Annual Report 2011 - Monarch

Institute of Physics

Annual Report 2011

Editorial notes

Published by: Institute of Physics Chemnitz University of Technology Reichenhainer Straße 70 09126 Chemnitz Germany Phone:

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Editors: Prof. Dr. Rudolf Bratschitsch DI DI(FH) Lutz Feige Layout & Design: DI DI(FH) Lutz Feige Photos: Cover: Physics Building, L. Feige Backside: Physics Building, L. Sprenger Inside: TUC, Press office, and wikimedia commons Print: Frick Kreativbüro & Onlinedruckerei e.K. www.online-druck.biz November 2012

Annual Report 2011

Table of contents

Foreword ............................................................................................... 3 Organizational chart ................................................................................ 4 Research highlights: Selected publications & awards .................................... 6 Publications Publications in reviewed journals ................................................... Conference proceedings ............................................................... Books and book chapters ............................................................. Invited talks ............................................................................... Conference contribution (talks and posters) .................................... Theses Habilitation thesis ............................................................... PhD theses ........................................................................ Diploma and master theses .................................................. Granted patents ..........................................................................

120 124 126 127 129 140 140 140 141

Scientific events .................................................................................. 142 "Physikalisches

Kolloquium" ................................................................... 143

Staff Permanent staff .......................................................................... Technical and support staff ........................................................... Workshop staff ........................................................................... Postdocs .................................................................................... PhD students .............................................................................. Diploma students ........................................................................ Master students .......................................................................... Guest scientists ..........................................................................

145 145 146 146 146 147 148 149

Funding, Projects ................................................................................. 152 Industrial collaborations ........................................................................ 154 Teaching ............................................................................................. 155 Public releations .................................................................................. 160 Press releases ..................................................................................... 166 How to reach us ................................................................................... 204

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Annual Report 2011

Foreword

2011 was another successful year for the Institut für Physik both in teaching and research. In this year, the first students finished the new bachelor course in physics and started their master studies. Most of them obtained very good results in the exams and B.A. thesis research, demonstrating that during adaption of the new system of academic degrees the high level of the internationally renown Diplomphysiker course could be maintained. Also, the students in our bachelor courses computational science as well as sensors and cognitive psychology made very good success. The latter, truly innovative course - which is unique in Germany - was very well received. The first students finished their second year. The broad research activities in the institute provide a sound basis also for higher academic education. In 2011, ten young scientists earned the degree of a Dr. rer. nat. (PhD) while Dr. Harald Graaf obtained the Dr. habilitatus degree in physics for his work on "Preparation and characterization of functional micro- and nanostructures". An important aim in or outreach programme is to make schoolchildren interested in natural sciences. For this purpose, the institute runs the Pupils Laboratory Wunderland Physik which has celebrated its 5th anniversary in 2011. During these five years, more than 8500 children enjoyed doing experiments on their own in this laboratory. Among the numerous research projects granted in 2011 to members of the institute, the following coordinated projects deserve special emphasis: i) the DFG research unit FOR 877 „From local constraints to macroscopic transport“ (2nd period 2011-2014; together with scientists from the University of Leipzig and TU Dresden), ii) the DFG research unit FOR 1497 „Zwillingspolymerisation von organisch-anorganischen Hybridmonomeren zu Nanokompositen“ (starting 2011; together with the Institut für Chemie of our university), and iii) the DFG research unit FOR 1713 "Sensoric Microand Nanosystems" (starting 2011; together with scientists of the Faculty of Electrical Engineering of Chemnitz University of Technology as well as scientists from Dresden). All these projects were based on joint applications with colleagues from other institutes and, hence, illustrate the strong interdisciplinary approach of our institute. Last not least it shall be mentioned that the 488. WE Heraeus Seminar entitled “Single Molecule Spectroscopy: Current Status and Perspectives” was held from July 12-15, 2011, in Chemnitz. Researchers from all over Germany as well as from abroad met in Chemnitz, the city where important results in this fascinating field of research had been obtained over the past twenty years.

Prof.Dr.rer.nat.habil.FrankRichter ExecutiveDirector

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Annual Report 2011

Organizational chart

Faculty of Natural Sciences Dean: Prof. Karl Heinz Hoffmann

Administration : Dekanatsrätin: Heike Rafeld Secretary: Annett Kurasch Institute of Chemistry

Institute of Physics Director:

Deputy Director:

2010/2011: Prof. Manfred Albrecht 2011/2012: Prof. Frank Richter

2010/2011: Prof. Frank Richter 2011/2012: Prof. Rudolf Bratschitsch

Experimental Physics

Chemical Physics (CHEMPHYS)

Complex Systems and Nonlinear Dynamics (KSND)

Dynamics of Nanoscopic and Mesoscopic Structures (DNMS)

Computational Physics (CPHYS)

Optical Spectroscopy and Molecular Physics (OSMP)

Theoretical Physics Simulation of New Materials (TPSM)

Physics of Thin Films (PHDS)

Theory of Disordered Systems (THUS)

Semiconductor Physics (HLPH)

Solid State Physics (PHFK)

Solid Surfaces Analysis (AFKO) Surface and Interface Physics (OFGF)

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Theoretical Physics

Finances: Katrin Krasselt

Electronics Workshop Mechanics Workshop

Annual Report 2011

Chemical Physics Prof. Dr. Robert Magerle

(CHEMPHYS) (@ www.tu-chemnitz.de/physik/CHEMPHYS)

Complex Systems and Nonlinear Dynamics Prof. Dr. Günter Radons

(@ www.tu-chemnitz.de/physik/KSND)

Computational Physics Prof. Dr. Karl Heinz Hoffmann

(CPHYS) (@ www.tu-chemnitz.de/physik/CPHYS)

Dynamics of Nanoscopic and Mesoscopic Structures Prof. Dr. Rudolf Bratschitsch

(PHDS) (@ www.tu-chemnitz.de/physik/PHDS)

Semiconductor Physics Prof. Dr. Dietrich R. T. Zahn

(HLPH) (@ www.tu-chemnitz.de/physik/HLPH)

Solid State Physics Prof. Dr. Frank Richter

(PHFK) (@ www.tu-chemnitz.de/physik/PHFK)

Solid Surfaces Analysis Prof. Dr. Michael Hietschold

(AFKO) (@ www.tu-chemnitz.de/physik/AFKO)

Surface and Interface Physics Prof. Dr. Manfred Albrecht

(OFGF) (@ www.tu-chemnitz.de/physik/OFGF)

Theoretical Physics - Simulation of New Matrials Prof. Dr. Angela Thränhardt

Theory of Disordered Systems Prof. Dr. Michael Schreiber

(OSMP)

(@ www.tu-chemnitz.de/physik/OSMP)

Physics of Thin Films Prof. Dr. Peter Häussler

(DNMS)

(@ www.tu-chemnitz.de/physik/DNMS)

Optical Spectroscopy and Molecular Physics Prof. Dr. Christian von Borczyskowski

(KSND)

(TPSM)

(@ www.tu-chemnitz.de/physik/TPSM) (THUS) (@ www.tu-chemnitz.de/physik/THUS)

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Annual Report 2011

Research highlights: Selected publications

M. Toader, M. Hietschold: "Tuning the Energy Level Alignment at the SnPc/Ag(111)Interface Using an STM Tip", J. Phys. Chem. C 115, 3099-3105 (2011) DOI: 10.1021/jp111478v M. Toader, M. Knupfer, D. R. T. Zahn, M. Hietschold: "Initial Growth of Lutetium(III) Bisphthalocyanine on Ag(111) Surface", J. Am. Chem. Soc., 133, 5538-5544 (2011) DOI: 10.1021/ja200168a M. Franke, R. Magerle: "Locally auxetic behavior of elastomeric polypropylene on the 100 nm length scale", ACS Nano 5, 4886 (2011) DOI: 10.1021/nn200957g E.-C. Spitzner, C. Riesch, R. Magerle: "Subsurface imaging of soft polymeric materials with nanoscale resolution", ACS Nano 5, 315 (2011) DOI: 10.1021/nn1027278 K. M. Whitaker, M. Raskin, G. Kiliani, S. T. Ochsenbein, N. Janßen, M. Fonin, U. Rüdiger, A. Leitenstorfer, D. R. Gamelin, and R. Bratschitsch: "Spin-on spintronics: Ultrafast electron spin dynamics in ZnO and ZnCoO sol-gel films", Nano Lett. 11, 3355-3360 (2011) DOI: 10.1021/nl201736p F. Lüttich, D. Lehmann, M. Friedrich, Z. Chen, A. Facchetti, C. von Borczyskowski, D. R. T. Zahn, H. Graaf: "Interface properties of OFETs based on an air-stable n-channel perylene tetracarboxylic diimide semiconductor", Phys. Status Solidi A, 585-593 (2011) DOI: 10.1002/pssa.201127592 F. Haidu, M. Fronk, O. D. Gordan, C. Scarlat, G. Salvan, and D. R. T. Zahn: "Dielectric function and magneto-optical Voigt constant of Cu2O: A combined spectroscopic ellipsometry and polar magneto-optical Kerr spectroscopy study", Phys. Rev. B 84, 195203 (2011) DOI: 10.1103/PhysRevB.84.195203 M. Bauer, R. Valiullin, G. Radons, J. Kärger: "How to compare diffusion processes assessed by single-particle tracking and pulsed field gradient nuclear magnetic resonance", Virtual Journal of Biological Physics Research 22, 161 (2011) DOI: 10.1063/1.3647875 T. Kosub, D. Makarov, H. Schletter, M. Hietschold, and M. Albrecht: "Interplay between the antiferromagnetic spin configuration and the exchange bias effect in [Pt/Co]8/CoO/Co3Pt trilayers", Phys. Rev. B 84, 214440 (2011) DOI: 10.1103/PhysRevB.84.214440 M. Grobis, C. Schulze, M. Faustini, D. Grosso, O. Hellwig, D. Makarov, and M. Albrecht: "Recording study of percolated perpendicular media", Appl. Phys. Lett. 98, 192504 (2011) DOI: 10.1063/1.3587635 B. Schulz, D. Täuber, J. Schuster, T. Baumgärtel, and C. von Borczyskowski: "Influence of mesoscopic structures on single molecule dynamics in thin smectic liquid crystal films", Soft Matter 7, 7431 – 7440 (2011) DOI: 10.1039/C1SM05434A

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S. Krause, P. F. Aramendía, D. Täuber and C. von Borczyskowski: "Freezing Single Molecule Dynamics on Interfaces and in Polymers", PhysChemChemPhys 13, 1754-1761 (2011) DOI: 10.1039/C0CP01713B S. Peter, M. Günther, F. Richter: "A comparative analysis of a-C:H films deposited from five hydrocarbons by thermal desorption spectroscopy", Vacuum 86, 667-671 (2012) DOI: 10.1016/j.vacuum.2011.07.037 O. Böhm, R. Leitsmann, P. Plänitz, C. Radehaus, M. Schreiber und M. Schaller: "k-restoring processes at carbon depleted ultralow-k surfaces", J. Phys. Chem. A 115, 8282-8287 (2011) DOI: 10.1021/jp202851p K. H. Hoffmann, P. Salamon, Y. Rezek and R. Kosloff, "Time-optimal controls for frictionless cooling in harmonic traps", EPL 96, 60015 (2011) DOI: 10.1209/0295Ͳ5075/96/60015 S. Thiem and M. Schreiber, "Generalized inverse participation numbers in metallic-mean quasiperiodic systems", Eur. Phys. J. B 83, 415-421 (2011) DOI: 10.1140/epjb/e2011-20323-7

The journal articles are reprinted with kind permission of the copyright owners.

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ARTICLE pubs.acs.org/JPCC

Tuning the Energy Level Alignment at the SnPc/Ag(111) Interface Using an STM Tip Marius Toader* and Michael Hietschold Chemnitz University of Technology, Institute of Physics, Solid Surfaces Analysis Group, D-09107 Chemnitz, Germany

bS Supporting Information ABSTRACT: The tip influence on the energy level alignment at the SnPc/Ag(111) interface has been addressed via scanning tunneling spectroscopy (STS). A collective effect characteristic for both molecular conformations up and down is reported to shift the corresponding first filled and empty levels toward the Fermi energy via a tip-sample distance decrease. The importance of the tin ion coupling to the metal electrodes is emphasized for the newly reported “cross-bending” effect as well as for a controllable tip-induced single-molecule switching and “nanowriting” within densely packed molecular arrays.

’ INTRODUCTION The strong demand toward higher and higher storage capacities involves a continuous miniaturization tendency of memory devices. Being beyond the limits of the semiconductor technology at the nanometer scale, molecular switches have become of great interest recently. Molecule-based memory and switching nanodevices require feasible molecules with bistable conformations that can be reversibly tuned via different external agents. Behind the molecular switches concept, an intense and extended work is carried out worldwide to address a comprehensive understanding from modeling via theory toward experimental characterization and final integration within functional devices. Therefore, switchable systems based on benzene-dithiolate molecules contacted between a gold surface and a gold STM tip have been modeled,1 whereas a high switching efficiency of organic molecules assembled between SW-CNTs has been proven theoretically.2 Rotaxane molecules were chemically and electrochemically reversibly switched,3 whereas a light-induced mechanical switching of adsorbed TTB-azobenzene molecules has been reported.4 A conductance switching of naphthalocyanine molecules has been found to occur via current-induced hydrogen tautomerization.5 Via external electric field, a molecular switching of lutetium triple-decker phthalocyanine complexes has been performed at a liquid/solid interface.6 The integration of rotaxane molecules within distinct inorganic elements allowed the development of a high-capacity moleculebased memory device.7 A bistable system switching between low and high conductance states has been achieved via integrating CoPc molecules within inorganic nanowire field-effect transistors, which induce a hysteresis in the electrical response.8 With the same final goal, a controllable spin manipulation between two spin states will address the novelty of the molecular spintronics. A r 2011 American Chemical Society

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theoretical approach to identify molecular nanomagnets9 as well as a Kondo temperature manipulation via a tip-induced singlemolecule switching from a saddle to a planar conformation of TBrPP-Co molecules have been reported.10 A reversible onoff switching between spin state 1/2 and 0 has been achieved via chemically induced NO attachment to the CoTPP molecules, which allows a spin controlling within the adsorbed molecules.11 However, the ability to control information accessible at the single-molecule level within densely packed self-assembled molecular layers requires a deep understanding of the electronic interface effects. In this work, the energy level alignment formed upon adsorption of “shuttlecock” shaped SnPc molecules on Ag(111) is determined via STS. Bistable molecular conformations “up” and “down” emphasize the suitability of such molecules for molecular data storage.12 A tip-induced molecule switching demands a comprehensive understanding of the tip influence on the interface electronic states. A fine-tuning of the molecular electronic levels is reported here via a tip-sample distance variation.

’ EXPERIMENTAL SECTION SnPc molecules, highly purified via temperature gradient sublimation, were evaporated on an atomically flat Ag(111) crystal surface held at room temperature using conventional organic molecular beam deposition (OMBD). The submonolayer coverage was grown with a corresponding evaporation rate of 1 nm/ min within a short exposure time (15s). A subsequent sample annealing to 380 K for 20 min was performed. An ultra-high Received: December 2, 2010 Revised: January 14, 2011 Published: February 3, 2011 3099

dx.doi.org/10.1021/jp111478v | J. Phys. Chem. C 2011, 115, 3099–3105

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The Journal of Physical Chemistry C

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Figure 1. High-resolution STM image for SnPc adsorbed on Ag(111) recorded in constant current mode using Isp = 100 pA and Vsp = -1 V (a), the optimized molecular structure of a free SnPc molecule: top and side view (b), enlarged nonplanar porphyrin ring (O represents the orthocenter of the N(isoindole) plane) (c), and the calculated energy diagram close to EF for a free SnPc molecule; the molecular orbital contours for the first filled and empty levels close to EF are also shown (d).

vacuum (base pressure low 10-10 mbar) variable-temperature STM (UHV VT-STM from Omicron) was used for imaging and spectra recording. All of the data presented in this work were achieved at a sample temperature of 30 K. The reported spectra were recorded using single-point spectroscopy and averaged over adjacent molecules. Spectra sets of 50-60 curves were used for each individual spectrum line shown within this work. The corresponding density of states representation via normalized differential conductivity (NDC) was done using the scanning probe image processor (SPIP).

’ RESULTS AND DISCUSSION Equivalent commensurate molecular structures are formed upon adsorption of SnPc on Ag(111). Packed within subsequent well oriented molecular rows (R and β) glided with respect to each other and with corresponding different in-plane orientation, SnPc molecules assemble in highly dense chess-board-like molecular superstructures (part a of Figure 1). Both bistable molecular conformations up and down (a consequence of the molecular nonplanarity (part b of Figure 1) are found to adsorb within R rows, whereas only down molecules are found within β rows. The up and down species are easily distinguishable due to a strongly different contrast of the central cavity: bright protrusion and shallow depression, respectively. The molecular nonplanarity is

found to be considerably reduced upon adsorption for both types of molecular conformations, which exhibit a similar molecular plane geometry with respect to the metal surface, as it will be shown later on. To analyze the electronic effects at the organic-metal interface, a comprehensive understanding of the free molecule in the gas phase is needed. Therefore, DFT calculations for the free SnPc molecule have been employed using Gaussian ’03 software with a corresponding UB3LYP method and LANL2DZ basic sets. The resulting optimized molecular geometric structure is presented in part b of Figure 1. In part c of Figure 1 an enlargement of the nonplanar porphyrin ring is shown. According to our calculations, a separation of 1.05 Å has been found between the Sn ion and the nitrogen (isoindole) plane (the projection of the Sn ion to the plane is marked by O in the part c of Figure 1). Values of 2.27 and 2.84 Å are measured for the SnNisoindole and Nisoindole-Nisoindole bond lengths, respectively. The values reported here are in very good agreement with the reference.13 The calculated energy diagram close to Fermi energy (EF) for a free SnPc molecule is shown in part d of Figure 1. The highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals are reported to be localized at -5.37 eV and 3.24 eV with respect to the vacuum level. Typically for the phthalocyanine molecules, the HOMO orbital consists of π electron 3100

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Figure 2. Evolution of the NDC spectra for down-R (a) and down-β (b) with respect to Isp using a Vsp = -1 V, the corresponding energy level shifts for HOMO and LUMO (c), the energy gap variation (d).

clouds delocalized over the molecular backbone. Because it shows no additional contributions from the metal ion or nitrogen atoms, the level position of this orbital upon adsorption is expected to be the same for both molecular conformations if they show a similar adsorption geometry of the molecular plane. The degenerate LUMO and LUMOþ1 orbitals were found to extend over the nitrogen atoms. A separation of 0.23 eV is reported between LUMOþ2 and LUMOþ3, which extend distinctively over the pyridine-nitrogens or isoindole-nitrogens, respectively. Dominated by Sn 5p like electron clouds the HOMO-1 orbital is expected to play a major role in the coupling of the molecule to the surface states. Obtaining information available at single-molecule level via STS has great advantage with respect to standard photoemission techniques where the signal is averaged over multi molecular domains or grains. The access toward understanding the coupling of single molecules with underlying electronic states can be efficiently provided by the STS which exhibits a high sensitivity to the local density of states (LDOS). Therefore, electron transport through single molecular junctions has been previously studied14-16 and new electronic states characteristic for particular submolecular features have been detected.17,18 Distinct possible perturbing aspects that may affect the tunnelling transport like tip consistency,19,20 temperature,21 or tip-sample distance22,23 have also been addressed. In spite of the wide usage of the STS for studying the organic-inorganic interfaces, there are only few reports that address the previously mentioned issue. On a weakly interacting substrate like highly oriented pyrolytic graphite (HOPG),

a tip-induced polarization of planar d8 metal phthalocyanines has been reported via tip-sample distance variation, which leads to a corresponding HOMO shift while LUMO remains pinned.22 However, when similar molecules (NiTPP which has a similar planar porphyrin ring but a slightly larger molecule-substrate distance) are adsorbed on metal substrates dominated by their free-electron like surface states the tip-sample distance variation is found to have no significant influence on the molecular levels.23 Tip influence on nonplanar phthalocyanine molecules like those used in this work adsorbed on metal surfaces has not been previously studied. According to the well-known tunnelling currentdistance dependence, a current set point (Isp) increase will allow a fine-tuned tip-sample approach. In Figure 2, a detailed evolution of the NDC spectra for down-R (a) and down-β (b) with respect to the current set point is shown. The first clearly resolved features below and above the EF are assigned to the first occupied and unoccupied molecular levels: HOMO and LUMO, respectively. A fine-tuning of the interface energy level alignment for both types of down species is observed. The corresponding energy level positions for HOMO and LUMO are plotted in part c of Figure 2. A systematic shift toward Fermi level via decreasing the tip-sample distance is reported to characterize both HOMO and LUMO independent of the molecular down species. In general, systematic and collective shifts toward lower or higher energies of both filled and empty states close to EF are known to induce a downwards or upwards band-bending at the interface. Therefore, a tuning of the energy alignment and charge injection at the organic/inorganic interface has been reported via 3101

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The Journal of Physical Chemistry C a metal top-contact formation24 or doping process.25,26 To our knowledge, there are no studies that report a systematic opposite shift of the HOMO and LUMO levels. Because no energy bands are created at the organic-metal interface for submonolayer coverage but rather discrete energy levels, we will refer to a corresponding energy shift by using the word “bending” (shift). We use for the first time the terminology “cross-bending” (crossshifting) to address the novelty of our report. Consequently, to the new interface effect, an accelerated energy gap reduction is found. Its corresponding evolution as a function of Isp is plotted within part d of Figure 2. An extrapolation to zero is required to determine the molecular energy gap independent of the electric field induced by the tunnelling tip. Closely related gap values have been estimated for down-R (1.81 eV) and down-β (1.86 eV) molecules, which are considerably lower than the one calculated for the free molecule (2.13 eV). The difference is mainly due to a charge transfer at the interface driven by the good coupling of the Sn ion with the metal surface states. However, additionally small contributions may occur from the DFT calculations, which are not known to provide an exact estimation of the gap energies. These values are found to be highly consistent with the energy splitting (1.7-1.9 eV) between the main core level components and corresponding shake-up satellites determined from the C 1s core level spectra (part 1 of the Supporting Information). A strong coupling between the Sn ion and the metal surface states is sustained by the shift observed in the Sn 3d core level spectra which is characteristic for a reduction effect of the Sn oxidation state (part 2 of the Supporting Information). Moreover, a reduction of the substrate work function was observed upon adsorption leading to the formation of a negative interface dipole (data not shown). Using optical spectroscopy, similar charging effects could be emphasized for PTCDA molecules adsorbed on gold metal surfaces, which shift the molecular energy levels for the first contact layer.27 The molecular gap gets saturated for both molecular down species to corresponding values of 1.22 eV (R) and 1.25 eV (β). The small difference is attributed to different adsorption sites adopted by the molecules as could be concluded from the analysis of the lattice parameters for the adlayer structure as well as from well-defined tip-induced molecular diffusion at the metal surface (data will be presented elsewhere). The “saturation” is presumably assigned to an equal coupling of the molecule to the metal electrodes namely the metal substrate and the tip. For a comprehensive understanding of the reported energy cross-bending at the interface, the metalorganic-metal (substrate-molecule-tip) heterojunction will be described as a donor-acceptor/donor-acceptor system. Within the heterojunction, the molecule itself can act as a bistable system, which can donate and accept electrons at the same time. However, the metal-molecule and molecule-tip interfaces cannot be described individually as two independent donor/ acceptor systems because a singular reason lies behind, emphasized by the simultaneous saturation of the both HOMO and LUMO shifts. When the tip-sample distance is decreased (higher Isp) only the tip-molecule separation is expected to be tuned because the molecule-substrate adsorption height should remain nearly constant. Via a negative sample bias, a tunnelling transport from the substrate into the tip via the molecular orbitals is enabled. A reduced tip-molecule distance will enhance the tunnelling transport at the corresponding interface, which enables a higher electron flow from the HOMO level into the tip. An emptying of this level is achieved, which determines a shift toward the EF. The excess of created positive charges delocalized

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over the molecular backbone might lead to consequently the formation of induced dipole moments and an additional local electric field at the molecule/substrate interface, which, nevertheless, will be immediately compensated by the large amount of surface free electrons via a backtransfer into the molecule. Driven by the high electron affinity of the N atoms, the electron backtransfer fills the LUMO, which gets shifted toward the EF as well. Therefore, a charge redistribution within the molecular ligand occurs and a new equilibrium state is reached. Very recently, Stadler et al.28 assumed for the first time a donation/backdonation effect at the SnPc/Ag(111) interface to explain the repulsive packing mechanism within the molecular adlayer, which consists at room temperature only from down molecules. Still, we have proven via coupling the molecules with two metal electrodes, the bistable donor/acceptor character of the SnPc molecules responsible for the observed energy cross-bending. A systematic increase of the background signal slope close to 2 eV below EF has been found and will be addressed later on. The previously described system can be reversibly switched via a voltage polarity change and turns the metal-organic-metal heterojunction into an acceptor-donor/acceptor-donor system. When a positive sample bias is used, a tunnelling transport from the tip into the substrate is achieved. Via decreasing the tip-sample distance, a higher tunnelling rate from the tip into the LUMO is enabled. A partially LUMO filling occurs which shifts the corresponding energy level position closer to EF (part a of Figure 3). Reverse as previously, opposite oriented dipole moments and local electric field induced at the molecule/ substrate interface accelerate a further transfer into the substrate. Strongly coupled to the metal surface states the Sn ion mediates the donation transfer (from the molecule into the substrate), which leads to a partial emptying of the HOMO-1. However, localized at lower energies, an instantaneous electron relaxation from HOMO occurs, which shifts the corresponding level position toward Fermi energy (part a of Figure 3). Therefore, a similar energy cross-bending effect is observed to occur at positive biases. In good agreement with the previous experiment, the tip independent (1.83 eV) and saturated (1.33 eV) energy gap values for down-β molecules were determined. A resonant tunnelling transport via the empty states allows the identification of additional molecular empty levels. The asymmetric feature located at ∼2.3 eV (part a of Figure 3, Isp = 50 pA) above the EF is reported to show a clear double-shoulder feature via a tipsample distance decrease (part a of Figure 3, Isp = 700 pA). The two corresponding levels (separated by ∼0.3 eV) are attributed to the LUMOþ2 and LUMOþ3 molecular levels. The change of the relative intensities denotes a contribution to the tunnelling transport mainly attributed to the Nisoindole at higher tip-sample separation, whereas the Npyridine grow considerably in importance as the tip approaches the sample. The observation is presumably assigned (sustained later on) to a tip-induced molecular geometry distortion, which might adjust the importance of distinct types of N atoms to the coupling of the molecule with the underlying electronic states. The weak but consistent feature at 1 eV above the EF, which acts more like a LUMO shoulder, is assigned to the LUMOþ1. A degeneracy lifting is reasonable to appear as a consequence of a different molecular adsorption geometry compared to the gas phase, which leads to an energy splitting of the otherwise degenerate LUMO/þ1. A systematic opposite evolution of the HOMO and LUMO intensities has been found. The corresponding ILUMO/IHOMO relative intensity ratio, plotted within part b of Figure 3, is 3102


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Figure 3. The evolution of the NDC spectra for down-β with respect to Isp using a Vsp = þ1 V (a); the variation of the ILUMO/IHOMO ratio; the legend indicates the down molecular species and used Vsp (b); the evolution of NDC spectra for up-R (solid blue lines) with respect to Isp using a Vsp = -1 V; the corresponding NDC spectra for down-R (interrupted black line) are shown for comparison (c); direct comparison of the down-R and up-R NDC spectra in the filled states region(d).

reported to show a similar tendency independent of the molecular down species or the used bias polarity. The trend gets saturated at the same tip-sample separation (300-400 pA) in good agreement with the observed cross-bending saturation (also part c of Figure 2). Moreover, the ratio is found to saturate at a corresponding value 1, which describes a tunnelling transport with an equal 1:1 tunnelling rate at the both substrate/molecule and molecule/tip interfaces. A final equilibrium state is reached at this point where a charge redistribution within the molecular backbone does not occur any more and an equal donoracceptor character is achieved. Available only as R species the Sn-up molecules are found to exhibit a similar cross-bending effect via a tip-sample distance variation (part c of Figure 3), driven by the same bistable donor/ acceptor character of the SnPc molecule. Because of a higher switching rate at higher current values (>300 pA), we found it difficult to record spectra with a good signal-to-noise ratio. However, as previously discussed, at this current set point a saturation effect occurs and therefore it is reasonable to assume that no significant changes will arise further. The NDC spectra of down-R molecules are also indicated for a better comparison (black interrupted lines in part c of Figure 3). The two molecular conformations are found to be differently coupled to the metal surface states due to a distinct location of the Sn ion with respect to the molecular plane: above for up and below for down. A better coupling for the down molecules will enable a charge transfer at

the interface, which lowers the LUMO position in comparison with the up molecules where this effect is suppressed. At a high tip-sample separation (Isp = 50 pA), there is a considerable difference (0.35 eV) between the LUMO position for up and down molecules (part c of Figure 3). However, at lower tipsample separations the LUMO levels are aligned for both molecular conformations. As previously predicted, the HOMO level arises always at the same energy for both molecular conformations sustaining a similar adsorption geometry of the molecular plane. Because the molecule/substrate interaction is mainly driven by the Sn ion for down molecules and by the N atoms for up molecules, a similar slight upward bending of the benzene rings occurs. The proposed similar adsorption geometries for both molecular conformations are indicated in the top insert in part a of Figure 4, in good agreement with previous reports.12,29 The strong feature characteristic for up molecules located at ∼2 eV below the EF is assigned according to our calculations and in good agreement with12 to the second highest occupied molecular orbital HOMO-1. A considerable signal intensity difference (between up and down molecules) is found for a high tip-sample separation (double headed arrow in part c of Figure 3 at Isp= 50 pA) at the indicated energy. A decrease of the corresponding intensity is reported via reducing the tip-sample distance, which is opposite with the previous findings for down molecules. A direct comparison between the down-R and up-R 3103

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Figure 4. Controllable tip-induced single-molecule switching, the proposed similar adsorption geometries for both molecular conformations are indicated (a); direct observation of the transition effect within the current-voltage curves (b); STM images before (top) and after (bottom) “nanowriting” within a molecular close-packed array; the corresponding contrast-enhanced frames are also shown (c).

NDC spectra in the filled states region for the highest and lowest tip-sample separation is shown in part d of Figure 3. The spectra line shape is consistent with highly resolved valence band ultraviolet photoemission spectra in the Fermi region (part 3 of the Supporting Information). At a low current set point (Isp = 50 pA), a strong feature from HOMO-1 arises for up molecules at -2.27 eV, whereas the signal for down molecules is featureless at this energy. At higher current set points, a similar feature is induced for down molecules (-2.43 eV at Isp = 600 pA), whereas a reduced signal is reported for up molecules (-2.23 eV at Isp = 300 pA). Despite different current set points, the HOMO position is found to be the same for both molecular conformations sustaining a similar saturation (starting with Isp = 300 pA) of the cross-bending effect applicable for the up molecules. The reported observations can be explained based on a tip-induced molecular planarization where the Sn ion position is tuned most probably due to a charge redistribution within the molecular backbone. An induced different charge separation within the molecule will affect the molecular dipole moment (calculated to be 1.25 D along the z axis for the free molecule) most probably via an induced change of the Sn ion oxidation state. Via hole attachment, the Sn3þ (smaller than Sn2þ) can accommodate into a planar molecular geometry allowing further movements toward a conformational change.12 In spite of our findings toward a bidirectional tendency for a conformational change, still a persistent separation of ∼0.2 eV is reported to characterize the HOMO-1 position of down and up species even after the saturation occurs. Located at lower energies, the HOMO-1 of down molecules denotes a Sn ion confinement to the surface states, which suppresses a backswitching effect toward an up

conformation. Attempts to use higher current values to switch from down to up end up with a molecule attachment to the tip. However, tip-induced up-down single-molecule switching is performed in a very controllable manner. Part a of Figure 4 depicts 8 subsequent frames recorded over the exact same area, where seven aligned up [1] molecules where controllably switched one by one to down [0] conformation. The corresponding binary representation (indicated within the right inset column) sustains the concept of molecule-based nanoengineering. Assigning 1 “bit” per molecule, from an approximate frame area of only 2 15 nm2, we estimate an incredibly high memory capacity of 1013 bits/cm2. Highly localized information access at the single-molecule level can be achieved via STS, which can be use to “read” (low Isp) and “write” (high Isp) information at the same time. A typical direct observation of the switching effect within the current-voltage curves is shown in part b of Figure 4. A current drop in the electrical response appears always at ∼2.4 eV below EF emphasizing the crucial importance of the HOMO-1 for a conformational change. The considerable difference in the electrical response between the two molecular conformations can be used as a feedback signal for switching recognition in future molecule-based switching/memory devices. Moreover, the concept toward molecular nanopatterning (nanowriting) is exemplified within part c of Figure 4. A molecular close-packed array has been controllably changed via singlemolecule switching toward a desirable pattern (part c of Figure 4, before (top frame) and after (bottom frame) nanowriting). The nanoletters “TUC” stay as a shortcut for “Technische Universit€at Chemnitz”. 3104


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’ CONCLUSIONS In summary, as a general remark, the crucial aspect of the tipsample distance for the local investigation at the nanoscale has been emphasized. Consequently, this issue has to be addressed for the STS reliability to avoid any kind of data puzzling. Moreover, a fine-tuning of the energy level alignment at the SnPc/Ag(111) interface has been performed via the tip-sample distance-dependent STS. A new type of interface effect namely an energy “cross-bending” is reported to arise via tuning the tipsample separation. The observation is proven to be driven by the bistable donor/acceptor character of the SnPc molecules. Distinct types of coupling to the metal surface states have been found for the two molecular conformations. However, a similar adsorption geometry of the molecular plane is emphasized. Tip-induced molecular planarization allows an irreversible up to down switching at the single-molecule level. The crucial importance of the Sn ion for the coupling to the metal electrodes has been discussed toward a comprehensive understanding of the reported observations. ’ ASSOCIATED CONTENT

bS Supporting Information. C 1s core level spectra, Sn 3d core level spectra, and valence band UP spectra close to EF. This material is available free of charge via the Internet at http://pubs. acs.org. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected](M.T.). E-mail: [email protected], fax: þ49 371 531 21639 (M.H.).

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(12) Wang, Y.; Kr€oger, J.; Berndt, R.; Hofer, W. A. J. Am. Chem. Soc. 2009, 131, 3639. (13) Zhang, Y.; Zhang, X.; Liu, Z.; Xu, H.; Jiang, J. Vibrat. Spectrosc. 2006, 40, 289. (14) Wang, Y. F.; Kr€oger, J.; Berndt, R.; Vazquez, H.; Brandbyge, M.; Paulsson, M. Phys. Rev. Lett. 2010, 104, 176802. (15) Takacs, A. F.; Witt, F.; Schmaus, S.; Balashov, T.; Bowen, M.; Beaurepaire, E.; Wulfhekel, W. Phys. Rev. B 2008, 78, 233404. (16) Song, Y. J.; Lee, K.; Kim, S. H.; Choi, B.-Y.; Yu, J.; Kuk, Y. Nano Lett. 2010, 10, 996. (17) Takada, M.; Tada, H. Jpn. J. Appl. Phys. 2005, 44 (7B), 5332. (18) Kr€oger, J.; Jensen, H.; Neel, N.; Berndt, R. Surf. Sci. 2007, 601, 4180. (19) Chen, L.; Hu, Z.; Zhao, A.; Wang, B.; Luo, Y.; Yang, J.; Hou, J. G. Phys. Rev. Lett. 2007, 99, 146803. (20) Hu, Z.; Chen, L.; Zhao, A.; Li, Z.; Wang, B.; Yang, J.; Hou, J. G. J. Phys. Chem. C 2008, 112, 15603. (21) Gyarfas, B.; Wiggins, B.; Hipps, K. W. J. Phys. Chem. C 2010, 114, 13349. (22) Gopakumar, T. G.; Meiss, J.; Pouladsaz, D.; Hietschold, M. J. Phys. Chem. C 2008, 112, 2529. (23) Deng, W.; Hipps, K. W. J. Phys. Chem. B 2003, 107, 10736. (24) Gorgoi, M.; Zahn, D. R. T. Appl. Surf. Sci. 2006, 252, 5453. (25) Yan, L.; Watkins, N. J.; Zorba, S.; Gao, Y.; Tang, C. W. Appl. Phys. Lett. 2001, 79, 4148. (26) Ding, H.; Gao, Y. Appl. Phys. Lett. 2008, 92, 053309. (27) Forker, R.; Golnik, C.; Pizzi, G.; Dienel, T.; Fritz, T. Org. Electron. 2009, 10, 1448. (28) Stadler, C.; Hansen, S.; Kr€oger, I.; Kumpf, C.; Umbach, E. Nature Physics 2009, 5, 153. (29) Baran, J. D.; Larsson, J. A.; Woolley, R. A. J.; Cong, Y.; Moriarty, P. J.; Cafolla, A. A.; Schulte, K.; Dhanak, V. R. Phys. Rev. B 2010, 81, 075413.

’ ACKNOWLEDGMENT This work was supported by the Deutsche Forschungsgemeinschaft (DFG) through GRK 1215: “Materials and Concepts for Advanced Interconnects”. We thank P. Shukrynau for technical support. Concerning the photoemission data, we also thank T. Toader for fruitful discussions and M. Vondracek for technical support. ’ REFERENCES (1) Emberly, E. G.; Kirczenow, G. Phys. Rev. Lett. 2003, 91, 183301. (2) Martins, T. B.; Fazzio, A.; da Silva, A. J. R. Phys. Rev. B 2009, 79, 115413. (3) Bissel, R. A.; Cordova, E.; Kaifer, A. E.; Stoddart, J. F. Nature 1994, 369, 133. (4) Comstock, M. J.; Levy, N.; Kirakosian, A.; Cho, J.; Lauterwasser, F.; Harvey, J. H.; Strubbe, D. A.; Frechet, J. M. J.; Trauner, D.; Louie, S. G.; Crommie, M. F. Phys. Rev. Lett. 2007, 99, 038301. (5) Liljeroth, P.; Repp, J.; Meyer, G. Science 2007, 317, 1203. (6) Lei, S.-B.; Deng, K.; Yang, Y.-L.; Zeng, Q.-D.; Wang, C.; Jiang, J.-Z. Nano Lett. 2008, 8, 1836. (7) Green, J. E.; Choi, J. W.; Boukai, A.; Bunimovich, Y.; JohnstonHalperin, E.; DeIonno, E.; Luo, Y.; Sheriff, B. A.; Xu, K.; Shin, Y. S.; Tseng, H.-R.; Stoddart, J. F.; Heath, J. R. Nature 2007, 445, 414. (8) Duan, X.; Huang, Y.; Lieber, C. M. Nano Lett. 2002, 2, 487. (9) Trif, M.; Troiani, F.; Stepanenko, D.; Loss, D. Phys. Rev. B 2010, 82, 045429. (10) Iancu, V.; Deshpande, A.; Hla, S.-W. Nano Lett. 2006, 6, 820. (11) W€ackerlin, C.; Chylarecka, D.; Kleibert, A.; M€uller, K.; Iacovita, C.; Nolting, F.; Jung, T. A.; Ballav, N. Nature Commun. 2010, 1, 61. 3105

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Initial Growth of Lutetium(III) Bis-phthalocyanine on Ag(111) Surface Marius Toader,† Martin Knupfer,§ Dietrich R. T. Zahn,‡ and Michael Hietschold*,† †

Institute of Physics, Solid Surfaces Analysis Group, and ‡Institute of Physics, Semiconductor Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany § Leibniz Institute for Solid State and Materials Research, IFW Dresden, D-01171 Dresden, Germany

bS Supporting Information ABSTRACT: The adsorption of lutetium(III) bis-phthalocyanine (LuPc2) on Ag(111) was investigated using scanning tunneling microscopy and spectroscopy (STM/STS). A comprehensive study was carried out toward understanding the driving mechanism responsible for the formation of the first and second monolayers (MLs). In both MLs, the adsorbed molecules are found to exhibit different in-plane orientations arranged according to a “chess-board” like pattern. Highly resolved STM images allowed an exact determination of the corresponding angle mismatch, which differs for the first and second MLs. The tunneling transport through individual molecules reveals a negative differential resistance (NDR) effect detectable within the currentvoltage curves. The corresponding density of states (DOS) representation is consistent with a resonant tunneling mechanism sustained by the valence band (VB) states close to the Fermi energy (EF) recorded via highly resolved ultraviolet photoemission spectroscopy (UPS).

’ INTRODUCTION Because of the strong demand of nanoscale technology for novel, low-dimensional active elements, single molecular magnets (SMM) grew considerably in importance. There is a tremendous interest in research that addresses possible suitable candidates for spintronics applications. A controllable spin manipulation at single molecule level was recently reported via a chemical switch.1 In this respect, rare earth (lanthanide) elements are of great interest due to their large magnetic moment and anisotropy. There are already reports that dedicate strategies toward SMM based on lanthanide ions.2 The π-conjugated organometallic complexes such as lanthanide bis-phthalocyanines have been proven to behave as magnets at single molecule level.3 Later, it was shown by the group of Ishikawa et al.4 that these systems exhibit quantum tunneling magnetization. Moreover, such work could be extended to dinuclear lanthanide complexes with phthalocyaninato ligands.5 Triple-decker complexes have been investigated6 and reported to exhibit an electric-driven molecular switching effect at liquid/solid interfaces.7 However, more extended work is dedicated to the double-decker SMM based on mononuclear lanthanide ions.8,9 Their suitability for organic-based field effect transistors was probed as well.10,11 Corresponding properties like photosensitivity12 and magnetic response13 have been successfully enhanced in hybrid complexes using carbon nanotubes. However, outstanding r 2011 American Chemical Society

performance of molecule-based nanodevices will strongly depend on the interfaces formed upon adsorption on distinct inorganic substrates, where the morphological and electronic properties deviate considerably with respect to bulk-like thick films. Therefore, a comprehensive understanding of organic/inorganic interface formation in the initial growth phase is needed. A preservation of the magnetic behavior was reported for adsorbed double-decker TbPc214,15 on metal surfaces. This is of great advantage as compared to the single plane counterpart CoPc where the magnetic spin is quenched for the first monolayer (ML).16 Different works address the adsorption of distinct lanthanide-based bisphthalocyanine complexes using STM.1720 However, highly resolved extended molecular close-packed arrays (small domains are reported19,20) are still missing. Moreover, there is a question concerning the exact in-plane orientation within highly densepacked structures. Information concerning the second ML formation in terms of morphology and electronic behavior is still missing as well. Therefore, in this work, the adsorption of lutetium(III) bis-phthalocyanine (LuPc2) on Ag(111) substrate is investigated. Distinct aspects concerning the morphology and electronic properties are addressed for the first and second MLs, and the observed deviations are discussed. Received: January 7, 2011 Published: March 18, 2011 5538

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Figure 1. STM images for LuPc2 adsorbed on Ag(111) recorded in constant current mode using a tunnelling current of 100 pA and a sample bias of 1 V (the inset shows the corresponding molecular structure for LuPc2 (a)), and of 2 V (the inset shows a highly resolved isolated molecule where the submolecular features are consistent with the delocalized π systems (b)).

’ EXPERIMENTAL DETAILS A variable-temperature STM (Omicron GmbH) operating under ultrahigh vacuum (UHV) conditions (base pressure e 2 1010 mbar) was used for recording the data presented. All STM/STS results were achieved at a corresponding temperature of 30 K. Electrochemically etched tungsten tips (cut from a polycrystalline W wire) were used. The STS data were recorded using single point spectroscopy by positioning the tip on top of the molecular center. Each single ST spectrum shown is averaged over approximately 40 curves obtained from adjacent molecules. The photoemission spectroscopy (PES) data were recorded in the normal emission (NE) mode at room temperature (RT) under similar UHV conditions. A photon energy of 55 eV was used to obtain the valence band PES data. The PES experiments were carried out at the Material Science end-station at the Elettra synchrotron radiation facility in Trieste. For both types of experiments, the same Knudsen cell was used to evaporate the molecules via organic molecular beam deposition. A relatively high deposition rate ∼0.5 nm/min (corresponding sublimation temperature of ∼410 C) was used to check the stability of the molecules during evaporation. Prior to deposition, the metal single crystal was cleaned in situ by repeated cycles of Arþ sputtering and subsequent annealing.

’ RESULTS AND DISCUSSION The molecular structure for lutetium(III) bis-phthalocyanine is shown in the inset of Figure 1a. Two 4-fold π conjugated phthalocyanine ligands, rotated by 45 with respect to each other, are bridged via a Lu(III) ion. When adsorbed on the Ag(111) surface, extended molecular arrays are formed (see the large scale STM image in Figure 1a). The presence of uncovered areas between molecular domains indicates an attractive moleculemolecule interaction (see the black arrows that point along the unit cell vectors). In good agreement with previous reports, which address the adsorption of similar YPc2 on Au(111),19 the smallest angle mismatch between one unit cell vector and one of the equivalent substrate directions was determined to be 15 (see Figure 1a and b). Moreover, well-defined domain edges are found to develop as well along the close-packed directions of the substrate (e.g., [110]) (see the white solid arrow) or along the

corresponding perpendicular directions (e.g., [112]) (see the white dotted arrow). This suggests that a considerable contribution from the moleculesubstrate interaction to the final packing mechanism exists. Consistent with the well-oriented sharp domain edges, molecular dot-chains are found to be formed within the second ML (marked by similar white arrows). Areas with a lower adsorption height (∼1.4 Å) can be identified as well and are attributed to single-decker molecular domains formed via a thermal decomposition during evaporation. Therefore, the lutetium(III) bis-phthalocyanine is decomposed sometimes into two single-decker molecular species. One preserves the metal consistency leading to the formation of Lu(II) monophthalocyanine (LuPc), while the other ligand is metal-free and can be identified as a deprotonated phthalocyanine (Pc without the inner H atoms). The two species are easily distinguishable within highly resolved STM images due to their distinct molecular appearance of the central cavity at a negative bias voltage: bright protrusion for LuPc and shallow depression for Pc (see Figure 1b, top-left corner). The appearance of lutetium monophthalocyanine is found to exhibit a strong bias polarity dependence, which is not the case for deprotonated Pc (see Supporting Information 1). The observation is presumably assigned to a higher density of filled states localized at the metal ion site, explained on the basis of a reduction effect of the Lu oxidation state via an electron flow from the substrate into the molecule mediated by the Lu ion and/ or isoindole N. Similar voltage polarity dependence was previously reported for fluorinated cobalt phthalocyanine adsorbed on Ag(110).21 Moreover, photoelectron spectroscopy has shown that there is also charge transfer to the metal center in the case of Co-porphyrins deposited on Ag(111), which supports our conclusion.22 Ordered square structures are found via intermixing the two single-decker molecular species, which adsorb preferentially along the equivalent underlying directions and preserve the 4-fold symmetry within the formed arrays. The lutetium(III) bis-phthalocyanine molecular domains are easily distinguishable due to their relatively high adsorption height of ∼4 ( 0.5 Å and distinct molecular appearance. Because of an effective decoupling from the surface states via the first Pc ring, 5539

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Figure 2. Voltage polarity dependence for molecular close-packed arrays within the first ML; each frame area is 10 10 nm2 (a). Charge distribution within the molecular ligand for the filled states close to EF determined experimentally for single molecules in the first ML (top) and second ML (middle) (each frame area is 3 3 nm2) and theoretically for gas-phase isolated molecules (bottom) (b). For all frames, the tunnelling current was 100 pA.

the unperturbed π electronic clouds delocalized over the upper ligand determine the final molecular appearance. Highly resolved submolecular features for isolated molecules (see the inset of Figure 1b) are consistent with the 16 π electronic systems per upper ligand calculated using density functional theory (DFT) (see Figure 2b). However, due to the nonplanar geometry, the outer π electronic clouds appear brighter than the inner ones. Therefore, the molecules are mostly identified as eight-lobe structures (different from the four-lobe shape characteristic for the single-decker phthalocyanine). Still, a clear identification of individual molecules within densely packed arrays is very difficult at this bias voltage. Assigning the shallow depressions to individual central cavities, the counted features per molecule do not fit those identified for isolated molecules (minimum 8), because four surrounding features have coordination 1 while the other four have coordination 2 (see Figure 1b). Therefore, different inplane orientations might be responsible for the lack of a precise identification, a fact that was only assumed in previous works.19 As it will be shown later on, the validity of this assumption will be proven via a precise determination. Moreover, this effect is accompanied by an extended overlap of the molecular wave functions between neighboring molecules, creating a mixed and complicated contrast appearance of the submolecular features. The situation is different at the well-oriented domain edges where the in-plane orientation can be easily determined. The upper phthalocyanine ring was found to be rotated by 45 with respect to a close-packed orientation of the substrate. Because of the relative rotation of the two ligands (45), the lower phthalocyanine ring is thus found to align one molecular axis with the underlying substrate direction. A considerable moleculesubstrate interaction is found to contribute to the first ML formation via an overlapping between the π electronic clouds and surface states. Adsorbed via a ππ stacking mechanism, the isolated molecules in the second ML are found to be rotated by 45 with respect to the underlying ones. The contrast appearance of the molecular arrays within the first ML is found to be strongly dependent on the bias polarity (see Figure 2a, where all of the frames are equivalent and rotated by integers of 15 with respect to each other). Symmetric with respect to EF, via increasing the absolute voltage value, the submolecular resolution is progressively lost.

Moreover, a better resolution is achieved at negative biases, most probably due to a higher symmetry close to the Fermi energy of the charge distribution within the molecular ligand for the filled orbitals (highest occupied molecular orbital HOMO/ 1) as compared to the degenerated unfilled orbitals (lowest unoccupied molecular orbital LUMO/þ1). Therefore, a detailed negative polarity dependence of the molecular appearance for isolated molecules within first and second MLs is shown in Figure 2b. The same contrast and light intensity were used to display the images (no artificial enhancement/reduction of the molecular appearance was introduced this way), which allow for a direct comparison. A similar charge distribution within the molecular ligand is reported independent of the investigated ML. Presumably, there is no (or very weak) influence of the substrate on the upper Pc ring. Via increasing the voltage, the outer π electronic clouds get broader, thus inducing a gradual quenching of the inner π orbitals. Consequently, a larger molecular appearance, which suppresses the submolecular features, considerably complicates an exact estimation of the inplane orientation. The observations are consistent with the charge distribution contours for HOMO and HOMO1 (calculated using Gaussian 03 software with the UB3LYP method and SDD basic sets) (see Figure 2b). Located at lower energies, the HOMO1 orbital shows a more pronounced localization of the inner π electronic clouds to the C atoms directly bonded to the isoindole N and a corresponding broader appearance of the outer π orbitals. As the scenario indicates, a study at lower bias voltages enables a higher submolecular resolution. However, despite our previous observation that there is no (or very weak) influence of the substrate on the upper Pc ring, an increasingly pronounced asymmetry of the molecule orbitals within the first ML is found, which is less noticeable within the second ML. The effect is due to the organic radical delocalized over the two Pc rings characteristic for the neutral lanthanide-based bis-phthalocyanines,23 which favors an intramolecular interaction between the ligands. Similar to the nonplanar MePc,24 the first Pc ligand direct in contact with the metal surface is reasonably expected to exhibit a slight geometry distortion upon adsorption. Moreover, different atomic configuration underneath the molecular backbone (as a consequence of the previously discussed alignment with the underlying substrate 5540


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Figure 3. Highly resolved STM images for molecular close-packed array in the first ML, 0.5 V, 100 pA (a); for R molecule, 3 3 nm2 (b); and for molecular close-packed array in the second ML, 1 V, 100 pA, 20 20 nm2 (c).

directions) will enable a different moleculesubstrate coupling along the two molecular axes. Consequently, an adsorptioninduced asymmetry of the first Pc ring is propagated to the top Pc ligand as a result of the intramolecular interaction. However, the interface confined effect is less noticeable within the second ML, which is effectively decoupled from the substrate via the first ML that acts as a buffer layer. The effect may have strong consequences on the self-assembly process and the corresponding electrical response of the molecules adsorbed within different layers, as will be shown later. A high magnification of a molecular close-packed array within the first ML is shown in Figure 3a, where a negative bias voltage of 0.5 V was used for recording. As predicted by the polarity dependence study, at this relatively low voltage, the molecular features are imaged with optimum sharpness and localization. The inner π orbitals are considerably enhanced, while the outer ones get better defined. Even though unresolved individually, the inner π systems appear as an inner ring. Efficiently, the different in-plane orientations are determined with high accuracy. Differently oriented molecules (R and β) with an in-plane angle mismatch of 15 are found to arrange according to a “chessboard” like pattern. The estimated angle is consistent with the previously determined minimum mismatch between the unit cell vector and one equivalent substrate direction. Moreover, this angle is different from the one proposed in ref 19, where an angle of 30 was used for modeling the molecular structure. However, we do not question the proposed model because the lower reactivity of the Au(111) surface might have a lower impact on the final structure. The subsequent types of molecular rows (R and β) are reported to be well oriented (see Figure 3a), which justifies the presence of previously discussed sharp domain edges, which always appear along the diagonal of the molecular unit cell. For an overview of the lattice parameters and proposed model, see Supporting Information 2. Interestingly, the submolecular features do not exhibit a similar equivalent contrast appearance. A high magnification of one R type molecule is shown in Figure 3b. A noticeable nonequivalent contrast is reported for the diagonally opposite features marked by white arrows. Correspondingly, the neighbor β type molecules manifest an opposite effect (refer to the black arrows). Presumably, the molecular features at the periphery have the same charge consistency (π character). Therefore, excluding an electronic effect, the observed nonequivalent contrast might be exclusively attributed to a slight geometrical distortion of the upper Pc ligand, most probably due to a steric repulsion as well as due to the previously

discussed intramolecular interaction. Additional contribution might occur from a vertical ππ interaction between upper and lower Pc ligands of neighboring molecules. Such an extended three-dimensional (3D) moleculemolecule interaction is highlighted for the double-decker molecules, which presents a real novelty as compared to single-decker counterparts, which manifest an exclusively in-plane interaction. Therefore, an extended overlap of the molecular wave functions enhances particular submolecular features to the detriment of other ones. Consequently, the difficulties encountered for these systems are justified for a precise assignment of the in-plane orientation within closely packed arrays. As previously mentioned, the isolated molecules in the second ML adsorb exactly on top of the underlying ones. Therefore, densely packed molecular arrays within second ML are formed according to a similar growth mechanism (see Figure 3c). An equivalent molecular lattice is achieved where molecules with different in-plane orientation arrange according to a similar “chess-board” like pattern. However, the angle mismatch in the second ML is reduced to one-half (7.5) as compared to the first ML. For a higher resolution of the second ML and a corresponding assignment of the in-plane orientation, refer to Supporting Information 3. The isolated molecules in the second ML (reported previously to exhibit a relative 45 rotation) rearrange the in-plane orientation within densely packed arrays, reaching a compromise driven by an additional moleculemolecule interaction. The small deviations observed for the second ML are assigned to a perturbed fine balance between the moleculesubstrate and moleculemolecule interaction. The first type of driving force is considerably reduced, while the second one grows in importance. The tunnelling transport through individual molecules adsorbed within first and second MLs is found to manifest negative slopes within the corresponding currentvoltage curves (Figure 4a). Known as the negative differential resistance (NDR) effect, the reported phenomenon is of great interest for electronic applications. Present in doped silicon,25,26 the NDR was reported theoretically27 and experimentally28,29 to be induced in organic-based hybrid devices as well. Moreover, multiple NDR events at single molecule level were reported to appear selectively as a function of the silicon doping type.30 Hence, the effect was observed only for negative sample bias on n-type silicon and for positive sample bias on p-type silicon. For singledecker cobalt phthalocyanine adsorbed on Au(111), the NDR occurs only in the part of negative sample bias and only for nickel tips positioned on top of the cobalt ion.31 Absent for tungsten 5541

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Figure 4. Currentvoltage curves recorded at single molecule level reveal NDR behavior, 1 V, 100 pA (a); the corresponding DOS representation (b); and VB spectra in the Fermi energy region recorded using synchrotron radiation (55 eV) for 0.7 nm (top) and 1.3 nm (bottom) of LuPc2 adsorbed on Ag(111) (BE = binding energy) (c).

tips, the effect was explained on the basis of a mechanism originating from a local orbital symmetry matching. To our knowledge, the NDR response in tunnelling transport through individual lanthanide-based bis-phthalocyanines has not been previously reported. One and two negative slopes were found to appear in the negative part of the sample bias for the first and second MLs, respectively (see Figure 4a). However, independent of the ML, two minima are identified within the investigated negative voltage range (2.5 ÷ 0 V). The corresponding energy separation is reduced via increasing the thickness. The behavior is consistent and strongly correlated with the observed deviation of the energy level positions encountered for the first and second MLs (Figure 4b). At a negative sample bias, the contribution to the tunnelling current comes mainly from the occupied states of the molecule. The first two occupied levels below EF are assigned to HOMO and HOMO1 orbitals. As it was shown in the previous discussion, there is an effective coupling between the first Pc ligand and metal surface states, which drives (contributes to) the self-assembly mechanism. It is reasonable to assume a moleculesubstrate interaction mainly driven by the N atoms, which are the main electron acceptors of the molecules. Therefore, a charge redistribution at the corresponding atom site is likely to appear. Consequently and consistent with this assumption, the HOMO1 (found to be more localized at the C site directly bonded to the isoindole N) is located at lower energy for the first ML as compared to the second ML. As previously mentioned, the intramolecular interaction is effectively propagating the substrate influence on the final electrical response of the molecules adsorbed within the first ML. Still, the effect is considerably reduced for the second ML, which is decoupled from the substrate via the first ML. However, this considerable difference is relatively small for HOMO level, because the inner π orbitals are more delocalized. The tip apex was slightly changed via an in situ local melting procedure to determine the corresponding influence on the energy level alignment. The results are found to be very similar independent of the tip shape (see Figure 4b). The occupied states, directly involved in the tunnelling transport, are reported to be more affected (an unidirectional

Figure 5. C 1s core level spectra for 1.3 nm of LuPc2 adsorbed on Ag(111) measured using synchrotron radiation (450 eV); the inset depicts the molecular structure for LuPc2 where the top Pc ligand is enhanced and the corresponding different types of C atoms are indicated.

shift toward higher energies with corresponding values in the range of 0.18 ÷ 0.21 eV) as compared to the almost undisturbed unoccupied states (similar shift in the range of 0.04 ÷ 0.05 eV). Therefore, in the following sequence, the discussed values obtained with tip #2 will be given in brackets. As already mentioned, the HOMO HOMO1 energy separation is reduced from 1.38 (1.36) eV for the first ML to 0.99 (0.99) eV for the second ML. Independent of the tip shape and corresponding introduced small shifts, the previously discussed energy separation is reproduced with a high accuracy. To check the observed behavior, highly resolved valence band spectra in the 5542


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Journal of the American Chemical Society Fermi level region were recorded for two molecular thicknesses using synchrotron radiation (see Figure 4c). A similar reduction of the HOMO HOMO1 energy separation is demonstrated via increasing the film thickness. The smaller values are mainly attributed to the averaging character of the photoemission technique. Therefore, an averaged signal extended over decomposed molecules and molecular domains formed at surface defect sites might introduce the reported deviations. However, the UPS data are of great importance to sustain a resonant tunnelling mechanism responsible for the observed NDR effect. This type of mechanism was used previously30 to explain the origin of the NDR. Moreover, the currentvoltage behavior as a function of molecular film thickness is highly consistent with the evolution of the energy level alignment at the organic/metal interface determined using STS and UPS. Additionally, the energy separation between the first unfilled levels above Fermi was determined to be 1.17 eV (1.14 eV assuming a shift similar to the one reported for tip #1) for the first ML and 0.75 (0.75) eV for the second ML. The averaged molecular gap is estimated to be 1.97 and 2.16 eV for the first and second MLs, respectively. Because of the unsignificantly small shifts introduced by the tip shape for the empty states, the molecular gap was estimated with an averaged error bar not exceeding 0.1 eV. Additionally, these values are consistent with the energy splitting (1.7 ÷ 1.9 eV) between the main core level components and corresponding shakeup satellites determined from the C 1s spectra (see Figure 5). Besides the main core level components, shakeup satellites are identified at higher energies caused by a kinetic-energy loss of photoelectrons via simultaneously excited ππ* transitions.32 Assigned as transitions from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO), the energy splitting between the main core level components and the corresponding satellite features can be considered as an estimative value for the molecular gap.33 A value of 2:1.98:4.20 is reported for the fitted intensity ratio described as (C-1þSC-1):(C-2þSC-2):(CHþSCH), which is in very good agreement with the numerical ratio of distinct types of carbon atoms identified within the molecular ligand, 2:2:4 (C1:C2:CH), denoting that a further decomposition of monophthalocyanine species is not likely to appear.

’ CONCLUSIONS The initial growth of lutetium(III) bis-phthalocanine on Ag(111) is found to be of high complexity in terms of morphology and electronic properties. A fine balance between the moleculesubstrate and moleculemolecule interaction drives the molecular self-assembly. Molecules adopting different in-plane orientation are reported to arrange according to a “chess-board” like pattern where an extended 3D moleculemolecule interaction was found. An exact determination of the angle mismatch was reported for the first (15) and second (7.5) MLs. There is no (or very weak) substrate influence on the upper ligand, which manifests a similar charge distribution independent of the adsorbed ML. However, a considerable coupling was found between the molecular orbitals of the first Pc ligand and the metal surface states. Consequently, the energy level positions are different for the molecules adsorbed within the first or second MLs. The tunnelling transport at the single molecule level is reported to show a NDR behavior enlarging the great application potential of lanthanide-based bis-phthalocyanine toward logic/memory

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devices. The observed phenomenon is consistent with a resonant tunnelling mechanism sustained by the STS and UPS data.

’ ASSOCIATED CONTENT

bS Supporting Information. Voltage polarity dependence of the appearance of single-decker phthalocyanine species. Lattice parameters and proposed structural model. High magnification of one molecular domain edge within the second ML. This material is available free of charge via the Internet at http:// pubs.acs.org. ’ AUTHOR INFORMATION Corresponding Author

[email protected]

’ ACKNOWLEDGMENT This work was supported by the Deutsche Forschungsgemeinschaft (DFG) through GRK 1215 “Materials and Concepts for Advanced Interconnects” and Research Unit 1154 “Towards Molecular Spintronics”. We thank P. Shukrynau for technical support. Concerning the photoemission data, we also thank T. Toader for fruitful discussions and M. Vondracek for technical support. ’ REFERENCES (1) W€ackerlin, C.; Chylarecka, D.; Kleibert, A.; M€uller, K.; Iacovita, C.; Nolting, F.; Jung, T. A.; Ballav, N. Nat. Commun. 2010, 1, 61. (2) Sessoli, R.; Powell, A. K. Coord. Chem. Rev. 2009, 253, 2328. (3) Ishikawa, N.; Sugita, M.; Ishikawa, T.; Koshihara, S.; Kaizu, Y. J. Am. Chem. Soc. 2003, 125, 8694. (4) Ishikawa, N.; Sugita, M.; Wernsdorfer, W. Angew. Chem. 2005, 117, 2991. (5) Ishikawa, N. Polyhedron 2007, 26, 2147. (6) Yoshimoto, S.; Sawaguchi, T.; Su, W.; Jiang, J.; Kobayashi, N. Angew. Chem., Int. Ed. 2007, 46, 1071. (7) Lei, S.-B.; Deng, K.; Yang, Y.-L.; Zeng, Q.-D.; Wang, C.; Jiang, J.Z. Nano Lett. 2008, 8, 1836. (8) Gonidec, M.; Luis, F.; Vílchez, .; Esquena, J.; Amabilino, D. B.; Veciana, J. Angew. Chem., Int. Ed. 2010, 49, 1623. (9) AlDamen, M. A.; Clemente-Juan, J. M.; Coronado, E.; MartíGastaldo, C.; Gaita-Arin~no, A. J. Am. Chem. Soc. 2008, 130, 8874. (10) Su, W.; Jiang, J.; Xiao, K.; Chen, Y.; Zhao, Q.; Yu, G.; Liu, Y. Langmuir 2005, 21, 6527. (11) Katoh, K.; Yoshida, Y.; Yamashita, M.; Miyasaka, H.; Breedlove, B. K.; Kajiwara, T.; Takaishi, S.; Ishikawa, N.; Isshiki, H.; Zhang, Y. F.; Komeda, T.; Yamagishi, M.; Takeya, J. J. Am. Chem. Soc. 2009, 131, 9967. (12) Cao, L.; Chen, H.-Z.; Zhou, H.-B.; Zhu, L.; Sun, J.-Z.; Zhang, X.-B.; Xu, J.-M.; Wang, M. Adv. Mater. 2003, 15, 909. (13) Kyatskaya, S.; Mascaros, J. R. G.; Bogani, L.; Hennrich, F.; Kappes, M.; Wernsdorfer, W.; Ruben, M. J. Am. Chem. Soc. 2009, 131, 15143. (14) Vitali, L.; Fabris, S.; Conte, A. M.; Brink, S.; Ruben, M.; Baroni, S.; Kern, K. Nano Lett. 2008, 8, 3364. (15) Stepanow, S.; Honolka, J.; Gambardella, P.; Vitali, L.; Abdurakhmanova, N.; Tseng, T.-C.; Rauschenbach, S.; Tait, S. L.; Sessi, V.; Klyatskaya, S.; Ruben, M.; Kern, K. J. Am. Chem. Soc. 2010, 132, 11900. (16) Chen, X.; Fu, Y.-S.; Ji, S.-H.; Zhang, T.; Cheng, P.; Ma, X.-C.; Zou, X.-L.; Duan, W.-H.; Jia, J.-F.; Xue, Q.-K. Phys. Rev. Lett. 2008, 101, 197208. (17) Ye, T.; Takami, T.; Wang, R.; Jiang, J.; Weiss, P. S. J. Am. Chem. Soc. 2006, 128, 10984. 5543

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(18) Miyake, K.; Fukuta, M.; Asakawa, M.; Hori, Y.; Ikeda, T.; Shimizu, T. J. Am. Chem. Soc. 2009, 131, 17808. (19) Zhang, Y. F.; Isshiki, H.; Katoh, K.; Yoshida, Y.; Yamashita, M.; Miyasaka, H.; Breedlove, B. K.; Kajiwara, T.; Takaishi, S.; Komeda, T. J. Phys. Chem. C 2009, 113, 9826. (20) Zhang, Y.; Guan, P.; Isshiki, H.; Chen, M.; Yamashita, M.; Komeda, T. Nano Res. 2010, 3, 604. (21) Toader, M.; Gopakumar, T. G.; Abdel-Hafiez, M.; Hietschold, M. J. Phys. Chem. C 2010, 114, 3537. (22) Bai, Y.; Buchner, F.; Kellner, I.; Schmid, M.; Vollnhals, F.; Steinr€uck, H.-P.; Marbach, H.; Gottfried, J. M. New J. Phys. 2009, 11, 125004. (23) Ishikawa, N.; Sugita, M.; Tanaka, N.; Ishikawa, T.; Koshihara, S.; Kaizu, Y. Inorg. Chem. 2004, 43, 5498. (24) Toader, M.; Hietschold, M. J. Phys. Chem. C 2011, 115, 3099. (25) Bedrossian, P.; Chen, D. M.; Mortensen, K.; Golovchenko, J. A. Nature 1989, 342, 258. (26) Lyo, I.-W.; Avouris, P. Science 1989, 245, 1369. (27) Ribeiro, F. J.; Lu, W.; Bernholc, J. ACS Nano 2008, 2, 1517. (28) Chen, J.; Reed, M. A.; Rawlett, A. M.; Tour, J. M. Science 1999, 286, 1550. (29) Yoon, W.-J.; Chung, S.-Y.; Berger, P. R.; Asar, S. M. Appl. Phys. Lett. 2005, 87, 203506. (30) Guisinger, N. P.; Greene, M. E.; Basu, R.; Baluch, A. S.; Hersam, M. C. Nano Lett. 2004, 4, 55. (31) Chen, L.; Hu, Z.; Zhao, A.; Wang, B.; Luo, Y.; Yang, J.; Hou, J. G. Phys. Rev. Lett. 2007, 99, 146803. (32) Peisert, H.; Knupfer, M.; Schwieger, T.; Fuentes, G. G.; Olligs, D.; Fink, J.; Schmidt, Th. J. Appl. Phys. 2003, 93, 9683. (33) Piper, L. F. J.; Cho, S. W.; Zhang, Y.; DeMasi, A.; Smith, K. E.; Matsuura, A. Y.; McGuinness, C. Phys. Rev. B 2010, 81, 045201.

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Locally Auxetic Behavior of Elastomeric Polypropylene on the 100 nm Length Scale Mechthild Franke* and Robert Magerle* Fakult€at f€ur Naturwissenschaften, Technische Universit€at Chemnitz, 09107 Chemnitz, Germany

A

uxetic materials are materials with a negative Poisson's ratio; they expand laterally when stretched. This unusual behavior was originally attributed to a microstructure forming a reentrant network.13 Meanwhile, additional mechanisms causing auxetic behavior and materials with corresponding microstructures on molecular as well as macroscopic length scales have been found,46 such as certain molecular networks,3,79 networks of dilating elastic elements,1012 expanding chiral honeycomb lattices,13,14 and rotating rigid units.1517 Nevertheless, auxetic materials rarely occur naturally. Particular processing steps are required for producing polymeric materials with auxetic behavior such as foams,1,18,19 microporous films and fibers,2024 and macroscopically perforated sheets.25,26 Among the large class of semicrystalline polymers with a natural microstructure, auxetic behavior has not been previously found. In these intrinsically nanostructured materials, 10 nm thick crystalline lamellae strengthen the material and act as physical cross-links for the polymer molecules. The spatial arrangement and mechanical stability of crystalline regions are important factors in determining the mechanical properties of the material.27 Previous micromechanical studies focused on averaged crystal orientation,2837 crystallinity during straining,34,36 and the study of crazing,38,39 which is a common failure mechanism of these materials. Here, we report on unexpected locally auxetic behavior in elastomeric polypropylene (ePP), a semicrystalline polymer with a low degree of crystallinity.40 Our results reveal a mechanism for auxetic behavior similar to the stretching mechanism proposed by Rothenburg et al.10 based on purely geometric arguments. Its manifestation in ePP is related to the intrinsic properties of the material on the nanometer scale. FRANKE AND MAGERLE

ABSTRACT We observe unexpected locally auxetic behavior in elastomeric polypropylene, a

semicrystalline polymer with a natural microstructure and a low degree of crystallinity. Our series of scanning force microscopy images show the nanomechanical deformation processes that occur upon stretching a thin film of elastomeric polypropylene. Upon uniaxial stretching, the angle between epitaxially grown lamella branches remains constant and the lamellae elongate, resulting in locally auxetic behavior (negative Poisson's ratio) on the 100-nanometer scale. This mechanism causing auxetic behavior, which was previously proposed on the basis of geometric arguments, appears to be an intrinsic property of certain semicrystalline polymers. KEYWORDS: negative Poisson's ratio . nanomechanics . semicrystalline polymers . thin films . scanning force microscopy

RESULTS AND DISCUSSION Figure 1a shows a scanning force microscopy (SFM) phase image of the surface of an ∼1 μm thick film of ePP before stretching. The 10 nm thick crystalline lamellae appear as bright lines because they are oriented perpendicular to the film surface.41 The polymer forms long mother lamellae on which short epitaxial branches grow, forming an angle of 80 between the mother and daughter lamellae.4244 The lamellae are straight before the film is stretched (Figure 1a). Upon stretching the film in the y-direction to ε = 40% (Figure 1b), the lamellae deform in various ways: some buckle, others bend, and others break up into smaller fragments. The deformations are not affine on the submicrometer scale. On larger length scales (>1 μm), the deformations follow the uniaxial stretching with negligible lateral contraction as given by the slit geometry. We compiled the series of SFM phase images during stretching into an animated image sequence (see Supporting Information), which gives an impression of the deformations that occur on the 100 nm scale as the film is stretched. Connection points between large clusters of lamellae become obvious as well as clusters of lamellae moving VOL. 5

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independently from each other. The deformation behavior of the crystal complex shown in Figure 1a and b resembles a tree branch that is pulled through a highly viscous liquid. This is plausible since the crystals are solid with a Young's modulus of 40 GPa along the chain direction,45 and the amorphous matrix is viscoelastic at room temperature.40,46,47 Furthermore, this mother lamella widens perpendicular to the stretching direction from 631 nm at ε = 0% to 701 nm at ε = 40%. FRANKE AND MAGERLE

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Figure 1. SFM phase images of an ePP film before (a) and after stretching the film in the y-direction to a global strain of ε = 40% (b). Quadrilaterals A, B, and C are shown in Figure 2. D and E mark bending lamellae. (c) Angle j between mother (M ) and daughter lamella (D ) as function of global strain ε. For the branching numbered in (a) the average angle j h over the interval from ε = 0% to ε = 40% is given and indicated with a solid line. The j-scale is the same for all angles.

We now address the deformation behavior of individual crystalline lamellae and their branchings displaying locally auxetic behavior on the 100 nm length scale. A striking feature is that the acute angles formed between mother and daughter lamellae remain unchanged up to global strains of ε = 40% (Figure 1c). The scatter corresponds to the accuracy of the measurement. The mean values are ∼80, in accordance with the epitaxial growth mechanism.4244 At strains larger than ε = 40%, some angles widen by ∼10 to 20. Figure 2 shows SFM phase images of lamellae that are arranged in such a way that they form irregular quadrilaterals with one diagonal oriented roughly along the stretching direction with sizes from ∼100 nm (Figure 2ac) to ∼1 μm (Figure 2d). The lamellae elongate up to 1.5 times their initial length (Figure 2). This large relative elongation of up to 50% is unexpected considering that deformations of crystalline lattices upon straining are on the order of only a few percent.48 On the 100 nm length scale, the quadrilaterals widen along the stretching direction as well as perpendicular to it. On the macroscopic scale, the deformation of a material perpendicular to the strain direction is described by Poisson's ratio. In analogy to this concept, we describe the deformation behavior of individual quadrilaterals by a local Poisson's ratio, ν = (Δd/d)/(Δl/l), where d and l are the width and length of the quadrilateral perpendicular and parallel to the stretching direction of the film, respectively, and Δd and Δl are the corresponding changes. ν = 0.68, 2.59, and 0.18 at ε = 60% for the cases shown in Figure 2a, b, c, respectively. On the 1 μm scale, the quadrilateral shown in Figure 2d elongates only along the stretching direction and keeps its width perpendicular to the stretching direction, corresponding to a local Poisson's ratio of ν = 0.0072. Also the right-hand branch of the crystal complex shown in Figure 1a widens perpendicularly to the stretching direction from 631 nm at ε = 0% to 701 nm at ε = 40%. A local widening perpendicular to the stretching direction is also visible in other regions of the film (see Supporting Information). Almost all the lamellae elongate. Furthermore, there is no correlation between the relative elongation of a lamella and the fact that a lamella is a mother or daughter lamella. In addition to the lamella length, we measured the angles of the quadrilaterals during stretching. The angles of the ∼100 nm large quadrilaterals change by less than 10 for ε < 40% (Figure 2ac), whereas those of the 1 μm large quadrilateral change up to 40 (Figure 2d). On the basis of the results of the deformation behavior of the angles between mother and daughter lamella (Figure 1), we conclude that angles that do not or only slightly deform are formed by epitaxially grown daughter lamellae; angles that change significantly are unlikely to be formed by VOL. 5

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ARTICLE Figure 2. Deformation behavior of individual crystal complexes: (ac) on the 100 nm scale, (d) on the 1 μm scale. SFM phase images at ε = 0%, ε = 60%, and after releasing the strain to ε = 27%, relative elongation of crystalline lamellae marked in the SFM images, and angles between these crystalline lamellae as a function of global strain ε (from top to bottom). The colors in the SFM images correspond to the colors of the data points. The lines show the expected behavior assuming no expansion of the quadrilaterals in the x-direction.

epitaxially grown daughter lamellae. The deformation behavior of quadrilaterals that do not deform perpendicular to the stretching direction can be directly derived from geometric relations (see the Materials and Methods section) and is shown as solid lines in Figure 2. The assumption of no deformations perpendicular to the stretching direction is motivated by the global constraints imposed on the film by the slit geometry. The model describes the trend and the magnitude of the measured relative lamella elongations for ε < 30% as well as the change of angles for the quadrilaterals with a local Poisson's ratio ν = 0.18 (Figure 2c) and 0.0072 (Figure 2d). However, the model fails for the quadrilaterals with a negative local Poisson's ratio (Figure 2a,b). It predicts a change of angles with increasing global strain ε. In contrast to this, the measured angles are constant for ε < 40%, as is also observed for other angles between mother and daughter lamellae (Figure 1). The local Poisson's ratio of the quadrilateral shown in Figure 2b is ν = 2.59. This value is smaller than 1, which indicates that this quadrilateral widens more than it elongates. A behavior where FRANKE AND MAGERLE

Figure 3. Sketches of the assumed deformation behavior of a quadrilateral of crystalline lamellae (left) and an individual crystalline lamella forming one side of the quadrilateral (right, viewed perpendicular to the lamella side) upon stretching the ePP film along the y-direction. The grain structure of the lamella is indicated. (a) Initial state, (b) after deformation. The lamella width w is constant. The volume V of the amorphous region enclosed by a quadrilateral is marked in gray. It increases upon stretching the film: V = V0(1 þ ε).

only the sides of the quadrilateral elongate while the angles stay constant corresponds to a local Poisson's ratio of ν = 1. On releasing the strain, the quadrilaterals shrink along the stretching direction. In contrast, VOL. 5

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their widths remain almost constant perpendicular to the stretching direction. This is accompanied by a shortening of the lamellae and changes of the angles of the quadrilaterals (Figure 2). Since the maximum global strain of ε = 61% is beyond the elastic limit of the material,20 we attribute the relaxation behavior to partially plastic deformations of the microstructure. We now discuss possible explanations of the observed deformation behavior during stretching. We observe that many crystalline lamellae break into smaller fragments, which supports the models of Strobl49 and Sirota,50 who proposed that each lamella is a mosaic of ∼10 nm large crystalline grains. Other lamellae, in particular those forming the large crystal complex shown in Figure 1 and the ∼100 nm large quadrilateral shown in Figure 2ac, elongate considerably while retaining their continuous shape even at large global strain. The elongation is an order of magnitude larger than the elongation of the lattice constant during straining.48 The apparent growth during straining can be explained with the block model of crystalline lamellae.49,50 One explanation is that the growth of the lamellae occurs at the grain boundaries between the small grains when they are pulled apart. An alternative explanation is a rearrangement of grains via motion of grain boundaries within a lamella (Figure 3). On length scales g 1 μm no deformations occur along the x-direction (Figure 2d). This is in accordance with the global constraints imposed on the film by the slit geometry. This fact and the assumption that the volume is conserved on length scales g 1 μm imply that the thickness h of the film is reduced to h/(1 þ ε) upon stretching the polymer film. We will show that this is an important factor causing the locally auxetic behavior. For ε = 60%, the film thickness should decrease by 37.5%. This is corroborated by an observed decrease of the height corrugation of the film surface. We can only speculate about the internal rearrangements of the crystalline lamellae during this change of shape. Lamellae are oriented perpendicular to the film surface and are known to extend throughout the entire film.41 Since we do not observe individual lamellae poking out of the film surface upon stretching the film, we assume that the height of each lamella is reduced by the factor (1 þ ε)1 (Figure 3). This decrease in lamella height is accompanied by the apparent growth of the crystalline region along the long axis of the lamella so as to conserve the volume of crystalline material within each lamella since the width of lamellae are known not to change during straining.29 The entanglements of polymer chains prevent the increase of the lamella width during deformations. This is the same reason that limits the growth of lamella width during crystallization.49 The local conservation of the volume of the crystalline material implies that the overall crystallinity of the sample does not change during straining. This agrees with observations that

Figure 4. Schematic diagram of the setup used in the micromechanics experiment. (a) Silicon substrate with a support frame and a polymer film (marked by a dashed line) deposited across the slit. The slotted substrate was cut from a silicon wafer with a water-jet-guided laser (Laser MicroJet, SYNOVA, Lausanne, Switzerland). (b) The substrate with the free-standing film is glued onto a piezoelectric-driven symmetric stretching device (d-Drive, Piezosystem Jena, Jena, Germany), and after the glue has hardened, the support frame is removed. (c) The free-standing polymer film is stretched and its microstructure is observed with SFM at the surface of the film. The movement of the piezo drive was calibrated using an optical microscope.

more than 300% strain is required for inducing additional crystallization of this material.34 The proposed deformation mechanism of quadrilaterals implies that the volume V of the amorphous region enclosed by a quadrilateral increases by the factor (1 þ ε) upon stretching the polymer film in the ydirection. The dilation of the volume V enclosed by a quadrilateral validates identifying this deformation behavior as locally auxetic deformation behavior. Furthermore, if the number of atoms within the volume V = V0(1 þ ε) does not change, the increase in volume corresponds to a reduction of the density by a factor (1 þ ε)1. This local density decrease is probably accompanied by a compression of the amorphous regions surrounding the expanding quadrilateral. Due to this micromechanical deformation mechanism, spatial density heterogeneities are expected to be generated on the 100 nm length scale upon stretching the polymer film. Since we do not observe a depression of the film surface inside the quadrilaterals or a squeeze-out of amorphous material in the vicinity of those quadrilaterals, we conclude that if such density heterogeneities are initially created by stretching the film, they relax within the time required to measure the SFM images (within an hour or more). This time is much larger than the time constant of stress relaxation in ePP, which ranges between 10 s and 30 min.46,47 Some very interesting and open questions in this context are the roles of molecular conformations within the amorphous phase, the topology of the network formed by the entanglements and polymer chains anchored in the crystalline regions, and the deformations of the molecular network upon stretching the film. VOL. 5

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Large-scale computer simulations based on molecular dynamics and/or Monte Carlo methods are required to resolve these questions. CONCLUSIONS The constant width of the crystalline lamellae and the volume conservation of crystalline material cause

MATERIALS AND METHODS We developed a sample preparation technique and a tensile straining setup that allow the deformations of individual crystalline lamellae at increasing degrees of strain to be imaged with scanning force microscopy. We investigated elastomeric stereoblock polypropylene polymerized by metallocene catalysis40 with a weight-average molecular weight of 153 kg/mol, an [mmmm] pentad content of 26%, which corresponds to 12% crystallinity,36 and a glass transition temperature of 5 C. An approximately 1 μm thick film of ePP was prepared by drop casting a 5 mg/mL ePP solution in decaline onto a NaCl crystal. The dried film was floated onto a water surface and transferred onto a slotted silicon substrate, as shown in Figure 4a. NaCl residues were removed with distilled water. The film was stepwise stretched in the y-direction to a maximum strain of ε = 61%. Afterward, the strain was stepwise reduced to ε = 27%, where ε is the global strain in the y-direction given by ε = (L L0)/L0, where L is the slit width and L0 = 150 μm is the initial slit width. To prevent damage to the tip and film, the SFM tip was retracted while varying the strain. After each stretching step, the same area of the free-standing polymer film was imaged with tapping mode SFM, as described previously.51 To correct for global displacements of the specimen, the series of images was registered by laterally shifting individual images to achieve a best fit. Angles and lamella lengths were measured using ImageJ.52 The relative elongation (l l0)/l0 of the individual lamellae was calculated from the initial length l0 of the lamellae and their length l at global strain ε. Figure 5a shows the deformations of a two-dimensional quadrilateral upon uniaxial elongation along its diagonal. The deformation of the left-hand side of the quadrilateral is shown in Figure 5b,c. The relations between the initial length of the side l0 and the lengths a and b and its length l at strain ε and the lengths a and b(1 þ ε) are given by the Pythagorean formula. From this, the relative elongation of a side of the quadrilateral is calculated to be (l l0 )=l0 ¼ [1þ2ε(1þε=2)sin2 (R0 )]1=2 The angle R0 is defined in Figure 5. The relation between the angle (R þ β) at strain ε and the initial angle (R0 þ β0) at strain ε = 0 can be easily derived from the geometric relations given in Figure 5.

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Acknowledgment. We thank N. Rehse and M. Jecke for their contributions to the design of the setup and sample preparation. We thank B. Rieger for providing the ePP, G. Schr€ oder-Turk and M. Neumann for useful discussions, and S. McGee for proofreading the manuscript. This work was supported by the Volkswagen Foundation and the Deutsche Forschungsgemeinschaft. Author contributions: R.M. designed the experiment together with N. Rehse and M. Jecke. M.F. performed the experiments and analyzed the data. M.F. and R.M. jointly interpreted the results and wrote the paper. Supporting Information Available: Movie showing an animated series of SFM phase images upon stretching the ePP film from ε = 0% to ε = 61%. In the movie, the image sequence has been added in reversed order after the maximum strain is reached. This facilitates observing the details of the micromechanics, while watching the movie in a continuous loop. Only every tenth image of the entire series is shown in the movie. This material is available free of charge via the Internet at http:// pubs.acs.org.

REFERENCES AND NOTES 1. Lakes, R. Foam Structures with a Negative Poisson's Ratio. Science 1987, 235, 1038–1040. 2. Evans, K. E.; Nkansah, M. A.; Hutchinson, I. J.; Rogers, S. C. Molecular Network Design. Nature 1991, 353, 124. 3. Evans, K. E. Auxetic Polymers: A New Range of Materials. Endeavour, New Series 1991, 15, 170–174. 4. Evans, K. E.; Alderson, A. Auxetic Materials: Functional Materials and Structures from Lateral Thinking!. Adv. Mater. 2000, 12, 617–628. 5. Yang, W.; Li, Z.-M.; Shi, W.; Xie, B.-H.; Yang, M.-B. On Auxetic Materials. J. Mat. Sci. 2004, 39, 3269–3279. 6. Liu, Y. P.; Hu, H. A Review on Auxetic Structures and Polymeric Materials. Sci. Res. Essays 2010, 5, 1052– 1063. 7. Wojciechowski, K. W. Constant Thermodynamic Tension Monte Carlo Studies of Elastic Properties of a Two-Dimensional System of Hard Cyclic Hexamers. Mol. Phys. 1987, 61, 1247–1258. 8. Wojciechowski, K. W. Two-Dimensional Isotropic System with a Negative Poisson Ratio. Phys. Lett. A 1989, 137, 60–64.

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Figure 5. (a) In-plane deformation of a quadrilateral upon uniaxial elongation along one of its diagonals. In the perpendicular direction, the quadilateral's width does not change. The sides elongate and the angles change upon this uniaxial elongation. (b) Left-hand side of the quadrilateral at ε = 0 and (c) at ε > 0.

the elongation of lamellae along their long axis. The epitaxial relationship between mother and daughter lamellae explains the mechanical stability of their connection during straining. As a result, the increase in length combined with the fixed angles between mother and daughter lamellae cause the locally auxetic behavior on the 100 nm length scale. This is a manifestation of the general, length-scale-independent mechanism for auxetic behavior that was proposed by Rothenburg et al.10 based on purely geometric arguments. Our results show that locally auxetic behavior is an intrinsic property of certain semicrystalline polymers. More broadly, our results demonstrate that a microstructure configuration of elements that only elongate upon straining while maintaining constant angles between them is a feasible route for the design of auxetic materials. An example of such a material might be R-polypropylene, where crystalline lamellae form a cross-hatch structure,43,44 which is a continuous network of ∼100 nm large quadrilaterals, like that in our work.

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9. Wojciechowski, K. W. Non-Chiral, Molecular Model of Negative Poisson Ratio in Two Dimensions. J. Phys. A: Math. Gen. 2003, 36, 11765–11778. 10. Rothenburg, L.; Berlin, A. A.; Bathurst, R. J. Microstructure of Isotropic Materials with Negative Poisson Ratio. Nature 1991, 354, 470–472. 11. Masters, I. G.; Evans, K. E. Models for the Elastic Deformation of Honeycombs. Compos. Struct. 1996, 35, 403–422. 12. Grima, J. N.; Farrugia, P. S.; Caruana, C.; Gatt, R.; Attard, D. Auxetic Behaviour from Stretching Connected Squares. J. Mater. Sci. 2008, 43, 5962. 13. Prall, D.; Lakes, R. S. Properties of a Chiral Honeycomb with a Poisson's Ratio of 1. Int. J. Mech. Sci. 1997, 39, 305–314. 14. Alderson, A.; Alderson, K. L.; Attard, D.; Evans, K. E.; Gatt, R.; Grima, J. N.; Miller, W.; Ravirala, N.; Smith, C. W.; Zied, K. Elastic Constants of 3-, 4- and 6-Connected Chiral and Anti-Chiral Honeycombs Subject to Uniaxial In-Plane Loading. Compos. Sci. Technol. 2010, 70, 1042–1048. 15. Grima, J. N.; Evans, K. E. Auxetic Behavior from Rotating Squares. J. Mater. Sci. Lett. 2000, 19, 1563–1565. 16. Grima, J. N.; Gatt, R.; Ravirala, N.; Alderson, A.; Evans, K. E. Negative Poisson's Ratios in Cellular Foam Materials. Mater. Sci. Eng., A 2006, 423, 214–218. 17. Grima, J. N.; Gatt, R.; Alderson, A.; Evans, K. E. An Alternative Explanation for the Negative Poisson's Ratios in R-Cristobalite. Mater. Sci. Eng., A 2006, 423, 219–224. 18. Bianchi, M.; Scarpa, F.; Banse, M.; Smith, C. W. Novel Generation of Auxetic Open Cell Foams for Curved and Arbitrary Shapes. Acta Mater. 2001, 59, 686–691. 19. Grima, J. N.; Attard, D.; Gatt, R.; Cassar, R. N. A Novel Process for the Manufacture of Auxetic Foams and for their ReConversion to Conventional Form. Adv. Eng. Mater. 2009, 11, 533–535. 20. Caddock, B. D.; Evans, K. E. Microporous Materials with Negative Poisson's Ratios. I. Microstructure and Mechanical Properties. J. Phys. D: Appl. Phys. 1989, 22, 1877–1882. 21. Alderson, K. L.; Webber, R. S.; Kettle, A. P.; Evans, K. E. Novel Fabrication Route for Auxetic Polyethylene. Part 1. Processing and Microstructure. Polym. Eng. Sci. 2005, 45, 568–578. 22. Ravirala, N.; Alderson, A.; Alderson, K. L.; Davies, P. J. Auxetic Polypropylene Films. Polym. Eng. Sci. 2005, 45, 517–528. 23. Pickles, A. P.; Alderson, K. L.; Evans, K. E. The Effects of Powder Morphology on the Processing of Auxetic Polypropylene (PP of Negative Poisson's Ratio). Polym. Eng. Sci. 1996, 36, 636–642. 24. Alderson, K. L.; Alderson, A.; Smart, G.; Simkins, V. R.; Davies, P. J. Auxetic Polypropylene Fibres Part 1Manufacture and Characterisation. Plast., Rubber Compos. 2002, 31, 344–349. 25. Grima, J. N.; Gatt, R. Perforated Sheets Exhibiting Negative Poisson's Ratios. Adv. Eng. Mater. 2010, 12, 460–464. 26. Bertoldi, K.; Reis, P. M.; Willshaw, S.; Mullin, T. Negative Poisson's Ratio Behavior Induced by an Elastic Instability. Adv. Mater. 2010, 22, 361–366. 27. Nielsen, L. E.; Landel, R. F. Mechanical Properties of Polymers and Composites, 2nd ed.; Marcel Dekker: New York, 1994; Vol. 90. 28. Aboulfaraj, M.; G'Sell, C.; Ulrich, B.; Dahoun, A. In Situ Observation of the Plastic Deformation of Polypropylene Spherulites Under Uniaxial Tension and Simple Shear in the Scanning Electron Microscope. Polymer 1995, 36, 731–742. 29. Hild, S.; Gutmannsbauer, W.; L€ uthi, R.; Fuhrmann, J.; G€ untherodt, H.-J. A Nanoscopic View of Structure and Deformation of Hard Elastic Polypropylene with Scanning Force Microscopy. J. Polym. Sci., Part B: Polym. Phys. 1996, 34, 1953–1959. 30. Hild, S.; Rosa, A.; Marti, O., Deformation Induced Changes in Surface Properties of Polymers Investigated by Scanning Force Microscopy. In Scanning Probe Microscopy of Polymers; Ratner, B. D.; Tsukruk, V. V., Eds.; American Chemical Society: Washington, DC, 1998; pp 110129. 31. Petermann, J.; Ebener, H. On the Micromechanisms of Plastic Deformation in Semicrystalline Polymers. J. Macromol. Sci. Part B Phys. 1999, 5&6, 837–846. 32. Godehardt, R.; Rudolph, S.; Lebek, W.; Goerlitz, S.; Adhikari, R.; Allert, E.; Giesemann, J.; Michler, G. H. Morphology and

Micromechanical Behavior of Blends of Ethene/1-Hexene Copolymers. J. Macromol. Sci. Part B Phys. 1999, 38, 817– 835. Kravchenko, R. L.; Sauer, B. B.; McLean, R. S.; Keating, M. Y.; Cotts, P. M.; Kim, Y. H. Morphology Investigation of Stereoblock Polypropylene Elastomer. Macromolecules 2000, 33, 11–13. Auriemma, F.; De Rosa, C. Stretching Isotactic Polypropylene: From “Cross-R” to Crosshatches, from γ-Form to R-Form. Macromolecules 2006, 39, 7635–7647. Auriemma, F.; De Rosa, C.; Corradi, M. Stereoblock Polypropylene as a Prototype Example of Elasticity via a FlipFlop Reorientation of Crystals in a Compliant Matrix. Adv. Mater. 2007, 19, 871–874. Boger, A.; Heise, B.; Troll, C.; Marti, O.; Rieger, B. Orientation of the R- and γ-Modification of Elastic Polypropylene at Uniaxial Stretching. Eur. Polym. J. 2007, 43, 3573–3586. Nozue, Y.; Shinohara, Y.; Ogawa, Y.; Sakurai, T.; Hori, H.; Kasehara, T.; Yamaguchi, N.; Yagi, N.; Amemiya, Y. Deformation Behavior of Isotactic Polypropylene Spherulite During Hot Drawing Investigated by Simultaneous Microbeam SAXS-WAXS and POM Measurement. Macromolecules 2007, 40, 2036–2045. Thomas, C.; Ferreiro, V.; Coulon, G.; Seguela, R. In Situ AFM Investigation of Crazing in Polybutene Spherulites Under Tensile Drawing. Polymer 2007, 48, 6041–6048. Hobbs, J. K.; Winkel, A. K.; McMaster, T. J.; Humphris, A. D. L.; Baker, A. A.; Blakely, S.; Aissaoui, M.; Miles, M. J. Some Recent Developments in SPM of Crystalline Polymers. Macromol. Symp. 2001, 167, 1–14. Dietrich, U.; Hackmann, M.; Rieger, B.; Klinga, M.; Leskel€a, M. Control of Stereoerror Formation with High-Activity “Dual-Side” Zirconocene Catalysts: A Novel Strategy to Design the Properties of Thermoplastic Elastic Polypropylenes. J. Am. Chem. Soc. 1999, 121, 4348–4355. Rehse, N.; Marr, S.; Scherdel, S.; Magerle, R. Three-Dimensional Imaging of Semicrystalline Polypropylene with 10 nm Resolution. Adv. Mater. 2005, 17, 2203–2206. Lotz, B.; Wittmann, J. C.; Lovinger, A. J. Structure and Morphology of Poly(propylenes): A Molecular Analysis. Polymer 1996, 37, 4979–4992. Norton, D. R.; Keller, A. The Spherulitic and Lamellar Morphology of Melt-Crystallized Isotactic Polypropylene. Polymer 1985, 26, 704–716. Sch€ onherr, H.; Wiyatno, W.; Pople, J.; Frank, C. W.; Fuller, G. G.; Gast, A. P.; Waymouth, R. M. Morphology of Thermoplastic Elastomers: Elastomeric Polypropylene. Macromolecules 2002, 35, 2654–2666. Sawatari, C.; Matsuo, M. Elastic Modulus of Isotactic Polypropylene in the Crystal Chain Direction as Measured by X-Ray Diffraction. Macromolecules 1986, 19, 2653–2656. Carlson, E. D.; Fuller, G. G.; Waymouth, R. M. Transient Birefringence of Elastomeric Polypropylene Subjected to Step Shear Strain. Macromolecules 1999, 32, 8094. Wiyatno, W.; Pople, J. A.; Gast, A. P.; Waymouth, R. M.; Fuller, G. G. Dynamic Response of Stereoblock Elastomeric Polypropylene Studied by Rheooptics and X-Ray Scattering. 2. Orthogonally Oriented Crystalline Chains. Macromolecules 2002, 35, 8498. Ovchinnikov, V. A.; Zhorov, V. A.; Baskaev, Z. P. Elasticity of the Crystal Lattice of Polyethylene Terephthalate. Mekhanika Polimerov 1972, 6, 982–986. Strobl, G. From the Melt via Mesomorphic and Granular Crystalline Layers to Lamellar Crystallites: A Major Route Followed in Polymer Crystallization?. Eur. Phys. J. E 2000, 3, 165–183. Sirota, E. B. Polymer Crystallization: Metastable Mesophases and Morphology. Macromolecules 2007, 40, 1043–1048. Dietz, C.; Zerson, M.; Riesch, C.; Franke, M.; Magerle, R. Surface Properties of Elastomeric Polypropylenes Studied with Atomic Force Microscopy. Macromolecules 2008, 41, 9259–9266. Abramoff, M. D.; Magelhaes, P. J.; Ram, S. J. Image Processing with ImageJ. Biophotonics Int. 2004, 11, 36–42.

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Eike-Christian Spitzner,* Christian Riesch, and Robert Magerle* Chemische Physik, Technische Universita¨t Chemnitz, D-09107 Chemnitz, Germany

T

he chemical composition and mechanical properties of the nearsurface region of polymeric materials play a crucial role for understanding structure formation phenomena such as surface segregation,1 wetting,2 and surface reconstructions,3 as well as adhesion4 and friction.5 Amplitude modulation atomic force microscopy (AM-AFM),6,7 also known as tapping mode AFM, is a versatile and widely used method for imaging polymeric surfaces as well as other soft matter, including biological cells.8,9 In AM-AFM, a cantilever with a sharp tip is excited to oscillate at (or near) its resonance frequency ␻0 and scanned along the surface of a specimen while keeping the oscillation amplitude A constant by adjusting the tip height using a feedback loop. These height changes reflect the shape of the sample surface. The simultaneously detected phase shift between the excitation signal and tip oscillation contains information about the local mechanical properties of the specimen. Compared to atomic force microscopy (AFM) in contact mode,10 AM-AFM minimizes the lateral forces acting on the sample; however, the indentation of the tip into compliant specimens cannot be neglected. For instance, on flat but mechanically heterogeneous surfaces, the AM-AFM feedback loop varies the height of the tip to keep the amplitude A constant. Thus, the height images do not necessarily represent the true shape of the surface.11 Furthermore, the phase images also include information from a certain volume below the surface due to tip indentation.12 In this article, we demonstrate a method which takes advantage of finite tip indentation to reconstruct depth-resolved images of material properties. The method is nonwww.acsnano.org

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Subsurface Imaging of Soft Polymeric Materials with Nanoscale Resolution

ABSTRACT Nondestructive depth-resolved imaging of ⬃20-nm-thick surface layers of soft polymeric materials

is demonstrated using amplitude modulation atomic force microscopy (AM-AFM). From a map of amplitude-phasedistance curves, the tip indentation into the specimen is determined. This serves as a depth coordinate for reconstructing cross sections and volume images of the specimen’s mechanical properties. Our method reveals subsurface structures which are not discernible using conventional AM-AFM. Results for surfaces of a block copolymer and a semicrystalline polymer are presented. KEYWORDS: surface properties · depth profiling · block copolymers · semicrystalline polymers · atomic force microscopy

destructive, offers subnanometer depth resolution, and complements other AFMbased volume imaging techniques that use ablation,13 ultrasonic excitation of the sample,14,15 or require certain assumptions about the specimen.16 Our approach relies on measurements of amplitude⫺phase⫺distance (APD) curves, where amplitude and phase are recorded as the tip⫺sample distance d is decreased. Knoll et al. used two-dimensional arrays of APD curves to determine the location of the true sample surface as given by the tip height h0 where attractive forces first cause a phase change.12 From this point on, the tip indentation z˜ can be determined by comparing the damped amplitude on the specimen with the damped amplitude on a noncompliant stiff surface.12,17 APD curves have also been used to describe and identify tip⫺sample interaction processes, such as energy dissipation,18⫺20 and different contributions to the origins of phase contrast.21 By plotting the energy dissipated per oscillation cycle Edis as a function of the amplitude set point ratio A/A0 (where A0 is the amplitude at a large tip⫺sample distance d), Garcia et al.19 identified different dissipation processes corresponding to different types of tip⫺sample interaction. Schro¨ter et al.21 introduced a simple model which

*Address correspondence to eike-christian.spitzner@ physik.tu-chemnitz.de, [email protected]. Received for review October 12, 2010 and accepted December 07, 2010. Published online December 21, 2010. 10.1021/nn1027278 © 2011 American Chemical Society

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Figure 1. (a) AM-AFM phase image of the surface of an SB film (A/A0 ⴝ 0.77). Bright (dark) areas correspond to PS (PB) microdomains below a PB top layer. The white line indicates the positions where A(d) and ␸(d) (shown in panels b and d, respectively) have been measured. The solid line in panel b shows the expected amplitude on a nondeformable surface. The curves are colored according to position (PS domains, PB domains, transition regions) as indicated in panel h. (d) Tip indentation z˜(d), (e) Edis(A/A0), (f) kTS(d), and (g) ␣eff/m(d) computed from APD data. (h) Schematic tip indentation z˜ as a function of position x for A/A0 ⬇ 0.5 and region classification scheme according to tip indentation.

separates the conservative and dissipative contributions to tip⫺sample interaction, permitting a better understanding of image contrast formation. RESULTS AND DISCUSSION Our subsurface imaging method combines information about material properties, contrast formation in phase images, and uses the tip indentation as a depth coordinate. This is accomplished by measuring twodimensional arrays of APD curves, where each curve contains information about the position of the true sample surface and the tip indentation, as well as depth-resolved information about the tip⫺sample interaction. The data analysis is described in the Materials and Methods section. We demonstrate this method on two polymeric model systems exhibiting nm-scale heterogeneities in the subsurface region. Both systems provide good contrast in AM⫺AFM phase imaging due to large differences in the mechanical properties of their respective components. The first system is a thin film of polystyrene-blockpolybutadiene (SB), which forms polystyrene (PS) cylin316

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ders embedded in a polybutadiene (PB) matrix22,23 (Figure 1a). We recorded 100 APD curves separated by 5 nm along the line perpendicular to the PS cylinders as indicated in Figure 1a. In Figure 1b,c, the amplitude A and phase ␸ are plotted as a function of tip⫺sample distance d. Plotting the tip indentation z˜ versus d shows identical slopes for all indentation curves up to d ⫽ 15 nm (Figure 1d). This point corresponds to an indentation of 10 nm, the depth where the tip first touches the glassy (hard) PS cylinders, pushing through the compliant (soft) PB matrix. This is in agreement with earlier results.12 In Figure 1e, the energy dissipated between the AFM tip and the sample per oscillation cycle, Edis, is plotted as a function of the set point ratio A/A0. Notably, all curves are congruent down to A/A0 ⫽ 0.91. This reflects the presence of a 10-nm-thick top layer of PB. Edis curves recorded on PS domains exhibit significantly different shapes and lower maximum values than those recorded on PB domains. We attribute the shape of the PB curves to viscoelastic dissipation processes19 and note the plateau-like shape of the PS curves, similar to those curves observed on crystalline regions of polypropylene.24 Figure 1 panels f and g show the analysis of the APD curves according to ref 21. Conservative and dissipative contributions to the total tip⫺sample interaction force are expressed by an additional tip⫺sample spring constant kTS and the effective damping parameter ␣eff/m. For kTS as well as for A and ␸, the curves recorded on PS and PB domains can be clearly distinguished. They split as d decreases, whereas for d ⬎ A0, where tip⫺sample interactions are negligible, the curves attain the same value. The set of ␣eff/m curves measured on PS domains can be identified by their lower maximum values (Figure 1f). Otherwise, the ␣eff/m curves measured on different domains exhibit the same shape. The quantities shown demonstrate a clear contrast between the two components of the SB film and deliver quantitative information about the tip⫺sample interaction. We now combine the knowledge about tip indentation z˜ for all tip⫺sample distances d (and the corresponding amplitude set points A/A0) with the quantities describing the tip⫺sample interaction (␸, Edis, kTS, and ␣eff/m) to create a depth-resolved image of the specimen. This requires no a priori information about the sample. In Figure 2, we plot ␸, Edis, kTS, and ␣eff/m as functions of lateral position x and depth z beneath the sample surface. Since surface roughness was not considerable, we set z ⬅ z˜. The resulting depth-resolved data shown in Figure 2 correspond to cross sections through the SB film. Panel a is a plot of ␸(x, z) containing data from all APD curves, where the z axis has been stretched by a factor of 2.5. The black regions indicate areas where the given depth (tip indentation) was not reached. The phase shift shows periodic variations in the local mechanical properties, corresponding to the www.acsnano.org

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regular spacing of PS cylinders. For detailed discussion, we selected two cylinders and plotted the aforementioned quantities on a magnified 1:1 scale (Figure 2b⫺e). In panel b, the phase shift ␸(x, z) gives a good impression of the general shape of the cylinders’ surface, as expected from the AM-AFM phase image, and shows a monotonous slope starting at z ⯝ 5 nm. The white lines indicate the tip indentation z˜ for the amplitude set points A/A0 ⫽ 0.999, 0.95, 0.90 (light tapping), and 0.80 (moderate tapping). These lines correspond to the lower tip inflection point when imaging with conventional AM-AFM. The phase values along one line would result in one line of the AM-AFM phase image. For several common A/A0 values, the tip inflection point visibly follows areas of nearly constant phase shift. This might partially explain the often poor phase contrast observed in AM-AFM imaging and its strong dependency on the amplitude set point A/A0.25 Edis(x, z) is plotted in panel c. Notably, most of the energy is dissipated in the soft matrix at positions between the PS cylinders at a depth of ⬃15 nm. Generally, Edis attains lower values above stiff objects, which leads to weak but visible lateral contrast at depths of only 2⫺3 nm. The remaining two panels, d and e, show kTS(x, z) and ␣eff/m(x, z). Both quantities exhibit almost constant values even for depths where ␸(x, z) has already notably increased. Furthermore, kTS and ␣eff/m grow with almost infinite slope close to the respective maximum tip indentation. Note that this drastic increase could not be completely resolved in panels d and e. To reconstruct a threedimensional image from depth-resolved data, we use thresholding to obtain the isosurfaces of a given quantity, which separate stiffer objects from the surrounding matrix. Starting with the notion of circular cylinder cross sections, ␸(x, z) reflects the general shape but does not allow the location of the cylinder surfaces to be determined due to the continuous increase of the phase signal for z ⬎ 5 nm. Edis is also not suitable for this purpose, leaving kTS(x, z) and ␣eff/m(x, z). The cylinder surface is indicated by a strong increase in the two parameters mentioned above. In kTS(x, z), slight shadows appear above the cylinders. In ␣eff/m(x, z), the cylinders appear broadened compared to kTS(x, z). The second system is a thin film of elastomeric polypropylene.26 Its surface properties and volume structure have been studied previously.24,27⫺30 We investigated a 250 ⫻ 250 nm2 surface area by recording 50 ⫻ 50 APD curves with 5-nm separation. From these data, we have reconstructed maps of kTS as a function of depth z and combined them into a volume image. In Figure 3a, the kTS isosurface is shown as yellow, enclosing the crystalline (hard) regions of ePP, whereas the amorphous (compliant) regions are shown as transparent. A cross section (x, z) along one lamella is presented

Figure 2. ␸ plotted as a function of depth z and position x along the white line shown in Figure 1a. (bⴚe) ␸(x, z), Edis(x, z), kTS(x, z), and ␣eff/m(x, z) for the two indicated cylinders in 1:1 scaling. The white lines in panel b show the tip indentation z˜ for different set points A/A0.

in Figure 3b. Figure 3c shows a conventional AM-AFM phase image of the area where the APD curves were measured. In Figure 3d,e, the kTS slices for three different depths are presented. The gray scale has been adapted to the respective minimum and maximum. In contrast to the AM-AFM phase image, where only the lateral extension of lamellae is discernible, Figure 3 panels a and b show the detailed three-dimensional shape of the lamella edges. The latter display height corrugations of ⬃5 nm (in the z direction) and ⬃15-nm-large blocks along the lamellae, supporting earlier findings that crystalline lamellae are formed from grains of this size.31 Furthermore, Figure 3b reveals the laterally heterogeneous thickness of the amorphous top layer as claimed in previous works.24,32 This is corroborated by Figure 3d, where no crystalline regions are visible at a depth of z ⫽ 1 nm. In contrast, more and more lamellae appear at z ⫽ 5 and 15 nm (Figure 3 panels e and f, VOL. 5 ▪ NO. 1 ▪ 315–320 ▪ 2011

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Figure 3. (a) Isosurface volume image reconstructed from normalized kTS maps representing the top 19 nm of the ePP specimen. (b) Cross section through the volume image shown in panel a along one lamella marked with a dotted line in panel c. (c) AM-AFM phase image of the same spot (A/A0 ⴝ 0.90). Crystalline lamellae appear bright, whereas dark regions indicate amorphous material. The viewing direction of the 3D volume image shown in panel a is indicated by a white arrow. (dⴚf) Normalized kTS maps for 1, 5 nm, and 15 nm depth, respectively.

respectively). At larger depths, the lamellae appear broadened compared to those closer to the surface. This can be explained by the influence of the conical shape of the tip, which becomes greater with increasing z.

MATERIALS AND METHODS Sample Preparation. Polystyrene-block-polybutadiene was obtained from Polymer Source, Inc., Canada, with weight averPB ⫺1 aged molecular weights MPS w ⫽ 13.6 kg · mol , Mw ⫽ 33.7 kg · mol⫺1 of the two blocks, and polydispersity Mw/Mn ⫽ 1.03. A 60-nm-thick film was prepared by spin-casting onto a silicon substrate from a 1 wt % solution in toluene, followed by annealing at 23 °C for 14 h in a nitrogen atmosphere with 70% partial pressure of chloroform vapor. This procedure results in polystyrene cylinders, which are aligned parallel to the surface and embedded in a polybutadiene matrix. Elastomeric polypropylene (ePP) with Mw ⫽ 160 kg · mol⫺1 and 36% crystallinity was synthesized using a dual-side metallocene catalyst as described in ref 26. A 240-nm-thick film was prepared by drop casting a 0.6 wt % decalin solution onto a silicon substrate. The sample was first heated to 150 °C in air to melt the polymer and then kept at 100 °C in a nitrogen atmosphere for 18 h to allow for slow crystallization. This leads to the formation of 15-nm-wide, crystalline lamellae surrounded by amorphous ePP. Atomic Force Microscopy. All AFM measurements were accomplished using NanoWizard I and II devices (JPK Instruments AG, Berlin, Germany) under ambient conditions with silicon cantilevers (Pointprobe NCH, NanoWorld AG, Neuchaˆtel, Switzerland). The cantilever parameters were as follows: quality factor Q ⫽

318


CONCLUSION The method presented in this work allows objects located at the same depth which exhibit different mechanical properties to be distinguished from mechanically identical objects at different depths. In a conventional AM-AFM phase image, both would yield a similar signal. As a volume imaging technique, the lateral resolution is equal to that of AMAFM and is mainly determined by the radius and shape of the tip. In contrast, the vertical resolution is only limited by the accuracy of the amplitude detection, which is ⬃0.5 nm in our case. Furthermore, while measuring APD curves, no lateral forces act on the sample and surface deformations due to tip indentation are reversible in most cases. The shape of hard objects embedded in a soft matrix can be reconstructed. However, no information is obtained from inside or below noncompliant objects. The depth range is limited by the tip indentation, which is primarily determined by the compliance of the material. For a given sample, the tip indentation can be increased by higher excitation amplitudes of the cantilever or by decreasing the lower limit of the amplitude in APD measurements. However, to avoid destruction of the specimen, a trade-off must be found. The presented approach turns the finite tip indentation during AM-AFM imaging on soft specimens into an advantage. By analyzing maps of APD curves, we obtain the true sample surface, tip indentation, and depth resolved images of material properties in the subsurface region. This is achieved using standard AFM equipment and it opens a broad range of new research opportunities in nanoscience and soft matter physics, as well as biology, where the structure of the near surface region is of particular interest.

420, resonance frequency ␻0 ⫽ 248.904 kHz, and spring constant k ⫽ 16.5 N/m (determined as in ref 33) for the measurements on SB. The excitation frequency ␻ ⫽ ␻0. For measurements on ePP, Q ⫽ 435, ␻0 ⫽ 287.939 kHz, k ⫽ 21.2 N/m, and ␻ ⫽ 287.795 kHz. APD Curves. Amplitude A and phase ␸ were recorded pointwise by decreasing the tip height h. This is technically similar to the force volume technique, which is based on measuring static forces as a function of distance.34⫺36 We measured APD curves at points separated by 5 nm along a line (in the case of SB) or a square grid (in the case of ePP). Data Analysis. The APD curves have been analyzed according to the methods described in refs 12, 21, and 19. The unperturbed (true) sample surface h0(x, y) is the position where attractive forces first cause a phase change when approaching the surface by decreasing the AFM tip height h.12 The tip⫺sample distance d is obtained by setting d ⬅ h ⫺ h0 ⫹ A0. For plotting depth-resolved data, as shown in Figure 2, h0(x, y) measured from successively acquired curves must be consistent, which is hampered by thermal drift affecting the AFM components controlling the tip height. Standard methods, such as linewise subtraction of a best-fit first-order polynomial, are well-suited for correcting these drift effects. The tip indentation z˜ ⫽ A(d) ⫺ d. In the case of considerable surface corrugation, slices with constant tip inden-

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Edis ) -

(

πkA ω A0 sin φ + A Q ω0

)

(1)

We use the phase convention of ref 21 where, in resonance, ␸ ⫽ ⫺90°. Equation 1 has been adapted accordingly. Conservative and dissipative contributions to the total tip⫺sample interaction force are expressed by an additional tip⫺sample spring constant kTS and the effective damping parameter ␣eff/m.21 The former is given by

(

kTS ) keff - k ) m ω2 + cos(φ)

)

F0 /m -k A

(2)

where m ⫽ k/␻20 is the vibrating mass and keff is the total effective spring constant. The effective damping parameter

Reff /m )

-sin(φ) F0 /m ω A

(3)

The quantity F0/m, where F0 represents the amplitude of the excitation force, is obtained by fitting the cantilever resonance curve.21 In the case of ePP, we investigated a 250 ⫻ 250 nm2 surface area by recording 50 ⫻ 50 APD curves with 5 nm separation. From these data, we have reconstructed maps of kTS as a function of depth z, ranging from 1 to 20 nm in steps of 0.5 nm, resulting in 39 slices. To accentuate the lateral differences in kTS, we subtracted each slice’s background from the slice itself; the background was calculated by blurring with a 25-nm-wide Gaussian filter. The resulting slices were then combined into an isosurface volume image using Amira V4.0 (Mercury Computer Systems, Inc.). Acknowledgment. We thank B. Rieger and A. Scho¨bel for providing the ePP, M. Neumann for sample preparation, and S. McGee for proofreading the manuscript. We acknowledge financial support from the Volkswagen Foundation.

REFERENCES AND NOTES 1. Puri, S. Surface-Directed Spinodal Decomposition. J. Phys.: Condens. Matter 2005, 17, R101. 2. Geoghegan, M.; Krausch, G. Wetting at Polymer Surfaces and Interfaces. Prog. Polym. Sci. 2003, 28, 261–302. 3. Rehse, N.; Knoll, A.; Konrad, M.; Magerle, R.; Krausch, G. Surface Reconstruction of an Ordered Fluid: An Analogy with Crystal Surfaces. Phys. Rev. Lett. 2001, 87, 035505. 4. Possart, W. Adhesion: Current Research and Applications; Wiley-VCH: Weinheim, Germany, 2005. 5. Persson, B. N. J. Sliding Friction. Surf. Sci. Rep. 1999, 33, 83– 119. 6. Zhong, Q.; Inniss, D.; Kjoller, K.; Elings, V. Fractured Polymer/Silica Fiber Surface Studied by Tapping Mode Atomic Force Microscopy. Surf. Sci. 1993, 290, L688–L692. 7. Garcıá, R.; Pe´rez, R. Dynamic Atomic Force Microscopy Methods. Surf. Sci. Rep. 2002, 47, 197–301. 8. Magonov, S. N.; Whangbo, M.-H. Surface Analysis with STM and AFM; VCH: Weinheim, Germany, 1996. 9. Tsukruk, V. V., Ed. Advances in Scanning Probe Microscopy of Polymers; Macromolecular Symposia, Vol. 167; Wiley-VCH: Weinheim, Germany, 2001. 10. Binnig, G.; Quate, C. F.; Gerber, C. Atomic Force Microscope. Phys. Rev. Lett. 1986, 56, 930–933. 11. Brandsch, R.; Bar, G.; Whangbo, M.-H. On the Factors Affecting the Contrast of Height and Phase Images in Tapping Mode Atomic Force Microscopy. Langmuir 1997, 13, 6349–6353.

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12. Knoll, A.; Magerle, R.; Krausch, G. Tapping Mode Atomic Force Microscopy on Polymers: Where Is the True Sample Surface? Macromolecules 2001, 34, 4159–4165. 13. Magerle, R. Nanotomography. Phys. Rev. Lett. 2000, 85, 2749–2752. 14. Shekhawat, G. S.; Dravid, V. P. Nanoscale Imaging of Buried Structures via Scanning Near-Field Ultrasound Holography. Science 2005, 310, 89–92. 15. Tetard, L.; Passian, A.; Thundat, T. New Modes for Subsurface Atomic Force Microscopy through Nanomechanical Coupling. Nat. Nanotechnol. 2010, 5, 105–109. 16. Bodiguel, H.; Montes, H.; Fretigny, C. Depth Sensing and Dissipation in Tapping Mode Atomic Force Microscopy. Rev. Sci. Instrum. 2004, 75, 2529–2535. 17. Ho¨per, R.; Gesang, T.; Possart, W.; Hennemann, O.-D.; Boseck, S. Imaging Elastic Sample Properties with an Atomic Force Microscope Operating in the Tapping Mode. Ultramicroscopy 1995, 60, 17–24. 18. Ho¨lscher, H. Quantitative Measurement of Tip⫺Sample Interactions in Amplitude Modulation Atomic Force Microscopy. Appl. Phys. Lett. 2006, 89, 123109. 19. Garcıá, R.; Go´mez, C. J.; Martinez, N. F.; Patil, S.; Dietz, C.; Magerle, R. Identification of Nanoscale Dissipation Processes by Dynamic Atomic Force Microscopy. Phys. Rev. Lett. 2006, 97, 016103. 20. Cleveland, J. P.; Anczykowski, B.; Schmid, A. E.; Elings, V. B. Energy Dissipation in Tapping-Mode Atomic Force Microscopy. Appl. Phys. Lett. 1998, 72, 2613–2615. 21. Schro¨ter, K.; Petzold, A.; Henze, T.; Thurn-Albrecht, T. Quantitative Analysis of Scanning Force Microscopy Data Using Harmonic Models. Macromolecules 2009, 42, 1114–1124. 22. Knoll, A.; Horvat, A.; Lyakhova, K. S.; Krausch, G.; Sevink, G. J. A.; Zvelindovsky, A. V.; Magerle, R. Phase Behavior in Thin Films of Cylinder-Forming Block Copolymers. Phys. Rev. Lett. 2002, 89, 035501. 23. Tsarkova, L.; Knoll, A.; Krausch, G.; Magerle, R. SubstrateInduced Phase Transitions in Thin Films of CylinderForming Diblock Copolymer Melts. Macromolecules 2006, 39, 3608–3615. 24. Dietz, C.; Zerson, M.; Riesch, C.; Franke, M.; Magerle, R. Surface Properties of Elastomeric Polypropylenes Studied with Atomic Force Microscopy. Macromolecules 2008, 41, 9259–9266. 25. Magonov, S.; Elings, V.; Whangbo, M.-H. Phase Imaging and Stiffness in Tapping-Mode Atomic Force Microscopy. Surf. Sci. 1997, 375, L385–L391. 26. Dietrich, U.; Hackmann, M.; Rieger, B.; Klinga, M.; Leskela¨, M. Control of Stereoerror Formation with High-Activity “Dual-Side” Zirconocene Catalysts: A Novel Strategy To Design the Properties of Thermoplastic Elastic Polypropenes. J. Am. Chem. Soc. 1999, 121, 4348–4355. 27. Karger-Kocsis, J. Polypropylene: Structure, Blends and Composites; Chapman & Hall: London, 1995; Vol. 1. 28. Rehse, N.; Marr, S.; Scherdel, S.; Magerle, R. ThreeDimensional Imaging of Semicrystalline Polypropylene with 10 nm Resolution. Adv. Mater. 2005, 17, 2203–2206. 29. Franke, M.; Rehse, N. Three-Dimensional Structure Formation of Polypropylene Revealed by in Situ Scanning Force Microscopy and Nanotomography. Macromolecules 2008, 41, 163–166. 30. Franke, M.; Rehse, N. Nucleation of Branches in Elastomeric Polypropylene. Polymer 2008, 49, 4328–4331. 31. Hugel, T.; Strobl, G.; Thomann, R. Building Lamellae from Blocks: The Pathway Followed in the Formation of Crystallites of Syndiotactic Polypropylene. Acta Polym. 1999, 50, 214–217. 32. Sakai, A.; Tanaka, K.; Fujii, Y.; Nagamura, T.; Kajiyama, T. Structure and Thermal Molecular Motion at Surface of Semi-Crystalline Isotactic Polypropylene Films. Polymer 2005, 46, 429–437.

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tation must be shifted by h0(x, y) to obtain a z coordinate with respect to the lab reference frame. In the case of our samples, surface roughness was not considerable (always ⬍2.5 nm) and no lateral features appeared;12,24 therefore we set z ⬅ z˜. The energy dissipated between the AFM tip and the sample per oscillation cycle is given by19

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33. Sader, J. E.; Chon, J. W. M.; Mulvaney, P. Calibration of Rectangular Atomic Force Microscope Cantilevers. Rev. Sci. Instrum. 1999, 70, 3967–3969. 34. Rotsch, C.; Radmacher, M. Mapping Local Electrostatic Forces with the Atomic Force Microscope. Langmuir 1997, 13, 2825–2832. 35. A-Hassan, E.; Heinz, W. F.; Antonik, M. D.; D’Costa, N. P.; Nageswaran, S.; Schoenenberger, C.-A.; Hoh, J. H. Relative Microelastic Mapping of Living Cells by Atomic Force Microscopy. Biophys. J. 1998, 74, 1564–1578. 36. Heinz, W. F.; Hoh, J. H. Spatially Resolved Force Spectroscopy of Biological Surfaces Using the Atomic Force Microscope. Trends Biotechnol. 1999, 17, 143–150.


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LETTER pubs.acs.org/NanoLett

Spin-on Spintronics: Ultrafast Electron Spin Dynamics in ZnO and Zn1xCoxO SolGel Films Kelly M. Whitaker,†,‡,§ Maxim Raskin,†,§ Gillian Kiliani,† Katja Beha,† Stefan T. Ochsenbein,‡ Nils Janssen,†,‡ Mikhail Fonin,† Ulrich R€udiger,† Alfred Leitenstorfer,† Daniel R. Gamelin,*,‡ and Rudolf Bratschitsch*,† † ‡

Department of Physics and Center for Applied Photonics, University of Konstanz, D-78464 Konstanz, Germany Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, United States

bS Supporting Information ABSTRACT: We use time-resolved Faraday rotation spectroscopy to probe the electron spin dynamics in ZnO and magnetically doped Zn1xCoxO solgel thin films. In undoped ZnO, we observe an anomalous temperature dependence of the ensemble spin dephasing time T2*, i.e., longer coherence times at higher temperatures, reaching T2* ∼ 1.2 ns at room temperature. Time-resolved transmission measurements suggest that this effect arises from hole trapping at grain surfaces. Deliberate addition of Co2+ to ZnO increases the effective electron Lande g factor, providing the first direct determination of the mean-field electron-Co2+ exchange energy in Zn1xCoxO (N0R = +0.25 ( 0.02 eV). In Zn1xCoxO, T2* also increases with increasing temperature, allowing spin precession to be observed even at room temperature. KEYWORDS: ZnCoO, solgel, spin dynamics, hole trapping, exchange energy, time-resolved Faraday rotation

D

opant-carrier exchange interactions in diluted magnetic semiconductors (DMSs) have been exploited to control the polarizations of carrier spins in all-semiconductor spintronics device structures such as spin light-emitting diodes and spin filters.1 Among DMSs, n-type Zn1xCoxO has received extraordinary attention over the past decade,24 ever since reports of room-temperature ferromagnetism in this material began to appear.5 Remarkably, the magnitude of the Co2+-electron exchange energy (N0R) has never been measured for this DMS. Magneto-optical experiments have been used to characterize the difference between Co2+-electron and Co2+-hole exchange energies in excitonic states, N0|Rβ|, but the presence of localized midgap states complicates the analysis of magneto-optical data in this and other Zn1xTMxO DMSs substantially.69 For Zn1xCoxO even the sign of N0(Rβ) remains ambiguous.10 Here, we describe the use of time-resolved Faraday rotation (TRFR) spectroscopy to directly probe the transient electron spin dynamics in chemically prepared ZnO and Zn1xCoxO solgel films. A strong dependence of the effective electron Lande g factor (g*) on x is observed, allowing the first direct experimental measurement of both the sign and magnitude of the Co2+-electron exchange energy N0R in Zn1xCoxO. Co2+ dopants greatly accelerate spin dephasing, but the solgel synthesis allows fine control of Co2+ concentrations even in the low doping regime. Coherent spin precession is observed at room temperature in all Zn1xCoxO films with doping below x ∼ 0.0025, and the apparent spin dephasing times (T2*) increase with rising temperature. This anomalous temperature dependence is r 2011 American Chemical Society

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attributed to thermally activated hole trapping at grain surfaces, a process not seen in epitaxial thin film or bulk ZnO preparations. To our knowledge, the results presented here represent the first direct measurements of carrier spin dynamics in any member of the highly investigated Zn1xTMxO series of DMSs. ZnO films were prepared by modification of a solgel synthesis method reported previously11 (see Supporting Information for details). To fabricate Zn1xCoxO films, a fraction of the Zn(OAc)2 was replaced by a stoichiometric amount of Co(OAc)2. Figure 1a shows a scanning electron microscope (SEM) image of an x = 0.0021 Zn1xCoxO solgel film on sapphire with a thickness of 50 nm. It displays a columnar structure with an average grain diameter of about 50 nm. Structural investigation by X-ray diffraction demonstrates that the solgel films are over 98% c-plane oriented (Figure 1b). Suitability of the magnetically doped solgel films for optical experiments is confirmed by broadband optical transmission measurements, which show a clear onset of absorption at the fundamental bandgap (Figure 1c). Magnetization measurements at a temperature of T = 2 K demonstrate paramagnetic saturation behavior that was modeled using eq 1, which describes the anisotropic magnetization of Co2+ in the trigonal cation site of wurtzite ZnO. The first term describes the zero-field splitting, and the second models the effect of the magnetic field, oriented Received: May 23, 2011 Revised: July 12, 2011 Published: July 12, 2011 3355

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Figure 1. Structural, optical, and magnetic characterization of a Zn1xCoxO solgel film with a cobalt concentration of x = 0.0021. (a) Scanning electron microscope image, showing the granular structure of the film. (b) X-ray diffraction measurement, demonstrating over 98% c-plane crystal orientation. (c) Optical transmission measurement, indicating absorption at the fundamental bandgap. (d) Magnetization data recorded at T = 2 K using a perpendicular applied field (dots) and calculated perpendicular magnetization curve for the same conditions (line).

Figure 2. Time-resolved Faraday rotation traces for ZnO and Zn1xCoxO films. Time-resolved Faraday rotation data collected at (a) T = 10 K and (b) room temperature. The experimental data (solid lines) were recorded with a transverse magnetic field of Bx = 1.4 T. Laser wavelengths were λ = 368 nm at T = 10 K and λ = 375 nm at room temperature. Exponentially damped sinusoidal fits are displayed as gray dotted lines.

perpendicular to the c axis. 1 2 H ¼ D ^Sz SðS þ 1Þ þ gx μB Bx ^Sx 3

ð1Þ

D = 0.337 meV is the axial zero-field splitting parameter, ^Sx and ^Sz are spin operators, S = 3/2 is the ground-state spin of Co2+, gx = 2.2791 is the in-plane g value of Co2+ in ZnO,12 μB is the Bohr

magneton, and Bx is the magnetic field applied perpendicular to the ZnO c axis. At these very low values of x, Co2+Co2+ interactions can be neglected, including potential short-range antiferromagnetic or long-range ferromagnetic coupling. The calculated magnetization curve in perpendicular orientation agrees well with the experimental data (Figure 1d). Time-resolved Faraday rotation measurements1315 were performed to study the electron spin dynamics in the solgel 3356

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Figure 3. Dependence of electron spin dephasing times T2* on temperature and Co2+ concentration. (a) Temperature dependence of T2* in undoped ZnO (open red squares), x = 0.0001 Zn1xCoxO (filled orange triangles), and x = 0.0006 Zn1xCoxO (green crosses) solgel films. Solid lines are linear fits to the data. (b) Co2+ concentration dependence of 1/T2* at T = 10 K (filled squares), and fit to eq 5 (solid line), yielding τ0 ≈ 0.25 ps. (c) Time-resolved differential transmission of the undoped ZnO film, measured at various temperatures and normalized at t = 0 ps time delay (T = 10, 100, and 300 K data shown). The curves are taken at wavelengths ranging from 375 nm (T = 300 K) to 368 nm (T = 10 K). (d) Fractional contribution of the slow carrier recombination process (τ2 ∼ 1700 ps at T = 298 K) from panel c plotted vs temperature.

films. In this ultrafast pumpprobe technique, 3 ps laser pulses in resonance with the fundamental absorption edge of the semiconductor are used to generate and probe spin-polarized excited carriers. Figure 2 shows TRFR traces of an undoped ZnO solgel film recorded at T = 10 K (Figure 2a) and room temperature (Figure 2b), along with parallel traces collected from Zn1xCoxO films at various Co2+ concentrations (vide infra). Exponentially damped oscillatory signals are observed that can be described using eq 2, where θF is the Faraday rotation angle, A is the amplitude, ωL is the Larmor precession frequency, t is the time delay, and T2* is the ensemble spin dephasing time. θF ðtÞ ¼ A expð t=T2 Þ cosðωL tÞ

ð2Þ

From ωL, g* can then be determined according to eq 3. g ¼

pωL μ B Bx

ð3Þ

Fitting the ZnO TRFR time trace yields g* = 1.99 at T = 10 K, which agrees well with electron g* values for epitaxial ZnO films.16 As reported previously,17,18 the hole spin dephases too quickly to be observed on the picosecond time scale, so our TRFR measurements selectively probe electron spins. Remarkably, TRFR signals in these solgel films persist up to room temperature and T2* increases with rising temperatures, in stark contrast with previous observations for epitaxial ZnO films.16 This surprising trend is illustrated in Figure 3a, which plots T2* over the full temperature range between T = 10 and 298 K for three different solgel Zn1xCoxO films including x = 0 (undoped ZnO). In the undoped ZnO sample, T2* increases by over a factor of 2, from 500 ps at T = 10 K to more

than 1 ns at room temperature. The opposite dependence of T2* on temperature was observed in an undoped ZnO film grown by molecular beam epitaxy (MBE) (data not shown). Solgel films of Zn1xCoxO show a similar temperature dependence of T2* as will be discussed below. The contrast with epitaxial films suggests that the anomalous T2* observed in these solgel ZnO films arises from their granularity (Figure 1a). Hole traps at the surfaces of ZnO nanocrystals have been proposed to slow down electronhole recombination and hence allow observation of extended electron spin coherence times.19 We believe that this mechanism is also active in the solgel films studied here. To test this hypothesis, carrier recombination dynamics were probed using the same pumpprobe setup by monitoring the time evolution of the transient transmission at the ZnO band-edge following photoexcitation. Figure 3c shows the differential transmission data at three different temperatures. Biphasic recombination dynamics are observed. These dynamics were fit with a biexponential function involving a short component (τ1 ∼ 20 ps at T = 10 K, amplitude A1), attributed to direct electronhole recombination, and a long component (τ2 ∼ 700 ps at T = 10 K, amplitude A2), attributed to recombination of the conduction-band electron with a trapped hole, as discussed previously.19 It is apparent from the transient differential transmission traces in Figure 3c that the slow component becomes more prominent as the temperature is raised. Figure 3d plots the relative amplitude of the slow component (A2/(A1 + A2)) determined from the biexponential fitting vs temperature, which shows a steady increase with rising temperature. These data suggest that hole trapping becomes increasingly important at higher temperature, a result that implies that hole trapping is thermally activated. Although the possibility that other thermally activated processes may also contribute to this anomalous temperature dependence cannot be completely excluded, the correlation between the temperature dependence of the transient differential transmission and that of T2* is a strong indication that the anomalous temperature dependence of T2* is linked to the increasingly slow carrier recombination dynamics at elevated temperatures. The data are consistent with a picture in which electronhole separation is thermally activated and subsequent charge recombination is slow. Two prominent changes are observed in the TRFR signal upon precise addition of Co2+ to the ZnO solgel films (Figure 2): an increase in ωL (i.e., an increase in g*) and a rapid decrease in T2*. The inset in Figure 4a plots g* vs x for 10 solgel films with different values of x, all measured at T = 10 K. Obviously, g* in Zn1xCoxO can increase by a factor of almost 2 with only small changes in x. The temperature dependence of g* was also measured (Figure 4a). In undoped ZnO, g* remains nearly constant between T = 10 and 298 K (g* = 1.982.00). In Zn1xCoxO, however, g* decreases with increasing temperature, approaching that of the undoped ZnO at high temperatures. This behavior reflects the existence of exchange coupling between the photoexcited electrons and the Co2+ dopants. These data therefore allow the electronCo2+ exchange coupling parameter, N0R, for Zn1xCoxO to be determined. Because of the relationship between g* and T2* found in these Zn1xCoxO films (vide infra), the data in Figure 4a were obtained by fitting just the short-time data (second oscillations) of each TRFR time trace. Within the mean-field and virtual-crystal approximations, g* for a conduction-band electron in a DMS can be described 3357

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Figure 4. Temperature and time dependence of the observed effective g factor in Zn1xCoxO. (a) Temperature dependence of g* in Zn1xCoxO with x = 0.0021 (filled black circles), 0.0013 (open blue diamonds), 0.0006 (green crosses), and 0.0000 (undoped ZnO, open red squares). Inset: Dependence of g* on Co2+ concentration in Zn1xCoxO solgel films, measured at T = 10 K. The line is calculated from eq 4 using N0R = +0.25 eV. (b) Time-resolved Faraday rotation trace for the x = 0.0006 Zn1xCoxO solgel film, recorded at T = 25 K. The dots plot quasiinstantaneous g* values as a function of time, and the line is a guide to the eye.

using eq 4 (ref 20). g ¼ gint

xN0 RÆSx æ μ B Bx

ð4Þ

The first term, gint, is the intrinsic electron g value in the absence of magnetic dopants. From the undoped ZnO films, gint = +1.98. The second term describes the perturbation to g* induced by electronCo2+ magnetic exchange coupling. ÆSxæ is the expectation value of the Co2+ spin perpendicular to the c axis of ZnO (i.e., along the magnetic field, Bx), and by convention is defined as a negative number. The temperature dependence of ÆSxæ is obtained from the numerical derivative of the eigenvalues of the axial spin Hamiltonian in eq 1 with respect to the magnetic field, weighted by the Boltzmann populations of each state. A global fit of the data in Figure 4a yields N0R = +0.25 ( 0.02 eV. The sign of N0R is determined unambiguously from the observation that g* increases rather than decreases with Co2+ doping (see eq 4). Curves based on this value of N0R are drawn as solid lines in Figure 4a, and agree very well with the experimental data over the entire temperature and concentration ranges. The solid line in the inset of Figure 4a has a slope corresponding to N0R = +0.25 eV. Hence, excellent agreement is achieved between the calculated and experimental data using N0R = +0.25 eV, for all 10 samples investigated and under all experimental conditions. Note that the strong dependence of g* on temperature makes measurements of N0R by TRFR in principle susceptible to systematic error from laser heating. The measurements here were therefore all performed at the lowest possible excitation powers (55 W/cm2 at T = 10 K) to minimize such heating effects (see Supporting Information). To our knowledge, this is the first experimental determination of N0R in Zn1xCoxO. A value of N0|Rβ| ≈ +0.8 eV has been reported for Zn1xCoxO MBE-grown films based on analysis of excitonic Zeeman splitting energies,10 but the analysis is complicated by the uncertainty in the valence band ordering in ZnO21,22 and the proximity of Co2+-centered photoionization transitions23 to the excitonic transitions. The observations of magnetoresistance and anomalous Hall effect in paramagnetic n-type Zn1xCoxO films24 certainly indicate the existence of sd exchange, but such data have always been analyzed25 using

N0R values estimated from other Co2+-based IIVI semiconductors (such as N0R = +0.28 eV and +0.18 eV for Cd1xCoxSe and Cd1xCoxS, respectively26,27). The value of N0R = +0.25 ( 0.02 eV reported here is independent of the above complications and should facilitate assessment of the magneto-electronic and magneto-optical properties of this material. Recent ab initio calculations on bulk Zn1xCoxO have suggested N0R = +0.34 eV (ref 6), which is in fair agreement with our experimentally determined value. Electron spin dephasing is strongly accelerated by introduction of Co2+ into the solgel ZnO films (Figure 3b). With as little as x = 0.0001, T2* drops from 600 to 250 ps at T = 10 K. At x = 0.0025, the TRFR signal is heavily damped with no visible oscillations remaining at T = 10 K (data not shown). Addition of Co2+ into the ZnO lattice clearly introduces a very effective dephasing mechanism. Nevertheless, large increases in T2* are still visible with increasing temperatures. The accelerated dephasing upon addition of magnetic impurities is attributed to local fluctuations of the magnetization,28 which in turn arise from thermal fluctuations of ÆSxæ and from microscopically inhomogeneous spatial distributions of the dopant ions (i.e., a breakdown of the virtual crystal approximation). As in magnetic resonance spectroscopy, the efficiency of this dephasing mechanism is directly related to the strength of the exchange interaction.29 The experimental dependence of T2* on x shown in Figure 3b can be modeled by eq 5 (ref 28).

" # ðÆδMz 2 æ þ ÆδMy 2 æÞ=2 1 γ2 τ0 2 2 ¼ ÆδM æ þ ÆδM æ þ x x cf Ne T2 1 þ ðgint μB Bx =p þ γÆMx æÞ2 τ0 2

ð5Þ Here, γ = xN0R/p describes the interactions between the electrons and the Co2+ ions, τ0 is the electron spin correlation time, Ne = xN0Ve is the average number of Co2+ ions within the volume of an electron (Ve), ÆδM2i æ = ÆM2i æ ÆMiæ2 is the variance of the Co2+ magnetization parallel (x) and perpendicular (y, z) to the applied magnetic field due to thermal fluctuations. The average magnetization along the field also varies due to local Co2+ concentration fluctuations, modeled by ÆδM2xæcf. For a Poissonian distribution of dopants, ÆδM2xæcf equals ÆMxæ. The average magnetization ÆMiæ and its second moment ÆM2i æ can be calculated by differentiating the eigenvalues of the axial Co2+ spin Hamiltonian (eq 1) with respect to the magnetic field once and twice, respectively, and weighting by the Boltzmann populations of each eigenstate. In this way, the data in Figure 3b could be fitted to eq 5 with τ0 as the only free parameter. The solid line in Figure 3b shows the best fit, obtained using a correlation time of τ0 = 0.25 ps. This fitted value of τ0 is very similar to the propagation time of electrons in ZnO calculated following ref 28 (τ0 ≈ 0.1 ps), lending credence to the conclusion that the accelerated dephasing observed with increasing x is indeed caused by magnetization fluctuations. A striking consequence of the relationship between electron Co2+ coupling and electron spin dephasing is that electrons interacting with the highest number of Co2+ ions have the largest g* but also dephase the quickest. Figure 4b shows a TRFR trace that illustrates this effect. Close inspection of the TRFR data for this Zn1xCoxO (x = 0.0006) sample reveals that the oscillation frequency is not constant but decreases with increasing delay times. In Figure 4b quasi-instantaneous g* values (green dots) were extracted for single-cycle windows within this TRFR trace using an autocorrelation function. From these data, we find that 3358


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Nano Letters g* decreases from 2.2 to 2.0 over the 400 ps time window of the TRFR trace. This apparent evolution of g* reflects the fact that TRFR measures an ensemble of spins in which those with smallest g* retain coherence longest because of the dependence of T2* on x described in Figure 3b. To our knowledge, the results presented here constitute the first measurement of ultrafast carrier spin dynamics on any ZnO DMS, a class of materials that has attracted extraordinary attention in recent years for potential spintronics applications.3032 In both ZnO and Zn1xCoxO solgel films, the ensemble electron spin dephasing times T2* grew longer at elevated temperatures. This unprecedented behavior in ZnO-based materials is attributed to inhibition of carrier recombination via thermally activated hole trapping. Through analysis of the electron’s effective g factor as a function of Co2+ concentration, the mean-field electronCo2+ exchange coupling parameter in Zn1xCoxO has been determined for the first time (N0R = +0.25 ( 0.02 eV). A key aspect of these experiments was the ability to synthesize optical-quality Zn1xCoxO films by a rapid, inexpensive wetchemical synthesis. This preparative approach has yielded ZnO films showing the longest room-temperature optically generated spin coherence times yet observed in any ZnO-based materials (1.2 ns). Moreover, it provided the flexibility needed to explore a broad experimental parameter space, which led to the discovery that TRFR in Zn1xCoxO could only be observed at very low values of x because of fast dephasing due to electronCo2+ exchange interactions. Beyond providing fundamental new insights into the spin dynamics of ZnO DMSs, these results thus highlight the importance of exploring solution-based preparations of magnetically doped oxides for optical spinmanipulation experiments. The demonstration here that it is possible to prepare ZnO and Zn1xCoxO films suitable for optical electron spin generation and detection using rapid solution techniques, with precise control over x, marks a promising advance in the development of flexible, low-cost preparative methods for incorporation of oxide DMSs into UV optical microcavities33 or related optoelectronic and optospintronic device structures.

’ ASSOCIATED CONTENT

bS

Supporting Information. Chemical preparation of Zn1x CoxO solgel films, technical specifications of the setups for structural, optical, and magnetic characterization, and description of the time-resolved Faraday rotation measurement. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]; Gamelin@chem. washington.edu. Author Contributions §

These authors contributed equally to this work.

’ ACKNOWLEDGMENT The authors acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) through priority program SPP 1285. Financial support from the US National Science Foundation (CHE 0628252-CRC to D.R.G.) is gratefully acknowledged.

LETTER

This work was supported by a grant from the Ministry of Science, Research and the Arts of Baden-W€urttemberg. Gillian Kiliani acknowledges the support of the Carl Zeiss Foundation.

’ REFERENCES (1) Fiederling, R.; et al. Injection and Detection of a Spin-Polarized Current in a Light-Emitting Diode. Nature 1999, 402, 787. (2) Kittilstved, K. R.; Liu, W. K.; Gamelin, D. R. Electronic structure origins of polarity-dependent high-Tc ferromagnetism in oxide-diluted magnetic semiconductors. Nat. Mater. 2006, 5, 291. (3) Liu, C.; Yun, F.; Morkoc-, H. Ferromagnetism of ZnO and GaN: A Review. J. Mater. Sci: Mater. Electron. 2005, 16, 555. (4) Coey, J. M. D.; Venkatesan, M.; Fitzgerald, C. B. Donor impurity band exchange in dilute ferromagnetic oxides. Nat. Mater. 2005, 4, 173. (5) Ueda, K.; Tabata, H.; Kawai, T. Magnetic and electric properties of transition-metal-doped ZnO films. Appl. Phys. Lett. 2001, 79, 988. (6) Chanier, T.; Virot, F.; Hayn, R. Chemical trend of exchange coupling in diluted magnetic II-VI semiconductors: Ab initio calculations. Phys. Rev. B 2009, 79, 205204. (7) Dietl, T. Hole states in wide band-gap diluted magnetic semiconductors and oxides. Phys. Rev. B 2008, 77, 085208. (8) Johnson, C. A.; et al. Sub-band-gap photoconductivity in Co2+ doped ZnO. Phys. Rev. B 2010, 81, 125206. (9) Johnson, C. A.; et al. Mid-gap electronic states in Zn1-xMnxO. Phys. Rev. B 2010, 82, 115202. (10) Pacuski, W.; et al. Effect of the s,p-d exchange interaction on the excitons in Zn1xCoxO epilayers. Phys. Rev. B 2006, 73, 035214. (11) Cao, Y.; et al. Low resistivity p-ZnO films fabricated by sol-gel spin coating. Appl. Phys. Lett. 2006, 88, 251116. (12) Koidl, P. Optical absorption of Co2+ in ZnO. Phys. Rev. B 1977, 15, 2493. (13) Awschalom, D. D.; Loss, D.; Samarth, N. Semiconductor Spintronics and Quantum Computation; Springer-Verlag: Heidelberg, 2002. (14) Chen, Z.; et al. Effects of disorder on electron spin dynamics in a semiconductor quantum well. Nat. Phys. 2007, 3, 265. (15) Chen, Z.; et al. Optical excitation and control of electron spins in semiconductor quantum wells. Phys. E (Amsterdam, Neth.) 2010, 42, 1803. (16) Ghosh, S.; et al. Room-temperature spin coherence in ZnO. Appl. Phys. Lett. 2005, 86, 232507. (17) Crooker, S. A.; et al. Terahertz Spin Precession and Coherent Transfer of Angular Momenta in Magnetic Quantum Wells. Phys. Rev. Lett. 1996, 77, 2814. (18) Crooker, S. A.; et al. Optical spin resonance and transverse spin relaxation in magnetic semiconductor quantum wells. Phys. Rev. B 1997, 56, 7574. (19) Janssen, N.; Whitaker, K. M.; Gamelin, D. R.; Bratschitsch, R. Ultrafast Spin Dynamics in Colloidal ZnO Quantum Dots. Nano Lett. 2008, 8, 1991. (20) Furdyna, J. K. Diluted magnetic semiconductors. J. Appl. Phys. 1988, 64, R29. (21) Reynolds, D. C.; et al. Valence-band ordering in ZnO. Phys. Rev. B 1999, 60, 2340. (22) Lambrecht, W. R. L.; et al. Valence-band ordering and magnetooptic exciton fine structure in ZnO. Phys. Rev. B 2002, 65, 075207. (23) Schwartz, D. A.; et al. Magnetic Quantum Dots: Synthesis, Spectroscopy, and Magnetism of Co2+- and Ni2+-Doped ZnO Nanocrystals. J. Am. Chem. Soc. 2003, 125, 13205. (24) Xu, Q.; et al. Paramagnetism in Co-doped ZnO films. J. Phys. D 2009, 42, 085001. (25) Dietl, T.; et al. Origin of ferromagnetism in Zn1xCoxO from magnetization and spin-dependent magnetoresistance measurements. Phys. Rev. B 2007, 76, 155312. (26) Gennser, U.; et al. Exchange energies, bound magnetic polarons, and magnetization in CdSe:Co and CdS:Co. Phys. Rev. B 1995, 51, 9606. (27) Kacman, P. Spin interactions in diluted magnetic semiconductors and magnetic semiconductor structures. Semicond. Sci. Technol. 2001, 16, R25. 3359

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Nano Letters

LETTER

(28) R€onnburg, K. E.; et al. Motional-Narrowing-Type Dephasing of Electron and Hole Spins of Itinerant Excitons in Magnetically Doped IIVI Bulk Semiconductors. Phys. Rev. Lett. 2006, 96, 117203. (29) Slichter, C. P. Principles of Magnetic Resonance; Harper & Row: New York, 1963. (30) Ohno, H.; et al. Electric-field control of ferromagnetism. Nature 2000, 408, 944. (31) Dietl, T.; et al. Zener Model Description of Ferromagnetism in Zinc-Blende Magnetic Semiconductors. Science 2000, 287, 1019. utic, I. Piezomagnetic (32) Abolfath, R. M.; Petukhov, A. G.; Z Quantum Dots. Phys. Rev. Lett. 2008, 101, 207202. (33) Thomay, T.; et al. Colloidal ZnO quantum dots in ultraviolet pillar microcavities. Opt. Express 2008, 16, 9791.

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Interface properties of OFETs based on an air-stable n-channel perylene tetracarboxylic diimide semiconductor 1

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Phys. Status Solidi A 209, No. 3, 585–593 (2012) / DOI 10.1002/pssa.201127592

3

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Franziska Lu¨ttich , Daniel Lehmann* , Marion Friedrich , Zhihua Chen , Antonio Facchetti , 1 2 1 Christian von Borczyskowski , Dietrich R. T. Zahn , and Harald Graaf 1

Optical Spectroscopy and Molecular Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany Semiconductor Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany 3 Polyera Corporation, 8045 Lamon Avenue, Skokie, IL 60077, USA 2

Received 4 October 2011, revised 23 November 2011, accepted 2 December 2011 Published online 29 December 2011

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Original Paper Phys. Status Solidi A 209, No. 3 (2012)

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Annual Report 2011

PHYSICAL REVIEW B 84, 195203 (2011)

Dielectric function and magneto-optical Voigt constant of Cu2 O: A combined spectroscopic ellipsometry and polar magneto-optical Kerr spectroscopy study Francisc Haidu,1 Michael Fronk,1,* Ovidiu D. Gordan,1 Camelia Scarlat,2 Georgeta Salvan,1 and Dietrich R. T. Zahn1 1

Institute of Physics, Chemnitz University of Technology, Reichenhainer Str. 70, D-09107 Chemnitz, Germany 2 Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Bautzner Landstraße. 400, 01328 Dresden, Germany (Received 5 July 2011; revised manuscript received 19 September 2011; published 23 November 2011)

Cuprous oxide is a highly interesting material for the emerging field of transparent oxide electronics. In this work the energy dispersion of the dielectric function of Cu2 O bulk material is revised by spectroscopic ellipsometry measurements in an extended spectral range from 0.73 to 10 eV. For the first time, the magneto-optical Kerr effect was measured in the spectral range from 1.7 to 5.5 eV and the magneto-optical Voigt constant of Cu2 O was obtained by numerical calculations from the magneto-optical Kerr effect spectra and the dielectric function. DOI: 10.1103/PhysRevB.84.195203

PACS number(s): 71.20.Nr, 78.20.Ci, 78.20.Ls

I. INTRODUCTION

Cuprous oxide (Cu2 O) is a p-type semiconductor due to copper vacancies1 or oxygen interstitials,2 with reported values of the band gap between 2 and 2.4 eV (see Table I). Cu2 O can be found as a natural crystal, named cuprite, or can be produced by oxidizing copper at high temperatures.3,4 Cu2 O was intensively investigated in the past as a possible candidate for inexpensive solar cell fabrication.1,5 Even though the theoretical limit of the power conversion efficiency for Cu2 O based solar cells is about 18%,6 the highest efficiency achieved was 2%.7 More recently, transparent conducting oxide (TCO)/Cu2 O heterojunction solar cells, such as ZnO/Cu2 O have also been investigated.8 However, efforts are still needed to improve the film characteristics, in particular the minority carrier transport length.9 On the other hand, Cu2 O was already used as injection material in metal-based transistors10 going into the direction of spin injection and as base material for diluted ferromagnetic semiconductors.11 Even though Cu2 O is known for decades, there are still divergent reports regarding its electronic and optical properties. Early optical measurements in a broad spectral range were reported by Brahms et al. (spectral range of 2.5 to 6.5 eV),12 Balkanski et al. (2–6 eV),13 and Tandon et al. (1.24–6.2 eV).14 Spectroscopic ellipsometry (SE) measurements performed by Ito et al.15 revealed well-separated features in the dielectric function. In the modeling of the ellipsometric data, Ito et al. used Lorentzian oscillators, while surface roughness (SR) was not considered.15 Due to their large tales, the use of Lorentzian peaks results in an absorption-like behavior even in the red and near-infrared (IR) range, in contradiction to the obvious transparency of cuprite in the red region of the electromagnetic spectrum. Cu2 O also received significant attention from a theoretical point of view. A detailed calculation of the electronic energy bands was reported by Dahl et al.,16 who obtained a direct band gap of 1.77 eV, thus slightly underestimating the ones obtained experimentally. However, modern density functional theory (DFT) calculations underestimate the band gap much more (0.5–0.8 eV, see Ref. 17 and references therein), while Hartree-Fock methods overestimate significantly the band gap (9.7 eV18 ). Table I provides a survey of the band-gap values obtained by different calculation methods. 1098-0121/2011/84(19)/195203(7)

The electronic structure was intensively studied by Ghijsen et al. with photoemission (PES) and inverse photoemission (IPES) measurements.19 More recent angular resolved PES (ARPES) measurements were compared with theoretical data of the Cu2 O band structure obtained using scGW20 and LDA + U21 methods. Even though progress has been made regarding the agreement between the theoretically and experimentally determined band structures, there still are some discrepancies between the measured and the calculated density of states.21 The scope of the present work is to extend the spectral range of known optical constants and to improve their accuracy in the spectral range already reported in previous studies. In addition, we report for the first time the magneto-optical material parameter Q, the so-called Voigt constant, in the near-IR to near-ultraviolet (UV) spectral range as a further support for future theoretical interpretation of the optical spectrum. For this purpose, we exploit the magneto-optical Kerr effect (MOKE) in polar geometry, which describes the change in the polarization state of light induced by reflection on a sample exposed to a magnetic field oriented perpendicular to the sample plane. Its origin lies in the modification of the dielectric properties of the material in the presence of a magnetic field. The effect can be described by the occurrence of Q in the off-diagonal components of the macroscopic dielectric tensor. In the polar MOKE geometry, as used in this work, the light propagates along the z direction and hence parallel to the magnetic field direction. Since Cu2 O is an optically isotropic material, the dielectric tensor has the following form: ⎞ ⎛ 1 iQ 0 ⎟ ⎜ ε = ε ⎝ −iQ 1 0 ⎠ . 0 0 1 While spectroscopic ellipsometry is commonly used to determine the optical constants of materials, generalized magneto-optical spectroscopic ellipsometry (see, e.g., Ref. 28) or MOKE spectroscopy in combination with SE (see, e.g., Ref. 29) is applied to obtain the off-diagonal dielectric tensor elements of oxides. The knowledge of the magneto-optical activity of the pure Cu2 O is needed when characterizing advanced heterostructures of Cu2 O/diluted ferromagnetic semiconductors

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©2011 American Physical Society

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HAIDU, FRONK, GORDAN, SCARLAT, SALVAN, AND ZAHN


TABLE I. Literature values for the band gap of Cu2 O determined by different measurement techniques and calculation methods. The abbreviations APW, OLCAO, H-F, FP-LAPW and PBE + GGA stand for Augmented Plane Wave, Orthogonalized Linear Combination of Atomic Orbitals, Hartree-Fock, Full Potential Linearized Augmented Plane Wave, Perdew-Burke-Ernzerhof + Generalized Gradient Approximation, respectively. Ref.

Band gap (eV)

Calculation method

Ref.

Diffuse reflectance Absorption Reflectance and transmittance Transmission PES + IPES

14 22 23 24 19

1.77 0.78 9.7 ∼0.5 0.54–1.97 0.53–2.36 0.7

APW OLCAO Periodic H-F FP-LAPW Different approaches Different approaches PBE + GGA

16 25 18 26 20 27 17

The investigated cuprite (Cu2 O) natural single crystal, with (100) surface orientation, one side polished, and having a thickness of 1 mm, was purchased from SurfaceNet GmbH. The crystal is translucent with a red color. Ellipsometric measurements were performed with two instruments: a commercial Variable Angle Spectroscopic Ellipsometer (VASE, J. A. Woollam Co. Inc.) and a Vacuum UltraViolet (VUV) ellipsometer,30 using synchrotron light as a source at BESSY II, Berlin. The VASE data were recorded from 0.73 to 4.99 eV photon energy with a 0.02 eV step at different incidence angles (65, 70, and 75◦ ). The VUV measurements were performed in the energy range from 4 to 10 eV with a step of 0.025 eV at the fixed angle of incidence (67.5 ± 0.5◦ ). The magneto-optical characterization was performed using a home-built MOKE spectrometer using the reflection anisotropy configuration31 in the energy range from 1.7 to 5.5 eV. The extension for MOKE measurements is realized using an electromagnet that can apply a magnetic field perpendicular to the sample surface (polar geometry).32 The setup measures the tilt θ K and ellipticity ηK of the polarization of the light reflected from the sample surface exposed to a magnetic field of 1.7 T. The magnetic moment of the Cu2 O sample was investigated using superconducting quantum interference device (SQUID; QD MPMS XL) magnetometry.

16

ε1

II. EXPERIMENT

of a virtually semi-infinite layer with a smooth surface,33 coincides with the true dielectric function of the material. The line shape of ε2 in Fig. 1 is similar to that of the dielectric function determined by Ito et al.15 However, a significant absorption tail well below 2.0 eV is noticeable. This cannot be real since, by bare eye, it can be seen that the crystal with a thickness of ∼1 mm is transparent for red visible light. Ito et al. also state that cuprite has a “reddish” color.15 Therefore, in a second step, a more sophisticated model was used to model the experimental data, i.e., by introducing SR. SR leads to light scattering at the sample surface, which, in turn, reduces the polarization degree of the reflected light beam. Depolarization effects and scattering may thus appear as absorption in the calculated dielectric function, when the SR is neglected. It is commonly accepted that semiconductor materials can be well described in the transparent range by a Cauchy dispersion layer, see, e.g., Ref. 34. We modeled the data in the energy range (0.7–2.1 eV) using an optical three-layer model that consists of a semi-infinite Cauchy layer (as substrate), a SR layer on top, and air. The SR was modeled as a layer consisting of a mixture of 50% material (having the same optical constants as the semi-infinite Cauchy layer) and 50% void using the

< ε1>,

or Cu2 O/magnetic TCO by magneto-optical means. This paper presents Kerr rotation and ellipticity data in the spectral range between 1.7 and 5.5 eV. From these, the Voigt constant is derived in a Kramers-Kronig (KK) consistent way, allowing the prediction of MOKE, Faraday, or magnetic circular dichroism (MCD) spectra of layer systems containing Cu2 O.

III. RESULTS AND DISCUSSIONS

4 0 Cu2O(100) bulk

12 SR - 11 nm

8 Cu2O(100)

4 1

2

3

4

5

6

7

8

0

Photon Energy (eV) FIG. 1. (Color online) The real (ε1 ) and imaginary (ε2 ) part of the effective dielectric function of cuprite (dashed black lines) determined assuming a single Cu2 O semi-infinite layer (upper inset). The real (ε1 ) and imaginary (ε2 ) part of the dielectric function of cuprite (full red lines) determined using a point-by-point fit, assuming a single Cu2 O semi-infinite layer covered with a layer simulating the SR (lower inset).

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A. Ellipsometry

The optical response of cuprite was determined in the spectral range from 0.73 to 10 eV by overlapping the data measured with the VASE and VUV ellipsometers in an energy region between 4 and 5 eV. The effective dielectric function was determined using the R WVASE32 (J. A. Woollam Company) analysis software and is plotted in Fig. 1 as dashed black line. For ideal samples, the effective dielectric function, defined as the dielectric function

experimental modeled ε

12

-4

ε2

2.02 2.17 2.2 2.17 2.4 ± 0.3

Measurement technique

< ε2>,

Band gap (eV)

Annual Report 2011

DIELECTRIC FUNCTION AND MAGNETO-OPTICAL VOIGT . . .

FIG. 2. (Color online) Example of AFM image of the Cu2 O crystal surface. The average rms roughness of all scans performed was determined to be 4.8 ± 0.4 nm.

effective medium approximation (EMA) algorithm based on the Bruggeman equation,35 which is implemented in the WVASE32 code. The calculated ellipsometric parameters and were fitted to the experimental ones, with the free parameters of the fit being the Cauchy dispersion parameters and the SR layer thickness. The upper boundary of 2.1 eV of the energy range of the fit was chosen slightly below the parity forbidden direct band gap of Cu2 O of 2.17 eV36 to avoid any absorption effects of higher order. The best match to the measured ellipsometric data, judging from the mean square error values and the optical inspection of the fit to experimental and curves, was obtained for a SR layer thickness of (11.0 ± 1.0) nm. This value agrees well with the results of atomic force microscopy (AFM) measurements, if one considers the thickness of the roughness layer to be double of the root mean square roughness (2 × rms = (9.6 ± 0.8) nm) of the scans, i.e., the double of the average plus/minus deviation from an average level. An example scan image is shown in Fig. 2. Afterwards a point-by-point fit of the ellipsometric parameters and in the whole spectral range (0.7 to 10) eV was performed to obtain the dielectric function of


FIG. 3. Dielectric function of Cu2 O determined by a point-bypoint fit (circles) and the fitted curve using Gaussian peaks (full line). The parameters of individual peaks (dashed lines, assigned by grey numbers) are given in Table II.

the substrate. The SR layer thickness was kept fixed (11 nm) during the point-by-point fit. A schematic drawing of the model is presented in the inset of Fig. 1. The resulting dielectric function is presented in Fig. 1 by a full red line. The noise is caused by the low light intensity of the VASE setup between 4.5 and 5 eV. Besides SR also the formation of other species on the surface, like CuO or Cu(OH)2 ,37 could influence the optical response in a similar manner. It is, however, difficult to distinguish their contribution from that of SR. The absorption onset resulting from our modeling with SR lies slightly below 2.5 eV. This corresponds to the optical transition from the valence band into the second conduction band (energy difference of 2.65 eV) considering the rather large exciton energies in Cu2 O of more than 0.1 eV.36 The direct band gap of 2.17 eV is, as mentioned, parity forbidden. Therefore, its contribution to absorption is so small that it can be neglected in the ellipsometry data evaluation. The dielectric function was then fitted with Gaussian peaks in ε2 to determine the position of the spectral features. The real part ε1 is calculated KK consistently from ε2 (see, e.g., Ref. 38). In Fig. 3 the real (ε1 ) and imaginary parts (ε2 ) of the dielectric function (empty circles) and the deconvolution using

TABLE II. Parameters of the Gaussian peaks used to model the imaginary part of the dielectric function. Peak 3 was used for better fit, although it does not present any well-defined feature in the spectra. Corresponding energy positions reported previously in literature are given in columns 5 to 7. Peak

Energy (eV)

Amplitude (a.u.)

Broadening (eV)

Energy (eV) 15

Energy (eV) 12

Energy (eV) 14

1 2 3 4 5 6 7 8 9 10

2.60 ± 0.02 2.72 ± 0.02 2.87 ± 0.02 3.48 ± 0.02 4.18 ± 0.02 4.62 ± 0.02 5.21 ± 0.02 6.33 ± 0.02 7.31 ± 0.02 9.68 ± 0.02

1.78 ± 0.05 3.32 ± 0.05 3.83 ± 0.05 13.76 ± 0.05 9.63 ± 0.05 7.13 ± 0.05 4.76 ± 0.05 1.16 ± 0.05 0.52 ± 0.05 1.88 ± 0.05

0.053 ± 0.020 0.112 ± 0.020 0.334 ± 0.020 0.773 ± 0.020 0.457 ± 0.020 0.649 ± 0.020 0.546 ± 0.020 0.885 ± 0.020 0.910 ± 0.020 1.190 ± 0.020

2.64 2.76

2.61 2.71

2.67

3.45 4.25

3.62 4.33 4.48; 4.74; 4.86 5.36 6.45

3.85 4.64 5.00

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Gaussian peaks (full lines) are shown. The energy position, the amplitude, and the broadening of the Gaussian peaks are given in Table II. As mentioned above, the fit with Gaussian peaks serves for the identification of the position of spectral features. Obviously, it would be more reasonable in the case of a crystalline semiconductor like Cu2 O to start off with a parabolic band model and subsequently extend it to a fully parametrized semiconductor model taking into account the band structure. However, a data fit with such a model is not possible from the experimental data alone, because of too many unknown parameters involved. B. Magneto-optical Kerr effect spectroscopy

The experimental MOKE spectrum of the Cu2 O crystal is presented in Fig. 4. The Kerr rotation of about 0.1 mrad observed for Cu2 O crystal lies in the same order as that observed for molecular films.39 In order to check the origin of the MOKE signal, the Cu2 O crystal was measured in a SQUID magnetometer at room temperature (which corresponds to the temperature of the MOKE experiments). To ensure a good sensitivity to small amount of magnetic species present in the sample the measurements were performed in an applied magnetic field of 6 T, i.e., by a factor of 3.5 larger than the applied field in the MOKE experiment. The signal obtained after diamagnetic correction exhibits neither paramagnetic contribution nor a hysteresis loop within the detection limits as visible in Fig. 5. This confirms that the Cu2 O crystal under study is purely diamagnetic and if any magnetic impurities are present, their magnetic response is negligible. Thus the magnetooptical signal observed by MOKE spectroscopy is an intrinsic property of the crystal. From the MOKE spectra together with the optical constants obtained by spectroscopic ellipsometry, the material Voigt constant Q can be determined as a free parameter by a point-by-point fitting procedure.40 The result is shown in Fig. 6

FIG. 4. (Color online) Experimental MOKE spectrum of Cu2 O (thin lines with symbols) and modeled using the KK-consistent Voigt constant Q (thick solid lines) and the dielectric function obtained by point-by-point fitting.

FIG. 5. (Color online) M-H curve of the Cu2 O crystal at 300 K obtained from SQUID magnetometry. The sample is found to be fully diamagnetic within the experimental sensitivity.

as thin line with symbols. Subsequently, the dispersion of the Voigt constant is modeled by a sum of KK-consistent Gaussian functions38 and their derivatives. This procedure is conducted following the Faraday term formalism described by Stephens.41 Stephens used the shape of absorption features for describing Faraday A terms and the derivative for B and C terms in the energy dispersion of magnetic circular dichroism (MCD). We adopt a similar procedure: as the typical line shape of features in the imaginary part ε2 of the diagonal elements of the dielectric tensor is well described by Gaussian functions, we use Gaussian functions as well as derivative-like-shaped features to calculate the Voigt constant spectrum of Cu2 O. The KK-consistent Gaussian function can

FIG. 6. (Color online) Energy dispersion of the Cu2 O Voigt constant modeled point-by-point from the MOKE data and the dielectric function (thin lines with symbols) compared to the Voigt constant modeled using KK-consistent functions (thick solid line; see Table III and Fig. 7)

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DIELECTRIC FUNCTION AND MAGNETO-OPTICAL VOIGT . . .

be written as38 2A Re gKK = √ π

Im gKK


√ √ E + E0 E − E0 D 2 ln2 − D 2 ln2 FWHM FWHM

E − E0 = A exp −4 ln2 FWHM

2

E + E0 − exp −4 ln2 FWHM

2 ,

with A being the amplitude, E0 the energy position, and FWHM the full width at half maximum value. D is the Dawson function, which can be calculated numerically. It is defined as x exp(t 2 )dt. D(x) = exp(−x 2 ) 0

The derivative of the Gaussian function is given by (under preservation of the odd symmetry around E = 0 eV, which accounts for time inversion invariance, taken into account by sign change at the negative energy half axis):

√ √ √

√ √ dg 4 ln2 E+E0 E−E0 4 ln2 4 ln2 Re 1− = (E+E0 )D 2 ln2 + 1− (E−E0 )D 2 ln2 √ dE FWHM FWHM FWHM FWHM FWHM π dg 8 ln2 Im = dE F W H M2

E − E0 (E − E0 ) exp −4 ln2 FWHM

The function parameters used in the present model are summarized in Table III. The deconvolution is presented in Fig. 7. The Gaussian peak 4, which is outside the spectral range measured by MOKE, is needed in the real part of Q and plays the role of a pole. Therefore its height and broadening are strongly correlated and its parameters are governed by a large uncertainty. The use of the Gaussian functions alone already yields a reasonable agreement between the experimental MOKE data and the model fit. The positions of the Gaussian peaks can be identified with maxima in the imaginary part of ε . This can also be seen by the comparison of the Tables II and III. The peaks in ε 2 at 3.48, 4.18, and 5.21 eV correspond quite reasonably to the ones in Q at 3.50, 4.30, and 5.21 eV. These features can therefore be attributed to Faraday B or C terms,41,42 although the broadening does not agree that well between ε2 and Q features. This discrepancy could be caused by the use of Gaussian peaks as an approximation for the true B-term line shape. B-term transitions have a nondegenerated ground state and a set of excited states, which are close to degeneracy, e.g., they would be degenerated in the next higher symmetry group. B terms therefore usually appear in pairs with the component peaks close in energy but with different signs. This situation is not found in the present data. C terms

2

E + E0 + (E + E0 ) exp −4 ln2 FWHM

2 .

arise from a degeneracy in the ground state, which is lifted in the presence of a magnetic field. The difference in the occupancy of the new “ground states” due to Boltzmann statistics is directly related to the oscillator strength of the C-term feature in MCD or Q, respectively. Consequently, these features are temperature dependent. At T = 0 K a C-term feature has its largest amplitude because the difference in occupancy of the ground and excited energy levels is maximum. For T →∞, a C-term feature does not completely vanish but transforms into a derivative-like line shape (similar to an A term). An A-term arises from an optical transition between a nondegenerated ground state and a degenerated excited state, the degeneracy of which is lifted in a magnetic field. From measurements performed at room temperature, it is often not possible to distinguish between an A and a C term. The Gaussian features in the present data are probably C terms because they do not appear in pairs with opposite signs. However, in order to unambiguously confirm this assignment, temperature-dependent measurements are planned. Care must also be taken because at the basis of the Faraday term formalism lies the assumption that the degenerated energy levels involved in the magneto-optical transitions undergo the normal Zeeman effect. This assumption applies well to atomic or molecular spectra,42 which correspond to transitions

TABLE III. Model function types and parameters of the Q dispersion. Peak 1 2 3 4 5 6

Type Gaussian derivative (1) Gaussian derivative (2) Gaussian (1) Gaussian (2) Gaussian (3) Gaussian (4)

Energy position (eV) 2.575 ± 0.010 2.655 ± 0.010 3.498 ± 0.020 4.301 ± 0.020 5.208 ± 0.020 6.29 ± 0.10

Amplitude (a.u.) −6

−(1.86 ± 0.20)×10 (1.92 ± 0.20)×10−6 (4.933 ± 0.020)×10−5 (2.394 ± 0.002)×10−4 (2.291 ± 0.020)×10−5 −(1.152 ± 0.010)×10−3

Broadening (eV) 0.080 ± 0.010 0.075 ± 0.010 0.524 ± 0.020 0.696 ± 0.020 0.391 ± 0.020 0.34 ± 0.10

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require at least one additional peak, which would have no correspondent structure in ε 2 . The presence of A terms suggests a nondegenerated ground state and a degenerated excited state for these sharp features. This line shape is consistent with the excitonic character of these two optical transitions, since the excited electronic states are accompanied by excitonic sublevels. IV. CONCLUSIONS

FIG. 7. Deconvolution of the Voigt constant dispersion of Cu2 O. The parameters are given in Table III.

The dielectric function ε = ε1 + iε2 of Cu2 O single crystal at room temperature was obtained by spectroscopic ellipsometry in the spectral range from 0.73 to 10.00 eV. This improves the present knowledge of ε over the photon energy compared to previous reports (1.2 to 5.2 eV).15 The model used for the numerical evaluation of the experimental data takes into account a small SR, which accounts for the obvious transparency of Cu2 O in the visible red spectral range and yields higher ε2 values in the energy range between 3.1 and 5.5 eV. In addition, the magneto-optical Voigt constant, which describes the influence of an external magnetic field on the off-diagonal elements of the dielectric tensor, was determined in the energy range between 1.7 and 5.5 eV at a magnetic field of 1.7 T. The Voigt constant was determined numerically, using an optical layer model, from the experimental MOKE spectrum and the dielectric function, and then a KK-consistent fit of its line-shape was obtained.

between discrete energy levels. The present empirical trial to adopt this formalism for a bulk semiconductor, Cu2 O, which is characterized by energy bands, appears to be successful regarding the agreement between fit and experimental data. However, for an accurate description of the line shape of the features, a band structure model would certainly be of great help. In the dielectric function, two sharp features appear at around 2.6 eV. At the corresponding position in the MOKE spectra, very weak features, not much higher than the noise level, can also be observed. The best agreement between experiment and calculated curve in this spectral range was obtained when using two Gaussian derivatives (A terms) with opposite signs. A description with Gaussian functions would

The authors gratefully acknowledge the Bundesministerium für Bildung und Forschung in the frame of the Nanett – Nano System Integration – Network of Excellence for financial support (Grant No. 03IS2011A). We also acknowledge the financial support of the Helmholtz Zentrum Berlin.

*

11

[email protected] A. E. Rakhshani, Solid-State Electron. 29, 7 (1986). 2 D. O. Scanlon, B. J. Morgan, G. W. Watson, and A. Walsh, Phys. Rev. Lett. 103, 096405 (2009). 3 T. Ito, H. Yamaguchi, K. Okabe, and T. Masumi, J. Mater. Sci. 33, 3555 (1998). 4 S. Mani, J. I. Jang, J. B. Ketterson, and H. Y. Park, J. Cryst. Growth 311, 3549 (2009). 5 B. P. Rai, Sol. Cells 25, 265 (1988). 6 J. J. Loferski, J. Appl. Phys. 27, 777 (1956). 7 A. Mittiga, E. Salza, F. Sarto, M. Tucci, and R. Vasanthi, Appl. Phys. Lett. 88, 163502 (2006). 8 S. H. Jeong, S. H. Song, K. Nagaich, S. A. Campbell, and E. S. Aydil, Thin Solid Films 519, 6613 (2011). 9 Y. Liu, H. K. Turley, J. R. Tumbleston, E. T. Samulski, and R. Lopez, Appl. Phys. Lett. 98, 162105 (2011). 10 R. G. Delatorre, M. L. Munford, R. Zandonay, V. C. Zoldan, A. A. Pasa, W. Schwarzacher, M. S. Meruvia, and I. A. Hümmelgen, Appl. Phys. Lett. 88, 233504 (2006). 1

ACKNOWLEDGMENTS

Y. L. Liu, S. Harrington, K. A. Yates, M. Wei, M. G. Blamire, J. L. MacManus-Driscoll, and Y. C. Liu, Appl. Phys. Lett. 87, 222108 (2005). 12 S. Brahms and S. Nikitine, Solid State Commun. 3, 209 (1965). 13 M. Balkanski, Y. Petroff and D. Trivich, Solid State Commun. 5, 85 (1967). 14 S. P. Tandon and J. P. Gupta, Phys. Status Solidi 37, 43 (1979). 15 T. Ito, T. Kawashima, H. Yamaguchi, T. Masumi, and S. Adachi, J. Phys. Soc. Jpn. 67, 2125 (1998). 16 J. P. Dahl and A. C. Switendick, J. Phys. Chem. Solids 27, 931 (1966). 17 M. M. Islam, B. Diawara, V. Maurice, and P. Marcus, J. Mol. Struct. Theochem 903, 41 (2009). 18 E. Ruiz, S. Alvarez, P. Alemany, and R. A. Evarestov, Phys. Rev. B 56, 7189 (1997). 19 J. Ghijsen, L. H. Tjeng, J. van Elp, H. Eskes, J. Westerink, G. A. Sawatzky, and M. T. Czyzyk, Phys. Rev. B 38, 11322 (1988).

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F. Bruneval, N. Vast, L. Reining, M. Izquierdo, F. Sirotti, and N. Barrett, Phys. Rev. Lett. 97, 267601 (2006). 21 ¨ A. Onsten, M. M˚ansson, T. Claesson, T. Muro, T. Matsushita, T. Nakamura, T. Kinoshita, U. O. Karlsson, and O. Tjernberg, Phys. Rev. B 76, 115127 (2007). 22 S. Brahms, S. Nikitine, and J. P. Dahl, Phys. Lett. 22, 31 (1966). 23 B. Karlsson, C. G. Ribbing, A. Roos, E. Valkonen, and T. Karlsson, Phys. Scr. 25, 826 (1982). 24 P. W. Baumeister, Phys. Rev. 121, 359 (1961). 25 W. Y. Ching, Y.-N. Xu, and K. W. Wong, Phys. Rev. B 40, 7684 (1989). 26 A. Martinez-Ruiz, M. G. Moreno, and N. Takeuchi, Solid State Sci. 5, 291 (2003). 27 T. Kotani, M. van Schilfgaarde, and S. V. Faleev, Phys. Rev. B 76, 165106 (2007). 28 H. L. Liu, K. S. Lu, M. X. Kuo, L. Uba and S. Uba, L. M. Wang, and H.-T. Jeng, J. Appl. Phys. 99, 043908 (2006). 29 J. Mistrik, T. Yamaguchi, M. Veis, E. Liskova, S. Visnovsky, M. Koubaa, A. M. Haghiri-Gosnet, Ph. Lecoeur, J. P. Renard, W. Prellier, and B. Mercey, J. Appl. Phys. 99, 08Q317 (2006). 30 R. L. Johnson, J. Barth, D. Fuchs, A. M. Bradshaw, and M. Cardona, Rev. Sci. Instrum. 60, 2209 (1989).

PHYSICAL REVIEW B 84, 195203 (2011) 31

D. E. Aspnes, J. P. Harbison, A. A. Studna, and L. T. Florez, J. Vac. Sci. Technol. A 6, 1327 (1988). 32 T. Herrmann, K. Lüdge, W. Richter, K. G. Georgarakis, P. Poulopoulos, R. Nünthel, J. Lindner, M. Wahl, and N. Esser, Phys. Rev. B 73, 134408 (2006). 33 R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1992), p. 327. 34 O. D. Gordan, M. Friedrich, and D. R. T. Zahn, Org. Electron. 5, 291 (2004). 35 D. A. G. Bruggeman, Ann. Phys. 416, 636 (1935). 36 D. A. Fishman, A. Revcolevschi, and P. H. M. van Loosdrecht, Phys. Status Solidi C 3, 2469 (2006). 37 S. L. Harmer, W. M. Skinner, A. N. Buckley, and L.-J. Fan, Surf. Sci. 603, 537 (2009). 38 D. De Sousa Meneses, M. Malki, and P. Echegut, J. Non-Cryst. Solids 352, 769 (2006). 39 B. Bräuer, M. Fronk, D. Lehmann, D. R. T. Zahn, and G. Salvan, J. Phys. Chem. B 113, 14957 (2009). 40 M. Fronk, B. Bräuer, J. Kortus, O. G. Schmidt, D. R. T. Zahn, and G. Salvan, Phys. Rev. B 79, 235305 (2009). 41 P. J. Stephens, Adv. Chem. Phys. 35, 197 (1976). 42 J. Mack, M. J. Stillman, and N. Kobayashi, Coord. Chem. Rev. 251, 429 (2007).

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How to compare diffusion processes assessed by single-particle tracking and pulsed field gradient nuclear magnetic resonance Michael Bauer,1 Rustem Valiullin,2,a) Günter Radons,1,b) and Jörg Kärger2 1 2

Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany Institute of Experimental Physics I, University of Leipzig, 04103 Leipzig, Germany

(Received 15 July 2011; accepted 19 September 2011; published online 13 October 2011) Heterogeneous diffusion processes occur in many different fields such as transport in living cells or diffusion in porous media. A characterization of the transport parameters of such processes can be achieved by ensemble-based methods, such as pulsed field gradient nuclear magnetic resonance (PFG NMR), or by trajectory-based methods obtained from single-particle tracking (SPT) experiments. In this paper, we study the general relationship between both methods and its application to heterogeneous systems. We derive analytical expressions for the distribution of diffusivities from SPT and further relate it to NMR spin-echo diffusion attenuation functions. To exemplify the applicability of this approach, we employ a well-established two-region exchange model, which has widely been used in the context of PFG NMR studies of multiphase systems subjected to interphase molecular exchange processes. This type of systems, which can also describe a layered liquid with layer-dependent self-diffusion coefficients, has also recently gained attention in SPT experiments. We reformulate the results of the two-region exchange model in terms of SPT-observables and compare its predictions to that obtained using the exact transformation which we derived. © 2011 American Institute of Physics. [doi:10.1063/1.3647875] I. INTRODUCTION

Diffusion is one of the omnipresent phenomena in nature and involved in most physico-chemical and biological processes.1 Often media, where the molecules perform their chaotic Brownian motion, do include different types of compartments, regions of different densities, or domains surrounded by semipermeable membranes. Diffusion properties in these spatially separated regions may, in general, be different. Altogether, this typically gives rise to very complex processes of diffusive mass transport including regimes of anomalous diffusion. To model such inhomogeneous systems, they may be represented to consist of a number of domains with different local diffusivities subjected to exchange processes between them. The most simple two-phase exchange model with an exponential exchange kernel has often been used to describe experimental results obtained using pulsed field gradient nuclear magnetic resonance (PFG NMR) technique.2 Such examples include, e.g., diffusive exchange between two pools of guest molecules in zeolite crystals and surrounding gas atmosphere3 and between extra- and intracellular water4 in biosystems. Recently, a new type of experimental approach, namely single-particle tracking (SPT) has emerged.5 It provides an alternative method for studying diffusion processes and for measuring their properties as well as some properties of the surrounding medium.6 In contrast to PFG NMR, where an ensemble of diffusing particles is investigated, SPT only observes individual tracer particles. In particular, fluorescent dye a) Electronic mail: [email protected]. b) Electronic mail: [email protected].

0021-9606/2011/135(14)/144118/13/$30.00

molecules, such as rhodamine B, in a solvent, e.g., tetrakis(2ethylhexoxy)-silane (TEHOS), which arranges in ultra-thin liquid layers,7 are excited by laser radiation. The emitted light of the dyes is captured with a wide-field microscope and recorded by a CCD camera. Hence, the obtained movies show diffusing spots representing a two-dimensional projection of the three-dimensional motion of the dyes. From a statistical point of view, such processes are known as observed diffusion8–10 or hidden Markov models11, 12 leading, in general, to the loss of the Markov property. A tracking algorithm detects the positions of the spots and connects them to trajectories.13 A basic quantity for the characterization of diffusion processes is obtained by taking two positions x(t) and x(t + τ ) from a trajectory separated by a time lag τ and by considering the rescaled squared displacement [x(t + τ ) − x(t)]2 /τ . This quantity is a local or microscopic diffusivity which fluctuates along a given trajectory or in an ensemble of diffusing particles. It is natural to extract the corresponding distribution of diffusivities from experiments by forming histograms of the observed rescaled squared displacements.14 Note that other definitions of diffusivity distributions may be found in the literature.15 For homogeneous diffusion processes the distribution of diffusivities is independent of the time lag τ , whereas for heterogeneous systems a non-trivial τ -dependence is observed. Therefore in analyzing heterogeneous systems, the distribution of diffusivities provides advantages over an analysis via mean squared displacements because in addition to its mean value it contains all information about the fluctuations.16 Furthermore, quantities such as the mean diffusion coefficient, obtained as the first moment of the distribution of diffusivities, are well

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defined, and thus time-dependent diffusion coefficients and their fluctuations can be calculated. The objective of this work is to investigate the connection between the two different techniques of measuring diffusion. SPT and PFG NMR are clearly related to each other, since both measure displacements of diffusing particles. For instance, the time lag between the observation of two positions in SPT corresponds to the time interval between two gradient pulses in PFG NMR. In both SPT and PFG NMR this time lag τ is a parameter, which can be tuned by varying the time between snapshots and by altering the temporal distance between gradient pulses, respectively. Furthermore, the signal attenuation in PFG NMR is related to the propagator in Fourier space, from which the distribution of diffusivities can be calculated. At first, it seems to be sufficient to compare the propagators obtained from both types of experiments directly. However, if diffusion processes with heterogeneities or anomalous behavior are considered, access to the propagator will be complicated or even hindered. In such cases, the distribution of diffusivities offers a well-defined analysis of the processes and a comparison of data from the two approaches is feasible. Moreover, it becomes possible to contrast results from time-averaged and ensemble-averaged quantities and detect anomalous diffusion leading to ergodicity breaking as reported recently.17 More generally, an improvement in the analysis of heterogeneous diffusion could benefit from the link between single-particle analysis and ensemble methods. Hence, analytical expressions for one- up to three-dimensional processes are derived which transform PFG NMR signal attenuation into the distribution of singleparticle diffusivities from SPT. For simple systems with heterogeneous diffusion the two-region exchange model of PFG NMR offers an analytical expression for the spin-echo diffusion attenuation.18 In conjunction with our transformation, this model provides an example, where the distribution of single-particle diffusivities can be calculated exactly and also the non-trivial time-lag dependence can be investigated. In this context we consider a two-layer liquid film on a homogeneous surface characterized by two distinct diffusion coefficients.16 This two-layer system corresponds exactly to the two-region exchange model of PFG NMR. In particular, its condition of exponential waiting times is fulfilled since a change in the diffusion coefficient is possible at any time and independent of the particles’ current positions. For a system comprising an arbitrary number of layers, exact asymptotic results for the dispersion of particles in the long-time limit have already been provided.19 We substantiate our findings by analyzing data from simulated single-particle trajectories of heterogeneous diffusion. To evaluate experimental limitations, we study the influence of a signal attenuation bounded to a certain range of k-values. The impact on the distribution of single-particle diffusivities will also be pointed out. The remainder of the paper is organized as follows. In Sec. II, we recall the basic principles of PFG NMR and underline the differences to SPT experiments. In particular, we discuss properties of both approaches and the connection between them. In this context, we introduce the distribution of single-particle diffusivities and provide expressions for the

J. Chem. Phys. 135, 144118 (2011)

well-known case of homogeneous diffusion. To apply our new concepts to some more elaborated systems, we consider in Sec. III heterogeneous diffusion in two-region systems, where analytical expressions of the PFG NMR signal attenuation exist. We outline the principles of the simulation of such systems in Sec. IV. In order to provide a simple relation between signal attenuation and distribution of diffusivities, we suggest an approximation in Sec. V to avoid the inconvenient Fourier transformation. This approximation is then compared to the exact expressions of the relation in Sec. VI for simulated data of the two-region system. Finally, in Sec. VII we address the issue of finite intensity of the magnetic field gradient pulses in the PFG NMR experiment and illustrate its influence on our exact transformation into the distribution of diffusivities. II. SIGNAL ATTENUATION AND DISTRIBUTION OF DIFFUSIVITIES

Diffusion measurement by PFG NMR is based on observing the transverse magnetization of nuclear spins in a constant magnetic field. Offering the highest sensitivity and occurring in numerous chemical compounds, in most cases the nuclei under study are protons. By superimposing, over two short time intervals, an additional magnetic field with a large gradient, the displacement of the nuclei (and hence of the molecules in which they are contained) in the time span between these two “gradient pulses” is recorded in a phase shift of their orientation in the plane perpendicular to the magnetic field with respect to the mean orientation. Hence, the distribution of the diffusion path lengths appears in the distribution of these phase shifts and, consequently, in the vector sum of the magnetic moments of the individual spins, i.e., in the magnetization.2, 20–22 Since it is this magnetization which is recorded as the NMR signal, molecular diffusion leads to an attenuation of the signal intensity during the PFG NMR experiments which is larger then the displacements in the time interval between these two gradient pulses are. The signal attenuation from PFG NMR may be shown to obey the relation2, 18, 20, 23 (τ, k) = dr p(r, τ ) exp(ikr) (1) with the ensemble-averaged conditional probability density (2) p(r, τ ) = dx p(x + r, τ |x) p0 (x), where p(x + r, τ |x) is the stationary probability density of a displacement r = (r1 , . . . , rd )T in d dimensions in the time interval τ and p0 (x) refers to the equilibrium distribution given by the Boltzmann distribution. Further, τ is the time interval between the two gradient pulses and represents the diffusion time in the PFG NMR experiment. According to the PFG NMR experiment, signal attenuation is measured in the direction of the applied field gradients. Thus, k in Eq. (1) is given by k = k eˆ , where eˆ denotes the unit vector in that direction. The quantity k is a measure of the intensity of the field gradient pulses. Assuming an isotropic system, without loss of generality, an arbitrary direction kˆ = (k, 0, . . . , 0)T may be considered. Obviously, the scalar product in the exponential


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of Eq. (1) picks out only the component r1 of the displacement r. Then, the signal attenuation 1 (τ, k) = (τ, kˆ = (k, 0, . . . , 0)T ) +∞ dr1 p1 (r1 , τ ) exp(ikr1 ), =

(3)

−∞

depends only on scalar values corresponding to the chosen direction and p1 (r1 , τ ) is the projection of the probability density, Eq. (2), on the considered direction, given by p1 (r1 , τ ) = · · · dr2 · · · drd p(r, τ ). (4) In NMR, p1 (r1 , τ ) in Eq. (3) is known as the mean propagator, i.e., the probability density that, during τ , an arbitrarily selected molecule has been shifted over a distance r1 in the direction of the applied field gradients. However, it should be noted that for heterogeneous systems, such as systems with regions of different mobility, p1 (r1 , τ ) may not be called propagator since it cannot evolve the system due to the loss of Markovianity. The reason is that, in general, p1 (r1 , τ ) of such systems does not satisfy the Chapman– Kolmogorov equation.24 Non-Markovian behavior, besides others, may also arise in systems which can be modeled by the fractional Brownian motion25 or by certain fractional diffusion equations.26 Further, the mean propagator in Fourier space as given by Eq. (1) corresponds to the incoherent intermediate scattering function. The details of this connection are given in the Appendix A for clarification. In contrast to the PFG NMR technique, which is ensemble-based as described above, SPT experiments allow to follow the trace of individual diffusing molecules. Therefore, by considering the displacement of a particular molecule in d dimensions it is natural to define a microscopic singleparticle diffusivity Dt (τ ) by the relation Dt (τ ) = [x(t + τ ) − x(t)]2 /(2d τ ),

(5)

where x(t) denotes the trajectory of an arbitrary stochastic process. Note that the term “microscopic” has been used before by Kusumi and co-workers27 to characterize the shorttime behavior of averaged squared displacements equivalent to the small τ limit of our mean diffusivity defined in Eq. (10) below. In the context of Markovian diffusion processes this limit also corresponds via jump moments to the diffusion terms appearing in Fokker-Planck equations.24 Here, we use the term microscopic in analogy to the statistical physics concept of microstates to distinguish it from ensemble based averages. For a given time lag τ , the microscopic single-particle diffusivity is a fluctuating quantity along a trajectory x(t) and we now ask for the probability p(D)dD that, under the so far considered conditions of normal diffusion, Dt (τ ) attains a value in the interval D . . . D + dD. Therefore, the distribution of single-particle diffusivities is defined as p(D, τ ) = δ (D − Dt (τ )) ,

(6)

where . . . denotes an average, which can be evaluated ei T ther as a time-average . . . = limT →∞ 1/T 0 . . . dt, which is accessible by SPT, or as an ensemble average, appropriate for NMR measurements. Note, however, that in SPT, T is

usually limited by the finiteness of the trajectory and complications arise due to the blinking and bleaching of the fluorescent dyes.28 However, advanced tracking algorithms in SPT reduce these effects13, 29 and arbitrary time lags τ between snapshots, which are only limited below by the inverse frame rate of the video microscope, can be accomplished. For experimental SPT data, the distribution of diffusivities is obtained by binning diffusivities into a normalized histogram according to Eq. (6). For ergodic systems, as considered here, time average and ensemble average coincide. By additionally assuming time invariance, Eq. (6) can be rewritten as r2 p(D, τ ) = dr δ D − p(r, τ ) (7) 2d τ with the probability density, Eq. (2), given by p(r, τ ) = δ(r − r(τ )). By performing the angular integration, Eq. (6) or Eq. (7) can also be expressed as ∞ r2 dr δ D − (8) pr (r, τ ), p(D, τ ) = 2d τ 0 in terms of the radial propagator pr (r, τ ), which is the probability density p(r, τ ) integrated over the surface of a d-dimensional sphere with radius r. The delta functions in Eqs. (7) and (8) simply describe a transformation of the coordinates from displacements to diffusivities. Hence, the distribution of diffusivities is a rescaled version of the propagator. This becomes obvious by expanding for r √ > 0, the delta function √ in Eq. (8) as δ[D − r 2 /(2d τ )] = d τ/(2D) δ[r − 2d τ D], which yields the relation √ dτ p(D, τ ) = pr ( 2d τ D, τ ). (9) 2D Furthermore, it should be noted that the distribution of singleparticle diffusivities is closely related to the self part of the van Hove function given in the Appendix A, which coincides with p(r, τ ) given by Eq. (2) for identical particles. Hence, the distribution of diffusivities is also a rescaled version of the van Hove self-correlation function and offers some beneficial properties for our investigations. The diffusivity D results as the mean of the microscopic single-particle diffusivities, Eq. (5). Therefore, for clarity, we denote it in the following as mean diffusivity. According to the definition of the distribution of diffusivities the mean diffusivity has to obey the relation ∞ dD D p(D, τ ). (10) D(τ ) = 0

It is thus obtained as the first moment of the probability density of diffusivities by a well-defined integration, avoiding any numerical fit. Obviously it may also depend on the time lag τ . In the special

t+τ case of free diffusion of a particle, x(t + τ ) − x(t) = t dt ξ (t ) is a fluctuating quantity taken from one realization of the Gaussian white noise ξ (t) with variance proportional to the diffusion coefficient. With Eq. (3), the mean propagator and the signal attenuation are seen to be


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interrelated by the Fourier transformation.18, 23 In the case of normal diffusion in one dimension one has r2 , (11) p1 (r1 , τ ) = (4πDτ )−1/2 exp − 1 4Dτ

1 (τ, k) = exp(−k 2 Dτ ).

(12)

10-3

0

10 10 p(D)

where D stands for the diffusivity. To avoid confusion we deviated from the usual way of denoting the diffusivity simply by D. This is because we use this notation to refer to microscopic single-particle diffusivities Dt (τ ). By inserting Eq. (11) into Eq. (3) the signal attenuation in PFG NMR experiments is seen to obey the well-known exponential relation

101

p(D)

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-1

10-2

10

-4

10-5

6 6.5 7 7.5 8 8.5 9 D

10-3 10

-4

10-5

0

2

4

6

8

10

D

Let us now consider a molecular random walk in a twodimensional plane. Equation (11) describes the probability of a molecular displacement in any arbitrarily chosen direction. For the probability that radial molecular displacements are within the interval r . . . r + dr one obtains, therefore, r2 1 exp − 2π r dr. (13) pr (r, τ ) dr = 4πDτ 4Dτ The mean squared displacement, ∞ 1 2 1 dr pr (r, τ )r 2 = D, r (τ ) = 4τ 4τ 0

(14)

obeys the well-known Einstein relation for normal diffusion in two dimensions. Inserting the corresponding propagator of homogeneous diffusion in two dimensions Eq. (13) into Eq. (7) yields the distribution of single-particle diffusivities p(D) = D−1 exp(−D/D).

(15)

In general, for homogeneous diffusion in d dimensions, the distribution of diffusivities is found to be 1 d D D d/2 exp − , (16) pd (D) = Nd D D 2 D where Nd can be obtained from the normalization condition and is explicitly given by ⎧ √ for d = 1 ⎪ ⎨1/ 2π for d = 2 . (17) Nd = 1 ⎪ ⎩ √ √ 3 3/ 2π for d = 3 Since the system is governed by only one diffusion constant, the dependence on τ vanishes in Eq. (16). However for heterogeneous diffusion, the distribution of single-particle diffusivities additionally depends on the time lag τ . Then, p(D, τ ) cannot generally be expressed by a simple exponential function as in Eq. (16). By inserting Eq. (15), the first moment of the distribution of diffusivities, Eq. (10), ∞ dD D/D exp(−D/D) = D, (18)

FIG. 1. Distribution of diffusivities from a simulated trajectory of a homogeneous diffusion process in two dimensions. The distribution agrees well with the exponential behavior expected from Eq. (15) and is independent of τ . The inset depicts deviations between simulation and Eq. (15) for large D due to insufficient statistics from finite simulation.

the mean diffusion coefficient of the system by ordinary integration. With Eq. (15) for diffusion in two dimensions, the distribution of the single-particle diffusivities in homogeneous systems is seen to result in an exponential. The semi-logarithmic plot of the number of trajectory segments governed by a particular single-particle diffusivity versus these diffusivities is correspondingly expected to yield a straight line. Its negative slope is defined as the reciprocal value of the mean diffusivity. Figure 1 depicts the distribution of diffusivities of a homogeneous diffusion process in two dimensions. The data are obtained from simulations of a system with diffusion coefficient D = 0.7 and gathered in a normalized histogram. For comparison, the solid line represents the analytical expression, Eq. (15), and shows a good agreement with the histogram. The inset of Fig. 1 shows deviations between simulated data and Eq. (15) for large D due to insufficient statistics originating from the finite sample in simulation. It is interesting to note that the shape of the distribution of diffusivities of homogeneous diffusion is similar to that of the attenuation function of PFG NMR diffusion measurements (Eq. (12)). One has to note, however, that now, in contrast to Eq. (12), the mean diffusivity D appears in the denominator of the exponent. From a semi-logarithmic plot of the PFG NMR signal attenuation versus k2 , the mean diffusivity thus directly results as the slope rather than its reciprocal value. In the simple cases of isotropic and homogeneous diffusion both the signal attenuation from PFG NMR and the distribution of diffusivities from SPT resulted in well-known and easily obtainable expressions. In the following we investigate a more elaborated two-region system exhibiting inhomogeneous diffusion.

0

is easily seen to be fulfilled for homogeneous systems and equals the mean squared displacement obtained in Eq. (14). Hence, with p(D, τ ), which is a rescaled van Hove self-correlation function, it becomes possible to determine

III. HETEROGENEOUS DIFFUSION IN TWO-REGION SYSTEMS

Let us now consider molecular diffusion in an isotropic two-region system. With the respective probabilities π i , the


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molecules are assumed to propagate with either the diffusivity D1 or D2 and to remain with the mean dwell times τ m (m = 1, 2) in each of these states of mobility. Thus, the observed diffusion process exhibits dynamic heterogeneities emerging as a time-dependent diffusion coefficient due to the exchange of particles between two regions with different diffusion coefficients. For such heterogeneous systems, the behavior of the distribution of single-particle diffusivities, in general, deviates from the mono-exponential decay. This is attributed to a superposition of many different exponentials of the type of Eq. (15) originating from trajectory segments which include layer transitions during the time lag τ . Thus, we denote the distribution of single-particle diffusivities by p(D, τ ) emphasizing its dependence on τ . Further, the superposition and accordingly the characteristics of the distribution of diffusivities strongly depend on the relation of dwell times and the time lag τ between observed positions.14 For short time lags compared to the dwell times, the exchange rates are very low. Then, the two diffusion processes can be separated into the two underlying processes. As a result, the probability density is the weighted superposition of the mono-exponential decays belonging to homogeneous diffusion inside each region. In the opposite case, for time lags much larger than both dwell times, the observation only reveals a long-term diffusion process with the mean diffusion coefficient of the system. Hence, the probability density is given by a mono-exponential decay parameterized by this mean diffusivity. In the case of a two-region system, the PFG NMR spinecho diffusion attenuation (and hence the Fourier transform of the mean propagator) has been shown to result as a superposition of two terms of the shape of Eq. (12) (Refs. 2 and 18) 1 (τ, k) = p1 (k) exp(−k 2 D1 (k)τ ) +p2 (k) exp(−k 2 D2 (k)τ ) with D1,2 (k)

∓

(19)

1 1 1 1 = + D1 + D2 + 2 2 k τ1 τ2

1 D2 − D1 + 2 k

1 1 − τ2 τ1

2

4 + 4 k τ1 τ2

1/2 ⎞ ⎠, (20)

p1 (k) = 1 − p2 (k), p2 (k) =

1 (π1 D1 + π2 D2 − D1 (k)). (21) D2 (k) − D1 (k)

It should be noted that the primed quantities in Eqs. (20) and (21) depend on the intensity of the magnetic field gradient being related to k and, thus, on the Fourier coordinate. Therefore, Eq. (19) cannot be considered as a superposition of separated populations of the two regions. It is rather the total interference of spin-echo attenuations observed from both regions. Further, the initial condition of a process described by Eqs. (19)–(21) has to be chosen in such a manner that for the

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initial time t = 0, the particles are located at a given position x and are already distributed stationarily between the regions. This is obvious since neither p1 (k) nor p2 (k) depends on t which would be necessary to converge to the stationary distribution. For any other initial distribution, Eq. (19) will only be valid in the limit of t → ∞. The signal attenuation can also be considered for the limiting cases. For τ → 0, i.e., τ τ 1 , τ 2 , the signal attenuation, 1 (τ, k) = π1 exp(−k 2 D1 τ ) + π2 exp(−k 2 D2 τ ),

decomposes into the superposition of two signal attenuations corresponding to each region. As discussed, two completely separated diffusion processes are observed. Hence, the inverse Fourier transformation leads to a superposition of the distribution of diffusivities of each region. In contrast, for τ → ∞, i.e., τ τ 1 , τ 2 , the mixing of the two regions leads to the observation of an effective mean diffusion process with a signal attenuation, 1 (τ, k) = exp(−k 2 (π1 D1 + π2 D2 )τ ),

(23)

containing the mean diffusion coefficient. Analogously, its inverse Fourier transform, i.e., the distribution of diffusivities, is only characterized by the mean diffusion coefficient D = π 1 D1 + π 2 D2 . A detailed deviation of the limiting cases is given in the Appendix C. IV. SIMULATION OF TWO-REGION SYSTEMS

In order to simulate heterogeneous diffusion, we consider a system with two regions where particles propagate with different diffusivities and can change their state of mobility. Following the experiment with rhodamine in TEHOS,16, 30 this two-region system is modeled by a bi-layer system with layer-dependent diffusion coefficients D1 and D2 , respectively. Such processes can formally be described as composite Markov processes31 or equivalently as multistate random walks,32, 33 which are known to be widely applicable. A recent biophysical application consists of changes in the diffusive behavior of molecules in membranes due to random changes of the molecules’ conformation.34 In the case of two states or regions the probability density of finding the particle at position x at time t is determined by the evolution equations ∂ pˆ 1 (x, t) = w12 pˆ 2 (x, t) − w21 pˆ 1 (x, t) + D1 ∇ 2 pˆ 1 (x, t), ∂t ∂ pˆ 2 (x, t) = w21 pˆ 1 (x, t) − w12 pˆ 2 (x, t) + D2 ∇ 2 pˆ 2 (x, t), ∂t (24) for each region with corresponding diffusion coefficients D1 and D2 . Within each region the motion of the molecules is accomplished by ordinary two-dimensional diffusion, i.e., random walkers experiencing shifts of the positions distributed according to a Gaussian with a variance defined by the diffusion coefficient in the region. The exchange between these two diffusive regions is simulated by a jump process governed by a master equation with jump rates wnm , which describe a transition from region m to n (m, n = 1, 2). The inverse of the


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jump rates wnm yields the mean dwell time τ m ,

(a)

(25)

for which particles remain in region m. Further, the stationary distribution between the regions, w12 w21 and π2 = , (26) π1 = w12 + w21 w12 + w21 is also dictated by the jump rates. With the stationary distribution the mean diffusion coefficient of the two-region system is given by D = π1 D1 + π2 D2 ,

2 layer

1 1 τ1 = and τ2 = , w21 w12

x 7

(b)

(27)

which is the weighted average of the diffusion coefficients belonging to each region.19 To investigate the effects of heterogeneous diffusion, simulation of the two-region system is performed with the following system parameters. The diffusion coefficients within each of the two regions are given by D1 = 0.1 and D2 = 1.0. The jump rates w21 = 8 and w12 = 4 yield the dwell times τ 1 = 0.125 and τ 2 = 0.25, respectively. Hence, the stationary distribution between the regions results in π1 = 1/3 and π2 = 2/3 and a mean diffusion coefficient D = 0.7 is obtained. The length of the time step in the simulation is chosen to be t = 0.01, which is much smaller than the dwell times to ensure diffusive motion of the particles within the regions. Simulation of Eq. (24) is depicted in Fig. 2(a). It shows the trajectory of a particle in a bi-layer system, where the particle jumps between the layers. In each layer, diffusion is governed by a different diffusion coefficient denoted by the color of the trajectory segments. Since in experiments with video microscopy only a two-dimensional projection of the process is observed, the trajectory is projected onto the x-y-plane in Fig. 2(b). As a consequence, information about the layer is obscured and can only be identified due to the color coding in the figure. Hence, in the projection it is unknown which diffusion coefficient currently governs the process. A description of such observed diffusion processes by the Fokker-Planck equation with time-dependent diffusion coefficient would become possible if all trajectories jump synchronously. Since in our bi-layer system the particles move independently, the process is more complicated. As a result of the projection, the observed process does not possess the Markov property anymore since, in general, the Chapman–Kolmogorov equation cannot be satisfied. The simulation provides an approach to study properties of an N-layer system, which is closely related to a system where the diffusion coefficient varies continuously with the z-coordinate. To avoid transient behavior in our simulation, the particle positions are initialized with their corresponding stationary distributions between the layers given by π i . It should be noted, however, that experimental results will be influenced by such transient effects if the tracer molecules require a sufficiently long time to distribute between the layers of the solvent. On the other hand, such slow relaxation is related to low exchange rates leading to almost complete separation of the two diffusive regions.14 This would allow for an appropriate bi-exponential fit of our distribution of diffusivities although

y

1

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3 2 1 0 -1 -2

-1

0

1

2

3

4

5

6

7

x FIG. 2. Single-particle trajectory from simulation of diffusion in a bi-layer system. (a) The particle performs diffusion with corresponding diffusion coefficients and jumps between the layers. (b) Projection of the trajectory shown in (a) onto the x-y-plane as usually observed by single-particle tracking. Information of the layer and the corresponding diffusion coefficient is lost in the projection and can only be identified due to the color code.

the weights do not correspond to the stationary distributions yet. To investigate the connection between spin-echo signal diffusion attenuation, as measured by PFG NMR, and distribution of single-particle diffusivities, as assessed by SPT, we simulated one particle. Next, we recorded squared displacements along the simulated trajectory of 107 time steps. The squared displacements are calculated from the changes of the particle positions and are divided by the time lag τ elapsed between the observations of the two positions. Hence, we obtain scaled squared displacement with the dimension of a diffusion coefficient. The thus obtained diffusivity is a fluctuating quantity along a trajectory. Finally, we gather them in a histogram counting their occurrences. The histogram contains data from a moving-time average since the diffusivities originate from single trajectories. Note that for ergodic systems ensemble averaging will yield identical results. After normalizing the histogram, we obtain a probability density referred to as the distribution of diffusivities. The distribution of diffusivities contains all information about the diffusivities of the process and their fluctuations. Following the experiment, only a fraction of the time steps is available for the distribution depending on the selected time lag. Thus, our resulting


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distributions of diffusivities depicted in log-linear plots have their lower boundary at 10−3 since data below suffer from insufficient statistics. V. APPROXIMATION OF DIFFUSIVITY DISTRIBUTIONS

Since an exact relation of the PFG NMR signal attenuations to distributions of diffusivities requires the inverse Fourier transformation, we are now going to use the set of Eqs. (19)–(21) for an approximation of the probability distribution of the single-particle diffusivities in a two-region system. We proceed in analogy with our treatment of the simple system with only one (mean) diffusivity. In either case the information about the probability distribution p(D, τ ) of the single-particle diffusivities D is clearly contained in the propagator. For the system with one diffusivity this propagator is given by Eq. (11). Its Fourier transform (Eq. (12), which is nothing else than the PFG NMR spin-echo diffusion attenuation curve) was found to coincide with the shape of the probability distribution of the single-particle diffusivities (Eq. (15)) with the only difference that the mean diffusivity, which represents the slope in the semi-logarithmic attenuation plots, appears in the denominator of the exponent in the distribution function p(D). In the two-region system, the PFG NMR spin-echo diffusion attenuation (and hence the Fourier transform of the propagator) is now found to be given by two exponentials (Eq. (19)) of the form of Eq. (12). Formally we may refer, therefore, to two populations with the relative weights pi and the effective (mean) diffusivities Di as quantified by Eqs. (20) and (21). Following the analogy of our simple initial system, as a first attempt, the resulting probability function of the single-particle diffusivities may be approximated by a corresponding superposition of two exponentials of the type of Eq. (15), ˜ ˜ )) = p1 (k) ˜ p(D, τ ) p(D, k(τ

1 ˜ exp(−D/D1 (k)) ˜ D1 (k)

˜ +p2 (k)

1 ˜ exp(−D/D2 (k)) ˜ D2 (k) (28)

˜ pi (k)

˜ Di (k)

with the parameters and as given by Eqs. (20) and (21). Since this approximation avoids Fourier transformation, a proper τ -dependence of k˜ has to be chosen for the primed quantities. It should be noted that the transformation of Eq. (19) from the Fourier space will only result in a superposition of two exponentials in real space if the primed quantities ˜ Hence, Eq. (28) could in Fourier space are independent of k. only serve as a rough approximation of the observed process. However, inserting Eq. (28) into Eq. (10), the mean diffusivity of the two-region system results in ˜ 1 (k) ˜ + p2 (k)D ˜ 2 (k) ˜ = π1 D1 + π2 D2 D = p1 (k)D

(29)

with the second equality resulting from the application of Eqs. (20) and (21). This is exactly the result which is wellknown19 and it should be noted that it does not depend on τ . Further on, we may consider the limiting cases k˜ → 0 and k˜ → ∞ which can be translated to r → ∞ and r → 0,

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respectively. Intuitively, large displacements r → ∞ are related to long observation times τ → ∞ and vice versa. This relation is substantiated by keeping k˜ 2 τ constant (see also Eq. (32)) where k˜ → 0 corresponds to τ → ∞ and vice ˜ )) and ˜ versa. Due to this, the respective limits of p(D, k(τ p(D, τ ) should coincide. As a result we obtain the expected expressions ˜ )) = lim p(D, τ ) ˜ k(τ lim p(D, τ →0

˜ k→∞

=

π1 D1−1

exp(−D/D1 ) + π2 D2−1 exp(−D/D2 ), (30)

and ˜ )) = lim p(D, τ ) ˜ lim p(D, k(τ τ →∞

˜ k→0

= D

−1

exp(−D/D).

Since the diffusivities and probabilities Di and pi occur˜ we ring in Eqs. (19)–(21) depend on the Fourier coordinate k, have referred to the probability density in this context as an ˜ )). Hence, Eq. (28) in the given ˜ approximated one, p(D, k(τ notation is unable to provide an approximation of the probability distribution function of the single-particle diffusivities over the whole diffusivity scale. This is in perfect agreement with the previous results14 where it has been shown that the distribution of diffusivities, in general, cannot be represented by a weighted superposition of the underlying homogeneous diffusion processes. However, such an approximation of the probability density might become possible by inserting an appropriately selected value for the Fourier coordinate. As a first trial, one may put k˜ −2 = Dτ ,

(32)

which ensures highest sensitivity with respect to the space scale covered during the experiments. Note that in PFG NMR experiments, the exponent in the signal attenuation, Eq. (12), is of the order of 1, which yields an easily observable PFG NMR spin-echo diffusion attenuation. Figure 3 depicts the distribution of diffusivities from a simulated two-dimensional trajectory in a two-region system with mean dwell times τ 1 = 0.125 and τ 2 = 0.25 for three time lags τ = 0.01, 0.2, and 1.0. Further, the approximation of the distribution of diffusivities from Eq. (28) is investigated ˜ Thus, the limiting case of completely for corresponding k. separated diffusion processes found for τ → 0 is simulated with τ = 0.01 τ 1 , τ 2 and compared with Eq. (28) for k˜ → ∞, i.e., Eq. (30). On the other hand, the second limiting case of mean diffusion emerging for τ → ∞ is obtained from simulation with τ = 1.0 τ 1 , τ 2 and comparison with Eq. (28) for k˜ → 0, i.e., Eq. (31). Fig. 3 clearly shows that simulated data from both limiting cases are recovered reason˜ In contrast, the distriably by Eq. (28) for corresponding k. bution of diffusivities reveals a more complicated behavior in the intermediate exchange regime between the limiting cases. Since the time lag τ = 0.2 is in the order of the mean dwell times, neither a mean diffusion process nor a weighted superposition of completely separated processes is observed. In particular, the distribution cannot be approximated by ˜ ). This is obvious, since with such an Eq. (28) with a given k(τ


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With the rescaled coordinates, √ r r = √ and k = k 2d τ , 2d τ

101

it is further simplified to 1 k Sd (k , D), p(D, τ ) = dk τ, √ 2d τ (2π )d

p(D,τ)

100 10-1

10

τ=0.01 ~ k→∞

-2

τ=0.2 k≈2.67 τ=1.0 ~ k→0

0

1

2

3

4

5

6

(35)

with Sd (k, D) being the Fourier transform of a uniform √ density on the surface of a d-dimensional sphere of radius D,

~

10-3

(34)

Sd (k, D) =

dr δ(D − r2 ) exp(−ikr).

(36)

D FIG. 3. Comparison of distribution of diffusivities (colored histograms) from a simulated two-dimensional trajectory with numerical approximation via Eq. (28) (solid lines) of a two-region system for time lags τ = 0.01, 0.2, and 1.0 and mean dwell times of τ 1 = 0.125 and τ 2 = 0.25. The limiting cases of k˜ → 0 and k˜ → ∞ approximate the simulated data reasonably. However, for τ = 0.2 in the order of the dwell times an intermediate k˜ ≈ 2.67, as suggested in Eq. (32), does not approximate the density sufficiently.

estimate of k˜ the dependence on k of the primed quantities of Eqs. (20) and (21) in Fourier space is neglected. Then, the inverse Fourier transformation of Eq. (19) as well as the transformation to the distribution of diffusivities would yield a simple superposition of two exponentials again. In general, this does not provide appropriate results for arbitrary dwell times and time lags.14 As a consequence, a general expression requires inverse Fourier transformation of the PFG NMR attenuation curve.

VI. EXACT RELATION BETWEEN SIGNAL ATTENUATION AND DISTRIBUTION OF DIFFUSIVITIES

In Sec. V, the approximation of the distribution of diffusivities by Eq. (28) was shown to reproduce the limiting cases of time lag τ as well as the correct mean value. Cases in between the limits did not deliver appropriate results. In order to produce proper results for arbitrary τ , we derive general formulae for the transformation of PFG NMR signal attenuations to distributions of single-particle diffusivities. Quite formally two steps have to be accomplished to derive a general expression of p(D, τ ) from (τ, k). As a first step, inverse Fourier transformation of Eq. (1) yields the propagator in real space. Further, the shift r between positions, as given by the propagator, can be translated into diffusivities via scaled squared displacements leading to the distribution of diffusivities as defined in Eq. (7). The two steps can be combined to directly obtain the probability density from signal attenuation. Depending on dimensionality d, the distribution of diffusivities is given by p(D, τ ) =

r2 dr δ D − 2d τ 1 dk (τ, k) exp(−ikr). (33) × (2π)d

Since Eq. (36) can be expressed analytically35 by √ √ Sd (k, D) = π a+1 D a 2a Ja (|k| D)(|k| D)−a

(37)

with a = d/2 − 1 and Ja (x) denoting the Bessel function of the first kind, the exact transformation of signal attenuations (τ, k) to distributions of diffusivities p(D, τ ) is accomplished without applying an inverse Fourier transformation. For isotropic systems, the signal attenuation (τ, k) depends only on the absolute value of k, i.e., the radial intensity of the field gradient k. Without loss of generality, an arbitrary direction k = (k, 0, . . . , 0)T may be considered and the corresponding signal attenuation is denoted by 1 (τ, k) = (τ, k = (k, 0, . . . , 0)T ). Then the following expressions are obtained for the distribution of diffusivities depending on the dimensionality of the system. For one-dimensional systems, Eq. (33) reduces to ∞ √ 1 k cos(k D). dk 1 τ, √ p(D, τ ) = √ 2τ π D 0 (38) The transformation for d = 2 can be written as √ 1 ∞ k kJ0 (k D), p(D, τ ) = dk 1 τ, √ (39) 2 0 4τ and for d = 3 one obtains √ k 1 ∞ k sin(k D) dk 1 τ, √ p(D, τ ) = π 0 6τ

(40)

using polar and spherical coordinates, respectively. The given transformations move the whole dependence on time lag τ to the signal attenuation. This is achieved by rescaling the k √ coordinate by 2d τ . Hence, a signal attenuation of an ensemble diffusing in a two-dimensional plane measured by PFG NMR is transformed into a distribution of single-particles diffusivities via Eq. (39). For homogeneous diffusion, Eq. (39) yields the expected probability of single-particle diffusivities, Eq. (15), by inserting the simple exponential relation, Eq. (12), as signal attenuation. Furthermore, the limiting cases of time lag τ are reproduced exactly by the presented transformations, Eqs. (38)– (40): For τ → 0 the distribution of single-particle diffusivities for the given dimensionality results in the superposition of two respective distributions of Eq. (16) denoting two separated, homogeneous diffusion processes. On the other hand,


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101 101

p(D,0.2)

100

p(D,τ)

100

10-1

10-2

kmax=2 kmax=5 kmax=8 kmax=10 kmax=12 kmax=15

0

1

2

3

4

τ=1.0 τ=0.5 τ=0.2 τ=0.05

D

10-1

10-2

10-3

0

1

2

3

4

5

6

7

8

D

FIG. 4. Comparison of distributions of single-particle diffusivities from a simulated two-dimensional trajectory (colored histograms) with distributions obtained by applying Eq. (39) for an exact transformation of the PFG NMR spin-echo signal diffusion attenuation, Eq. (19), of a two-region system for time lags τ = 0.05, 0.2, 0.5, and 1.0 and mean dwell times τ 1 = 0.125 and τ 2 = 0.25 (solid lines). The data agree well with each other for each τ . Further, the dependence on τ is apparent, which is typical for diffusion in heterogeneous media.

FIG. 5. Transformation of Eq. (39) of PFG NMR spin-echo signal diffusion attenuation by integration up to kmax (solid lines) due to experimentally bounded intensity k of the field gradient pulses. The distribution of singleparticle diffusivities (colored histogram) from a simulated two-dimensional trajectory will only be obtained reasonably if k is given over the whole intensity scale. For smaller intervals of k deviations become clearly visible as well as oscillations introduced by the inverse Fourier transformation.

for τ → ∞, the resulting distribution of single-particle diffusivities for the given dimensionality is also of the type of Eq. (16), respectively, and depends only on the mean diffusion coefficient of the system. A detailed derivation of the limiting cases is given in the Appendix C. To examine the transformations, the same parameters, for which the approximation via Eq. (28) failed, are used again, now applying Eq. (39) for an exact transformation of the PFG NMR signal attenuation relation, Eq. (19), into the distribution of single-particle diffusivities. The results are depicted in Fig. 4 and again the distribution of diffusivities from a simulated two-dimensional trajectory is given for comparison. For each of the chosen τ = 0.05, 0.2, 0.5, and 1.0, a perfect agreement is obvious, confirming the relation between the two approaches. Moreover, Fig. 4 clearly illustrates how the distribution of diffusivities depends on τ and reveals a transition from a non-exponential behavior to a mono-exponential decay. For small τ corresponding to diffusion in separated regions, it deviates considerably from a mono-exponential behavior. However, for long-term observations (τ → ∞) only a mean diffusion process is observed due to averaging of the motion in both regions. Consequently, this yields a mono-exponential decay of the distribution of diffusivities. This transition reveals the heterogeneity of the diffusion process.14 Hence, in order to characterize diffusive motion the distribution of diffusivities has to be investigated for its dependence on the time lag τ .

Figure 5 illustrates the influence of finite k on the distribution of single-particle diffusivities obtained for τ = 0.2. If with the maximal applied kmax the respective spin-echo signal is not sufficiently attenuated, the transformation of the signal attenuation from a finite interval will yield significant deviations from the expected probability distribution. As a consequence, the first moment, i.e., the mean diffusion coefficient of the system, is altered accordingly. Furthermore, due to the bounded signal attenuation, the inverse Fourier transformation introduces oscillations since only a limited range of the spectrum contributes to the values in real space. The reason is the integrand in Eqs. (38)–(40) which will only vanish for large k if 1 decays faster than the remainder. This effect may clearly be identified in Fig. 5. In order to obtain reasonable results, the signal must be attenuated to a sufficient extent. Simulated data of two-dimensional diffusion processes have shown that the attenuation should fall below 10−4 of its maximum at kmax to suppress oscillations. This has to be considered when dealing with experimental data. The necessity of fast decaying 1 becomes especially important for large time lags τ . In the case of small time lags τ →0√ our rescaling of the k coordinate in Eqs. (38)–(40) √ leads to k/ τ → ∞ in the second argument of 1 (τ, k/ 2d τ ). Thus, for small τ , signal attenuation becomes more pronounced and reduces the influence of the bounded k. Moreover, signal attenuation is closely related to the incoherent structure factor,36 as demonstrated in the Appendix A, dealing with similar limitations. A possible solution is to split the integral into two parts, integrating numerically up to the experimental limit kmax and assuming an analytical expression for the remaining part. Since the oscillations in the approximate densities of Fig. 5 seem to be induced by the hard cutoff at the wavelength k = kmax , a possible strategy in reducing these oscillations may lie in applying an appropriate window function as in spectrum estimation procedures. We tested this option

VII. INFLUENCE OF EXPERIMENTALLY BOUNDED k

PFG NMR spin-echo diffusion attenuation functions can only be measured up to a finite intensity k of the magnetic field gradient pulses. However, to generate the distribution of diffusivities exactly, the signal attenuation has to be given over the whole intensity scale. Hence, the effect of an experimentally bounded Fourier coordinate k has to be considered.


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fusive motion offers new approaches for the evaluation of data. Hence, the methods of analysis may benefit from each other. This becomes especially relevant for systems with heterogeneities, where the distribution of diffusivities exhibits a dependence on the time lag. For more elaborated processes it may even not become stationary and enables to assess nontrivial properties of such systems. Since the distribution of diffusivities can be measured easily and contains more information from the propagator than well-established methods, it should be used for future analysis of experimental data.

101 kmax=2 kmax=5 kmax=8 kmax=10 kmax=12 kmax=15

p(D,0.2)

100

10-1

10-2

10-3

0

1

2

3

4

5

6

7

8

D FIG. 6. Same situation as in Fig. 5, but the densities are now obtained by replacing the sharp cutoff at k = kmax by a smooth cutoff resulting from applying a half Hann window. A considerable improvement is achieved, especially if the value kmax is not too small.

by applying a half Hann window to smoothen the cutoff. The best results were obtained for a window decaying from the value one at k = 0 to zero at k = kmax . The obtained results are very convincing if the cutoff value kmax is not too small as can be seen in Fig. 6. VIII. CONCLUSIONS

We investigated the connection between the signal attenuation measured by pulsed field gradient nuclear magnetic resonance and the distribution of single-particle diffusivities obtained from single-particle tracking. Due to their interrelations with the diffusion propagator of the system, the distribution of diffusivities is expressed by a general transformation of the signal attenuation. In the special case of a system involving two different states of diffusive mobility, the tworegion exchange model of PFG NMR offers analytical expressions and allows for a comparison of analytical and simulated data. An approximation of the distribution of single-particle diffusivities via two populations with relative weights avoids the inverse Fourier transformation. Even in this simple system, such an approximation will only yield appropriate results if the time lag is much larger or much smaller than the dwell times. These cases correspond to an observation of the mean diffusion of the system and a process of completely separated diffusive motion without transition between the regions, respectively. Thus, in general, to obtain a proper distribution of single-particle diffusivities for diffusion in two-region systems, the exact transformation of the respective NMR signal attenuations is necessary. Only in this way we found perfect agreement of the experimental and analytical data. However, since PFG NMR data in some systems cannot be measured over a sufficiently large dynamic range, the inverse Fourier transformation may introduce deviations and oscillations. In these cases, the data analysis has to be performed with care and may require the use of additional information. In summary, the investigated connection between two popular methods to experimentally observe and analyze dif-

ACKNOWLEDGMENTS

We gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft (DFG) for funding of the research unit FOR 877 “From Local Constraints to Macroscopic Transport”. We also thank the anonymous referees for their valuable suggestions, which helped to improve the paper considerably. APPENDIX A: CORRESPONDENCE BETWEEN INCOHERENT INTERMEDIATE SCATTERING FUNCTION AND SIGNAL ATTENUATION

The signal attenuation of PFG NMR and the incoherent intermediate scattering function as well as the dynamic structure factor are closely related. In this appendix, their correspondence is illustrated briefly and further details can be found in Refs. 18, 37, and 38. The observed motion of tracer particles can be analyzed by the self part of the van Hove time-dependent pair correlation function, N 1 δ(r − (xi (τ ) − xi (0))) , (A1) Gs (r, τ ) = N i=1 describing the correlation of N individual particles.39 Its spatial Fourier transformation, S(k, τ ) = dr Gs (r, τ ) exp(ikr), (A2) leads to the incoherent intermediate scattering function, S(k, τ ) =

N 1 exp(ik(xi (τ ) − xi (0))), N i=1

(A3)

which is linked to the velocity autocorrelation function of the particles. Furthermore, the incoherent intermediate scattering function S(k, τ ) is related to the dynamic structure factor S(k, ω) known from neutron scattering via Fourier transformation in τ , i.e., the power spectrum of S(k, τ ), where ω denotes a frequency. For ergodic systems, S(k, τ ) can be obtained from an arbitrary particle, S(k, τ ) = exp(ik(x(τ ) − x(0))) 1 dx dx exp(ik(x − x ) p(x, τ, x , 0), = 2 V (A4)


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where V is the normalization and p(x, τ, x , 0) denotes the joint probability of a particle to be located initially at x and at time τ at position x. The joint probability can be expressed by the conditional probability, p(x, τ, x , 0) = p(x, τ |x , 0) p0 (x ).

(A5)

Since during time τ the particle accomplished a displacement r, its positions are interrelated by x = x + r. Due to translation invariance, without loss of generality, x = 0 leads to the propagator in Fourier space, 1 dr exp(ikr) p(r, τ ) = (τ, k), (A6) V corresponding to the signal attenuation in PFG NMR as introduced in Eq. (1). Hence, signal attenuation and incoherent intermediate scattering function coincide. Furthermore, for identical particles without restrictions by the boundaries the averaging over the particles in Eq. (A1) can be omitted and Gs (r, τ ) is equal to p(r, τ ) given by Eq. (2). For isotropic systems the self part of the radial van Hove time-dependent pair correlation function, N 1 δ (r − |xi (τ ) − xi (0)|) , (A7) Gs (r, τ ) = N i=1 considers only absolute values of the displacements. Again, for identical particles without restrictions by the boundaries an arbitrary particle can be considered and Gs (r, τ ) is equal to pr (r, τ ). APPENDIX B: RELATION BETWEEN EVOLUTION EQUATIONS AND PFG NMR SIGNAL ATTENUATION

For Eq. (24), i.e., the evolution equations of the probability density to find a particle at position x at time t, the moments of the random variable x can be obtained via the characteristic functions. By introducing the vector p(k, t) comprising the characteristic functions of each region and the matrix W(k) consisting of the elements

2 W(k)nm = wnm + −Dn k − wln δnm , (B1) l

the Fourier transform of Eq. (24) can be written elegantly as d p(k, t) = W(k) p(k, t), dt

(B2)

p(k, t) = exp(t W(k)) p(k, 0)

(B3)

where

is easily seen to be the solution. For the two-region system the initial distribution p(k, 0) = (π1 , π2 )T is given by the equilibrium distribution between the regions. Applying the spectral decomposition the matrix exponential in Eq. (B3) for the two-region system can be written as exp(t W(k)) =

2 α=1

exp(tμα (k)) Aα (k),

(B4)

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where μ1,2 (k) =

1 (−D1 k2 − D2 k2 − λ ± D(k)) 2

denotes the eigenvalues and,

D(k) ± η(k) ±2w12 1 A1,2 (k) = , 2D(k) ±2w21 D(k) ∓ η(k) (B6) represent the corresponding matrices from the dyadic product of the right- and left-eigenvectors with λ = w21 + w12 ,

(B7)

η(k) = −D1 k2 + D2 k2 − w21 + w12 ,

(B8)

D(k) = {(D1 k2 + D2 k2 + λ)2 − 4D1 D2 k4 −4D1 k2 w12 − 4D2 k2 w21 }1/2 .

(B9)

Finally, the signal attenuation obtained from PFG NMR corresponds to the projection of the characteristic function π (τ, k) = 1 1 exp(τ W(k)) 1 , (B10) π2 where k = k eˆ is measured in the direction of the applied field gradient denoted by the unit vector eˆ . Since for isotropic systems an arbitrary direction can be considered, Eq. (B10) results in the expressions given in Eqs. (19)–(21) for the tworegion system. APPENDIX C: EXACT TRANSFORMATION OF LIMITING CASES

By choosing k = k eˆ , the isotropic signal attenuations for dimensionality d in Eqs. (38)–(40) ⎧√ ⎪ ⎨ 2 for d = 1 k for d = 2 , with u = 2 1 τ, √ ⎪ u τ ⎩√ 6 for d = 3 are considered in an arbitrary direction of the applied field gradient with intensity k. The exponent of Eq. (B10) is given by

−w21 w12 k 2 D1 0 k eˆ − 2 . =τ τW √ u u τ w21 −w12 0 D2 (C1) Based on these expressions the limiting cases are discussed separately. 1. Limiting case τ → 0

In the limiting case of τ → 0, only the diagonal matrix on the right-hand side of Eq. (C1) remains. Hence, the matrix exponential can be expressed by the exponentiation of the


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diagonal elements and Eq. (B10) reduces to k 1 τ, √ u τ ⎛ ⎞ 2

k 0 ⎜ exp − u2 D1 ⎟ π1 = 1 1 ⎝ , (C2) 2 ⎠ π2 0 exp − uk 2 D2 yielding a superposition of two exponentials corresponding to separated regions. This is in agreement with the previous findings since for short times τ no exchange between the regions occurs. Obviously, this result is not restricted to the tworegion system but holds for an arbitrary number of diffusion states. Applying the presented transformations Eqs. (38)–(40) for dimensionality d to the obtained signal attenuation results in a distribution of diffusivities which is the superposition of two distributions of diffusivities for homogeneous diffusion in each region as given by Eq. (16), respectively.

c = (4D1 w12 + 4D2 w21 )

τ μ1

−w12 w12

.

(C4)

Due to the projection in the signal attenuation Eq. (B10) 1 1 A2 (0) = 0 0 , (C5) the contribution from A2 (0) vanishes. Thus, for τ → ∞ only eigenvalue μ1 contributes to the spectral decomposition. Moreover, μ1 = 0, which explains that the contribution from the diagonal matrix in Eq. (C1) cannot be neglected. Then, √ according to Eq. (B4), the exponential of τ μ1 (k eˆ /(u τ )) is required, which is given by k eˆ 1 −a − λτ + (a + λτ )2 − b − cτ τ μ1 = √ 2 u τ (C6) with a = D1

k2 k2 + D2 2 , 2 u u

b = 4D1 D2

k4 , u4

(C8)

After further simplification, Eq. (C6) reduces to c k eˆ 1 τ μ1 −a − λτ + λτ + a − √ 2 2λ u τ c (C9) =− , 4λ

2. Limiting case τ → ∞

1 w21 A2 (0) = λ −w21

(C7c)

The square root in Eq. (C6) can be rewritten as (a + λτ )2 − b − cτ 2a c 1 a2 − b 1 − 2 + = λτ 1 + λ λ τ λ2 τ 2 1 2a c 1 1 = λτ 1 + − 2 +O . 2 λ λ τ τ2

which results in

In the limiting case of τ → ∞, the situation is more complicated. Arguing analogously to the case of τ → 0 does not result in an appropriate expression. If the diagonal matrix on the right-hand side of Eq. (C1) is neglected, the signal attenuation will reduce to 1 yielding only its normalization. Hence, this limiting case is addressed by involving the spectral decomposition. The matrices Eq. (B6) are given by τ →∞ k eˆ −−→A1,2 (0), A1,2 √ u τ

1 w12 w12 A1 (0) = , (C3) λ w21 w21

k2 . u2

k eˆ √ u τ

−(π1 D1 + π2 D2 ) = −D

k2 , u2

k2 u2 (C10)

by applying Eq. (C7c) and Eqs. (26) and (29). Hence in the limiting case of τ → ∞, the signal attenuation, k k2 (C11) = exp −D 2 , 1 τ, √ u u τ depends only on the mean diffusion coefficient of the tworegion system. By integrating the signal attenuation Eq. (C11) for the limiting case τ → ∞ with the presented transformations Eqs. (38)–(40) for dimensionality d, as expected, the respective distributions of diffusivities, Eq. (16) are obtained, which correspond to homogeneous diffusion with the mean diffusion coefficient D. To conclude, the derivation of the two limiting cases reveals the properties of the distribution of single-particle diffusivities and its dependence on τ . Starting from the limiting case τ → ∞, where only eigenvalue μ1 contributes, the weight of μ2 increases for decreasing τ . This is reflected in the distribution of diffusivities by the dependence on τ as presented in Fig. 4. It describes the transition from a mean diffusion process to two completely separated diffusion processes for τ → ∞ and τ → 0, respectively. It should be noted that for the self part of the van Hove function the limiting cases cannot be determined. However, for the distribution of diffusivities, which is a rescaled van Hove self-correlation function, both limits are well-defined. 1 Diffusion in Condensed Matter, edited by P. Heitjans and J. Kärger, 2nd ed.

(C7a)

(C7b)

(Springer-verlag, Berlin, 2005). S. Price, NMR Studies of Translational Motion, Cambridge Molecular Science (Cambridge University Press, Cambridge, New York, 2009). 3 M. Krutyeva and J. Käger, Langmuir 24, 10474 (2008). 4 M. Nilsson, E. Alerstam, R. Wirestam, F. Staohlberg, S. Brockstedt, and J. Lätt, J. Magn. Reson. 206, 59 (2010). 2 W.


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J. Saxton and K. Jacobson, Annu. Rev. Biophys. Biomol. Struct. 26, 373 (1997). 6 A. Zürner, J. Kirstein, M. Düblinger, C. Bräuchle, and T. Bein, Nature (London) 450, 705 (2007). 7 C.-J. Yu, A. G. Richter, A. Datta, M. K. Durbin, and P. Dutta, Phys. Rev. Lett. 82, 2326 (1999). 8 A. Dembo and O. Zeitouni, Stochastic Proc. Appl. 23, 91 (1986). 9 F. Campillo and F. L. Gland, Stochastic Proc. Appl. 33, 245 (1989). 10 R. Das, C. W. Cairo, and D. Coombs, PLOS Comput. Biol. 5, e1000556 (2009). 11 L. R. Rabiner, Proc. IEEE 77, 257 (1989). 12 R. J. Elliott, L. Aggoun, and J. B. Moore, Hidden Markov Models, Stochastic Modelling and Applied Probability, Vol. 29 (Springer, New York, 1995). 13 M. Heidernätsch, M. Bauer, D. Täuber, G. Radons, and C. von Borczyskowski, Diffus. Fundam. 11, 111 (2009). 14 M. Bauer, M. Heidernätsch, D. Täuber, C. von Borczyskowski, and G. Radons, Diffus. Fundam. 11, 104 (2009). 15 M. J. Saxton, Biophys. J. 72, 1744 (1997). 16 I. Trenkmann, D. Täuber, M. Bauer, J. Schuster, S. Bok, S. Gangopadhyay, and C. von Borczyskowski, Diffus. Fundam. 11, 108 (2009). 17 A. Lubelski, I. M. Sokolov, and J. Klafter, Phys. Rev. Lett. 100, 250602 (2008). 18 J. Kärger, H. Pfeifer, and W. Heink, in Advances in Magnetic Resonance, edited by J. S. Waugh (Academic, San Diego, 1988), Vol. 12, pp. 1–89. 19 C. Van den Broeck and R. M. Mazo, J. Chem. Phys. 81, 3624 (1984). 20 B. Blümich, Essential NMR, (Springer-Verlag, Berlin, 2005), Vol. 1. 21 R. Kimmich, N. Fatkullin, M. Kehr, and Y. Li, Anomalous Transport– Foundations and Applications, edited by R. Klages, G. Radons, and I. M. Sokolov (Wiley VCH, Berlin, 2008), Chap. XVII, pp. 485–518.

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Valiullin and J. Kärger, Anomalous Transport–Foundations and Applications, edited by R. Klages, G. Radons, and I. M. Sokolov (Wiley VCH, Berlin, 2008), Chap. XVIII, pp. 519–544. 23 J. Kärger and W. Heink, J. Magn. Reson. 51, 1 (1983). 24 C. W. Gardiner, Handbook of Stochastic Methods, 3rd ed., Springer Series in Synergetics, Vol. 13 (Springer-Verlag, Berlin, 2004). 25 B. B. Mandelbrot and J. W. Van Ness, SIAM Rev. 10, 422 (1968). 26 Anomalous Transport–Foundations and Applications, edited by R. Klages, G. Radons, and I. M. Sokolov (Wiley VCH, Berlin, 2008). 27 A. Kusumi, Y. Sako, and M. Yamamoto, Biophys. J. 65, 2021 (1993). 28 J. Schuster, J. Brabandt, and C. von Borczyskowski, J. Lumin. 127, 224 (2007). 29 I. F. Sbalzarini and P. Koumoutsakosa, J. Struct. Biol. 151, 182 (2005). 30 A. Schob and F. Cichos, J. Phys. Chem. B 110, 4354 (2006). 31 N. G. van Kampen, Stochastic Processes in Physics and Chemistry, 2nd ed. (North-Holland, Amsterdam, 1992). 32 J. W. Haus and K. W. Kehr, Phys. Rep. 150, 263 (1987). 33 G. H. Weiss, Aspects and Applications of the Random Walk (NorthHolland, Amsterdam, 1994). 34 N. Malchus and M. Weiss, Biophys. J. 99, 1321 (2010). 35 S. Vembu, Q. J. Math. 12, 165 (1961). 36 G. Fleischer and F. Fujara, in NMR–Basic Principles and Progress, edited by P. Diehl, E. Fluck, H. Günther, R. Kosfeld, J. Seelig, and B. Blümich (Springer-Verlag, Berlin, 1994), Vol. 30, Chap. IV, pp. 159–207. 37 J. P. Boon and S. Yip, Molecular Hydrodynamics (Dover, New York, 1991). 38 J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids, 3rd ed. (Academic, Amsterdam, 2006). 39 L. van Hove, Phys. Rev. 95, 249 (1954).


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Interplay between the antiferromagnetic spin configuration and the exchange bias effect in [Pt/Co]8 /CoO/Co3 Pt trilayers Tobias Kosub,*,† Denys Makarov,† Herbert Schletter, Michael Hietschold, and Manfred Albrecht Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany (Received 12 August 2011; revised manuscript received 23 September 2011; published 28 December 2011) The exchange bias effect in [Pt/Co]8 /CoO/Co3 Pt trilayers was studied. The individual reversal of the ferromagnetic layers was analyzed for two cooling configurations in which the magnetic moments were aligned parallel or antiparallel to each other. The exchange bias fields of the ferromagnetic films can be set independently for each configuration, depending on their respective initial magnetization orientations. Still, magnetic coupling between both the [Pt/Co]8 and the Co3 Pt layers is unambiguously observed below the blocking temperature of the antiferromagnetic CoO. This phenomenon is studied by looking at isolated magnetic reversal processes in minor loops and is explained by temporary modifications of the CoO bulk spin structure. Specifically, we suggest that the frozen part of the antiferromagnetic grains is responsible for the coupling. DOI: 10.1103/PhysRevB.84.214440

PACS number(s): 75.70.−i, 68.65.Ac, 75.50.Ee, 75.60.Ej

I. INTRODUCTION

Magnetism is a collective phenomenon governed by interactions at the atomic scale, resulting in ferromagnetic (F), ferrimagnetic, or antiferromagnetic (AF) arrangement of atomic moments in solids. The most intriguing effects arise when magnetic materials revealing different intrinsic coupling (i.e., F and AF) are brought in contact. One of the prominent examples is the appearance of unidirectional anisotropy as a result of exchange coupling between F and AF layers, first discovered by Meiklejohn and Bean in 1956.1 This unidirectional anisotropy, also known as exchange bias (EB), leads to the shift (biasing) of the hysteresis loop of the F layer,2,3 which is of great application relevance for the fabrication of magnetic sensor devices.4,5 Although the phenomenon of EB has been studied for more than half a century, many aspects have not yet been explored in detail. Thus, even the origin (bulk or interfacial) of the EB effect is not yet clear. It is generally accepted that EB results from the exchange coupling between F and uncompensated AF spins at the F/AF interface.6 The microscopic way in which this coupling translates into EB is more controversial, and many models have been proposed.7–13 Morales et al.14 have recently performed a thorough experimental investigation of the EB effect in an epitaxial trilayer consisting of Ni/FeF2 /permalloy with in-plane easy axis of magnetization in the F layers. It was unambiguously demonstrated—by investigating the EB effect for two cooling configurations, where the F layers are aligned parallel or antiparallel to each other—that the EB effect in this stack has substantial influence on the bulk AF spin configuration. In this paper, we investigated the EB effect in a polycrystalline [Pt/Co]8 /CoO/Co3 Pt trilayer with an out-of-plane easy axis of magnetization. The magnetic properties of the F layers were optimized to assure a substantial difference in coercive field, thus allowing the preparation of different magnetic states at the interface to the AF CoO. We explore how the reversal of the F1/AF interface affects the bulk AF spin configuration, which can be probed via the EB effect at the other F2/AF interface. This study provides an insight into the influence of the bulk AF spin configuration on the EB effect in the trilayer stack employing a rather thin AF CoO layer. Moreover, we 1098-0121/2011/84(21)/214440(6)

focus on the novel coupling effect between the two F layers across the AF layer, which leads to intriguing changes in the magnetization reversal behavior when comparing single F/AF subsystem minor loops and full loops of the complete F/AF/F trilayer.

II. EXPERIMENTAL DETAILS

A 5-nm-thick Co3 Pt alloy with a perpendicular magnetic easy axis and with a coercive field of ∼600 Oe at 300 K was chosen as a magnetically hard layer. The Co3 Pt films were prepared on thermally oxidized Si(100) wafers with a 100-nm-thick SiO2 layer by direct current (DC)–magnetron ˚ cosputtering of Co and Pt with rates of 0.22 and 0.1 A/s, respectively. A composition of Cox Pt100−x with x = 73±1 was determined by Rutherford backscattering spectroscopy. A series of EB Co3 Pt samples was prepared by introducing the samples into the sputter chamber again and depositing an additional 1-nm-thick Co layer, followed by the oxidation of the Co layer at ambient conditions. This procedure also led to an oxidation of the top Co3 Pt surface.15 Superconducting Quantum Interference Device-Vibrating Sample Magnetometer (SQUID-VSM) measurements of the single CoO layer showed no magnetic signal at room temperature, indicating the complete oxidation of the deposited Co layer. As a magnetically softer layer, a [Pt(0.77 nm)/Co(0.28 nm)]8 multilayer film was chosen, revealing a coercivity of 50 Oe at room temperature and full remanence. This film was prepared by alternating DC–magnetron sputtering of Co and Pt species on the CoO/Co3 Pt starting the multilayer stack with a cobalt layer. A 2-nm-thick Pt capping layer was used to protect the samples from oxidation. All metal layers were sputter deposited at room temperature using Ar as a sputter gas at a pressure of 3.5 × 10−3 mbar. In addition to the [Pt/Co]8 /CoO/Co3 Pt trilayer, reference samples consisting of CoO/Co3 Pt and [Pt/Co]8 /CoO bilayers were prepared for comparison. Structural characterization of the samples was performed using transmission electron microscopy (TEM) in both conventional and high-resolution modes. A cross-sectional TEM image is shown in Fig. 1(a), revealing the three layers of

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grains of ∼10 nm for the Co3 Pt alloy film and ∼15 nm for the [Pt/Co]8 multilayer stack. Magnetic characterization was done in in-plane and out-ofplane geometry of the applied magnetic field using a Quantum Design SQUID-VSM with a maximum field of 70 kOe. The measurements were carried out in the temperature range between 10 and 300 K. Bulk cobalt(II) oxide develops an AF order below its Néel temperature TN of ∼290 K, although a blocking temperature TB of ∼100 K was measured for both CoO/Co3 Pt and [Pt/Co]8 /CoO systems. The used measurement routine included a warming process to 320 K followed by setting the field to +70 kOe to saturate both F layers in the same direction. Then, the cooling field Hcool was set. With Hcool applied, the samples were cooled to the desired measurement temperature Tmeas , at which hysteresis loops were acquired. After the cooling procedure, the sample was trained to equilibrium (20 cycles with a maximum field of 20 kOe). Tmeas and Hcool were varied to investigate the dependence of the coercivity HC and the EB field HEB on both parameters.

(a)

Pt

[Pt/Co]8

CoO

Co3Pt 3 nm

SiO2 (b1)

(b2) III. MAGNETIC PROPERTIES OF THE REFERENCE F/AF BILAYERS

[Pt/Co]8 CoO Co3Pt

Moment ( emu)

(c)

40

Hcool = +70 kOe

20 0 Tmeas(K):

-20

10 65

-40 -3

300

-2

-1

0 1 H (kOe)

2

3

FIG. 1. (Color online) (a) TEM cross-sectional image taken on the [Pt/Co]8 /CoO/Co3 Pt (from top to bottom) trilayer grown on thermally oxidized Si(100). (b) Sketch revealing the magnetic configuration in the F layers in the [Pt/Co]/8 CoO/Co3 Pt stack (b1) after positive saturation and (b2) after exposing the initially saturated layer stack to a reverse magnetic field with a strength larger than HC of the [Pt/Co]8 layer at room temperature (−400 Oe). (c) Evolution of the hysteresis loop of the [Pt/Co]8 /CoO/Co3 Pt trilayer after cooling in a field of Hcool = +70 kOe down to the measurement temperature.

the stack. The larger thickness of the CoO layer of ∼3 nm compared to its nominal value is related to the oxidation at the top of the Co3 Pt layer15 and at the first Co layer of [Pt/Co]8 multilayer stack. Analysis of the grain sizes revealed that the CoO layer consists of rather small crystallites with a mean grain size of ∼3 nm. However, larger grains with sizes of more than 5 nm were also observed. At the same time, the F films have a grainy film morphology with substantially larger

A study of the EB effect in a single Co3 Pt layer biased by a thin CoO AF film was recently presented.15 In agreement with an earlier work by Yamada et al.,16 Co3 Pt alloy films grown on planar amorphous SiO2 substrates reveal a preferential out-ofplane easy axis of magnetization. The saturation magnetization of the alloy film was estimated to be about MS,Co3 Pt = (900 ± 140) emu/cm3 , thus resulting in a total moment per unit area of ∼405 μemu/cm2 . Being coupled to the CoO layer, the system reveals a shift of magnetic hysteresis loops and an enhancement of the coercivity of the Co3 Pt layer. An interfacial coupling constant JEB,Co3 Pt of 0.19 ergs/cm215 was estimated following the method by O’Grady et al.13 for grainy AF films. [Pt/Co]8 multilayer films grown on CoO reveal a welldefined, out-of-plane easy axis of magnetization with a saturation magnetization of MS,[Pt/Co] = (520 ± 80) emu/cm3 . In comparison with the Co3 Pt alloy, the [Pt/Co]8 multilayer stack has a saturation magnetization, which is smaller by almost a factor of 2. However, because the thickness of the [Pt/Co]8 multilayers is about twice as large as that of the Co3 Pt film, the moment per sample area of the two F layers is similar (∼416 μemu/cm2 for [Pt/Co]8 ). This is important in the following discussion of the EB effect in the [Pt/Co]8 /CoO/Co3 Pt trilayer stack with opposite orientation of magnetic moments in the F layers. The [Pt/Co]8 /CoO bilayer system exhibits a strong EB effect with an interfacial coupling constant of JEB,Co/Pt = 0.29 ergs/cm2 . The latter is in agreement with the study by Maat et al.,17 where a value of 0.25 ergs/cm2 was estimated for a CoO/[Co/Pt] bilayer. IV. F/AF SUBSYSTEMS IN THE TRILAYER STACK: MINOR LOOP ANALYSIS

Because of the different coercivities of the hard and soft layer, a double-step hysteresis loop is observed when the complete layer stack is measured at room temperature [Fig. 1(c), square symbols]. This enables the possibility of preparing distinct magnetic states with either parallel or antiparallel

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INTERPLAY BETWEEN THE ANTIFERROMAGNETIC SPIN . . .

Norm. Magn. Moment

(a)

Norm. Magn. Moment

(b)

2

trilayer bilayer

Tmeas = 10 K

1 0 Parallel

-1

[Pt/Co]8

-2

CoO Co3Pt Antiparallel

2

[Pt/Co]8

1

CoO Co3Pt

0 -1 trilayer bilayer

-2 -3

-2

-1

0 1 H (kOe)

2

3

FIG. 2. (Color online) Overlay of the hysteresis loops measured at Tmeas = 10 K comparing trilayer minor [Pt/Co]8 loops (closed symbols) and reference [Pt/Co]8 /CoO bilayer full loops (open symbols) after cooling the samples in a field of (a) Hcool = +400 Oe and (b) Hcool = −400 Oe, respectively. The orientations of the magnetic moments in the trilayer stack for the different field cooling processes are also sketched. Minor loops are plotted with respect to the total moment of the fully saturated trilayer stack; therefore, the vertical shifts of the soft layer minor loops are related to the saturated harder Co3 Pt layer.

magnetic orientation of the F layers [Fig. 1(b)] in the samples when cooling below TB in a certain cooling field. The evolution of the hysteresis loops of the [Pt/Co]8 /CoO/Co3 Pt trilayer with Tmeas after cooling the stack in a field of +70 kOe [Fig. 1(c)] was recorded. In this case, both F layers stay aligned parallel to each other as sketched in Fig. 1 (b1). Whereas the hysteresis loop measured at room temperature is symmetric, the decrease of the measurement temperature results in an asymmetric hysteresis loop triggered by the onset of the EB effect, resulting (1) in a loop shift and (2) different magnetization reversal mechanisms for the ascending and descending branches for the individual F layers.18,19 Under these conditions (parallel cooling alignment of the two F layers), the analysis of the coercive and EB fields for different Tmeas and Hcool revealed that the HC and HEB values of the softer F layers in the trilayer stack are quite similar to those values of the reference bilayer sample. In Fig. 2, the full hysteresis loop of the [Pt/Co]8 /CoO reference bilayer system is compared to the [Pt/Co]8 reversal in the trilayer stack. For the latter, only a minor loop of the [Pt/Co]8 reversal was measured. Thus, in this study, the orientation of the magnetic moment of Co3 Pt was fixed and only the magnetization reversal of the softer [Pt/Co]8 layer was followed. This


measurement scheme is mimicking conventional investigation of the EB effect in F/AF bilayers. The matching of trilayer minor hysteresis loops and bilayer hysteresis loops [Fig. 2(a)] confirms that in the parallel configuration, the hard Co3 Pt layer at the opposite interface does not notably influence the EB field and coercivity of the soft [Pt/Co]8 layer. However, as the CoO/Co3 Pt and [Pt/Co]8 /CoO interfaces were in the same magnetic state [Fig. 1 (b1)] after the field cooling procedure, the presented data do not answer the question whether the two interfaces are dependent or independent of each other. Therefore, a different cooling state with antiparallel orientation of the magnetic moments of the two F layers [Fig. 1 (b2)] was realized by cooling the sample in a field of Hcool = −400 Oe after initial saturation of both F layers in the same direction in a field of +70 kOe. The applied reverse magnetic field of −400 Oe does not influence the magnetic state of the Co3 Pt layer.15 Comparing the [Pt/Co]8 minor loops measured after cooling in such an antiparallel configuration [Fig. 2(b), filled circles] to those measured after cooling in a parallel configuration [Fig. 2(a), filled squares] clearly proves that the EB effect of the [Pt/Co]8 /CoO bilayer is independent of the relative arrangement of the two F layers: the minor loops appear unaffected apart from the expected sign change of the loop shift. A similar behavior was observed while measuring at various temperatures below the blocking temperature. Thus, analysis of the minor loops of [Pt/Co]8 suggests that the EB effect is of interfacial origin and that the bulk AF spin configuration plays a negligible role when using a strong antiferromagnet. This finding is different from that in the work of Morales et al.,14 where a weak AF material was used, which might explain the altered bulk AF spin configuration. Furthermore, the identical [Pt/Co]8 minor loops for the two cooling configurations show that a possible magnetic coupling between the two F layers (i.e., orange peel coupling20 and Ruderman-Kittel-Kasuya-Yosida-type coupling21 ), preferring one relative alignment over the other, is of minor importance, because no change in the loop shift was observed. In Fig. 3, a summary of the measured HC and HEB fields of the [Pt/Co]8 layer [Fig. 3(a)] and Co3 Pt layer [Fig. 3(b)] in the trilayer stack is given. Whereas the values for [Pt/Co]8 could be obtained from the minor loop measurements [Fig. 2, closed symbols], we had to evaluate both antiparallel [Fig. 3(c)] and parallel [Fig. 3(d)] cooling configurations to determine the left and right coercive fields of the Co3 Pt layer. The HC and HEB values for the Co3 Pt layer in the stack show good agreement with those of the bilayer reference samples.15 V. F/AF/F TRILAYER STACK: FULL LOOP ANALYSIS

As already pointed out, when looking at the isolated reversal of the [Pt/Co]8 layer (minor loops, black curves in Fig. 4), no dependence on the cooling state is found apart from the expected sign change of the loop shift. However, even though the EB can be set independently for each F/AF interface and commensurately with respect to the bilayer reference systems, the two present EB subsystems are not magnetically decoupled from each other, as becomes evident when analyzing the full hysteresis loops [Fig. 4, red (gray) curves]. When measuring full loops of the trilayer stack, which

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FIG. 3. (Color online) Temperature dependences of the coercive (upward triangles) and EB fields (downward triangles) of each of the F layers in the trilayer stack: (a) [Pt/Co]8 and (b) Co3 Pt. Hysteresis loops measured at various temperatures showing the evaluation method of the (c) left (after antiparallel cooling) and (d) right (after parallel cooling) coercive fields of the Co3 Pt layer. The Co3 Pt coercive fields are the ones at which the hysteresis loop crosses the dashed line, which represents no total Co3 Pt moment at simultaneous [Pt/Co]8 saturation. The presented coercivity is defined as HC = 12 (HC,right − HC,left ).

now includes the reversal of the harder Co3 Pt layer, the reversal of the [Pt/Co]8 layer is substantially altered: (1) there is a clear merging of the hysteresis loop branches of the soft and hard layers, and (2) the descending branch measured after parallel cooling [Fig. 4(a)] and the ascending branch measured after antiparallel cooling [Fig. 4(b)] reveal that the reversal of the softer [Pt/Co]8 happens in a substantially smaller field than in the corresponding minor loops. These drastic effects, which become even more obvious by looking at the first derivative dm/dH of the corresponding loops [Figs. 4(c) and 4(d)], can only be caused by a modification of the bulk CoO spin structure, because this is the connecting element between the two F-AF subsystems. The derivative of the descending branch of the full hysteresis loop measured after cooling in parallel configuration is shown in Fig. 4(c). It supports two intriguing details of the present F-AF-F coupling mechanism. First, the derivative reveals the presence of two peaks, of which the one at the low field region is related to the reversal of the soft [Pt/Co]8 film and a part of the Co3 Pt film. While the nucleation field (i.e., the onset of magnetization reversal) of ∼1.0 kOe remains rather similar for the [Pt/Co]8 film when comparing minor and full loops, the average switching field expressed by the dm/dH peak position has changed from approximately 1.7 kOe (minor loop) to 1.6 kOe (full loop). This change indicates that the reversal of [Pt/Co]8 occurs earlier in the full loop. Second, the derivative of the full loop is lower than that of the minor loop for applied fields between 1.7 and 2.0 kOe. This is suggestive for the mutual nature of the present F-AF-F

coupling mechanism: If, in contrast, only the reversal of the softer [Pt/Co]8 caused a simultaneous switching of parts of the harder Co3 Pt, we would expect a derivative that is always equal to or greater than that of the [Pt/Co]8 minor loop. The mutual stimulation for magnetization reversal between the two F layers is even more pronounced on the ascending branch of the hysteresis loop measured after antiparallel cooling [Figs. 4(b) and 4(d)]. Here, although the nucleation field remains unchanged, the magnetization reversal commences in a much lower field. Similar data are given in Fig. 5 for measurements done at 40 and 65 K. For higher temperatures (Tmeas > TB ), evidence of F-AF-F coupling vanishes, which means that the dm/dH curves of the trilayer full loops track exactly the ones for the corresponding [Pt/Co]8 minor loops (not shown). This behavior can be explained in the following way: The AF layer consists of magnetically exchange-decoupled CoO grains,13,15 the interfacial AF/F coupling energy is JEB , and the anisotropy energy of the AF grains can be expressed by the product KAF ·tAF (tAF : thickness of the AF layer).9,22 CoO is a rather strong AF with a high anisotropy constant KAF of 29 × 107 ergs/cm3 .23 However, the mean size of the CoO grains is ∼3 nm, resulting in a reduced thermal stability. The magnetic spin configuration of such an AF grain can be altered if the torque induced by a strongly exchange-coupled F layer is sufficient (JEB comparable to or greater than KAF ·tAF ), which was proposed by Meiklejohn and Bean.9,22,24 In a realistic sample, the grain size distribution leads to finite widths of the distributions of JEB and KAF ·tAF for a given Tmeas . Therefore,

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FIG. 4. (Color online) Hysteresis loops measured at Tmeas = 10 K of the [Pt/Co]8 /CoO/Co3 Pt trilayer after cooling in (a) parallel (Hcool = +400 Oe) and (b) antiparallel (Hcool = −400 Oe) configurations. Full loops are presented as open symbols, and [Pt/Co]8 minor loops are shown as filled symbols. The [Pt/Co]8 minor loops were measured while going to negative (positive) saturation from the plateau region of the hysteresis loop at +1.0 (−1.0) kOe and back. The first derivatives dm/dH of the outer full and minor loop branches are presented in panels (c) and (d). The inset images show the cooling configuration.

at a certain measurement temperature Tmeas < TB , both cases with JEB < KAF ·tAF (frozen spin configuration) and JEB > KAF ·tAF (rotatable AF net moment) are expected. Those AF

-2 5 4

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FIG. 5. (Color online) Derivatives of merged hysteresis loop branches and respective minor loop branches as shown in Figs. 4(c) and 4(d) but for temperatures of (a) 40 K and (b) 65 K.

grains with a rotatable net moment cannot contribute to the loop shift, which is created by the AF grains with a frozen spin structure.6 To understand the F-AF-F coupling, both shares of AF grains (rotatable net moment and frozen structure) have to be considered individually. First, the grains with rotatable net moments are considered. By changing the magnetic configuration of the trilayer stack at Tmeas , we introduce frustrations in the bulk AF spin configuration, affecting the magnetization reversal behavior of both F layers. However, by looking at the minor loops shown in Figs. 4(a) and 4(b) (black curves), we see that they are identical despite experiencing the Co3 Pt layer in its cooling state [Fig. 4(b)] and antiparallel to its cooling state [Fig. 4(a)]. Therefore, the spin structure in the AF grains with rotatable net moments is only altered in a way that does not significantly affect the opposing F layer—e.g., only in the interfacial regions. This finding is in agreement with the recent work by Xu et al.25 where F/AF subsystems in a trilayer stack with an in-plane easy axis of magnetization are found to be decoupled when the thickness of the FeMn AF layer is above a critical thickness of a few nanometers corresponding to the two interfacial layers influenced by EB. The conclusions regarding AF grains with rotatable net moments make it appear rather unlikely that they can substantially influence the magnetization reversal of individual F layers in the trilayer stack. Thus, we focus now on the AF grains with a frozen spin structure. Those grains have maintained their net moment throughout the training procedure (cycling the field 20 times with a maximum field of 20 kOe). Still, when an adjacent F domain is reversed, the AF spin structure is exposed to the same magnetic torque given by the AF/F exchange coupling, which leads to the flip of the net moment in the AF grains with

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rotatable moments. As, however, the rigid (frozen) AF spin structure cannot absorb this torque in the form of flipped spins, a collective disturbance of the spin structure is expected.26 This disturbance leads to a temporary reduction of the EB effect on both AF/F interfaces. This event allows the reversal of the F layers in a weaker external field compared to the one needed with the AF layer undisturbed. Therefore, the observed, mutually stimulated reversal of the two F layers in trilayer full hysteresis loops originates from the frozen part of the AF spin structure. If there are no AF grains with a frozen spin structure above the blocking temperature, the F-AF-F coupling is expected to vanish as observed experimentally. VI. CONCLUSIONS

We explored the EB effect in a polycrystalline [Pt/Co]8 /CoO/Co3 Pt trilayer stack with [Pt/Co]8 and Co3 Pt layers possessing out-of-plane easy axes of magnetization. The analysis of the magnetization reversal process of the trilayer after cooling in either parallel or antiparallel orientation of the magnetic moments of the two F layers clearly revealed the occurrence of a coupled magnetization reversal of the two F layers, which is mediated by a temporary disturbance of

*

[email protected] Present address: Institute for Integrative Nanosciences, IFW Dresden, D-01069 Dresden, Germany. 1 W. H. Meiklejohn and C. P. Bean, Phys. Rev. 102, 1413 (1956). 2 A. E. Berkowitz and K. Takano, J. Magn. Magn. Mater. 200, 552 (1999). 3 J. Nogués and I. K. Schuller, J. Magn. Magn. Mater. 192, 203 (1999). 4 B. Dieny, P. Humbert, V. S. Speriosu, S. Metin, B. A. Gurney, P. Baumgart, and H. Lefakis, Phys. Rev. B 45, 806 (1992). 5 J. S. Moodera, L. R. Kinder, T. M. Wong, and R. Meservey, Phys. Rev. Lett. 74, 3273 (1995). 6 F. Radu and H. Zabel, Springer Tracts Mod. Phys. 227, 97 (2007). 7 D. Mauri, H. C. Siegmann, P. S. Bagus, and E. Kay, J. Appl. Phys. 62, 3047 (1987). 8 A. P. Malozemoff, Phys. Rev. B 35, 3679 (1987). 9 M. D. Stiles and R. D. McMichael, Phys. Rev. B 60, 12950 (1999). 10 U. Nowak, K. D. Usadel, J. Keller, P. Miltényi, B. Beschoten, and G. Güntherodt, Phys. Rev. B 66, 014430 (2002). 11 D. Suess, M. Kirschner, T. Schrefl, J. Fidler, R. L. Stamps, and J.-V. Kim, Phys. Rev. B 67, 054419 (2003). 12 J. Nogués, J. Sort, V. Langlais, V. Skumryev, S. Suriñach, J. S. Muñoz, and M. D. Baró, Phys. Rep. 422, 65 (2005). 13 K. O’Grady, L. E. Fernandez-Outon, and G. Vallejo-Fernandez, J. Magn. Magn. Mater. 322, 883 (2010). 14 R. Morales, Z.-P. Li, J. Olamit, K. Liu, J. M. Alameda, and I. K. Schuller, Phys. Rev. Lett. 102, 097201 (2009). †

the spin configuration in the frozen AF grains below. The performed study suggests that the bulk part of the AF grains in EB systems is influenced by the magnetization reversal of the F layer. This effect cannot be observed in classic F/AF bilayers. In contrast, when a F/AF/F trilayer stack is investigated, the second ferromagnet at the opposite interface of the thin AF layer acts as a sensor that allows one to observe the modification of the AF volume spin arrangement induced by the reversal event of a F layer. The magnetic F-AF-F coupling discussed here leads to cross talk between F layers through the frozen grains of the AF material via a propagating magnetic excitation. This propagation experiences rather low damping as no absorption of the magnetic torque takes place.26 At the same time, the charge current resistance of the insulating CoO is rather high. Hence, such F-AF-F systems are potentially interesting for the generation of pure spin currents.27,28 ACKNOWLEDGMENTS

The authors thank C. Schubert and C. Brombacher for fruitful discussions, M. Daniel and G. Beddies for RBS data analysis and B. Mainz for TEM sample preparation.

15

T. Kosub, C. Schubert, H. Schletter, M. Daniel, M. Hietschold, V. Neu, M. Maret, D. Makarov, and M. Albrecht, J. Phys. D Appl. Phys. 44, 015002 (2011). 16 Y. Yamada, W. P. Van Drent, E. N. Abarra, and T. Suzuki, J. Appl. Phys. 83, 6527 (1998). 17 S. Maat, K. Takano, S. S. P. Parkin, and E. E. Fullerton, Phys. Rev. Lett. 87, 087202 (2001). 18 M. R. Fitzsimmons, P. Yashar, C. Leighton, I. K. Schuller, J. Nogués, C. F. Majkrzak, and J. A. Dura, Phys. Rev. Lett. 84, 3986 (2000). 19 J. Camarero, J. Sort, A. Hoffmann, J. M. Garc´ıa-Mart´ın, B. Dieny, R. Miranda, and J. Nogués, Phys. Rev. Lett. 95, 057204 (2005). 20 J. Moritz, F. Garcia, J. C. Toussaint, B. Dieny, and J. P. Nozières, Europhys. Lett. 65, 123 (2004). 21 S. S. P. Parkin, N. More, and K. P. Roche, Phys. Rev. Lett. 64, 2304 (1990). 22 M. G. Blamire, M. Ali, C.-W. Leung, C. H. Marrows, and B. J. Hickey, Phys. Rev. Lett. 98, 217202 (2007). 23 J. Kanamori, Prog. Theor. Phys. 17, 177 (1957); 17, 197 (1957). 24 W. H. Meiklejohn and C. P. Bean, Phys. Rev. 105, 904 (1957). 25 Y. Xu, Q. Ma, J. W. Cai, and L. Sun, Phys. Rev. B 84, 054453 (2011). 26 K. H. Michel and F. Schwabl, Z. Physik 238, 264 (1970). 27 S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnár, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001). 28 A. Hoffmann, Phys. Stat. Sol. 4, 4236 (2007).

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APPLIED PHYSICS LETTERS 98, 192504 共2011兲

Recording study of percolated perpendicular media Michael Grobis,1,a兲 Carsten Schulze,2 Marco Faustini,3 David Grosso,3 Olav Hellwig,1 Denys Makarov,2,b兲 and Manfred Albrecht2 1

San Jose Research Center, Hitachi Global Storage Technologies, 3403 Yerba Buena Rd., San Jose, California 95135, USA 2 Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany 3 Laboratoire de Chimie de la Matière Condensée de Paris, CNRS, Université Pierre et Marie Curie-Paris 6, 75252 Paris Cedex 05, France

共Received 31 March 2011; accepted 11 April 2011; published online 11 May 2011兲 We examine the magnetic recording properties of percolated perpendicular media 共PPM兲 fabricated by depositing a Co/Pt multilayer film on top of nanoperforated templates created by self-assembly. We characterize the recording performance by examining the magnetic transition jitter in patterns written to the media using a hard disk drive write head. The transition jitter is lowest in the media created using the template with the highest perforation density, which demonstrates a route for further improving PPM-based recording media. © 2011 American Institute of Physics. 关doi:10.1063/1.3587635兴 The demand for higher storage capacities is one of the driving forces in the development of innovative magnetic materials. Magnetic recording based on granular CoCrPt– SiO2 alloy perpendicular media is expected to face fundamental limitations at areal storage densities above 1 Tbit/ in.2 共Ref. 1兲 and several novel concepts for magnetic recording are being explored to achieve higher areal densities. One of the proposed approaches is bit patterned media2 in which each bit is defined by single-domain magnetic island. Various manufacturing methods are under development to produce high quality arrays of magnetic islands for magnetic recording.3–5 An alternative recording scheme based on percolated perpendicular media 共PPM兲 has been introduced recently.6,7 PPM consists of an exchange coupled magnetic film with a dense distribution of defects which serve as pinning sites for magnetic domain walls. Hence, the pinning sites define bit boundaries in the PPM recording concept.8,9 Several experimental realizations of PPM are already known codeposition of magnetic material and nonmagnetic oxides,10,11 magnetic films on anodized alumina templates,12,13 and the deposition of hard magnetic materials on arrays of nonmagnetic nanoparticles,14,15 to name a few. Recently, an alternative route toward the fabrication of PPM based on the deposition of hard magnetic films on nanoperforated membranes fabricated by an organic/ inorganic self-assembly process16 was suggested. The nanoperforations act as pinning sites for the magnetic domain walls. Furthermore, the exchange coupling between the magnetic material inside the nanoperforation and the continuous film outside can be used for tuning the pinning strength. The fundamental aspects of the interplay between magnetostatic and exchange coupling as well as further details on the template formation and their structural characterization have been presented elsewhere.17,18 Here, we concentrate on the recording performance of this type of PPM. By means of static read/write tests we examine the influence of both perforation size and period on the recording performance.19 a兲

Electronic mail: [email protected]. b兲 Present address: Institute for Integrative Nanosciences, IFW Dresden, Helmholtzstraße 20, 01069 Dresden, Germany. 0003-6951/2011/98共19兲/192504/3/$30.00

The formation of the nanoperforated template is based on chemical deposition, invoking the self-assembly of blockcopolymer micelles together with inorganic precursors, resulting in the formation of inorganic ZrO2 membranes with nanoperforations.16,20,21 Two types of templates were employed as follows: a nanoperforated template with an average perforation diameter of 67 nm and a period of about 110 nm, and a nanoperforated template with an average perforation diameter of 17 nm and an average period of 34 nm. Size and period of the perforations were verified using scanning electron microscopy 关SEM, Figs. 1共a兲 and 1共b兲兴. The as-prepared nanoperforated ZrO2 membranes were used as templates for the deposition of Co/Pt multilayer films as described in detail in Refs. 17 and 18. Using dc-

FIG. 1. SEM micrographs of nanoperforated ZrO2 membranes with 共a兲 110 nm period and 67 nm diameter and 共b兲 34 nm period and 17 nm diameter. 共c兲 MOKE hysteresis loops taken on the sample with 110 nm period 共solid line兲 and 34 nm period 共dotted line兲.

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© 2011 American Institute of Physics

Author complimentary copy. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

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magnetron sputter deposition 共Ar pressure: 8.3⫻ 10−3 mbar兲 at room temperature, a 4.8-nm-thick Pt seed layer was deposited onto the substrates followed by 8 repetitions of a Co 共0.28 nm兲/Pt 共0.76 nm兲 bilayer and a Pt cover layer of 1.91 nm nominal thickness to prevent the stack from oxidation. In addition, a reference sample grown on a planar SiO2共100 nm兲 / Si共100兲 substrate was prepared. The hysteresis loops acquired using magneto-optical Kerr effect 共MOKE兲 magnetometry in polar detection geometry are shown in Fig. 1共c兲. On the sample with the larger nanoperforations, a two-step hysteresis loop is observed as follows: the first transition at about 1.5 kOe corresponds to the nucleation of reversed magnetic domains followed by the propagation of their domain walls through the planar part of the sample. The deposition of magnetic material inside the large perforations leads to the formation of exchange decoupled magnetic nanodots whose magnetization is reversed at higher fields, about 3.8 kOe, with a broad switching field distribution resulting from the size distribution of the individual nanodots.17 In this work, only the first transition is of interest. The hysteresis loop taken on the sample grown on small perforations shows only a single, sharp switching event at about 2 kOe that is attributed to partial exchange coupling between the continuous film and the nanodots.18 Characterization using a superconducting quantum interference device magnetometer allowed for estimation of the uniaxial anisotropy constant, which was found to be Ku = 2 ⫻ 106 ergs/ cm3. Assuming an exchange constant of A = 10−6 ergs/ cm, this results in a magnetic domain wall width of about ␦B = 23 nm. The recording performance of these two samples was investigated by scanning magnetoresistive microscopy using conventional hard disk read/write heads.19 The magnetic write width and magnetic read width of these heads is about 110 nm and about 70 nm, respectively. The read/write tests were carried out at a head speed of 50 ␮m / s. Alternating bit patterns of different periodicity were written to the initially saturated sample in pulsed mode with a duty cycle of 0.1%. Please note that the domains written on the planar reference sample spread over several microns and can be easily moved by residual fields in the write and read elements in the head. Figure 2 shows the read back image for various bit patterns written on the two samples under study. The size of the magnetic domains that can be written by a recording head is limited by the spacing between pinning sites induced by the nanoperforated template. Due to the template period of 110 nm on the sample with the larger perforations, the minimum bit pitch is expected to be on the order of 200 nm. In this case, domains written with smaller bit pitch merge together as observed experimentally 关Fig. 2共a兲兴. In contrast, on the sample with a period of 34 nm, the individual domains can be clearly separated even at a bit pitch as low as 100 nm 关Fig. 2共b兲兴. Analysis of the recording performance of the PPM was carried out by investigating the bit transition jitter, which reflects the minimum bit pitch that can be used in a recording application.22–24 The exact relationship between bit pitch and transition jitter depends on other factors in the recording system, such as the allowed error rate, but roughly the minimum useable bit pitch is five to ten times larger than the transition jitter.25 The bit transition jitter was measured by analyzing the read back waveform for the bit pattern with 500 nm bit

Appl. Phys. Lett. 98, 192504 共2011兲

FIG. 2. Read back image for various written bit pitches on PPM grown on a nanoperforated ZrO2 membrane with an average perforation diameter and period of 共a兲 67 nm and 110 nm and 共b兲 17 nm and 34 nm, respectively.

pitch. The signal was split into 1-␮m-long segments 关Figs. 3共a兲 and 3共b兲兴 and the position of the zero-crossings of the signal within each section were extracted. The standard deviation of the transition positions gives the transition jitter 关Figs. 3共c兲 and 3共d兲兴. As the down-track extent of the write head is smaller than 500 nm and the head field is pulsed once per bit, the transition jitter for the leading edge of the head is larger than for the trailing edge due to the asymmetric geometry of the write head. For nanoperforations with a diameter of 67 nm and a period of 110 nm, the leading edge jitter is 85 nm and the trailing edge jitter is 55 nm. These numbers are highly improved by writing on perforations with 17 nm diameter and 34 nm period, where the leading edge jitter is 27 nm and the trailing edge jitter is 12 nm. The difference between the jitter values for the leading and trailing edge is due

FIG. 3. Evaluation of transition jitter of the data bit written with 500 nm bit pitch. Read back signal vs down track position on perforations with a period of 共a兲 110 nm and 共b兲 34 nm showing various bit transitions. The images are a repartitioning of a single trace acquired on the center of a track into a stack consisting of segments of 1 ␮m in length, i.e., twice the written bit pitch. Histogram of the transition positions within each 1 ␮m interval measured on the sample with 共c兲 110 nm perforation period and 共d兲 34 nm perforation period.


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to the larger magnetic field gradient on the trailing edge of the write head. If single uncorrelated pinning sites determine the read back transition locations, the jitter would be equal to half of the perforation period. The 110 nm perforation period sample follows this rule while jitter in the 34 nm perforation sample is a third of the period. The smaller jitter most likely stems from cross-track averaging by the reader, whose crosstrack response has a ⬃70 nm full-width at half-maximum. The transition jitter is expected to be further reduced by increasing the perforation density, increasing of the homogeneity of the template, and improving the structural and magnetic properties of the recording layer. In conclusion, the recording performance of PPM based on magnetic films grown on nanoperforated membranes was investigated. On templates with 67-nm-large perforations with a period of 110 nm, it was possible to stabilize single bits at a bit pitch of about 200 nm. The feasibility of achieving a bit pitch of less than 100 nm was demonstrated on a template with a perforation period of 34 nm. Further optimization of the magnetic layer stack, including the use of a soft magnetic underlayer, hard 共scratch resistant兲 overcoat and lubricant, might still increase the recording performance of this type of PPM. Financial support by the European Commission via the FP7 project TERAMAGSTOR 共Grant No. 224001兲 and by the German Science Foundation 共Grant No. DFG AL 618/10兲 is kindly acknowledged. D. Weller and A. Moser, IEEE Trans. Magn. 35, 4423 共1999兲. R. M. H. New, R. F. W. Pease, and R. L. White, J. Vac. Sci. Technol. B 12, 3196 共1994兲. 3 B. C. Stipe, T. C. Strand, C. C. Poon, H. Balamane, T. D. Boone, J. A. Katine, J.-L. Li, V. Rawat, H. Nemoto, A. Hrotsune, O. Hellwig, R. Ruiz, E. Dobisz, D. S. Kercher, N. Robertson, T. R. Albrecht, and B. D. Terris, Nat. Photonics 4, 484 共2010兲. 4 S. Sun, C. B. Murray, D. Weller, L. Folks, and A. Moser, Science 287, 1989 共2000兲. 5 O. Hellwig, J. K. Bosworth, E. Dobisz, D. Kercher, T. Hauet, G. Zeltzer, 1 2

Appl. Phys. Lett. 98, 192504 共2011兲

Grobis et al.

J. D. Risner-Jamtgaard, D. Yaney, and R. Ruiz, Appl. Phys. Lett. 96, 052511 共2010兲. J.-G. Zhu and Y. Tang, J. Appl. Phys. 99, 08Q903 共2006兲. 7 D. Suess, J. Fidler, K. Porath, T. Schrefi, and D. Weller, J. Appl. Phys. 99, 08G905 共2006兲. 8 W. R. Eppler, B. K. Cheong, D. E. Laughlin, and M. H. Kryder, J. Appl. Phys. 75, 7093 共1994兲. 9 P. F. Carcia, D. Coulman, R. S. McLean, and M. Reilly, J. Magn. Magn. Mater. 164, 411 共1996兲. 10 D. E. Laughlin, Y. Peng, Y.-L. Qin, M. Lin, and J.-G. Zhu, IEEE Trans. Magn. 43, 693 共2007兲. 11 A.-C. Sun, J.-H. Hsu, P. Kuo, and H. Huang, IEEE Trans. Magn. 43, 2130 共2007兲. 12 M. T. Rahman, N. N. Shams, Y.-C. Wu, C.-H. Lai, and D. Suess, Appl. Phys. Lett. 91, 132505 共2007兲. 13 M. T. Rahman, N. N. Shams, C. H. Lai, J. Fidler, and D. Suess, Phys. Rev. B 81, 014418 共2010兲. 14 D. Makarov, E. Bermúdez-Ureña, O. G. Schmidt, F. Liscio, M. Maret, C. Brombacher, S. Schulze, M. Hietschold, and M. Albrecht, Appl. Phys. Lett. 93, 153112 共2008兲. 15 C. Brombacher, M. Saitner, C. Pfahler, A. Plettl, P. Ziemann, D. Makarov, D. Assmann, M. H. Siekman, L. Abelmann, and M. Albrecht, Nanotechnology 20, 105304 共2009兲. 16 A. Fisher, M. Kuemmel, M. Järn, M. Linden, C. Boissière, L. Nicole, C. Sanchez, and D. Grosso, Small 2, 569 共2006兲. 17 D. Makarov, P. Krone, D. Lantiat, C. Schulze, A. Liebig, C. Brombacher, M. Hietschold, S. Hermann, C. Laberty, D. Grosso, and M. Albrecht, IEEE Trans. Magn. 45, 3515 共2009兲. 18 C. Schulze, M. Faustini, J. Lee, H. Schletter, M. U. Lutz, P. Krone, M. Gass, K. Sader, A. L. Bleloch, M. Hietschold, M. Fuger, D. Suess, J. Fidler, U. Wolf, V. Neu, D. Grosso, D. Makarov, and M. Albrecht, Nanotechnology 21, 495701 共2010兲. 19 A. Moser, D. Weller, M. E. Best, and M. F. Doerner, J. Appl. Phys. 85, 5018 共1999兲. 20 M. Kuemmel, J. Allouche, L. Nicole, C. Boissière, C. Laberty, H. Amenitsch, C. Sanchez, and D. Grosso, Chem. Mater. 19, 3717 共2007兲. 21 C. Sanchez, C. Boissière, D. Grosso, C. Laberty, and L. Nicole, Chem. Mater. 20, 682 共2008兲. 22 A. Moser, K. Rubin, and M. E. Best, IEEE Trans. Magn. 37, 1872 共2001兲. 23 J.-G. Zhu, X. Lin, and W. Messner, IEEE Trans. Magn. 36, 23 共2000兲. 24 G. J. Tarnopolsky and P. R. Pitts, J. Appl. Phys. 81, 4837 共1997兲. 25 J. T. Olson, J. Park, and R. Wood, private communication 共March 29, 2011兲. 6


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C

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99.9%), Merck) and then spin-coated at a rotational speed of about 100 Hz. Using a liquid crystal concentration of about 100 mg ml1 is a reliable method to prepare homogeneous films with a thickness between 200 and 250 nm. We used silicon wafers as substrates with either native silicon oxide or 100 nm of thermally grown silicon oxide (Center for Microtechnologies, Chemnitz). Substrates were cleaned by piranha solution (60% sulfuric acid, 40% hydrogen peroxide) in an ultrasonic bath at 70 C. Before the dilution of the liquid crystal, dye molecules were dissolved in toluene at very dilute concentrations (around 1010 mol l1 and close to 109 mol l1 in LC). Single tracer molecules are identified by the typical blinking (fluorescence intermittency).13,15 We obtained LC films with homogeneous and flat LC–air interfaces as identified by AFM experiments. Samples were heated (annealed) up to 35 C (above the (bulk) smectic–nematic phase transition at 33.5 C) for half an hour. At this temperature the LC films remain in the nematic phase. Further heating into the isotropic phase results in dewetting of the film with formation of droplets. For this reason we restricted ourselves to temperature cycling into the nematic phase. As (single) tracer molecules we used two different perylene diimides (PDIs) shown in Scheme 1. One of them (o-PDI: N,N0 di-hexadecyl-perylene-3,4,9,10-tetracarboxdiimide) orients with its long molecular axis parallel to the LC director13 while the other one (no-PDI: N,N0 -di-propyl-1,6,7,12-tetra-(4-heptyl-phenoxy)-perylene-3,4,9,10-tetra-carboxdiimide) has no preferred orientation in a LC film. The orientational behavior of PDI dye

molecules has been discussed recently in more detail.13 The optical transition dipole moment of PDI is parallel to the long axis of the chromophoric backbone. Therefore in the case of o-PDI the dipole moment is oriented parallel to the LC director. When the dipole moment is perfectly perpendicular to the substrate, no fluorescence emission will be detected. However, the orientation will not be perfectly parallel to the director and the order parameter of the LC will be always less than 1. This implies that considerably reduced fluorescence intensity can be observed. In fact, experimentally we always observe significantly less o-PDI molecules than no-PDI though the absolute concentration is approximately the same. To monitor diffusion of PDI dye molecules we used a homebuilt widefield microscope.13 PDI molecules were excited at 514 nm (argon ion laser Innova 70C, Coherent). Separating the reflected and the fluorescent light we got a fluorescence image of the sample using an electron multiplying CCD-camera (Andor iXon 885) operating at a frame rate of 50 fps. The analysis of the observed diffusion time traces was performed by single molecule tracking either via reconstruction of the diffusion trajectories and calculation of mean square displacements from which the diffusion coefficient for each tracked molecule (time scale >1 s) is determined, or via calculating diffusivities following the procedure described recently.16 The latter approach provides information on shorter time scales than msd analysis as this method does not average over a total trajectory but identifies the translational steps between two subsequent CCD frames. This implies a temporal resolution of 20 ms and a time scale between 1 s and 20 ms. A much faster time resolution is obtained via fluorescence correlation spectroscopy (FCS) in a confocal setup13 resulting in a time range of 1–106 s. For FCS measurements the dye concentration was about 108 mol l1 in toluene. AFM images have been obtained by a Nanowizard (JPK Instruments). Reflection and fluorescence images have been obtained on typical length scales of 10 10 mm by a laser scanning microscope (Zeiss LSM 510). Further experimental details about the setups and experimental procedures are given elsewhere.13

Results Formation of mesoscopic structures

Scheme 1 Structure of tracer dye molecules (o-PDI and no-PDI) and 8CB.

7432 | Soft Matter, 2011, 7, 7431–7440

Directly after sample preparation we did not find any differences in structure between films prepared on silicon wafers with native oxide or those with an oxide layer of 100 nm thickness. However, after annealing the films into the nematic phase and slowly cooling down to the smectic phase at room temperature, two different types of mesoscopic structures emerged, depending on which kind of substrate was used. For samples on thermally grown oxide we observe focal conic domains (LC-FCDs) that are known to form on silicon substrates17 due to the random planar anchoring condition for 8CB molecules. Scheme 2 shows schematically the structure of one FCD. The optical identification of a FCD was achieved by taking fluorescence images of a sample with a high concentration of o-PDI. These molecules align with their transition dipole parallel to the director of 8CB.13 Accordingly, the probability of optical excitation as well as the probability of emission into the This journal is ª The Royal Society of Chemistry 2011

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Scheme 2 Schematic presentation of a FCD with incorporated o-PDI. Preferred directions of emission of o-PDI molecules in different areas of a focal conic domain are indicated by arrows.

direction of observation is increased if the molecules are—in the center of a FCD—oriented with their long axis parallel to the substrate. Since the excitation was performed with linearly polarized laser light, both emission and reflection depend on the angle between molecular orientation and polarization of the laser. So finally for a circular FCD one obtains textures that look like two circles connected in the center of the domain.18 Exactly this kind of texture is found in our samples as shown in Fig. 1 both in reflection and fluorescence. The fluorescence image reveals the orientation of the dipole moment of the dye molecules, i.e. the brighter areas correspond to the areas where the molecules are mainly aligned along the direction of polarization of the light. On the other hand the reflection image shows the reflectivity of the surface according to the Fresnel equations, therefore providing information about the surface of the film. Thus the fluorescence image is a lot easier to interpret regarding the director orientation inside the liquid crystal. However the reflection image was also necessary as it was used to identify the structure of the samples containing dye molecule with single molecule concentration. We obtained a size distribution of the FCD between 0.5 and 1.5 mm diameter, which is slightly narrower than the one observed for thicker films.19 We did not find any regular arrangement of the domain centers. However, for the annealed samples on native oxide we found a completely different structure (LC-TF) which is characterized

Fig. 1 Reflection (left) and PDI fluorescence (right) image of PDI doped 8CB on silicon with 100 nm oxide. Characteristic textures (see text) demonstrate the presence of focal conic domains (LC-FCDs). Open circles indicate the typical diameter of a single domain. Images were obtained from the same area of the film. The arrow marks the direction of linear polarization of incident light.

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Fig. 2 Left: AFM-image of an annealed film on native oxide which shows terrace-like structures (TF). Right: cross-section along the white line of the left image which shows step sizes of multiples of about 3 nm which corresponds to the 3.2 nm height of one smectic double layer of 8CB.

by AFM as a terraced surface surrounding deep holes. This structure remains stable for days. A typical AFM-image is shown in Fig. 2 together with a cross-section through one of the holes. While AFM only reflects height profiles the microscopic structure of the terraced holes remains open and would need detailed optical experiments similar to those reported by van Effenterre et al.20 Presently such experiments are out of scope, since we are not yet able to correlate the statistical appearance of AFM detected TF (revealing varying shape, depth and distribution) with precise optical data, which would be necessary to describe a possibly TF related birefringence. An overall measurement of birefringence is not decisive with respect to TF which reflects only a minor part of the total film volume. To the best of our knowledge, such a structure has not been reported yet. The overall structure reminds us of the coexistence of two LC phases as described by Garcia et al.4 However, in the corresponding experiment only two defined film thicknesses were found, and the structures appeared as a new phase at the smectic–nematic transition. In contrast, we clearly see several steps. In the cross-section through one of the holes (Fig. 2, right) one can identify characteristic step heights related to the change of the film thickness. The respective height is always found to be about 3 nm or a multiple of it. As this corresponds to the typical thickness of smectic bilayers of 8CB,21 we conclude that the structure near the air–LC interface consists of parallel smectic layers without any bending of the layers as would be characteristic for a FCD. As the depth of the holes was found to be not deeper than 85 nm, the holes are not an indication for dewetting, given the fact that we have an overall total film thickness close to 225 nm. A similar structure has been described by Overney et al.22 But in that case the structure was formed in the solid phase of the LC due to internal strain caused by different thermal expansion coefficients of the substrate and the (solid) LC. In our case the mobility of the molecules in the smectic phase should inhibit any strain caused by expansion. Terraced steps have also been observed in the case of wetting 8CB droplets on silicon wafers with native oxide using scanning polarization force microscopy.23 Therefore the strong interaction with the silicon substrate certainly plays a role. Diffusion trajectories To obtain information about the influence of the observed mesoscopic structures on diffusion we used single PDI molecules Soft Matter, 2011, 7, 7431–7440 | 7433

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as tracer molecules for dynamic processes in LC-FCD or LC-TF. We identify trajectories related to the projection of the lateral diffusion of single molecules over at least 50 frames separated by Dt. Along those trajectories we calculate mean square displacements and make use of the two-dimensional Einstein–Smoluchowski equation


Dmsd ¼ limDt/N msd(Dt)/(4Dt),

probability distributions p(ddiff, Dt) of scaled squared displacements ddiff ¼ r2/(4Dt) are analyzed,16 where Dt is the time lag between succeeding frames. Since our data are related to a projection of the three dimensional diffusion into the plane parallel to the substrate, we have to consider two-dimensional diffusion. The probability density for diffusivities can now be written as

(1)

to calculate diffusion coefficients Dmsd. By this a diffusion coefficient is ascribed to each trajectory. In Fig. 3 the obtained diffusion coefficients are shown for both types of PDI in the case of LC-FCD and LC-TF in comparison to the respective (LC) films before annealing. The Dmsd distributions are fitted with the assumption of only one Gaussian, which is certainly only a rough approximation. The absolute range of Dmsd is in qualitative agreement with Dk and Dt for self-diffusion of 8CB in the smectic phase.24 For this comparison the difference in dye diameter has been taken into account.13 Only for no-PDI we observe for both substrates a slight increase of the peak value of the distribution of the diffusion coefficient Dmsd. The increase is more significant for LC-TF, where the average diffusion coefficient is increased by about 30% together with a strong broadening of the distribution (FWHM) of the coefficients. All data for Dmsd are collected in Table 1.

Probability distributions of diffusivities Since the trajectory analysis considers only traces of more than 50 sequential frames, relatively fast diffusion processes are underestimated. Such processes might show up, however, when analyzing probability distributions of single diffusivities.13 In this approach all squared displacements r2 between all traced molecules in succeeding frames are calculated. With these data

p(ddiff, Dt) ¼ Ddiff1 exp(ddiff/Ddiff)

(2)

An elegant way to analyze experimental data is to use an integrated form of p(ddiff, Dt), i.e. the complementary cumulative probability distribution C(ddiff, Dt).25 The solutions for the twodimensional case are given by the exponential function C(ddiff, Dt) ¼ 1 P(ddiff, Dt) ¼ exp(ddiff/Ddiff),

(3)

which yields a straight line in a semilog-plot. In the case of heterogeneous or anomalous diffusion, experimental data will deviate from this straight line. Then instead of eqn (3) a multiexponential fit to the cumulative probability distributions C(ddiff, Dt) ¼

P

iAi

exp(ddiff/Ddiff,i).

(4)

can be used to obtain diffusion coefficients Ddiff,i.13,16 Since only no-PDI shows a noticeable dependence on structure formation, we applied the analysis only to this tracer molecule. The plots in Fig. 4 clearly show a multi-exponential behavior which is an indication for the presence of more than one diffusion process, as was already evident in Fig. 3 and Table 1 from the analysis of Dmsd. The diffusion dynamics of no-PDI in 8CB films on 100 nm SiOx can be divided into three basically different time regimes: a slow one, which represents (partially) immobile molecules (sticking on the substrate surface13), a medium one (A1, A2),

Fig. 3 Diffusion coefficients Dmsd for o-PDI (left) and no-PDI (right) in LC, LC-FCD and LC-TF films on 100 nm SiOx (bottom) and native SiOx (top). The fitted data are collected in Table 1.

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View Online Table 1 Diffusion data from trajectory (Dmsd) and diffusivity analysis (Ddiff)a Dye

Si/SiOx

8CB

Dmsd/mm2 s1

FWHM/mm2 s1

o-PDI

Native

LC LC-TF LC LC-FCD LC LC-TF LC LC-FCD

2.6 0.3 2.4 0.3 2.6 0.3 2.4 0.3 2.9 0.3 3.8 0.5 2.6 0.3 3.0 0.3

1.8 0.2 1.5 0.2 2.1 0.2 2.4 0.2 1.5 0.2 3.0 0.3 2.0 0.2 2.7 0.2

100 nm no-PDI

Native 100 nm

Ddiff,1/mm2 s1

2.9 0.2 2.4 0.3 2.4 0.3

Ddiff,2/mm2 s1

3.4 0.2 3.8 0.6 3.8 0.6


a The real diffusion coefficient in single molecule tracking experiments is about 50% higher than the apparent diffusion coefficient.35 The values in the table are therefore scaled by a factor of 1.5 compared to those depicted in Fig. 3 and 4.

For 8CB films on 100 nm oxide we clearly observe two components Ddiff,1 ¼ 2.4 mm2 s1 and Ddiff,2 ¼ 3.8 mm2 s1, which nearly do not change in magnitude upon formation of FCD. According to diffusivity analysis Ddiff,2 is a relatively strong component, which shows up only weakly in msd analysis, probably because this type of analysis is less sensitive to relatively fast components. In that respect analysis of diffusivities is superior to msd analysis. The situation for native oxide is distinct from the one of 100 nm oxide. For both cases temperature cycling leads to faster diffusion. In the case of LC-TF only one medium component Ddiff,2 can be detected, which increases from 2.9 to 3.4 mm2 s1 after annealing. Also for LC-FCD an enhancement of diffusion can be observed. Here the amplitude A2 for Ddiff,2 increases from 0.29 to 0.37. Fig. 4 Probability distributions of ddiff (data points) on two different oxides for no-PDI, together with (broken lines) multi-exponential fits (representing diffusion on slow, medium and fast time scales) of LC (top), LC-TF (bottom left) and LC-FCD (bottom right). The fitted data are collected in Table 2.

which is in the range of the trajectory analysis, and a much faster one (A3) with a very small relative amplitude. Data were fitted with up to 3 diffusion coefficients. All related data are collected in Table 2. Since fluorescence is quenched close to the substrate,26 no immobile PDI is observed in the case of native oxide. In the medium time regime all Dmsd and Ddiff are in rough qualitative agreement with each other. The fastest regime (Ddiff,3 > 30 Ddiff,2) cannot be detected in the trajectory analysis but shows up as a very small contribution for all configurations (a similar fast component will show up more clearly in the fluorescence correlation spectroscopy as will be described later on). In the following we will concentrate on details in the medium time regime.

Fluorescence correlation spectroscopy The time resolution of the widefield based methods (trajectory and single step analysis) is restricted by the exposure time of the CCD camera of 20 ms. Nevertheless, diffusivity analysis shows a small but very fast contribution, which cannot be related to the intrinsic translational (self-)diffusion typical for 8CB, but to an additional inherent heterogeneous structure.13 In order to get a better time resolution we applied fluorescence correlation spectroscopy (FCS), which can be used to measure the dynamic behavior related to an area not larger than the size of the illuminating laser focus. Scanning the laser focus over the sample provides local information on dynamic processes below milliseconds with a lateral precision of about 20 nm. In a previous paper13 we have argued that the relevant time scale experimentally observed by FCS is slower than predicted for molecular rotational motion. Also in the present experiments we neglect the

Table 2 Analysis of diffusivities (Ddiff,i in mm2 s1) for no-PDIa 8CB

Si/SiOx

A0

A1

Ddiff,1

A2

Ddiff,2

A3

Ddiff,3

LC LC-TF LC LC-FCD

Native

— — 0.17 0.01 0.12 0.01

— — 0.54 0.02 0.51 0.02

— 2.4 0.3 2.4 0.3

0.9999 0.00005 0.999 0.0005 0.29 0.02 0.37 0.02

2.9 0.2 3.4 0.2 3.8 0.6 3.8 0.6

0.0001 0.00005 0.001 0.0005 0.0004 0.00005 0.0008 0.00005

105 30 105 30 105 30 105 30

100 nm

a

Ai corresponds to the relative contribution of a multiexponential fit according to eqn (4). The real diffusion coefficient in single molecule tracking experiments is about 50% higher than the apparent diffusion coefficient.35 The values in the table are therefore scaled by a factor of 1.5 compared to those depicted in Fig. 4.


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(too fast) intrinsic molecular rotation. The FCS method makes use of the fluorescence intensity autocorrelation function


G2(s) ¼ hI(t)I(t + s)i/hI(t)i2

(5)

In the case of structure formation such as LC-FCD or LC-TF one might expect a spatial dependence of the dynamics when analyzing areas with about 500 nm resolution (the lateral focal diameter of the exciting laser). Diffusion in the z-direction would not influence the correlation function as our film thickness is considerably smaller than the focal depth of the laser, which is on the order of 0.9 mm. In the following we first concentrate on the investigation of LC-FCD. For simplicity let us neglect the coupled rotation in the case of o-PDI at the moment and consider the expectation for lateral diffusion only. Outside a FCD diffusion Dt perpendicular to the LC director will be easily detected due to the lateral 2-D projection, while close to the center of a FCD mostly diffusion Dk parallel to the director will be detected. Diffusion Dk in bulk 8CB is roughly twice the diffusion coefficient perpendicular to the director Dt.24 Furthermore, the fluorescence emission intensity of o-PDI molecules is stronger in the direction of observation when the optical dipole is oriented along the director in the center of a FCD (see Scheme 2). This leads to a higher fluorescence intensity of o-PDI in the FCD and thus we expect a higher amplitude of the correlation function in the center of a FCD. As no-PDI does not align along the LC director, a homogeneous fluorescence intensity distribution is expected for this molecule. Due to sensitivity reasons, we were not able to determine the location of FCD in the single molecule setup directly as we succeeded according to Fig. 1. Therefore we measured the FCS signal at positions along randomly chosen lines across the sample. We assume that measurements are performed statistically in the center of a domain, between two domains or in an intermediate region. The variations in autocorrelation functions G2,norm in each plot of Fig. 5 are related to different lateral positions of the laser focus on the LC-FCD sample. The respective amplitudes of the fluorescence signals have been normalized to 2 for direct comparison. It is clearly evident that the spread in decay times is significantly higher for o-PDI as compared to no-PDI. As we will discuss later in more detail, for o-PDI we find a strong variation of the amplitude A of the correlation function by more than a factor of 2. However, for no-PDI no significant position dependence of amplitudes or characteristic times has been found. Experimentally determined FCS curves cannot be fitted assuming normal diffusion according to Arag on and Pecora.27 There are several possibilities for such a deviation from the ‘‘normal’’ behavior as has been discussed elsewhere.13 As shown by Hac et al.28 improvement can be obtained assuming e.g. two dynamic processes according to G2(s) ¼ 1 + A1/(1 + s/sD1) + A2/(1 + s/sD2).

(6)

Fig. 5 Examples of normalized autocorrelation functions G2,norm before and after the formation of FCD for no-PDI (bottom) and o-PDI (top). We scanned the confocal spot over the sample in steps of typically 200 nm.

G2(s) ¼ 1 + A/[1 + (s/sD)a],

with a < 1. This approximation contains both lateral diffusion processes (medium time scale of diffusivity analysis) and much faster ones. Table 3 collects the corresponding fitting results. First of all, there is an average decrease of about 30% for o-PDI when comparing characteristic times sD for LC and LCFCD. At the same time the parameter a of the anomalous dynamics remains constant so that the general form of the autocorrelation function remains unchanged. Standard deviations s(sD) are much smaller for no-PDI as compared to o-PDI. For a deeper insight into the correlation between the amplitude A of the correlation function and the related characteristic time sD for o-PDI we (arbitrarily) scanned through a focal conic domain. Since FCD diameters are in the range of about 1 mm, we scanned the confocal spot over the sample in steps of 200 nm at an arbitrarily chosen line across the sample. For a typical example the amplitude A shows a clear maximum at d ¼ 0.5–0.75

Table 3 Analysis of data from fluorescence correlation spectroscopy Dye

8CB

sDa/ms

s(sD)b/ms

aa

s(a)b

o-PDI

LC LC-FCD LC LC-FCD

3.31 2.22 2.69 2.22

0.60 0.68 0.26 0.19

0.46 0.50 0.59 0.55

0.04 0.03 0.05 0.06

no-PDI

Despite the complex behavior of the autocorrelation function, in this publication we approximate the complex behavior while assuming anomalous dynamics and therefore fitted the data according to the following analytical approximation28 7436 | Soft Matter, 2011, 7, 7431–7440

(7)

a Characteristic times sD and a (eqn (7)) averaged over all spatial positions. b Standard deviation.


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Fig. 6 Correlation between the amplitude A of the autocorrelation function and the characteristic time sD for o-PDI. Bottom left: sD as a function of the corresponding amplitude A for two independent measurements. The absolute values of A depend on the arbitrarily chosen ‘‘scanning line’’ across a typical sample (top left). Bottom right: amplitude A and sD as a function of the spatial position d along an arbitrarily chosen scan across the sample (through a FCD) with steps of length 200 nm. Lines are for eye guide. The broken line denotes half of the maximum intensity. On top right an image section of 2 microns size is shown for comparison. Note that the graphs on top have been selected from a different sample than the data shown below.

mm which corresponds to a minimum of sD (please note the inverse scale) (Fig. 6, bottom right). The spatial widths of both curves are close to 1 mm as expected for a FCD shown in Fig. 6 (top). The amplitude A is related to the absolute fluorescence intensity, for which a maximum should be obtained for parallel orientation of o-PDI with respect to the surface. This finding is expected at the center of a FCD in the case of o-PDI since that dye follows the orientation of the LC director (see Scheme 2). The experimental data nicely show that they reflect the fluorescence intensity distribution within a FCD shown in the upper part of Fig. 6. Note, however, that FCS data and FCD imaging have been taken from different samples due to experimental reasons. As shown in Fig. 6 (left) we find that sD is decreasing with increasing amplitude A. The increase of A is in agreement with the expectation that in the center of a FCD the fluorescence intensity is higher (see Scheme 2). It can also be seen in Fig. 6 (left), that the absolute range of sD and A is varying for different measurements. The reason for this is that (as mentioned earlier) we were not able to select defined areas of the FCD so that a scan through the center of a domain would result in a larger difference in the values for sD and A (blue triangles) than a scan along boundary areas of the FCD. This leads to a smaller spread of absolute values (green circles). But also in this case the relation between amplitude and correlation time is quite obvious. For both PDI molecules the averaged sD tentatively decreases (see Table 3) for LC-FCD as compared to the non-tempered LC films, which points towards overall faster dynamics. Effects are much smaller for no-PDI, since no-PDI does not follow the orientation of 8CB molecules. We have also performed FCS experiments on LC-TF, which, however, did not show any difference in characteristic times sD when comparing with LC data. This journal is ª The Royal Society of Chemistry 2011

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Discussion While the formation and structure of FCDs are well documented,14,17 the formation of TFs has not yet been reported. The appearance of a TF is not surprising since it shows up for a thickness close to the known threshold thickness associated with FCD formation.14 It most likely reveals a change of anchoring when comparing the two substrates, due to the underlying silicon. It demonstrates that planar anchoring on native oxide is weaker. In order to assess the critical thickness at which TFs appear, films of varied thickness might be studied. However, since the focus of our experiments is on the implementation of single molecule detection schemes into the field of LC structure formation, thinner films on native oxide escape the detection due to strong fluorescence quenching caused by the silicon substrate. Additionally, thicker films would escape the detection due to the increase of optical background signal intensity. Nevertheless, more detailed experiments are needed to clarify the exact conditions of TF formation which is beyond the scope of the present experiments, which concentrate on the influence of mesoscopic structures on diffusion dynamics. However, at the end of the discussion we will draw some conclusions related to the TF structure based on merely diffusion dynamics. Such suggestions are naturally limited and need further proof by more detailed future experiments. In Scheme 3 we suggest a possible structure of a TF based on related reports in the literature and— as will be discussed later—our proposals deduced from diffusion experiments only. The suggested structure shown in Scheme 3 consists of a planar alignment of 8CB on the substrate, then a (newly formed) intermediate nematic layer that turns the director orientation via bend deformation from a parallel orientation of the nematic layer directly at the interface to the Soft Matter, 2011, 7, 7431–7440 | 7437

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Scheme 3 LC film structure as suggested by dye diffusion measurements on no-PDI in 8CB on native silicon oxide after annealing.

smectic layers far away from the surface. The presence of flat smectic layers has been shown by AFM for the top 100 nm of LC-TF (see Fig. 2). A similar molecular structure has been proposed by Lacaze et al.29 for thin 8CB films on MoS2. The same authors also proved theoretically that the energy for such a transition from a smectic phase into the nematic one is comparable to the energy for layer deformation similar to the one in focal conic domains.30 A distortion of layers close to the silicon substrate was also found using scanning force polarization microscopy on wetting droplets by Xu et al.23 Studies of anchoring strength and structural transitions of 8CB, 10CB and 12CB confined to alumina pores by Zumer et al. reveal a strong influence of ambient conditions on structure formation in the case of weak anchoring strength.31 Thus the observed holes in our films may occur on distortion sites due to the influence of surface induced distortions or as a memory effect of evaporated residual solvent. Comparison of LC-FCD and LC-TF structures With respect to structure formation the fundamentally different behavior of the 8CB films on native and on 100 nm silicon oxide are not immediately obvious. We have annealed both substrates only slightly above (35 C) the smectic–nematic transition (33.5 C), since we found dewetting above the nematic–isotropic transition. Somewhat below the (bulk) smectic–nematic and the nematic–isotropic phase transition Garcia et al.4 observed a thick–thin (of typically 20–40 nm) coexistence, respectively, upon temperature increase, which depends on the absolute film thickness of 8CB on native oxide substrates. This coexistence is metastable and persists upon re-entrance into the smectic phase. However, the reason for the coexistence of different film thicknesses remains unclear. Especially the increase of the surface will cost energy. It is not obvious, why such a structure should be energetically preferable compared to a homogeneous film, as LCTF consists of parallel layers in the vicinity of the air–LC 7438 | Soft Matter, 2011, 7, 7431–7440

interface as shown in Fig. 2. Therefore the most likely explanation is that the LC-TF surface topography is a remaining instability at the smectic–nematic transition comparable with the one observed at the nematic–isotropic transition of 8CB.6 If so, the terrace formation and the observed increase in diffusion coefficient would be two independent effects as has been argued above. Xu et al.23 observed steps via AFM at the edge of a smectic 8CB droplet on a Si wafer covered by native oxide at room temperature using scanning polarization force microscopy. They report step heights of 3.2 nm corresponding to an 8CB smectic double layer placed on a wetting trilayer (consisting of one planar monolayer and a slightly distorted smectic double layer). We suggest that our experiments can be explained by a combination of both previously reported observation: (i) a thin–thick coexistence (or ‘‘merging’’ 8CB droplets with a typical hole depth on the order of 20–40 nm) and (ii) smectic steps formed at the ‘‘walls’’ of the holes. Guo and Bahr14 observed the formation of FCDs in the smectic phase of thick 8CB droplets on native oxide upon temperature cycling well into the isotropic phase. Since we performed temperature cycling only into the nematic phase, the absence of FCDs in the current experiments is not necessarily in contradiction with those of literature data. Guo and Bahr also report14 that 8CB anchoring on native oxide becomes less favored as compared to a polymer or silane coated native oxide. This observation emphasizes that the chemical and physical properties of the interface are of crucial importance for adequate wetting conditions. Moreover, long-range van der Waals interactions with the underlying Si substrate will have additional impact.32 Such long range interactions with Si can certainly be neglected in the case of thermally grown (100 nm) oxide. To the best of our knowledge, 8CB has not been investigated on such a substrate. For this reason we presently do not have direct experimental evidence, whether anchoring of 8CB on 100 nm oxide takes place in the same way as on native oxide. In fact previous single molecule diffusion experiments13 show differences for very thin 8CB films depending on the kind of substrate, which might be related to differences in the film structure close to the interface. It has to be pointed out, however, that the formation of mesoscopic structures is already observed by temperature cycling through the (bulk) smectic–nematic phase transition without entering the isotropic phase. Another reason for the different behavior of 8CB on the two substrates might be an increase of surface roughness due to the thermal growth process of the 100 nm oxide. However, our AFM experiments have shown a surface roughness of only 0.3 nm for both types of substrates. Finally let us turn to the diffusion dynamics, which will be discussed separately for FCD and TF. For non-tempered 225 nm LC films we did not observe pronounced differences for dynamics in films prepared on native or on 100 nm oxide substrates. This finding is independent of whether we used single molecule tracking or FCS. After annealing (diffusion) dynamics remain the same for o-PDI on long (>20 ms) time scales (single molecule tracking), but change upon mesoscopic structure formation (FCD) on short ( Dt), while a considerable part of FCS detected dynamics on short time scales has been related to heterogeneous diffusion on short length scales.


Thermally grown oxide: focal conic domain (FCD) related diffusion dynamics Also in the present experiments we assign the broad spread of diffusion coefficients observed on long time scales by tracking experiments on long time scales to diffusion parallel (Dk) and perpendicular (Dt) to the LC director,13 which differ in bulk 8CB by about a factor of 2. For no-PDI two components D1 and D2 are evident from fits to the probability distribution of diffusivities on the expected time scale. Upon FCD formation the contribution of the component D2 clearly increases. This observation can be explained by the presence of a faster or at least an increase of the faster component in the center of the FCD. Since no-PDI diffusion is not influenced by the projection of the transition dipole, the finding of faster diffusion in FCS upon FCD formation for no-PDI points to a real increase of diffusion dynamics for no-PDI. The situation is different for o-PDI, for which we observe only one (broad) distribution of diffusion coefficients (Fig. 3). Since oPDI follows the LC director the component Dk might be suppressed in non-structured films as the transition dipole is perpendicular to the substrate. Diffusion parallel to the director within the FCD would, however, be detected more effectively due to an increased fluorescence emission into the direction of observation (see Scheme 2). Contrary to expectations, no fast diffusion coefficient is emerging on long time scales from the broad distribution shown in Fig. 3. We therefore suggest that either Dk and Dt are of the same order of magnitude or the contribution of diffusion within the domains is too small as compared to regions outside the FCD. Single molecule tracking results are obtained on long time scales by widefield detection, which does not directly relate diffusion to the spatial position in a FCD. This limitation is overcome by FCS which additionally extends the dynamic range to times below 20 ms. On short time scales (FCS) we observe a slight decrease (10–20%) of sD both for o-PDI and no-PDI (see Fig. 5). This corresponds to an overall increase of decorrelation which is more pronounced for o-PDI as compared to no-PDI (see Table 3). However the finding from tracking data seems to be in contradiction to observations following FCS analysis. As already mentioned, FCS data are related also to dynamic processes other than lateral diffusion. While diffusing o-PDI molecules follow the orientation of the smectic layers within a FCD this leads to a rotation of the dielectric dipole of o-PDI which will decorrelate the fluorescence signal. The same process, however, leads to the identification of the position of a FCD, while scanning the laser focus across the sample. In the center of a FCD decorrelation becomes faster, since o-PDI follows the director orientation within a single FCD while diffusing (see Fig. 6). As it is not possible to distinguish between the two effects (translation and rotation) using FCS we cannot conclude, which one has a higher impact on our results. However both lead to a reduction of the This journal is ª The Royal Society of Chemistry 2011

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characteristic time so that the center of the domain can be clearly identified. The defect line in the center of the FCD is rather small, approximately on the order of one smectic layer which relates to some nanometres.33 The dimensions of the defect core are reduced with decreasing temperature as within the defect the molecules are in an undercooled isotropic phase. In the experiment the temperature is as much as 17 K below the isotropic phase. Given that the area of our focus is several hundred nanometres, the probability of a dye molecule being inside the defect is negligible. For this reason, the contribution of molecules entering the defect line itself is negligible within our measurements. Native oxide: terrace formation (TF) related diffusion dynamics For no-PDI we find a significant increase of the mean values and the spread of diffusion coefficients for LC-TF both with msd and diffusivity analysis as shown in Fig. 3 and Tables 1 and 2. o-PDI is basically not influenced by TF formation. AFM results on TF indicate that the smectic structure persists even at the walls of the holes (see Fig. 2). Since (on long time scales) there is no change of diffusion close to the walls of the holes an intriguing hypothesis is that basically diffusion parallel to the walls will be affected. Since o-PDI follows very closely the LC director we expect an increase of Dk. However, due to the 2-D projection and in combination with the orientation of the emitting dipole such an influence is hidden both in molecule tracking and FCS experiments. Since no-PDI does not follow the orientation of the director very closely, an increase of Dk becomes more easily detectable as is experimentally observed. However, there might be an alternative explanation based on comparison with results from FCS. When studying LC-TF films with FCS on short time scales, one obtains the surprising result that the characteristic times sD are not decreased although single molecule tracking of no-PDI does show a faster diffusion in LC-TF as compared to LC (see Fig. 3 and Tables 1 and 2). Furthermore, it is noticeable that this discrepancy only occurs for native oxide while the results on 100 nm oxide are consistent comparing trajectory and FCS analysis. A possible explanation might be related in the case of LC-TF to an unknown arrangement of the smectic layers close to the interface. A major difference for fluorescence measurements on native oxide as compared to thermal oxide is the presence of non-radiative transitions,26 which quench the fluorescence of molecules close to the substrate. For example, at a distance of 20 nm above the substrate the fluorescence intensity is reduced by more than 60%.26 This effect does not influence the measurements of single molecule tracking as the exposure time (20 ms) is longer than the mean first passage time. In contrast, in the case of FCS all information of areas close to the surface is suppressed in the case of both LC and LC-TF because this method only analyzes the temporal evolution of the fluorescence intensity. Keeping this in mind we conclude, that there is no change in diffusion upon TF formation above about 40 nm from the surface (no changes in FCS). At the same time we observe an increase of the diffusion coefficient averaged over the total film thickness (see Fig. 3 and Table 2). A possible molecular configuration that agrees with both observations is the assumption that Soft Matter, 2011, 7, 7431–7440 | 7439

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upon annealing an intermediate nematic layer (with a faster diffusion)24 is newly formed directly above the ‘‘substrate’’ layer (see Scheme 3). Since we do not observe FCDs or hemicylinders, but homogeneous flat surfaces besides the terraced holes, surface domains as suggested by Zappone et al. for 8CB on mica3 are probably not an explanation for the present findings for diffusion in thin 8CB films. Considering that the switching of the director orientation in the nematic phase can be completed within 30 nm,34 and assuming that the diffusion coefficient in the nematic phase is two to three times the diffusion coefficient in the smectic phase for 8CB,24 rough calculations would lead to an increase of the diffusion coefficient averaged over the total film of up to 30%, which is in agreement with our results collected in Tables 1 and 2. The observation that this strong increase of the diffusion coefficient only occurs for the no-PDI molecules might be explained by the fact that those molecules do not fit properly in the LC matrix and thus would prefer to stay in the less oriented nematic phase. In contrast, o-PDI molecules follow the LC orientation. However the molecules are remarkably much larger than the LC molecules (see Scheme 1). For this reason o-PDI prefers the smectic phase with the higher order parameter.

Conclusions We studied the influence of the formation of mesoscopic structures upon the diffusion of single fluorescent PDI molecules in 200 nm thick 8CB films. Depending on the thickness of the silicon oxide layer above the Si wafer we could identify two fundamentally different LC structures. On 100 nm (thermally grown) oxide we observed the formation of the well known focal conic domains (FCDs) whereas on native oxide we found a terraced structure (TF). In the latter case the analysis of the diffusion suggests that surface melting of the smectic layers occurs. In the case of the formation of FCD we could show that the two tracer molecules o-PDI and no-PDI behave differently if analyzed locally by FCS. In the case where the tracer molecule follows the LC director (o-PDI) we can map out the diffusion dynamics related directly to a single FCD. The combination of single molecule tracking and FCS allows for a detailed investigation of various aspects of mesoscopic structure formation at high spatial resolution and in combination with adapted tracer molecules. Though the presence of mesoscopic structures is evident, the physical base of TF is far from being understood. Further systematic investigations varying temperature, humidity and film thickness are needed in combination with theoretical models to systematically understand TF formation and to extend these first observations on molecular diffusion in mesoscopic liquid crystal films towards a general understanding of structure related dynamics.

Acknowledgements We thank the German Science Foundation (DFG, FOR 877 ‘‘From Local constraints to macroscopic transport’’) for financial support. H. Graaf, TU Chemnitz, kindly synthesized the PDI dyes. We would like to thank one of the referees to point out to us valuable information on mesoscopic structure formation in relation to substrate properties. 7440 | Soft Matter, 2011, 7, 7431–7440

Notes and references 1 J. B. Fournier, I. Dozov and G. Durand, Phys. Rev. A, 1990, 41, 2252. 2 J.-P. Michel, E. Lacaze, M. Goldmann, M. Gailhanou, M. de Boissieu and M. Alba, Phys. Rev. Lett., 2006, 96, 027803. 3 B. Zappone, E. Lacaze, H. Hayeb, M. Goldmann, N. Boudet, P. Barois and M. Alba, Soft Matter, 2011, 7, 1161. 4 R. Garcia, E. Subashi and M. Fukuto, Phys. Rev. Lett., 2008, 100, 197801. 5 D. van Effenterre, R. Ober, M. P. Valignat and A. M. Cazabat, Phys. Rev. Lett., 2001, 87, 125701. 6 S. Schlagowski, K. Jacobs and S. Herminghaus, Europhys. Lett., 2002, 57, 519. 7 M. Vilfan, T. Apih, P. J. Sebastiao, G. Lahajnar and S. Zumer, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2007, 76, 051708. 8 J. J. Skaife and N. Abott, Langmuir, 2000, 16, 3529. 9 D. K. Yoon, M. C. Choi, Y. H. Kim, M. W. Kim, O. D. Lavrentovich and H.-T. Jung, Nat. Mater., 2007, 6, 866. 10 G. Friedel and F. Grandjean, Bull. Soc. Fr. Mineral. Crystallogr., 1910, 33, 409. 11 T. Kawai, S. Yoshihara, Y. Iwata, T. Fukaminato and M. Irie, ChemPhysChem, 2004, 5, 1606; T. Kawai, A. Kubota, K. Kawamura, H. Tsumatori and T. Nakashima, Thin Solid Films, 2008, 516, 2666; M. P. Lettinga and E. Grelet, Phys. Rev. Lett., 2007, 99, 197802; E. Grelet, M. Lettinga, M. Bier, R. van Roij and P. van der Schoot, J. Phys.: Condens. Matter, 2008, 20, 494213. 12 F. Kulzer, T. Xia and M. Orrit, Angew. Chem., Int. Ed., 2010, 49, 854. 13 B. Schulz, D. T€auber, F. Friedriszik, H. Graaf, J. Schuster and C. von Borczyskowski, Phys. Chem. Chem. Phys., 2010, 12, 11555. 14 W. Guo and C. Bahr, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2009, 79, 011707; W. Guo, PhD thesis, G€ ottingen 2009. 15 F. Cichos, C. von Borczyskowski and M. Orrit, Curr. Opin. Colloid Interface Sci., 2007, 12, 272. 16 D. T€auber, M. Heidern€atsch, M. Bauer, G. Radons, J. Schuster and C. von Borczyskowski, Diffus. Fundam. J., 2009, 11, 107; I. Trenkmann, D. T€auber, M. Bauer, J. Schuster, S. Bok, S. Gangopadhyay and C. von Borczyskowski, Diffus. Fundam. J., 2009, 11, 108. 17 W. Guo, S. Herminghaus and C. Bahr, Langmuir, 2008, 24, 8174. 18 I. I. Smalyukh, S. V. Shiyanovskii and O. D. Lavrentovich, Chem. Phys. Lett., 2001, 336, 88. 19 J. P. Bramble, S. D. Evans, J. R. Henderson, T. J. Atherton and N. J. Smith, Liq. Cryst., 2007, 34, 1137. 20 D. van Effenterre, R. Ober, M. P. Valignat and A. M. Cazabat, Phys. Rev. Lett., 2001, 87, 125701; D. van Effenterre and M. P. Valignat, Eur. Phys. J. E, 2003, 12, 367. 21 S. Bardon, R. Ober, M. P. Valignat, F. Vandenbrouck, A. M. Cazabat and J. Daillant, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 1999, 59, 6808. 22 R. M. Overney, E. Meyer, J. Frommer, H.-J. G€ untherodt, G. Decher, J. Reibel and U. Sohling, Langmuir, 1993, 9, 341. 23 L. Xu, M. Salmeron and S. Bardon, Phys. Rev. Lett., 2000, 84, 1519. 24 S. V. Dvinskikh, I. Furo, H. Zimmermann and A. Maliniak, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 2002, 65, 061701. 25 C. Hellriegel, J. Kirstein, C. Br€auchle, V. Latour, T. Pigot, R. Olivier and S. Lacombe, J. Phys. Chem. B, 2004, 108, 14699. 26 L. Danos, R. Greef and T. Markvart, Thin Solid Films, 2008, 516, 7251. 27 S. R. Arag on and R. Pecora, J. Chem. Phys., 1976, 64, 1791. 28 A. E. Hac, H. M. Seeger, M. Fidorra and T. Heimburg, Biophys. J., 2005, 88, 317. 29 E. Lacaze, J. P. Michel, M. Goldmann, M. Gailhanou, M. de Boissieu and M. Alba, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2004, 69, 041705. 30 E. Lacaze, J.-P. Michel, M. Alba and M. Goldmann, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2007, 76, 041702. 31 T. Jin, B. Zalar, A. Lebar, M. Vilfan, S. Zumer and D. Finotello, Eur. Phys. J. E, 2005, 16, 159. 32 A. Sarlah and S. Zumer, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 2001, 64, 051606; R. Seemann, S. Herminghaus and K. Jacobs, Phys. Rev. Lett., 2001, 86, 5534; P. Ziherl and S. Zumer, Eur. Phys. J. E, 2003, 12, 361. 33 M. Kleman, J. Phys., 1977, 38, 1511. 34 M. P. Valignat, S. Villette, J. Li, R. Barberi, R. Bartolino, E. DuboisViolette and A. M. Cazabat, Phys. Rev. Lett., 1996, 77, 1994. 35 D. Montiel, H. Cang and H. Yang, J. Phys. Chem. B, 2006, 110, 19763; M. Heidern€atsch, Master thesis, TU Chemnitz, 2009.


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Freezing single molecule dynamics on interfaces and in polymers

Downloaded by Technische Universitat Chemnitz on 08 June 2012 Published on 08 December 2010 on http://pubs.rsc.org | doi:10.1039/C0CP01713B

Stefan Krause,*a Pedro F. Aramendia,b Daniela Taübera and Christian von Borczyskowskia Received 4th September 2010, Accepted 3rd November 2010 DOI: 10.1039/c0cp01713b Heterogeneous line broadening and spectral diffusion of the fluorescence emission spectra of perylene diimide molecules have been investigated by means of time dependent single molecule spectroscopy. The influence of temperature and environment has been studied and reveals strong correlation to spectral diffusion processes. We followed the freezing of the molecular mobility of quasi free molecules on the surface upon temperature lowering and by embedding into a poly(methyl methacrylate) (PMMA) polymer. Thereby changes of optical transition energies as a result of both intramolecular changes of conformation and external induced dynamics by the surrounding polymer matrix could be observed. Simulations of spectral fluctuations within a two-level system (TLS) model showed good agreement with the experimental findings.

Introduction Single molecule spectroscopy (SMS) using probe molecules in soft matter1 and at interfaces2,3 has been extensively used to study molecular dynamics.4 In material and biological sciences single emitters which are extremely sensitive to interactions with the environment and related dynamics constitute ideal nano-probes for polymers,5,6 amorphous solids,7 glasses8–11 and proteins.12,13 Heterogeneous media result often in fluctuations of spectroscopic observables such as emission, absorption, luminescence decay rates, translational or rotational motion. Heterogeneities are either of static or dynamic nature. With ensemble experiments it is in most cases impossible to discriminate between these two assignments. SMS, however, is an ideal tool to circumvent such limitations. Recent SMS investigations of heterogeneous media can be either related to low temperature experiments with high spectral resolution,8–10,14,15 determining spectral diffusion and spectral line width, or to experiments at room temperature, which in most cases deal with rotational diffusion16–18 or fluorescence lifetime fluctuations.19–22 Investigations of spectral diffusion and the related time dependency of optical transition energies are rare at elevated temperatures since intrinsic line broadening precludes from investigating relatively small spectral jumps which are typical for interactions of a chromophore with the environment. However, molecules with pronounced internal degrees of freedom such as intra-molecular charge transfer or internal deformations evidence spectral fluctuations detectable even at room temperature and give the opportunity to follow dynamical processes of the nanoscopic a

Institute of Physics and nanoMA (Center for nanostructured Materials and Analysis), Chemnitz University of Technology, 09107, Chemnitz, Germany. E-mail: [email protected]; Fax: +49 (0)371 531 837418; Tel: +49 (0)371 531 37418 b Dept. Quı´mica Inorgańica, Universidad de Buenos Aires, C1428EHA, Buenos Aires, Argentina

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environment by time dependent measurement of the fluorescence emission spectra of the single emitters.23–25 The intentions of the present paper are twofold. On one side, we aim at first steps to unravel how internal molecular degrees of freedom will couple as a function of temperature to external properties of the amorphous environment which can be twolevel systems,8 free volumes,22 meta basins20 or low frequency vibrations.7 Secondly, we will investigate the behaviour of a probe molecule when changing the constraints imposed by the environment for example by replacing a heterogeneous interface such as SiO2 by a polymer matrix. A suitable molecular system for our goals should have well defined conformers, which is e.g. realized for perylene diimide (PDI) molecules with appropriate substituents.22,26,27 First single molecule experiments on this type of dyes revealed strong spectral fluctuations (spectral diffusion) due to the mobility of attached phenoxy (bay) groups capable to change their positions relative to the chromophoric perylene backbone and the properties of the backbone itself.28–30 As a result the molecules exhibit differences in the optical transition energy of up to 0.27 eV making spectral fluctuations easily observable also under ambient conditions. Though a qualitative assignment of the observed spectral fluctuations to specific dynamic interactions is in most cases so far reported quite obvious, a quantitative analysis is often missing. Basically such a quantitative analysis will only be successful via correlation of several spectroscopic observables such as wavelength and fluorescence intensity including temperature variation. Recently we have shown that such correlations exist.30 This enables us to investigate in the present paper quantitatively the freezing of spectral dynamics both upon lowering temperature and/or upon transferring the probe molecules from an interface allowing for a high degree of mobility into a polymer which restricts on the one hand mobility to a larger extent but enhances small fluctuations due to polymer dynamics on the other. This journal is

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Experimental Dialkyl (DAP), monopyridyl (PP) and dipyridyl perylene diimides (DPP) were synthesized by Wu¨rthner and Sautter.27 (For structures see Fig. 6.) To prepare single molecule experiments, glassware was cleaned with acetone and ethanol followed by heating up to 60 1C in a Hellmanex II solution. Small amounts of the original solution of dye molecules in toluene were diluted in spectroscopic toluene (Merck) to achieve a concentration of about 1011 mol l1. To ensure clean substrates, silicon wafers with a 100 nm thick thermally grown oxide layer (ENAS, Chemnitz) were first treated with acetone and ethanol and then placed for at least one hour into a mixture of 3 : 2 H2SO4 and H2O2 in an 80 1C ultrasonic bath. Remaining contaminations on the substrates were eliminated by annealing those 20 to 30 s with a gas flame. The purity with respect to luminescence was verified with a standard wide field microscope (excitation wavelength lex = 514 nm). Spatially well separated single molecules on the substrate were achieved by spin coating the toluene solution at 3000 rpm followed by evaporation of the remaining toluene. The preparation of PMMA samples followed the same procedure. To achieve a 5 nm to 10 nm thick polymer film on the sample, 20 mg of PMMA were dissolved in 4 ml of the final mixture of toluene and dye molecules. Spin coating was performed under same conditions as for pure SiO2 samples. Vacuum pumping for at least 1 h in the cryostat at room temperature ensured complete toluene evaporation. Single molecule spectroscopy and microscopy experiments were performed with a home built confocal laser scanning microscope. A 532 nm Nd:YAG laser (Spectra Physics) was used as the excitation light source. The beam was scanned with the scanning mirror of a control scan stage (Newport) and then focused through the cryostat cover glass (0.5 mm) onto the sample with a 63 cover glass corrected objective (Carl Zeiss Jena) with a numerical aperture of NA = 0.75. All experiments were performed under vacuum condition (105 mbar–106 mbar) in a Janis Research Cryostat. For low temperature measurements the Cryostat was cooled with liquid helium to 4.2 K. The fluorescence signal was separated from the excitation light via a 542 nm long pass filter (Omega Optical). A 30 : 70 beam splitter allowed for recording simultaneously images with an avalanche photodiode (Perkin Elmer) and single molecule spectra with a monochromator (300 lines per mm grating, Acton Research Corporation, SpectraPro 275) equipped with a liquid nitrogen cooled CCD camera (Princeton Instruments, ST-121) allowing for spectral resolution of (2.3 0.2) nm at 600 nm wavelength and for a 200 mm entrance slit (note that the positioning accuracy of spectral emission peaks is slightly improved for high signal to noise ratio). Evaluation of single molecule spectra was performed by an adapted Matlab fitting algorithm.

Results PP has in comparison to DPP only one pyridyl group. The other one is replaced by a single butyl chain. It is expected that—as shown in Fig. 1—PP and DPP are close to an upright position of the transition dipole moment as might be confirmed by recent experiments according to the procedure suggested by Hohlbein and Hu¨bner.31 We already investigated the orientation of these types of molecules by means of such 3D This journal is

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Fig. 1 Top: Structure of N,N0 -bis(pyridyl)-1,6,7,12-tetrakis(3-hydroxyphenoxy)perylene-3,4:9,10-tetra-carboxylicaciddiimide (DPP). The figure shows an extended conformation of DPP. The pyridyl groups (see coloured circles) allow for directed attachment of the molecule to the silanol groups on the SiO2 surface (see enlarged scale). Scheme of a PMMA embedded DPP molecule. Bottom: The phenoxy groups in the bay position allow for a strong coupling to the polymer environment.

orientation measurements.32 The experiments revealed indeed a side-on orientation for the molecules functionalized with pyridyl groups such as PP and DPP. As these measurements yielded a large amount of interesting data it would go beyond the scope of this paper. Presently detailed experiments related to this subject are underway. In the case of DAP even both groups are replaced by butyl chains. The structural formula of DPP is depicted in Fig. 1. DPP, PP and DAP (structural formulas are additionally shown in Fig. 6) contain 4 bay groups which give rise to at least 5 conformers.29 They are different regarding their relative orientation with respect to the perylene moiety. The two limiting conformers are those where all bay groups are extended or folded, with respect to the perylene backbone. The intermediate ones are those where only 1, 2 or 3 bay groups are folded.29 While changes in conformation on SiO2 due to transitions between different conformers have been observed recently, the situation is expected to be different for a polymer host which strongly restricts large movements of the phenoxy groups. The question whether a coupling of the polymer dynamics to the optical transition dipole is possible or even useful for characterisation will be further dıscussed. Phys. Chem. Chem. Phys., 2011, 13, 1754–1761

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Fig. 2 Fluorescence emission spectra of single DPP molecules at 293 and 4.2 K on SiO2 (a) and in PMMA (b and c), respectively. Excitation wavelength lex = 532 nm and laser power Pex = 20 mW. The example in (c) shows a fluorescence emission spectrum which can be observed for only 5% of the investigated molecules in PMMA at 4.2 K.

We investigate single PDI molecules deposited on to a SiO2 surface or embedded into thin films of PMMA. Fig. 2 shows typical fluorescence emission spectra of single DPP molecules at 293 K and 4.2 K on a SiO2 surface (top) and in PMMA (middle), respectively. Spectral shape and line width are only slightly reduced upon temperature decrease. This is very similar to recently reported results.33 Such behaviour is observed for most of the molecules which cover in total a transition energy region of 1.94 eV to 2.21 eV.32 The broad range of emission is due to conformational changes of the bay groups with respect to the chromophoric PDI backbone.29,30 In PMMA at 4.2 K, a few molecules show narrow spectra which are within the range of our experimental resolution as shown for comparison in the bottom graph in Fig. 2. At 293 K, and especially on SiO2, such narrow spectra could not be observed. This broadening is due to spectral diffusion even at 4.2 K as is shown in Fig. 3(a) for spectrally resolved wavelength jumps of PP in PMMA. Spectral fluctuations could be detected because they occurred on time scales larger than the integration time for a single spectrum. The fluorescence time trace at the top of Fig. 3 shows fluctuations both in spectral positions and fluorescence intensities. Spectra with an integration time of 0.5 s are shown at various observation times in Fig. 3(b), while a ‘‘sum’’-spectrum of the 4 spectra is shown below. The individual spectra are still considerably broadened. The time trace reveals that at least two types of spectral fluctuations are evident: large spectral jumps of 60 meV, which occur rarely, and frequent jumps of about 15 meV and less. The intensity fluctuations are correlated with the spectral jumps. Owing to such spectral fluctuations, unbroadened line widths cannot be detected as long as the integration time is larger than the time scale of spectral jumps. The sum spectra as an example represents such a resulting line broadening. To investigate the time dependent spectral processes more in detail we fitted the fluorescence spectra of single molecules by up to four Gaussian lines yielding the peak positions, line widths and amplitudes. Fig. 4 shows the distribution of line widths (FWHM) of the highest energy emission band for the two environments at 4.2 K and 293 K. 1756

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Fig. 3 (a) Spectral time trace of PP in PMMA at 4.2 K. Red (yellow) dots mark the positions of the respective fluorescence origin (vibronic side band). Consecutive spectra are plotted in a gray scale map and exhibit small fluctuations of about 15 meV during the whole observation time and two large spectral jumps of about 60 meV. The numbers 1–4 mark single fluorescence spectra which are representative for the four observed spectral states. They are displayed in (b). The time trace of the integrated intensity shows clear correlation of spectral jumps and intensity changes. (c) Sum spectra of all single frames of (a).

In principle comparison of ensemble FWHMs and FWHMs of a single emitter observed for a very long time allows us to investigate the break down of ergodicity but it requires very long measuring times for one single molecule. A single molecule will especially for long times explore the same energy landscape like the ensemble as long as it is not restricted by its nanoscopic environment to a certain energy range (molecule 1 in Fig. 4). The environment might thus prevent single molecules from exploring the total energy landscape (molecule 2 in Fig. 4). In that case ergodicity breaks down. From the observations we conclude that for some of the molecules ergodicity applies for others it does not. The overall behaviour shown in Fig. 4 seems to be quite complex. At T = 293 K both the covered range and the width of the related line width distribution are larger for SiO2 (especially towards large FWHMs) as compared to those for PMMA. From this we conclude that the extent of spectral diffusion is, on the scale of our observation time, larger for SiO2 than for PMMA. This is reasonable, since PMMA will reduce the degree of spatial (and rotational) mobility for DPP which is apparently more ‘‘floppy’’ on a SiO2 surface. The extremely broad line widths on SiO2 are due to the fact that on the scale of the integration time of 0.5 s DPP explores a broader range of conformers. This is in line with observations of Ishikawa and coworkers from lifetime fluctuations and intensity time traces.34 The behaviour seems to become quite opposite at 4.2 K. While on SiO2 the average FWHM is reduced by at most a factor of 2 while maintaining a similar width in distribution (excluding the tail at large line widths for 293 K), the average width is less reduced in PMMA, but the width of the distribution is apparently much broader at 4.2 K as compared to 293 K. The related distributions are close to Gaussian ones in all cases besides the one for DPP in PMMA at 4.2 K, which seems to be a superposition of several distributions. This interpretation implies that PMMA freezes This journal is

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spectral diffusion, on a time scale faster than 0.5 s, covers a range of about 30 meV–60 meV, nearly independent of temperature. In PMMA some of the DPP molecules maintain at 4.2 K the same FWHM as at 293 K while others exhibit line widths as narrow as the experimental resolution (see the bottom spectrum in Fig. 2). Spectral diffusion slower than 0.5 s can be detected as discrete spectral jumps (see Fig. 3). To analyze these jumps, we use the difference of the maxima of two consecutive emission spectra DE = Ei+1 Ei where i denotes the number of the spectrum within the spectral time trace. Fig. 5 shows the distribution of spectral jumps for SiO2 and PMMA at 293 K and 4.2 K on a log–lin scale. The noise limited jump width is close to 3 meV which is obtained for DPP in PMMA at 4.2 K. Spectral jumps larger than 25 meV are in all cases nearly completely frozen at 4.2 K. For SiO2 at 293 K we observe spectral jumps of up to 120 meV for DPP. Similar large changes in the optical transition energy have for example also been reported for conjugated polymers and were addressed to strongly distance dependent interactions of two or more chromophores35,36 in a polymer chain. As we investigate well separated single molecules we assign conformational changes of bay groups of DPP as the reason for the observed fluctuations.29 Only very few large jumps between 25 meV and 120 meV are observed for DPP in PMMA (see Fig. 3 (top)). The jump width distribution at 4.2 K is shown on an enlarged energy scale in Fig. 6 together with additional data for PP and DAP in PMMA. The distributions show in all cases a characteristic central shape, which can be fitted with three Gaussian distributions (one for the noise and a second and third for small spectral diffusion resulting in positive or negative energy differences left and right of the center) and in the case of PP and DAP two additional ‘‘side-bands’’ separated by 15 meV–20 meV from the central peak of the distribution. We like to mention that the range of spectral diffusion is in all cases larger for PP and especially for DAP than for DPP. We assign this to the replacement of the pyridyl group(s) by one or two flexible butyl chains, preventing a double anchoring of the molecules (DAP) to the matrix. It is obvious from Fig. 6 that Fig. 4 Top: full width at half maximum (FWHM) distributions for DPP fluorescence emission spectra on SiO2, in PMMA, for 293 K and 4.2 K. Spectra were collected in time traces for 25–50 molecules. For each molecule a maximum of 200 frames were recorded or less for bleaching molecules. Bottom: two time dependent single molecule spectra of DPP in PMMA at 293 K. The spectrum of molecule 1 shows strong spectral fluctuations where molecule 2 emits at constant wavelength during the observation time. As a result molecule 1 represents the ensemble distribution of FWHMs for the first emission peak more precisely (see distributions for DPP in PMMA at 293 K on the right).

at least a few DPP–environment configurations with FWHM differences of a factor of 5. The temperature behaviour of FWHM distribution in PMMA can be explained by a coalescence of different conformations due to temperature increase. The overall behaviour of FWHM in connection with the rare but nevertheless present narrow line spectra suggests that This journal is

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Fig. 5 Distribution of spectral jump widths for DPP on SiO2, and in PMMA, at 293 K and 4.2 K. The distributions are shown on a log-in scale to emphasise large spectral jumps which occur with a very low probability.


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In the case of spectral diffusion we are interested in the cumulative distribution of the squared amplitude of spectral jumps. This gives us the opportunity to gain exact spectral diffusion coefficients despite the fact that the obtained spectral trajectories consist at most of 200 data points for a single molecule which is not sufficient to extract values according to the model of mean squared displacement.38 To proceed we define a spectral diffusivity


ds ¼

DE 2 2t

ð1Þ

where DE2 is the square of the energy difference of two consecutive spectra belonging to one single molecule and t represents the time difference between the two spectra. We calculate the spectral diffusivity between every pair of data points and sort them in descending order according to the probability of the respective occurrence. The complementary cumulative distribution Cs(ds) = 1 Ps(ds)

Fig. 6 Comparison of jump width distributions for DPP, PP and DAP molecules in PMMA at 4.2 K. The center peak was fitted by 3 Gaussian functions and represents small spectral fluctuations and broadening through noise. In the case of PP and DAP two additional Gaussian functions represent spectral jumps between 3 (3) meV and 40 (40) meV.

the butyl chain(s) in the case of PP and DAP are responsible for the coupling to external dynamics of the surrounding polymer since they enhance spectral diffusion processes strongly.

(2)

with Ps(ds) as the cumulative distribution representing the probability to measure a value smaller than ds, can be obtained by plotting the ratio j/N as a function of the diffusivity (j is the position of the jth data point in the sorted diffusivity row and N the overall number of events). Despite the fact of a finite energy space explored by the different molecule–environment conformations, a spectral diffusion coefficient Ds can be determined. In cases of fast diffusion processes the cumulative distribution curve would exhibit a small negative gradient and thus a high diffusion coefficient Ds, whereas slow processes lead to a large negative gradient and a related small Ds as has been shown in the case of translational diffusion in liquids.37,39 Application of this formalism to the spectral diffusion of DPP results in complementary cumulative distributions (complementary functions) as shown in Fig. 7 at 293 K and

Discussion To describe spectral diffusion more quantitatively we borrow ideas from translational diffusion analytics. The model of complementary cumulative distributions allows in the case of 2-dimensional spatial diffusion the determination of diffusion coefficients.37 As a matter of fact, the 2-dimensional spatial diffusion transfers to a 1-dimensional one in energy (wavelength) space. To emphasize the difference between spatial and spectral diffusion we label the spectral entities with the suffix ‘‘s’’. Formally we define in this way diffusion coefficients very similar to those in spatial diffusion. For the model of complementary cumulative distributions it is not necessary that the system is ergodic. The complementary cumulative distributions are derived from a straightforward statistical analysis. Of course diffusion coefficients will differ between the time average measurement and the ensemble average measurement if the system is not ergodic. However, one has to be aware that e.g. fast diffusion does not imply that spectral jumps occur very frequently, but that large (rare) spectral jumps are effectively realised per time unit t. 1758

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Fig. 7 (a) Complementary functions for spectral jump widths of DPP molecules on SiO2, in PMMA, for 293 K and 4.2 K. The blue lines represent the fits to the sum of three error functions. (b–d) Ratio of the fitting functions for SiO2 (293 K and 4.2 K), PMMA (293 K and 4.2 K) and for 293 K (PMMA and SiO2). The vertical dashed line in (d) marks the region of diffusivities which are dominated by the experimental noise (values below 10 meV2 s1). The horizontal lines represent maximum and minimum values of the ratio of complementary functions for PMMA and SiO2 at 293 K.

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4.2 K for SiO2 and PMMA. The apparently ‘‘multicomponent’’ behaviour indicates, in coherence with our expectations, that the spectral diffusion cannot be associated with a simple Brownian-type diffusion of a single distinct emissive state, but with the presence of at least two emissive states of discernible energy. This is in line with the assumption that spectral diffusion takes place e.g. as a result of conformational changes where different conformers are separated by energy barriers and exhibit different realisation probabilities. The cumulative distributions can be fitted by a sum of i error functions (see eqn (3)), where each value of Ds,i describes a well defined ‘‘diffusion’’ process.40 The individual fitting function is described by sffiffiffiffiffiffiffiffiffiffi!# " X ds Cs ðds Þ ¼ Ai 1 erf 2D s;i i ð3Þ X Ai ¼ 1: i

A is the amplitude of the fitting function which is assigned to one diffusion process. The error function in general is defined as 2 erfðzÞ ¼ pffiffiffi p

Zz

et dt: 2

ð4Þ

0

Experiments at 293 K for DPP in PMMA show a broad distribution of ‘‘spectral diffusion coefficients’’. Thereby the amplitudes for large spectral jumps are low indicating their infrequence. The curves in Fig. 7(a) are fitted by a sum of 3 error functions where the first one represents noise related values, the second one small spectral diffusion processes and the third one large spectral diffusion processes. At 4.2 K the overall behaviour remains very similar but the probability for large and small spectral jumps is reduced by at least one order of magnitude as can be seen from the ratio of the two curves for PMMA at 293 K and 4.2 K shown in Fig. 7(c). As expected, lowering the temperature freezes the spectral diffusion very effectively for large and small spectral jumps, which have to be assigned to conformational changes and polymer dynamics that are not completely frozen out as can be seen from Fig. 3. Room temperature data for DPP on SiO2 show a somewhat different behaviour. For diffusivities ds o 200 meV2 s1 there seems to be also a similar distribution of various diffusion processes but with larger diffusion coefficients than for DPP in PMMA. However, for ds > 200 meV2 s1 this behaviour crosses over to an apparent single diffusion coefficient of Ds (SiO2, 293 K) = (659 24) meV2 s1 (gained from the fitting function in Fig. 7(a)), which we assign to be related to conformational changes. Lowering the temperature nearly freezes large conformational jumps (see Fig. 7(b)) and the overall behaviour at 4.2 K is very similar to that in PMMA. The most obvious difference between the two environments occurs for small spectral jumps. In the case of SiO2 the reduction of such fluctuations is much less dependent on the temperature. Whereas in the polymer matrix the temperature plays a more important role. This is reflected in the much higher probability for small fluctuations at 293 K in PMMA (Fig. 7(d), which shows the ratio of the complementary This journal is

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distribution function for PMMA and for SiO2 at 293 K). It is clearly visible that the amount of small spectral fluctuations overweighs in comparison to SiO2. In contrast large spectral changes in PMMA in the region of 500 meV2 s1 appear with a probability of only 20% compared to SiO2. The described temperature and matrix dependence can also be identified in the spectral jump width distribution shown in Fig. 5 and 6. The distribution plot of spectral jumps for PP and DAP in PMMA provides strong evidence for the existence of individual two-level systems (Fig. 6), which are obviously not seen in Fig. 7. However, from Fig. 6 it becomes clear that such an ‘‘isolated’’ two-level system is rare and not detectable in the cumulative distribution shown in Fig. 7 for all molecules, but should be seen in the cumulative distribution of a single molecule. The spectral time trace and the cumulative distribution are shown in Fig. 8 for a single PP molecule. Contrary to results shown in Fig. 7 an upper limit of diffusivity becomes visible in the diffusivity range around 500 meV2 s1. Fig. 8(a) clearly shows that two distinct levels can be assigned with a separation of about 15 meV to 25 meV. This separation is very close to the ‘‘side bands’’ of the jump width distribution in Fig. 6 (middle). We assign this behaviour to a coupling of the optical transition to a distinct and well defined two-level system repeatedly reported in the literature.7,8 Such distinct transitions within the two-level system are observed more often for PP and DAP in PMMA as compared to those for DPP on SiO2 and in PMMA, though they are also present in these systems. We like to mention that the assigned two-level systems are not necessarily related to TLS of the amorphous materials due to the fact that the related energy differences between the two states appear also on SiO2 but with a lower probability. This is additionally confirmed by recent publications on the influence of TLS (contributing only a

Fig. 8 (a) Spectral time trace of a single PP molecule in PMMA at 4.2 K. The time evolution exhibits discrete jumps between two states. (b) Complementary function for the spectral time trace shown above. The red line represents a fit consisting of two error functions. The fitting procedure reveals a spectral diffusion coefficient of Ds = (110 2) meV2 s1.


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Fig. 9 (a) Simulated time trace of fluorescence emission peaks with energies of the two states of 2.000 and 1.982 eV (indicated by the red dashed lines) and a Gaussian distributed noise of 3 meV. The ratio of occupation of the energetically high and low levels was chosen to be the same as that experimentally observed (1 : 5.5, see Fig. 8(a)). (b) Complementary cumulative distribution function representing the two-level systems time trace in (a).

fraction of 1 meV to energy differences) and low frequency modes (causing predominantly broadenings of the line width) on line shapes and spectral fluctuations.7 From this we conclude that the polymer dynamics allow for distinct switching between specific intramolecular conformers. A cumulative distribution has been simulated for jumps in a two-level system while considering experimental noise. The energy difference between the two states and the ratio of occupation of energetically lower and higher states were estimated from the experimental data of Fig. 8(a) to DE = 18 meV and rTLS = 5.5. In the simulation, we assumed a noise of 3 meV for the position of the maximum of the spectrum, with a Gaussian distribution around the two energy levels. It has to be emphasised that this is only an approximation. For a more accurate description of the noise one has to consider that a mixture of the two states can appear due to the integration time of 0.5 s. This will cause intermediate states within the spectral time trace. The results for simple Gaussian distributed noise around the states are shown in Fig. 9. Comparison with experiment shows a qualitative agreement on a single molecule level. Both, experimental and simulated curves exhibit two components: one fast decaying component which represents the noise and a second slow decaying component which can be assigned to the observed diffusion processes. This confirms the assumption that the low temperature spectral fluctuations for PP in PMMA can be described via a two-level system.

Conclusions The outlined single molecule spectroscopy studies of perylene diimide molecules under different conditions revealed a complex behaviour of spectral line widths and spectral diffusion processes. The spectral line widths did not show the expected strong temperature dependence known from low temperature fluorescence excitation experiments. Even at 4.2 K emission line widths were only reduced by a factor of about 2. We assign this unexpected broadening behaviour to spectral fluctuations on a time scale far below our experimental time resolution. Less than 5% of the investigated molecules exhibit narrow emission lines in the region of our spectral resolution 1760

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confirming that line broadening can in principle be reduced by lowering the temperature. The temperature influence on observable spectral dynamics in the time scale of 0.5 s showed, in contrast, a much stronger correlation. Large spectral jumps of up to 120 meV could be especially observed on SiO2 at room temperature due to the high degree of freedom of the bay groups. As this is not the case in PMMA large spectral fluctuations were already reduced at 293 K. At low temperatures these phenomena were almost completely reduced for DPP molecules. In contrast to these observations a slight difference in the chemical structure of the dye molecules (PP and DAP) changed the situation in PMMA at low temperatures dramatically. For PP and especially DAP a strong enhancement of spectral fluctuations was observed at 4.2 K which we interpret as a coupling of the butyl chain(s) to the surrounding environment.

Acknowledgements We like to thank Frank Wu¨rthner (Wu¨rzburg University) for a kind donation of DPP, PP and DAP. We acknowledge financial support by the German Science Foundation within the research unit ‘‘From Local Constraints to Macroscopic Transport’’ (SFG 877) and the DAAD for supporting exchange between the University of Chemnitz and the University of Buenos Aires. PFA is a Research Fellow from CONICET (Consejo Nacional de Investigaciones Cientı´ ficas y Tećnicas, Argentina).

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View Online 17 H. Uji-i, S. M. Melnikov, A. Deres, G. Bergamini, F. De Schryver, A. Herrmann, K. Mu¨llen, J. Enderlein and J. Hofkens, Polymer, 2006, 47, 2511–2518. 18 R. A. L. Valleé, T. Rohand, N. Boens, W. Dehaen, G. Hinze and T. Basche, J. Chem. Phys., 2008, 128, 154515. 19 R. A. L. Valleé, M. Van Der Auweraer, F. C. De Schryver, D. Beljonne and M. Orrit, ChemPhysChem, 2005, 6, 81–91. 20 R. Valleé, M. Van der Auweraer, W. Paul and K. Binder, Phys. Rev. Lett., 2006, 97, 217801-1–217801-4. 21 R. Valleé, N. Tomczak, L. Kuipers, G. Vancso and N. van Hulst, Phys. Rev. Lett., 2003, 91, 038301-1–038301-4. 22 R. A. L. Valleé, M. Cotlet, M. Van Der Auweraer, J. Hofkens, K. Mu¨llen and F. C. De Schryver, J. Am. Chem. Soc., 2004, 126, 2296–2297. 23 C. Blum, F. Stracke, S. Becker, K. Mu¨llen and A. J. Meixner, J. Phys. Chem. A, 2001, 105, 6983–6990. 24 R. A. L. Valleé, P. Marsal, E. Braeken, S. Habuchi, F. C. De Schryver, M. Van der Auweraer, D. Beljonne and J. Hofkens, J. Am. Chem. Soc., 2005, 127, 12011–12020. 25 K. L. Wustholz, E. D. Bott, B. Kahr and P. J. Reid, J. Phys. Chem. C, 2008, 112, 7877–7885. 26 F. Wu¨rthner, Pure Appl. Chem., 2006, 78, 2341–2349. 27 F. Wu¨rthner and A. Sautter, Org. Biomol. Chem., 2003, 1, 240–243. 28 J. Hofkens, T. Vosch, M. Maus, F. Ko¨hn, M. Cotlet, T. Weil, A. Herrmann, K. Mu¨llen and F. C. De Schryver, Chem. Phys. Lett., 2001, 333, 255–263.

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Contents lists available at ScienceDirect

Vacuum journal homepage: www.elsevier.com/locate/vacuum

A comparative analysis of a-C:H films deposited from five hydrocarbons by thermal desorption spectroscopy S. Peter*, M. Günther, F. Richter Chemnitz University of Technology, Institute of Physics, D-09107 Chemnitz, Germany

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0042-207X/$ e see front matter 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.vacuum.2011.07.037

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ARTICLE pubs.acs.org/JPCA

k-Restoring Processes at Carbon Depleted Ultralow-k Surfaces Oliver B€ohm* Material Calculation, GWT-TUD GmbH, Annabergerstrasse 240, 09125 Chemnitz, Germany, and Institut f€ur Physik, Technische Universit€at Chemnitz, 09107 Chemnitz, Germany

Roman Leitsmann,* Philipp Pl€anitz, and Christian Radehaus Material Calculation, GWT-TUD GmbH, Annabergerstrasse 240, 09125 Chemnitz, Germany

Michael Schreiber Institut f€ur Physik, Technische Universit€at Chemnitz, 09107 Chemnitz, Germany

Matthias Schaller Dresden Module Two GmbH & Co. KG, GLOBALFOUNDRIES, 01109 Dresden, Germany ABSTRACT: In this study we investigate the silylation of OH groups with different silazanes. In particular we use density functional theory and the nudged elastic band method to study the different reaction mechanisms. For the silylation reaction of hexamethyldisilazane and trimethylaminosilane with silanol, the minimum energy paths as well as the activation and reaction energies are discussed in detail. From minimum energy reaction paths we found that all studied silazanes react exothermically. Bis(dimethylamino)dimethylsilane shows the most exothermic silylation reaction with the lowest activation energies. Therefore, it is a good candidate for the chemical repair of porous films in the semiconductor k-restoring process.

’ INTRODUCTION The decreasing feature size of integrated circuits (ICs) leads to several problems. Due to smaller distances between conduction paths and conduction layers the resistance capacitance (RC) delay increases.1,2 To reduce the RC delay, new materials have been developed. For example aluminum was replaced by copper as conduction material. Another possibility is the application of materials with a small dielectric constant (k-value) between the connection paths. Smaller, in this case, means that the k-value lies below that of silicon dioxide, which was used for a long time in the fabrication process of ICs. One group of those materials is porous organosilicates (SiOC:H) which are commonly known as ultralow-k (ULK) materials. They are produced by chemical vapor deposition (CVD), plasma enhanced chemical vapor deposition (PECVD), or spin on procedures from different precursors such as trimethylsilane, octamethylcyclotetrasiloxane, methylsilsesquioxane, and others.25 An important step in device production is the plasma etching of trenches or vias. A commonly used group of etch gases are fluorocarbons (CF). The plasma etching leads to damage of the ULK material. During the etching process, CF polymerization6,7 at the side walls and carbon depletion occurs.8 After the etching r 2011 American Chemical Society

process, the resulting CF film must be removed. Both the plasma etching and the removal of the CF film with classical cleaners, i.e., dHF, lead to the formation of OH groups and the ULK surface gets more hydrophilic.9 Due to moisture uptake, the k-value increases dramatically. To restore the k-value, a typical repair process is performed in which a repair molecule reacts with one or more OH groups. An optimal repair molecule should react only with OH groups and retain the ULK structure. Furthermore, the carbon concentration should be increased. Most repair molecules contain hydrophobic methyl groups. One important type of repair molecules is the group of silazanes, which can be used as a gas or solved in a hydrophobic liquid.10 A widely studied repair molecule is hexamethyldisilazane (HMDS).11 Chaabouni et al.9 showed that a treatment of the damaged ULK material with HMDS results in a decrease in the RC delay and the leakage current. But due to the silylation of the OH groups a larger molecule such as trimethylsilane (TMS) replaces the hydrogen of the OH Received: March 28, 2011 Revised: June 14, 2011 Published: June 17, 2011 8282

dx.doi.org/10.1021/jp202851p | J. Phys. Chem. A 2011, 115, 8282–8287

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Table 2. Bond Lengths, Bond Angles, and Torsional Angles of HMDS (Distance R, Å; Bond and Torsional Angles, deg) parameter

Figure 1. Silylation reaction of a repair chemical with one reactive group.

this work

experimental24

theoretical25

R(NSi)

1.75

1.738

1.7421.757

R(SiC) R(CH)

1.88 1.10

1.876 1.104

1.8761.895

R(NH)

1.02

0.98

1.0031.014

— (SiNSi)

132.7

131.3

130.4134.6

110.7

— (NSiC)

107.3111.7

— (SiNH)

113.6

112.7114.8

dih(SiNSiH)

0.2

02.0

107.0112.0

Figure 2. Silylation reaction of a repair chemical with two reactive groups.

Table 1. Total Energies of Products, Educts, and TSs as Well as the Activation and Reaction Energies Calculated with the DZVP and TZV2P Basis Set parameter

DZVP

TZV2P

85.688

85.712

Eproducts, au

85.701

85.726

ETS, au

85.646

85.671

ΔEreacn, kJ/mol

34.10

36.72

ΔEact., kJ/mol

110.17

107.55

educts

E

, au

group, which results in a screening of adjacent OH groups.11,12 Thus, an optimization of the repair process can be achieved by using repair molecules that minimize the steric hindrance effect. To optimize the repair process, a fine grasp of the silylation process is necessary. Unfortunately there exist no theoretical studies about the reaction mechanism of repair chemicals with two reactive groups. Therefore, in this work we study the silylation reactions of HMDS, trimethylaminosilane (TMAS), and bis(dimethylamino)dimethylsilane (DMADMS) with silanol in the gas phase. Silanol is used to represent a fragment of the ULK surface. Therefore, these reactions represent a model of the repair process at ULK surfaces. The different pre- and postreaction complexes, transition states (TS), and the reaction and activation energies are discussed in detail.

’ THEORY Computational Methods. All calculations were done using density functional theory (DFT) within the generalized gradient approximation (GGA). The specific GGA functional is parametrized according to Perdew, Burke, and Ernzerhof (PBE).13 We use the CP2K/Quickstep package14 with a Gaussian-augmentedplane-wave basis set (GAPW). The PBE functional provids a high accuracy in most cases but without calculating an expensive exact exchange correlation part such as in the M06 and M06-2X functionals which have recently been developed.15 For the position space representation of the valence electrons we use

Figure 3. Molecular structure of the silazanes: (a) HMDS, (b) TMAS, and (c) DMADMS. The indicated bond lengths are given in angstroms.

mainly the Gaussian double-ζ Molopt basis set with polarization function (DZVP), which strongly reduces the basis set superposition error (BSSE).16 The interactions with remaining ions are modeled by the GoedeckerTreterHutter (GTH) pseudopotentials.17 To determine the minimum energy reaction paths (MERP)18 and the TSs, we use the climbing image nudged elastic band (CI-NEB) method1923 as implemented in CP2K. Silylation Reactions. The silylation of OH groups with silazanes occurs through a proton transfer. In general, repair chemicals can be classified by the number of reactive groups. In this work we consider repair chemicals with one and two reactive groups, where the number of reactive groups is identical with the number of possible silylated OH groups. Due to steric hindrance effects we restrict ourselves to repair chemicals where only one OH group is silylated with a TMS group in the case of one reactive group (see Figure 1) or two OH groups are silylated by dimethylsilane in the case of two reactive groups (see Figure 2). It must be mentioned that the reaction with two reactive groups takes place in two steps (one for each OH group). Thus, we have to study two MERPs for this type of silylation process. 8283

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dx.doi.org/10.1021/jp202851p |J. Phys. Chem. A 2011, 115, 8282–8287

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ARTICLE

Figure 4. MERPs of the silylation reactions of (a) HMDS, (b) TMAS, (c) DMADMS, and (d) DMDMADSO with silanol. The reaction coordinate corresponds to the CRMSD. The total energy of the educts is taken as energy zero.

A well-studied repair molecule with one reactive group is HMDS, where the silylation reaction is given by

are given by

Equation 1 shows that one of the reaction products is TMAS, which is a typical repair chemical by itself. Therefore, to understand the impact of HMDS on ULK materials containing OH groups, one has to study the silylation reaction with TMAS as well. It is given by

As a representative molecule with two reactive groups we study DMADMS. The two steps of the silylation reaction

with DMA = dimethylamine and DMDMADSO = 1,1-dimethyl1-(dimethylamino)disiloxane. In addition one has to keep in mind that eq 3 and eq 4 are not independent from each other. There is a strong dependency on the distance between the two OH groups, due to the finite length of DMADMS. This is an important difference between the silylation with HMDS and TMAS. TMAS reacts independently from the position of the first silylated OH group. 8284


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Table 4. Energies and Lengths of the Postreaction Complexes of the Silylation Reactions as Well as the Mulliken Charges of the Hydrogen and Oxygen Atoms (Energy E, kJ/ mol; Distance R, Å; Mulliken Carges Q,e) R(H 3 3 3 N)

Q(H)

Q(O)

E

TMAS 3 3 3 (CH3)3SiOSiH3 NH3 3 3 3 (CH3)3SiOSiH3 DMA 3 3 3 DMDMADSO

2.25

0.106

0.540

4.25

2.32

0.103

0.535

7.27

2.52

0.114

0.523

6.91

DMA 3 3 3 (CH3)2Si(OSiH3)2

2.32

0.112

0.525

10.07

postreaction complex

Figure 5. Molecular structure of the prereaction complexes (a) HMDS 3 3 3 H3SiOH, (b) TMAS 3 3 3 H3SiOH, (c) DMADMS 3 3 3 H3SiOH, and (d) DMDMADSO 3 3 3 H3SiOH. The hydrogen bridge bonds are indicated by black dotted lines.

Table 3. Energies and Lengths of the Hydrogen Bonds between Silanol and Repair Molecules as Well as the Mulliken Charges of the Hydrogen and Nitrogen (Energy E, kJ/mol; Distance R, Å; Mulliken charges Q, e) prereaction complex

R(H 3 3 3 N)

Q(H)

Q(N)

E

HMDS 3 3 3 H3SiOH TMAS 3 3 3 H3SiOH

1.87

0.144

0.464

27.86

1.81

0.143

0.376

37.23

DMADMS 3 3 3 H3SiOH DMDMADSO 3 3 3 H3SiOH

1.74

0.142

0.136

33.05

1.75

0.127

0.127

31.99

’ RESULTS Wave Function Convergence. To test the accuracy of the basis set used, we have performed calculations with a DZVP and a triple-ζ Molopt basis set with two polarization functions (TZV2P). Table 1 shows the activation and reaction energies of the silyation from silanol with HMDS, calculated with the different basis sets. The differences of the reaction energies as well as the activation energies are smaller than 2.6 kJ/mol. Therefore, an adequate accuracy can be achieved by using the DZVP basis set. Since NEB calculations are computationally very demanding, all other calculations are carried out using a DZVP basis set. Geometry Optimization. The geometries of all educts and products of eqs 14 have been optimized, until the remaining HellmannFeynman forces are smaller than 25 meV/Å. To confirm the results of our calculations, we have compared the geometry of HMDS with experimental and theoretical data (Table 2). Our structural results are in good agreement with other works. The calculated bond lengths are slightly larger than in the experiment. This is a typical result of the used GGA functional. The torsional angle dih(SiNSi-H) is only slightly different from zero. Therefore, the used methods describe the planar Si2NH skeleton very well. This is in full agreement with experimental26 and theoretical27 results. The structures of

HMDS, TMAS, and DMADMS are shown in Figure 3 for illustration. Minimum Energy Reaction Paths. To understand the reaction process of eqs 14, we have calculated the MERPs with the CI-NEB method. NEB methods determine a discrete representation of the MERP. One advantage of the CI-NEB is the determination of the TS, which coincides with the highest energy image of the calculated MERP. Moreover, NEB methods can discover pre- and postreaction complexes and possible further TSs, which is impossible with many classical TS search methods such as diagonalization of the Hessian. For each NEB we used more than eight images, where the first and the last points are optimized during the calculation. The starting geometries for the products and educts are constructed from the optimized geometries of the corresponding single molecules. As reaction coordinate, we use the cumulative root-mean-square deviation (CRMSD): vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k u N X uX t CRMSDk ¼ ð5Þ jrji rji 1 j2 i¼2

where CRMSDk is the CRMSD of the NEB image k, N the number of particles, and rij the position vector of the particle j and NEB image i, respectively. The calculated MERPs are shown in Figure 4. The energies of the first and the last points are the sum of the energies of the single molecules. One can see that pre- and postreaction complexes exist. All studied reaction paths show only one TS with significantly higher energy. The reaction path of HMDS with silanol shows a small increase in energy between 0 and 4 Å . This is a result of small rotations of the HMDS molecule due to the steric hindrance of the SiN bond by the six methyl groups; i.e., the energy change is only an electrostatic effect. Between 4 and 6.3 Å the formation of the TS complex proceeds, where the hydrogen of the OH group comes close to the nitrogen and the SiN bond is stretched. Beyond 6.3 Å the educts are formed. The MERP of TMAS with silanol possesses its prereaction complex directly ahead of the formation of the TS complex. In comparison with HMDS there is no rotation of the repair molecule. This may be a result of the lower steric hindrance effect. The MERPs of the two steps of the silylation process with DMADMS are slightly different from the MERPS of HMDS and TMAS with silanol. Both possess a second TS with a very small activation energy of 5.5 kJ/mol for DMADMS 3 3 3 H3SiOH and 3.1 kJ/mol for DMDMADSO 3 3 3 H3SiOH. This is again a result of changes in the electrostatic potential due to some rotations of the repair molecules; i.e., there are no changes in the NSi, OH, and SiO bond lengths. The impact of these small TSs to the reaction rate can be neglected, because the TS energies at 7.8 and 10.5 Å, for DMADMS 3 3 3 H3SiOH and 8285

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Table 5. Typical Interatomic Distances in TSs as Well as Their Mulliken Charges (Distances R, Å; Mulliken Charges Q, e) TS

R(O 3 3 3 H)

R(O 3 3 3 Si)

R(Si 3 3 3 N)

R(N 3 3 3 H)

Q(N)

1.55

2.18

1.95

1.08

0.283

1.50

2.23

1.93

1.09

0.110

HMDS 3 3 3 H3SiOH TMAS 3 3 3 H3SiOH DMADMS 3 3 3 H3SiOH

1.52

2.25

1.98

1.08

0.071

DMDMADSO 3 3 3 H3SiOH

1.60

2.24

1.95

1.07

0.083

Table 6. Reaction and Activation Energies of the Different Silylation Reactions (kJ/mol) reaction

reaction energy

activation energy

HMDS + H3SiOH

34.10

110.17

TMAS + H3SiOH

36.55

105.31

DMADMS + H3SiOH

43.02

84.83

DMDMADSO + H3SiOH

46.99

71.13

DMDMADSO 3 3 3 H3SiOH, respectively, are much higher (larger than 71.13 kJ/mol). But the existence of these TSs shows that the energy landscape is more puckered due to the higher complexity of the molecules. Altogether our calculations show that all four calculated MERPs correspond to elementary reactions; i.e., they proceed in one single step. Pre- and Postreaction Complexes. As mentioned before, the silylation reactions 14 possess pre- and postreaction complexes. All prereaction complexes are formed by a hydrogen bond between the OH group of the silanol and the nitrogen of the repair molecule (see Figure 5). We obtained energies of the hydrogen bond between 24.65 and 37.23 kJ/mol. The strongest hydrogen bond is found between silanol and TMAS (Table 3). Furthermore, we found postreaction complexes in all calculated MERPs. The energy gain due to the formation of these complexes is between 4.25 and 10.07 kJ/mol (see Table 4). In all postreaction complexes the hydrogen atom of the HN bond is orientated toward the oxygen. Therefore, the energy gain is mainly an electrostatic effect. Due to the fact, that the energies are very small and the (H 3 3 3 O) distances are relatively large, the postreaction complexes play no important role in the praxis. At room temperature the products should exist separately. Therefore, no additional activation energy will be necessary to remove the nitrogen compounds from the ULK material after the repair process. Transition States. As mentioned before, during the silylation process a proton transfer from the OH group of the silanol to the nitrogen of the silazane molecule occurs. This is accompanied by an increasing SiN bond length and the formation of a siloxan bond. To give an explanation for the different activation energies, we inspect the geometry of the corresponding TSs. In particular the most changing interatomic distances, which are the O 3 3 3 H distance, the H 3 3 3 N distance, the Si 3 3 3 N distance, and the OSi distance between the silanol and the silicon atom of the stretched Si 3 3 3 N bond, are compared in Table 5. In all TSs the transfer of the hydrogen to the nitrogen atom is nearly completed, which means that it is chemically bound to the nitrogen atom. The inspection of the Mulliken charges of the prereaction complexes (see Table 3) and TSs (see Table 5) shows that all reactions occur with a proton transfer. The O 3 3 3 H distance lies

between 1.50 and 1.60 Å, which is a typical hydrogen bond length. Due to the same reaction mechanism, all TSs possess similar geometries. Reaction and Activation Energies. In a first-order approach we identify the free reaction energy with the reaction energy, which is the most important parameter for the proceeding of a reaction. The reaction energies are calculated as differences of the energies of the pre- and postreaction complexes. A second characteristic parameter of the reaction is the activation energy, because it is the most limiting factor for the velocity of a reaction. We calculate the activation energies from the differences of the TS and prereaction complex energies. The calculated energies are shown in Table 6. All reaction energies are negative, which means that the corresponding reactions are exothermic. The reaction of DMADMS with silanol and its consecutive reaction are more exothermic compared to the silylation reaction of HMDS and TMAS. Furthermore, the activation energies of the silylation reaction with DMADMS and its consecutive reaction are smaller. Therefore, the silylation with DMADMS should proceed faster and more efficiently, which makes DMADMS an attractive repair chemical. A closer look at the Mulliken charges of the nitrogen atom of the prereaction complexes and the TSs (see Table 3 and Table 5) compared to the activation energies (see Table 6) shows that the activation energy decreases with increasing Mulliken charge of the nitrogen atom. This appears to be reasonable, because a more negative nitrogen atom leads to a higher SiN bond energy due to the electrostatic interaction with the positive silicon atom. Summary. We have investigated the silylation reactions of different silazanes with silanol using ab initio methods. In particular we have calculated the MERPs of the respective reactions using the CI-NEB method. All reactions show negative reaction energies, which implies exothermic reactions. This shows that silazanes are promising candidates to restore the k-value in ULK materials due to the silylation of OH groups. A close inspection of the MERPs shows that the studied silazanes tend to build prereaction complexes with OH groups. Therefore, silazanes may be used as passivation molecules, to protect damaged ULK surfaces from moisture uptake. A direct comparison of the reaction and activation energies of the silylation reaction of HMDS and DMADMS shows that the silylation with DMADMS is more efficient. DMADMS reacts not only faster and the reaction is more exothermic but it also can avoid the well-known problem of the steric hindrance effect of HMDS and TMAS, which should make DMADMS a very attractive repair chemical for industrial usage. Moreover, we found that there is a direct impact of the partial charge of the nitrogen atom in silazanes on the reaction and activation energy of the OH-group silylation; i.e., an increasing Mulliken charge leads to decreasing activation and increasing reaction energies, which is an important fact for discovering new repair chemicals. 8286


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’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (O.B.); [email protected] (R.L.).

’ ACKNOWLEDGMENT This project has been funded in line with the technology funding for regional development (ERDF) of the European Union and by funds of the Free State of Saxony (SAB F€ordervorhaben Grant No. 13507). ’ REFERENCES (1) Singer, P. Semicond. Int. 1998, 21, 90. (2) Maex, K.; Baklanov, M. R.; Shamiryan, D.; Iacopi, F.; Brongersma, S. H.; Yanovitskaya, Z. S. Appl. Phys. Rev. 2003, 93, 8793. (3) Gates, S. M.; Neumayer, D. A.; Sherwood, M. H.; Grill, A.; Wang, X.; Sankarapandian, M. J. Appl. Phys. 2007, 101, 094103. (4) Chapelon, L. L.; Arnal, V.; Broekaart, M.; Gosset, L. G.; Vitiello, J.; Torres, J. Microelectron. Eng. 2004, 76, 1. (5) Kwak, S.; Jeong, K.; Rhee, S. J. Electrochem. Soc. 2004, 151, F11. (6) Smirnov, V. V.; Stengach, A. V.; Gaynullin, K. G.; Pavlovskya, V. A.; Raufb, S.; Ventzek, P. L. G. J. Appl. Phys. 2007, 101, 053307. (7) Leitsmann, R.; B€ohm, O.; Pl€anitz, P.; Radehaus, C.; Schaller, M.; Schreiber, M. Surf. Sci. 2010, 604, 1808. (8) Lee, S.; Woo, J.; Jung, D.; Yang, J.; Boo, J.; Kim, H.; Chae, H. Thin Solid Films 2009, 517, 3942. (9) Chaabouni, H.; Chapelon, L. L.; Aimadeddine, M.; Vitiello, J.; Farcy, A.; Delsol, R.; Brun, P.; Fossati, D.; Arnal, V.; Chevolleau, T.; Joubert, O.; Torres, J. Microelectron. Eng. 2007, 84, 2595. (10) Gun’ko, V. M.; Vedamuthu, M. S.; Henderson, G. L.; Blitz, J. P. J. Colloid Interface Sci. 2000, 228, 157. (11) Rajagopalan, T.; Lahlouh, B.; Chari, I.; Othman, M. T.; Biswas, N.; Toma, D.; Gangopadhyay, S. Thin Solid Films 2008, 516, 3399. (12) Kondoh, E.; Asano, T.; Arao, H.; Nakashima, A.; Komatsu, M. Jpn. J. Appl. Phys. 2000, 39, 3919. (13) Perdew, J.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (14) VandeVondele, J.; Krack, M.; Mohamed, F.; Parrinello, M.; Chassaing, T.; Hutter, J. Comput. Phys. Commun. 2005, 167, 103. (15) Zhao, Y.; Truhlar, D. G.; Chari, I.; Othman, M. T.; Biswas, N.; Toma, D.; Gangopadhyay, S. Theor. Chem. Acc. 2008, 120, 225 (Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue). (16) VandeVondele, J.; Hutter, J. J. Chem. Phys. 2007, 127, 114105. (17) Goedecker, S.; Treter, M.; Hutter, J. Phys. Rev. B 1996, 54, 1703. (18) Braslavsky, S. E. Pure Appl. Chem. 2007, 79, 370. (19) Jonsson, H.; Mills, G. Phys. Rev. Lett. 1994, 72, 1124. (20) Mills, G.; Jonsson, H.; Schenter, G. K. Surf. Sci. 1995, 324, 325. (21) Jonsson, H.; MillsG.Jacobsen, K. W. Nudged Elastic Band Method for Finding Minimum Energy Paths of Transitions. In Classical and Quantum Dynamics in Condensed Phase Simulations. Proceedings of the International School of Physics; Berne, B. J., Ciccotti, G., Coker, D. F.; World Scientific: Singapore, 1998. (22) Henkelmann, G.; Uberuaga, B.; Jonsson, H. J. Chem. Phys. 2000, 113, 9901. (23) Henkelmann, G.; Jonsson, H. J. Chem. Phys. 2000, 113, 9978. (24) Fjeldberg, T. J. Mol. Struct. 1984, 112, 159. (25) Olson, E. W.; Standard, J. M. J. Mol. Struct. 2005, 719, 17. (26) Robiette, A. G.; Sheldrick, G. M.; Sheldrick, W. S.; Beagley, B.; Cruickshank, D. W. J.; Monaghan, J. J.; Aylett, B. J.; Ellis, I. A. Chem. Commun. (London) 1968, 909. (27) Fleischer, H.; McKean, D. J. Phys. Chem. A 1999, 103, 727.

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Annual Report 2011

December 2011 EPL, 96 (2011) 60015 doi: 10.1209/0295-5075/96/60015

www.epljournal.org

Time-optimal controls for frictionless cooling in harmonic traps K. H. Hoffmann1(a) , P. Salamon2 , Y. Rezek3 and R. Kosloff3 Institut f¨ ur Physik, Technische Universit¨ at Chemnitz - D-09107 Chemnitz, Germany Department of Mathematical Sciences, San Diego State University - San Diego, CA 92182-7720, USA 3 Fritz Haber Research Center for Molecular Dynamics, Hebrew University of Jerusalem Jerusalem 91904, Israel 1

2

received 21 July 2011; accepted in final form 14 November 2011 published online 15 December 2011 PACS PACS PACS

02.30.Yy – Control theory 05.10.-a – Computational methods in statistical physics and nonlinear dynamics 37.10.Jk – Atoms in optical lattices

Abstract – Fast adiabatic cooling procedures have important implications for the attainability of absolute zero. While traditionally adiabatically cooling a system is associated with slow thermal processes, for the parametric quantum harmonic oscillator fast frictionless processes are known, which transfer a system from an initial thermal equilibrium at one temperature into thermal equilibrium at another temperature. This makes such systems special tools in analyzing the bounds on fast cooling procedures. Previous discussions of those systems used frictionless cooling assuming real frequencies of the oscillator. Using a control with imaginary frequencies (repulsive potential) revises previous implications for the possible operation of a quantum refrigerator. Here we discuss these requisite revisions in the context of the third law of thermodynamics. In addition to minimum time controls, which are always of the bang-bang form, fast frictionless processes with a continuous variation of the frequency have been presented previously in the literature. Such continuous variation controls have been experimentally verified by cooling a Bose-Einstein condensate, while minimum time controls still await verification. As some implementations may indeed not be able to implement the instantaneous jumps in frequency required by bang-bang controls, constraining the rate of change in the frequency calls for ramped bang-bang solutions. We present such solutions and compare their performance to the continuous controls used in the experiment. c EPLA, 2011 Copyright

The third law of thermodynamics is also called the unattainability principle [1–4]. In a dynamical interpretation absolute zero is unattainable as the cooling rate from a thermal bath with falling temperature declines as well and approaches zero together with an appropriate power of the temperature [5]. The relation of the cooling rate to the bath temperature depends crucially on the thermodynamic cooling process used. In particular, the times needed for cooling processes in an adiabatic fashion are important. In that context the frictionless cooling of particles in harmonic traps, which gained a lot of recent attention (see [6–16] and references therein), are of relevance. Here the interesting question is how these processes can be performed in the minimum time. A number of different methods have been suggested and implemented [6–8,10,17]. We feel it fair to say that the problem has turned out to be much richer than initially imagined. Our previous study considered only the case (a) E-mail:

[email protected]

where the particles are confined by attractive harmonic potentials [17]. It turns out that allowing the potential to become repelling during the process can achieve even shorter times [6–8,10,11]. When the potentials can become arbitrarily strong, frictionless transfer can be achieved in zero time [6,7,11]. We note however that this would require the energy of the oscillator to become infinite. It is natural to set bounds on the strength, i.e. the curvature, of achievable potentials but at large values of such a bound a new complication arises. Stefanatos et al. [11] have shown that the structure of the minimum time solution changes at sufficiently large values of the bound insofar as more jumps in the frequency outperform the three-jump solutions that are optimal for more moderate values of the largest frequency achievable in the control. Here we focus on such problems for which three-jump controls are optimal. This applies for example when the initial frequency coincides with the maximum allowed frequency, the case of interest for refrigeration. As argued in [5] the maximum allowed frequency is used as the initial

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K. H. Hoffmann et al. state for the adiabatic cooling branch to ensure maximum population in the ground state. Our previous solution was correct for this case, provided imaginary frequencies are used in the formulas (28) and (29) presented in [17]. The aim of this paper is twofold. Our first aim is to discuss the implications of the optimal three-jump bangbang control on the cooling rate of a quantum refrigerator. Contrary to the restrictions in [17] we here allow the potential to become repelling, which leads to much larger cooling rates. The second aim of this paper is to consider the addition of continuity requirements for the controls. Such requirements have been implemented by a number of authors based on Ermakov invariants added to the control problem and have resulted in smooth controls which have been tested empirically [7,8,10,11,15]. Here we take a different approach which directly constrains the rate with which the potential can be changed. We present a special type of optimal control, which we call ramped bang-bang. Such ramped bang-bang control considerably shortens the time needed to achieve a frictionless transition from one thermal state to one at a different temperature when compared to continuous controls obtained from the approach advocated by Chen et al. [7,8] based on Ermakov invariants. In this paper we analyze the parametric harmonic oscillator, i.e. a particle of mass m in a quadratic, timedependent potential. Its Hamiltonian is given by ˆ 2. ˆ = 1 Pˆ 2 + 1 k(t)Q (1) H 2m 2 As we will allow the potential to become repelling we use the force constant k(t) instead of the frequency ω(t) = k(t)/m which will become imaginary in that case. The dynamics can be completely described by the expectation values of three time-dependent operators: namely the expectation values of the momentum squared ˆ 2 , and the correlation Pˆ 2 , the position squared Q ˆ ˆ ˆ ˆ ˆ D ≡ QP + P Q. These will be collective labelled as x = ˆ 2 , D). ˆ (Pˆ 2 , Q Substituting these operators into the Heisenberg-equation and taking expectation values leads to three linear coupled differential equations, describing the dynamics that we need to control ˙2 ˆ Pˆ = f1 (x, k) = −k(t)D, 2 ˆ ˆ˙ = f2 (x, k) = D/m, Q ˆ 2 . ˆ˙ = f3 (x, k) = 2Pˆ 2 /m − 2k(t)Q D

(2) (3) (4)

Starting from a thermal equilibrium with ki , our goal is to reach the target state, thermal equilibrium with kf , in minimal time tf tf f0 (x, k)dt = dt. (5) ti

ti

ˆ i,f ) = 0 and Pˆ 2 (ti,f ) Thermal equilibrium implies D(t 2 ˆ and Q (ti,f ) have to fullfill the equipartition requireˆ 2 (ti,f ). ment, i.e. Pˆ 2 (ti,f )/m = k(ti,f )Q

For the parametric oscillator the desired state transition is achieved by a suitable control of the force constant k(t). We first turn to the case where the control k(t) is limited in size by kmin k(t) kmax . Experimentally this amounts to a maximum confining potential in a harmonic trap, or conversely, to a maximum repelling potential. Thus the control is free to vary within these constraints, but cannot exceed them. In order to find the fastest adiabatic transition we solve an optimal control problem, with the dynamics eqs. (2)–(4) as constraints. The technical details of that problem were discussed in [17], so we here restrict ourselves to the important features of that control problem. The objective of the control problem f0 (x, k) = 1 is especially simple. The linear dependence of the dynamics on the control k(t) leads to a linear dependence of the control Hamiltonian H, H=

λn fn (x, k) = H0 + σk,

(6)

n=0

where the λn are the adjoint variables, and H0 and σk are the two terms of H, which are zeroth and first order in k respectively. The Pontryagin maximality principle [18] requires that the value of the control must maximize H. Thus when the switching function σ, i.e. the coefficient of the control, is positive, k must be as large as possible and when σ is negative, k must be as small as possible. Since away from the constraints set by the inequalities kmin k(t) kmax the value of k is not constrained, this amounts in our problem to jumps in k. Such jumps must terminate on the boundary arcs k(t) = kmax or k(t) = kmin which can be used as segments of the optimal trajectory. In addition to jumps and boundary arcs, the optimal control for such problems can also have singular branches [17,19,20], along which the switching function σ vanishes identically over a time interval. For this problem, however, we can prove directly that singular branches are never included in the optimal control which must therefore be of the bangbang type, jumping between and waiting at the extreme allowed k’s. The proof is presented in [17,21], which shows that continuously varying k(t) can never be part of an optimal control. For a further discussion of singular control problems we refer the reader to [22] for quantum problems in general and to [23,24] for spin control problems in particular, for classical systems see [25,26]. The number of jumps needed to reach our target state turns out to be three. However, depending on the size of kmax multi-jump bang-bang controls with more than three jumps can outperform the three-jump control [27]. For the discussion here, we restrict ourselves to the threejump control which allows a closed-form description and which is the only case of interest for use in refrigeration for which we always want ki = kmax . Cooling the system by a three-jump control requires a jump from the initial ki to the minimum possible k1 = kmin , hold k constant for a wait time τ1 , then jump to the maximum possible k2 = kmax , hold k constant for a wait time τ2 , and finally

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Time-optimal controls for frictionless cooling in harmonic traps to determine the temperature dependence of the cooling rate as the temperature of the cold bath approaches zero. 2 For the temperature dependence of the cooling rate it is 1.0 important to know how the times τ1 and τ2 vary as kf approaches zero. As already pointed out, both times can 0.5 become arbitrarily small if k1 = −k2 approaches infinity for fixed kf . However, if we choose fixed k1 and k2 and 0.0 then vary kf things are different. In that case it can be 0.0 0.2 0.4 0.6 0.8 1.0 shown that τ1 diverges with −log kf as the leading term kf while τ2 remains finite. For the special choice k1 = −ki and Fig. 1: (Colour on-line) For the optimal three-jump bang- k2 = −k1 one obtains 1.5

1

bang control the two waiting times τ1 and τ2 are shown for ki = −k1 = k2 = 1. Note that τ1 diverges for kf → 0.

jump to kf . This leaves us with two wait times τ1 and τ2 as adjustable parameters. Adjusting these times allows us to reach the target state in the minimum time. Summerizing the optimal three-jump bang-bang solution is ⎧ ⎪ ⎪ki , for t = 0, ⎨ k1 , for 0 < t τ1 , (7) k3J (t) = k2 , for τ1 < t < τ1 + τ2 , ⎪ ⎪ ⎩ kf , for t = τ1 + τ2 . For any values of the intermediate frequencies k1 and k2 , the values of τ1 and τ2 given in [17] can be used by allowing ω 2 to become negative 1

Arccosh(r1 ), τ1 = 2 −k1 /m

(8)

1 Arccos(r2 ), τ2 = 2 k2 /m

(9)

√ √ 2k1 (k2 + kf ) ki − (k1 + k2 )(k1 + ki ) kf √ , (k2 − k1 ) kf (k1 − ki ) √ √ 2k2 (k1 + ki ) kf − (k1 + k2 )(k2 + kf ) ki √ . r2 = (k1 − k2 ) ki (k2 − kf )

− log(kf /ki ) , 4 ki /m

(12)

π τ2 = . 4 ki /m

(13)

This leads to implications for the cooling rate R. Let τc and τh be the times spent in contact with the cold and hot heat bath, respectively, and let τadi = 2(τ1 + τ2 ) be the time needed for the adiabats. Further denote the population (i.e. the expectation of the number operator) for a system in equilibrium with the cold or hot (i = c, h) temperature bath by ωi

kb T i − 1). neq i (ωi , Ti ) = 1/(e

(14)

Following the same approach as in [5] one finds R = F (τc , τh , τadi )G(ωc , ωh , Tc , Th ),

(15)

eq G(ωc , ωh , Tc , Th ) = ωc (neq c − nh )

(16)

with and

where r1 =

τ1 =

F (τc , τh , τadi ) =

(10)

(11)

Here we made already use of the fact that in the follow< 0. For the case of cooling ( kf /m = ωf < ωi = ing k 1 ki /m), the smaller k1 and the larger k2 are, the faster the process. The fastest three-jump process with τ1 = τ2 = 0 is obtained in the limit −k1 = k2 → ∞. In order to make contact with experiments [28] the following values were usedby [7]: ωi = 250 × 2π Hz and ωf = 2.5 × 2π as well as γ = ωi /ωf = 10. In fig. 1 we show how the times τ1 and τ2 change as a function of kf for the case k2 = −k1 . The choice to set k1 = −k2 is motivated by the fact that the same harmonic potential can be made repelling or attractive by a phase shift in case it is created by an optical lattice. The bang-bang control presented above is of relevance in a dynamical interpretation of the third law. In [5] optimal bang-bang controls were used in a quantum refrigerator

(eΓτc − 1)(eΓτh − 1) , − 1)(τadi + τc + τh )

(eΓτh +Γτc

(17)

where Γ is the relaxation rate for establishing thermal equilibrium while in contact with a bath. Maximizing F with respect to the relative size of the isochoric times leads to τc = τh , which allows us to introduce z ≡ Γτc = Γτh . We can now ask how much time we should spend on the isochores (z) for a given time spent on the adiabats (τadi ), by setting the derivative of F with respect to z to zero. This yields the equation 2z + Γτadi = Sinh(z).

(18)

Taking the limit where the time spent on the adiabats is long, this equation becomes Γτadi ≈ ez /2. Within that approximation we can rewrite R as R∗ = G(ωc , ωh , Tc , Th )/τadi .

(19)

We now want to find an upper bound on R∗ for Tc decreasing towards zero. To find such a bound we maximize R∗ for fixed Th and ωh with respect to ωc . Note that G as

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K. H. Hoffmann et al. 0

80

oscillator in finite time. Such controls have also been used experimentally [10]. The control is based on the existence of invariants of motion [29–32] for a harmonic oscillator. These invariants depend on a function of time b(t), which is intimately connected to the time-dependent frequency of the oscillator via an Ermakov equation

100

¨b + ω(t)2 b = ω 2 /b3 . i

20 40 60

120 140 140 120 100

80 60 log Tc

40

20

0

Fig. 2: (Colour on-line) The optimal frequency ωc,opt in a quantum refrigerator decreases close to linearly with decreasing Tc . 1.9 1.8 1.7 Aopt 1.6 1.5 1.4 − 140 − 120 − 100 − 80 − 60 log Tc

− 40

− 20

0

Fig. 3: (Colour on-line) The maximum cooling rate Ropt decreases roughly as −Tc /log Tc . Here Aopt = Ropt (−log Tc )/Tc is shown.

well as τadi depend on ωc . This leads to a transcendental equation for ωc , which suggests ωc,opt ∝ Tc for small Tc . Figure 2 shows ωc,opt as a function of Tc . The close to diagonal graph supports the above suggestion. Inserting ωcopt ∝ Tc into R∗ would then lead to Ropt ∝ −Tc /log Tc . This is checked in fig. 3, where Aopt =

− log Tc opt R Tc

(20)

is shown as a function of Tc , showing the slightly lower decrease within the range analyzed. This is consistent with the hypothesis that the third law constrains the cooling rate beyond the requirements due to the second law, and is the closest approach to the rate expected from the second law yet. We note however that further requirements on the adiabatic cooling process might lead to slower cooling rates than Ropt ∝ −Tc /log Tc . In [8] the effect of limits on the time averaged energies of the oscillator levels during the adiabatic move are discussed showing that such requirements lead to the same limitations on the cooling rate as the requirement of positive intermediate frequencies. We now turn to our second aim, namely controls with a continuity requirement. In a recent paper by Chen et al. [7,8] a smooth control was suggested which allows an adiabatic transition between thermal states of a harmonic

The function b(t) is dimensionless and scales with the time tf , which is available to change the system from a thermal equilibrium state at t = 0 with ω(0)2 = ωi2 = k(0)/m = ki /m to the final equilibrium state at t = tf with ω(tf )2 = ωf2 = k(tf )/m = kf /m. The reduction in the frequency ratio corresponds to the reduction in temperatures and is characterized by γ = ωi /ωf . In order to insure a continuous k(t) = mω(t)2 at t = 0 and at t = tf with k(t) = ki for t < 0 and k(t) = kf for t > tf b(t) must ˙ fulfill b(0) = 1, b(0) = 0, and ¨b(0) = 0 as well as b(tf ) = γ, ˙ f ) = 0, and ¨b(tf ) = 0. In [7] a polynomial ansatz fullb(t filling the above conditions is presented b(t) = 6(γ − 1) (t / tf )5 − 15(γ − 1)(t / tf )4 + 10(γ − 1)(t / tf )3 + 1. Based on this ansatz the ensuing continuous control kC (t, tf ) —called C-control in the following— can be determined from eq. (21). Note that kC (t, tf ) will depend on t and tf separately, and not only on t/tf . For each tf this control can now be compared to the optimal three-jump bang-bang control. As both controls allow the transition in arbitrarily short time provided that also a negative k, i.e. a repelling potential, is allowed, one needs to compare the controls for the same system constraints. These constraints are given by the ability to control k(t) during the transition, i.e. the extreme values reachable for k. max (tf ) = For a given kC (t, tf ) we thus determine kC min max01500°C) auf der Basis von Schottky-Kontakten", AIF "Erweiterte Methoden zur Nanocharakterisierung" (SMINT), DFG "Erzeugung und Untersuchung spintronischer Schichtsysteme", SAB Project "Spintronik" "Femtosecond Quantum Optics with Semiconductor-Metal Schwerpunktprogramm "Ultrafast Nanooptics"

Hybrid

Nanostructures",

DFG-

“Driven Diffusion in Nanoscaled Materials”, DFG-Forscherguppe "From Local Constraints to Macroscopic Transport" "Großserienfähige Produktionstechnologien für leichtmetallund faserverbundbasierte Komponenten mit integrierten Piezosensoren und –aktoren (PT-PIESA)", Teilprojekt A3: Dünnschichttechnologien für metallbasierte piezoelektrische Module, DFG-Sonderforschungsbereich / Transregio 39 "Growth, Structure, and Magnetic Properties of FePt Nanostructures on NaCl(001) Surfaces", DAAD Project (Frankreich), DAAD "Grundlegende Erforschung eines neuen kostengünstigen Erzeugung von Solarzellen auf Silizium-Basis", BMBF

Verfahrens

zur

drucktechnischen

"Halbleiternanopartikel als berührungsfreie optische Sonden in organischen Feldeffekttransistoren", DFG-Einzelantrag "In-Line Solarzellen-Fertigung auf Siliziumbasis (SoSi)", SMWA "Interplay between microscopic structure and intermolecular charge transfer processes in polymerfullerene bulk-heterojunctions", DFG-Schwerpunktprogramm "Elementarprozesse der Organischen Photovoltaik" "Local-field enhancement of magneto-optical effects in magneto-plasmonic nanostructures", DAAD Project (Ukraine) "Lyapunov instability of large dynamical systems: methods and application", DFG-Einzelantrag "Magnetische Mikro-/Nanostrukturen für Sensor-Anwendungen", DFG-Forscherguppe „Sensorische Mikro- und Nanosysteme“ "Magnetisches Kraftmikroskop (HR-MFM)", Forschungsgroßgerät "Magnetismus von nanoskaligen schränkten Dimensionen", DFG

- 152 -

CoCrPt-SiO2-Filmen

in

templatbedingt

geometrisch

einge-

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"Materialien und Konzepte für fortschrittliche Metallisierungssysteme", IRTG (Teilprojekt), DFG "Materials and Concepts Graduiertenkolleg, DFG

for

Advanced

Interconnects

and

Nanosystems",

Internationales

"Neuartige austauschgekoppelte Nanomagnete", D.A.CH. Project "Nukleation von Spinordnung in niederdimensionalen kollodialen Partikelsystemen", DFG "Oblique angle deposition by Fe-Ni film growth onto curved surfaces", DAAD Project (India) "Physics of high energy ion generation during explosive and thermo-magnetic instabilities in laser plasmas", DAAD "Physikalische Grundlagen des In-Mold Printing", Teilprojekt zum DFG-Projekt "Integration von Drucktechnologien in den Spritzgießprozess", DFG "Präparation und Charakterisierung ein- und zweidimensionaler optisch aktiver Nanostrukturen mittels Rastersondenlithographie", DFG "Präparation und Charakterisierung nanostrukturierter Magnetwerkstoffe Berücksichtigung des Exchange Bias-Effekts", Landesinnovationspromotion

unter

besonderer

"Prozessstabilität spanender Bearbeitungsprozesse", BMBF-Verbundprojekt VispaB "Quantum Dot Spins in High-Q Optical Resonators: Schwerpunktprogramm "Semiconductor Spintronics"

Spin

Meets

Cavity

QED",

DFG-

"Raman Investigations of In(Ga)As/Al(Ga)As self-assembled quantum dot structures: from ensembles to single quantum dots", DFG "Resonance- and plasmon-enhanced optical spectroscopy of semiconductor semiconductor-metal nanoparticles", Alexander von Humboldt Stiftung

and

coupled

"Sensorische Mikro- und Nanosysteme, DFG-Forschergruppe, DFG "Software für parallele irreguläre Algorithmen" - Projekt: "TP 2: Effiziente Simulationsmethoden für Anomale Diffusion auf zufälligen Fraktalen", DFG "Spektroskopische Untersuchungen von magnetischen Forschergruppe „Towards Molecular Spintronics“

molekularen

Materialien",

DFG

"Spitzenforschung und Innovation in den Neuen Ländern - Kompetenznetzwerk für Nanosystemintegration", TP: Nanoskalige Materialsysteme, NEMS/MEMS-Systemintegration und materialintegrierte Sensorik, BMBF Kompetenznetzwerk NANETT "Static and dynamic properties of curved multilayer nanomagnets on self-assembled particles", FGNSF Project (MWN) "Statistical Analysis of Bibliometric Indices", DAAD PPP mit Griechenland (IKYDA) "Strukturelle und magnetische Eigenschaften von FePdCu Legierungen", DAAD Project (Polen) "Synthese und Modifizierung siliziumorganischer Verbindungen zur Herstellung photovoltaisch aktiver, nanostrukturierter Schichten", SMWK "Tailoring light-matter coupling for femtosecond quantum optics with single defect centers in diamond", Research Group of the German Science Foundation (DFG) "Diamond Materials and Quantum Application", DFG "Terabit Magnetic Storage Technologies", EU Project "TERAMAGSTOR", EU "Towards Molecular Spintronics", DFG-Forschergruppe, DFG "Tuning Molecular Architectures at the Liquid-Solid Interface by Controlling Solvent Polarity and Concentration of Molecules", DAAD-Promotionsstipendium "Zwillingspolymerisation", DFG-Forschergruppe, DFG

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Industrial collaborations

AQcomputare Gesellschaft für Materialberechnung mbH, Dr. Philipp Plänitz, Chemnitz, "Silylation of hydroxil groups" ASMEC, Radeberg (www.asmec.de) Fraunhofer-Institut für Elektronische Nanosysteme (ENAS) Chemnitz, "Nanokomposit-basierte lowcost Sensoren" Globalfoundries, Module Two GmbH & Co. KG, M. Schaller, Dresden, "Ultra-low k surfaces" GWT-TUD GmbH, Andreas Werner, Chemnitz, "Ab initio Tunnelstromberechnung" Hitachi GST, San Jose, USA, "Magnetic recording materials and concepts" INNOVENT e. V. Technologieentwicklung Jena Leica Microsysteme Handelsgesellsch. m. b. H. Wien, Österreich, Demo Lab in Physics Building MICROTEC Gefell GmbH, "Beschichtung von Ni-Membranen mit Kohlenstoff, Abscheidung von Korrosionsschutzschichten auf Mikrofonmembranen, Untersuchungen an Mikrofonkapseln mittels Lichtmikroskopie, SEM und EDX, Untersuchung der Zusammensetzung von Targetmaterialien mittels EDX" NRU GmbH, INOVAP Innovative Vakuum- und Plasmatechnik GmbH Dresden, Porzellanfabrik Hermsdorf, TRIDELTA Thermporzess, DOIT Mechatronik GmbH, "Entwicklung eines neuen adaptierbaren HochTemperaturMessSystems (HTMSys) zur Kontaktmessung in hochtemperaturigen flüssigen und gasförmigen Medien", OC Oerlikon Balzers AG (Balzers, FL), "Thermoelectrica" Robert Bosch GmbH, "Virtualisierung der spanenden Bearbeitung in der Maschinenentwicklung und der Prozessoptimierung"

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Teaching

Courses offered by the Institute of Physics: x x x

Physics Computational Science Sensors and Cognitive Psychology

Bachelor Bachelor Bachelor

Master Master

Diploma

WS 2010/2011: hours per week

VL - Vorlesung, Ü – Übung, P - Praktikum S- Seminar, T - Tutorium

VL

Ü

Anleitung zum Computerpraktikum

1

1

Atome - Moleküle

4

Computational Science: Strukturen

3

Computergestützte Datengewinnung Computerphysik/Irreversible Prozesse

S

4

4

2

2

4

2 2

2

Einführung in die Nichtlineare Dynamik

3

Elektrodynamik

4

4

Elektrodynamik-Optik

4

2

3

2

Empirisch-Experimentelles Forschen, Gruppe 1

20

Experimentalphysik: Komplexe Materialien

2

3

Kerne und Elementarteilchen

2

1

Kognition

2

Laborpraktikum (Orientierungspraktikum) Magnetismus

6 4

Mathematische Grundlagen

2 4

Mechanik, Thermodynamik, Elektrodynamik, Optik

4

14

Mechanik-Thermodynamik

4

4

Messen, Interpretieren, Verarbeiten

T

3

Computerpraktikum Device-Related Solid State Physics II

P

1

4 12

6 2

4

Methodenpraktikum Analytik an Festkörperoberflächen

6

Methodenpraktikum Chemische Physik

6

Methodenpraktikum Dynamik nanosk. und mesosk. Strukturen

6

2

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Annual Report 2011

Methodenpraktikum Halbleiterphysik

6

Methodenpraktikum Komplexe Systeme und Nichtlineare Dynamik

6

Methodenpraktikum Oberflächen- und Grenzflächenphysik

6

Methodenpraktikum Optische Spektroskopie und Molekülphysik

6

Methodenpraktikum Physik dünner Schichten

6

Methodenpraktikum Physik fester Körper

6

Methodenpraktikum TP – Simulation neuer Materialien

6

Methodenpraktikum Theoretische Physik – insb. Computerphysik

6

Methodenpraktikum Theorie ungeordneter Systeme

6

Nanophysics - Physics of mesoscopic systems

2

1

Oberseminar

1

Physik

2

3

Physik (mit Experimenten)

6

18

Physik Teil 1 Mechanik und Thermodynamik

2

1

Physikalisches Kolloquium

2

4

Physikalisches Praktikum (Fortgeschrittenenpraktikum)

8


6

Physikalisches Praktikum (Gruppe 1)

24

Scientific English for Scientists

2 2

Statistische Physik ökonomischer Prozesse I

2

Struktur und Eigenschaften kondensierter Materie

1 1

Studentisches Tutorium

2

Surfaces, Thin films and Interfaces

2

Theoretische Mechanik / Quantenmechanik

4

Theoretische Physik (Kontinuumsphysik)

4

Tutorien für CS, Ph und SeKo

- 156 -

1 4 4 13

Annual Report 2011

SS 2011:

VL

Atome - Moleküle

2

Ausgewählte Kapitel der modernen Physik

2

Computational Science: Prozesse

3

Ü

P

S

1

3

Computergestützte Datenauswertung

2

2

Computergestützte Datengewinnung

2

2


4

4

4

Energie und Energiewandlung Geschichte der Physik

2 4

2

Informatik 2

6

4


2

1

Kondensierte Materie

2

1

Mathematische Grundlagen Mechanik, Thermodynamik, Elektrodynamik, Optik

2 4

2

2 12


6


6

Methodenpraktikum Dynamik nanoskop. und mesoskop. Strukturen

6


6


6


6


6


6


6


6

Methodenpraktikum Theoretische Physik – insbesondere Computerph

6


6

Microscopy and analysis on the nano scale

T

4

Nanophysik

1 2

Naturwissenschaftliche Grundlagen der Sensorik

2

Numerik für Physiker

2

2

1 4

1

Oberseminar

2

Physik

2


1

Physik Teil 2 Elektrizitätslehre und Optik

2

2

2 8

2

4

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Annual Report 2011

Physik tiefer Temperaturen/Ordnungsphänomene Physikalisches Kolloquium

2

1

2


12

Physikalisches Praktikum (in 4 Gruppen)

2

Polymerphysik

2

Quantenmechanik

4

Relativistische Physik - Allgemeine Relativitätstheorie

2 2

1

Scientific English for Scientists Semiconductor physics / Nano structures

2 3

1

Spezialisierungspraktikum

72

Stochastische Prozesse

3

9

Struktur der Materie

4

8

4


1

TP1: Analyse theoretisch-physikalischer Probleme Thermodynamik/Statistische Physik

1

4

2

2

2

6


14

Vertiefungspraktikum

8

WS 2011/2012:

VL

Ü

Anleitung zum Computerpraktikum

1

1

Atome - Moleküle

4

Computational Science: Strukturen

3

Computergestützte Datengewinnung Computerphysik/Irreversible Prozesse

S

4

4

3 2

2

4

2

Computerpraktikum Device-Related Solid State Physics II

P

2 2

Einführung in die Nichtlineare Dynamik

3

Elektrodynamik

4

4


4

2

Empirisch-Experimentelles Forschen, Gruppe 1

3

2 20

Experimentalphysik: Komplexe Materialien

2

3


2

1

- 158 -

T

Annual Report 2011

Kognition

2

Laborpraktikum (Orientierungspraktikum) Magnetismus

6 4

Mathematische Grundlagen

2 4

Mechanik, Thermodynamik, Elektrodynamik, Optik

4

14

Mechanik-Thermodynamik

4

4

Messen, Interpretieren, Verarbeiten

1

4 12

2 4


6


6

Methodenpraktikum Dynamik nanosk. und mesosk. Strukturen

6


6


6


6


6


6


6


6

Methodenpraktikum Theoretische Physik – insb. Computerphysik

6


6

Nanophysics - Physics of mesoscopic systems

2

6

2

1

Oberseminar

1

Physik

2

3


6

18

Physik Teil 1 Mechanik und Thermodynamik

2

1

Physikalisches Kolloquium

2

4


8


6


24

Scientific English for Scientists

2 2

Statistische Physik ökonomischer Prozesse I

2


1 1

Studentisches Tutorium

2

Surfaces, Thin films and Interfaces

2

Theoretische Mechanik / Quantenmechanik

4

Theoretische Physik (Kontinuumsphysik)

4


1 4 4 13

- 159 -

Annual Report 2011

Public releations

13.01.2011

Tag der offenen Tür Vorstellung der Studiengänge: Prof. Richter, Physik Prof. Radons, Computational Science Prof. von Borczyskowski, Sensorik und kognitive Psychologie Ó Special Physik: Prof. Albrecht, "Magnetismus in der Nanowelt – vom Elektronenspin zur Festplatte" Ó Special Computational Science: Prof. Radons, "Fraktale überall – Eine Entdeckungsreise durch Natur und Technik" Ó Unterstützung bei Standbetreuung und Laborführungen: Prof. M. Albrecht, Prof. P. Häussler, Dr. T. Franke, Dr. E. Fromm, Dr. S. Seeger, M. Heidernätsch, G. Steinbach, J. Seemann, M. Stiehler, M. Pleul, T. Baumgärtel, M. Dehnert, P. Matthes, M. Melzer, S. Röper, C. Schulze, H. Weber Ó

Ó

Organisation besonderer Betreuung von Schülern des Johannes-Kepler-Gymnasiums im Rahmen ihrer Berufsorientierung (in Zusammenarbeit mit der meteor GmbH) Press release p.168

16.01.2011

Dr. Beddies, Dr. Hempel, "Wie kommt der Strom in die Steckdose" Vortrag im Rahmen der Kinderuniversität Besucherrekord mit ca. 700 Kindern und ihren Eltern/Großeltern

Press release p.167 Press release p.169

21.-23.02.2011

Dr. Beddies, "Wasserstoff – Energieträger der Zukunft" Schülerworkshop im Schülerlabor

Press release p.170

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Annual Report 2011

09.03.2011

Regionalausscheid der 12. Sächsischen Physikolympiade Ó Ó

Dr. Seeger: Logistische Unterstützung und Organisation des Rahmenprogramms für die 154 Teilnehmer der 6.-10. Klasse Dr. Hempel, Dr. Franke, Experimentalvorlesung "Wettkampf im Physikstadion: E-Feld gegen H-Feld"

Press release p.176

17.03.2011

Festveranstaltung 50 Jahre Mathematikolympiade Ó Ó

Festveranstaltung im Institut für Physik Dr. Seeger, Dr. Beddies, Führungen und Laborbesichtigungen im Institut für Physik

Press release p.177

18.03.2011

"Parcour der Wissenschaft" im Hauptgebäude der Universität Ó Ó

Auftaktveranstaltung zum "Jahr der Wissenschaft" Experimentierstrecke im Hauptgebäude StraNa

Press release p.178 Press release: http://www.tu-chemnitz.de/tu/presse/aktuell/2/3474 Press release: http://www.tu-chemnitz.de/tu/presse/aktuell/1/3514

18.03.2011

Verteidigung der BeLL-Arbeiten am Johannes-Kepler-Gymnasium Ó Ó

Jurymitarbeit: Dr. Seeger 8 Arbeiten durch TU-Chemnitz betreut, davon durch Dr. Seeger: G. Haase, "Entwicklung von Messsensoren zur Kontrolle trainingsrelevanter Daten"

Press release: http://www.tu-chemnitz.de/tu/presse/aktuell/2/3507

09.04.2011

Landesausscheid der 12. Sächsischen Physikolympiade Ó Ó

Organisation vor Ort: Dr. Seeger Festvortrag: Prof. C. von Borczyskowski, "Über das Wasser wandeln"

Press release p.180

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Annual Report 2011

14.04.2011

Girl's Day 2011 Ó Ó Ó

Dr. G. Beddies, "Mit Energie in die Zukunft" Prof. G. Salvan, "Von der Schönheit des Forschens" mit über 20 Teilnehmern pro Veranstaltung 'ausgebucht'

Press release p.179

02.05.2011

Eröffnung der Festwoche "175-Jahre TU Chemnitz" Ó

Unterstüztung der Festveranstaltung auf dem Theaterplatz durch das Institut für Physik, René Krone, Dr. Seeger, Studierende der Fachschaft


04.05.2011

Eröffnung der Jubiläumsausstellung im Industriemuseum Ó

Unterstützung des Universitätsarchivs bei Vorbereitung und der Bereitstellung von Exponaten


06.05.2011

Alumni-Treffen

09.-14.05.2011

TU Chemnitz zu Gast in der Sachsenallee Ó Organisation: TU-Chemnitz, Dr. S. Seeger, P. Furchheim Ó Präsentation des Insituts 2011-05-14: Prof. M. Albrecht, "Von Analytik bis Unordnung" Prof. P. Häussler, "Tieftemperaturphysik"

Press release p.182

14.05.2011

Dr. G. Hempel Ó Ó

Experimentalvorlesung im Rahmen der Museumsnacht logistische Unterstützung durch Dr. Seeger

Press release p.184

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Annual Report 2011

15.05.2011

Dr. S. Seeger, "Der Traum von Fliegen" Ó Ó

Vortrag im Rahmen der Kinderuniversität ca. 600 Kinder und deren Eltern/Großeltern

Press release p.185

28.05.2011

„Langer Tag der Wissenschaft” (Tag der offenen Tür) Ó Ó Ó

Vorstellung der Studiengänge des Instituts Informationsstand mit Experimenten "Physik – Wissenschaft für Gourmets"

Press release p.186

01.06.2011

Dr. Beddies, Vorschulkinder zum Kindertag im Schülerlabor

Press release p.189

10.06.2011

Festveranstaltung "5 Jahre Schülerlabor" Ó

Physikalische Experimente im Schülerlabor

Press release p.190

21.06.2011

Vortrag im Rahmen der Jubiläumsausstellung 175-Jahre Chemnitz Ó

27.-28.06.2011

Dr. Müller, Dr. Seeger, "Naturlehre in der Ausbildung in Vergangenheit und Gegenwart"

18. Schülersommerschule Ó Ó

Dr. H.-R. Berger, "Mit Einstein durch Zeit und Raum" Gastredner Prof. Metin Tolan, "Die Physik bei Star-Trek"

Press release p.192

15.07.2011

Spezialistenlager Mathematik Ó

Dr. Franke, Dr. Seeger, "Tiefe Temperaturen/Optimierung"

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Annual Report 2011

25.08.2011

Bildungsmesse Gymnasium Plauen Ó Ó

02.09.2011

Prof. M. Hietschold, "Wie kann man Atome sehen" Dr. S. Seeger, "Studienmöglichkeiten am Institut für Physik"

„Spätschicht” im Rahmen der "Tage der Industriekultur" Ó Ó

Rahmenthema "Elektromoblität" über 300 Gäste

Press release: http://www.tu-chemnitz.de/tu/presse/aktuell/3/3824 Press release: http://www.tu-chemnitz.de/tu/presse/aktuell/2/3858

19.-23.09.2011

Praktikumsleitertagung 2011/Workshop der Vorlesungsassistenten Ó Ó

Tagungsorganisation: Dr. Beddies, Dr. Franke, Dr. Hempel, Dr. Prehl Durchführung Firmenausstellung: Dr. Seeger

Press release p.194 Press release p.196

22.09.2011

Prof. M. Wobst, Dr. Hempel, "Vorschule der Experimentalphysik" Ó Ó

Experimentalvortrag im Rahmen der Jubiläumsausstellung im Industriemuseum Logistische Unterstützung durch Martin Stiehler und Dr. Seeger

Press release p.195

17.10.2011

Herbstuniversität Ó Ó

27.10.2011

CareerNet-Projekttage mit Schülern Ó

27.10.2011

Vortrag im Rahmen der Phänomenia, Stollberg

Radio PSR Familienspass Ó

10.12.2011

Vorstellung der Studiengänge am Institut

Dr. S. Seeger, "Der Traum vom Fliegen" Ó

12.11.2011

Prof. M. Hietschold, "Postkarten aus der Nanowelt" Dr. S. Seeger, "Studiengänge am Institut für Physik"

Dr. Seeger, Dr. Gruner, Experimente und Demonstrationen in Zusammenarbeit mit der Kinderuniversität auf dem Stand der TU Chemnitz

175-Jahre TU-Chemnitz, Jubiläumsveranstaltung Physik Ó

Gastsprecher Prof. G. Huber, "Laser – Geschichte, Anwendung, Ausblick"

Press release: http://www.tu-chemnitz.de/tu/presse/2011/12.06-08.24.html

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Annual Report 2011

17.12.2011

175-Jahre TU-Chemnitz, Jubiläumsveranstaltung Physik Ó

Prof. F. Richter, "Das Vakuum – Wozu ist das Nichts nütze?"

Press release p.200

21.12.2011

Dr. Hempel, Dr. Lißner, Weihnachtsvorlesung Ó

"Alles muss raus – Experimente die uns schon immer gefallen haben"

Press release p.202

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Annual Report 2011

Press releases

The following articles were published by the press office at the Chemnitz University of Technology on the webpages. ( @ www.tu-chemnitz.de/tu/presse/aktuell/)

Contact: Technische Universität Chemnitz Pressestelle Straße der Nationen 62, Raum 185

- 166 -

Phone:

++49/371/531-10040

Fax:

++49/371/531-10049

Email:

[email protected]

Internet:

http://www.tu-chemnitz.de/tu/presse/index.html.en

Annual Report 2011

Schüler

Wie kommt der Strom in die Steckdose? Kinder-Uni der TU Chemnitz lädt am 16. Januar 2011 ein zu einer hochspannenden Reise in die Welt der Technik - Am Ende gibt es eine Überraschung Stellen wir uns einmal vor, es gäbe keinen Strom. Es würde abends kein Licht mehr funktionieren, der Fernseher bliebe schwarz und auch das Radio würde keinen Ton mehr von sich geben. Doch was genau ist eigentlich Strom? Woher kommt er und wie kommt er von der Steckdose in ein technisches Gerät? Diese und andere Fragen werden am 16. Januar 2011 unter Hochspannung in der Kinder-Uni Chemnitz mit vielen physikalischen Experimenten erklärt. Dr. Gunter Beddies und Dr. Gottfried Hempel vom "Wunderland Physik" der Technischen Universität Chemnitz greifen dabei tief in den Fundus der Versuchsaufbauten. Ihr Experimentalvortrag beginnt um 10.30 Uhr im Raum N 115 des Hörsaalgebäudes an der Reichenhainer Straße 90. Am Ende erhält jeder Juniorstudent passend zum Thema eine Überraschungstüte. Dr. Gunter Beddies vom "Wunderland Physik" lädt gemeinsam mit Dr. Gottfried Hempel (nicht im Bild) zur Kinder-Uni ein. Foto: Bildarchiv der Pressestelle/Uwe Meinhold

Weitere Informationen: http://www.tu-chemnitz.de/kinderuni

Kontakt: Brita Stingl, Telefon 0371 531-13300, E-Mail [email protected] Mario Steinebach 04.01.2011

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Annual Report 2011

Schüler

Zeitreise in die berufliche Zukunft Berufsorientierung etwas früher: Schüler der 9. Klassen des Chemnitzer Johannes-Kepler-Gymnasiums besuchen am 13. Januar 2011 Unternehmen und Hochschulen, darunter die TU Chemnitz 50 Schüler der 9. Klassen des Chemnitzer Johannes-Kepler-Gymnasiums verlassen am 13. Januar 2011 ihre Schule und erleben einen besonderen Tag zur Berufsorientierung. Sie besuchen Unternehmen und Universitäten der Region. "Unser Anliegen ist es, den Schülern schon vor ihrem Praktikum in der 10. Klasse im Rahmen des fächerverbindenden Unterrichtes Einblicke in die Berufswelt zu ermöglichen und ihnen damit den Weg zu einem geeigneten Studium oder zu einer Ausbildung zu erleichtern", sagt der Schulleiter des Gymnasiums, Oberstudiendirektor Stephan Lamm. Betreut wird dieses Projekt von der meteor gmbh Unternehmensberatung+Schulung+Coaching in Chemnitz, gefördert wird es von der Bundesagentur für Arbeit. "Die Neunklässler konnten sich im Vorfeld entscheiden, wo sie gern Berufsluft schnuppern wollen. Deshalb trennen sich an diesem Tag auch ihre Wege", berichtet Projektleiterin Franziska Freund von meteor. Praxisorte seien BMW, Siemens, arc solutions, Obermeyer albis bauplan, die Braustolz Brauerei, der Chemnitzer Polizeisportverein, Apotheken, Kindertagesstätten und - bei Gymnasiasten naheliegend - auch die Technische Universität Chemnitz und TU Bergakademie Freiberg. "Nach dem Praxistag werten die Schüler gemeinsam mit ihren Lehrern ihre Erfahrungen aus und bereiten einen Vortrag vor, den sie am 1. Februar vor Lehrern, anderen Mitschülern und Vertretern des Bildungsträgers und der Arbeitsagentur präsentieren", ergänzt Lamm. Die Schüler besuchen auch den Stand des Institutes für Physik, wo sich dieses Mal alles um Magnetismus dreht. Foto: Bildarchiv der Pressestelle/Wolfgang Thieme

Doch bevor dies soweit ist, nutzen beispielsweise 13 der 50 Gymnasiasten am 13. Januar den "Tag der offenen Tür" der Chemnitzer Universität, um sich umfassend zu informieren. Dabei stehen laut Aussage von Freund insbesondere die Studienmöglichkeiten in der Chemie, Physik, Informatik und Psychologie im Mittelpunkt. "Die Schüler werden von den Mitarbeitern einiger Fakultäten bei Rundgängen und bei der Durchführung praktischer Versuche etwa zum Magnetismus betreut", berichtet Dr. Steffen Seeger vom Institut für Physik, der in die Organisation des Berufsorientierungstages eingebunden ist. Zudem besuchen sie zahlreiche Vorträge. Weitere Informationen erteilen der Schulleiter des Johannes-Kepler-Gymnasiums Chemnitz, Stephan Lamm, Telefon 0371 488-8500, sowie Franziska Freund von der meteor gmbh, Telefon 03722 4017888. Mario Steinebach 10.01.2011

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Annual Report 2011

Schüler

Den "einfachsten Motor der Welt" gab es in der Überraschungstüte Besucherrekord an der Kinder-Uni der TU Chemnitz: 700 Kinder wollten mit ihren Eltern und Großeltern am 16. Januar 2011 wissen, wie Strom in die Steckdose kommt - Elektrischer Wind sorgte für Spannung Es herrschte Hochspannung im größten Hörsaal der Chemnitzer Uni. 700 Kinder wollten wissen, wie der Strom in die Steckdose gelangt. Ihre Eltern und Großeltern verfolgten die Vorlesung der Kinder-Uni per Liveschaltung im Nachbarhörsaal oder auf den Treppen neben den Hörsaalbänken. Dr. Gunter Beddies und Dr. Gottfried Hempel vom "Wunderland Physik" der Technischen Universität Chemnitz gaben auf die Frage eine einfache Antwort: "Natürlich von hinten! Über Kabel." Aber damit gaben sich die Juniorstudenten nicht zufrieden und wollten mehr über den Strom erfahren. Angesichts der mehr als 30 Versuche, die Stunden vorher im Hörsaal aufgebaut wurden, war natürlich auch mehr zu erwarten. Was folgte, war eine einzigartige Experimentiershow. Die beiden Physiker der TU zeigten, wie man Blitze erzeugen kann. Sie grillten eine Bockwurst Physiker mit Leib und Seele: Dr. Gunter Beddies und Dr. Gottfried von innen heraus mit Strom, ließen eine Gurke erglühen und zeigten, wie Hempel (v.l.) zeigten den Juniorstudenten spannende Versuche. Foto: Mario Steinebach man Ladungsteilchen mit "Löffeln" transportieren kann. Mit Hilfe des "elektrischen Windes" konnten sie sogar eine Kerze beinahe auspusten. Sie demonstrierten zudem, wie man mit Licht das "Auto der Zukunft" antreiben und mit Wind oder Wasser Strom erzeugen kann. Viele Kinder staunten, dass selbst Äpfel oder Zitronen als Stromquelle dienen können. Viel Beifall erhielt Michelle von Lienen aus Chemnitz. Die zwölfjährige Schülerin stellte sich für einen Versuch zur Verfügung, bei dem deutlich wurde, was es heißt, wenn einem buchstäblich die Haare zu Berge stehen. Die langen blonden Haare von Michelle wurden mit Hilfe des so genannten Van-de-Graff-Generators statisch aufgeladen. Da die Haare alle dieselbe Ladung trugen, haben sie sich daher abgestoßen und standen plötzlich in alle Himmelsrichtungen. Und auch einen Exkurs in die Welt des Magnetismus unternahmen die Physiker. In einem entfernten Hörsaal ließ Dr. Hempel mit Strom eine Magnetnadel beeinflussen, die Bilder erschienen per Videokonferenzschaltung auf den Großleinwänden in den Hörsälen. Außerdem zeigten die Physiker, wie man mit drei Elektromagneten und einer Blechdose einen simplen Motor bauen kann. Und damit die Juniorstudenten auch zu Hause das Gelernte vertiefen können, erhielten sie eine Überraschungstüte mit Bastelanleitung für den angeblich "einfachsten Motor der Welt". Weitere der gezeigten Versuche dürfen die Kinder jedoch nicht zu Hause nachmachen. Darauf haben die Referenten mehrfach hingewiesen. Denn Strom ist auch sehr gefährlich. Für zwei Kinder war die Experimentiervorlesung, die das Wintersemester der Kinder-Uni beendete, ein unvergessliches Erlebnis. Jennifer Pilath und Killian Kober aus Chemnitz, die ihren sechsten bzw. elften Geburtstag feierten, hatten den Start ihrer Party einfach in den Hörsaal verlegt. Natürlich durften sie gemeinsam mit ihren Freunden in der ersten Reihe sitzen. Auch sie wollen bei der nächsten Kinder-Uni am 17. April 2011 wieder gern mit dabei sein. Dann dreht sich alles um den Sport, mehr wird noch nicht verraten - denn etwas Spannung muss bleiben. Weitere Informationen: http://www.tu-chemnitz.de/kinderuni Kontakt: Brita Stingl, Telefon 0371 531-13300, E-Mail [email protected] Mario Steinebach 16.01.2011

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Annual Report 2011

Schüler

Mit wenig Energie durch die Ferien "Wunderland Physik" und "Fortis Saxonia" laden im Jahr der Wissenschaft und im Jubiläumsjahr der TU zum Schülerworkshop "Wasserstoff - Energieträger der Zukunft" ein - Anmeldeschluss: 14. Februar 2011 Schüler, die mehr über die Verwendung von Wasserstoff als Energieträger erfahren wollen, sollten sich die letzte Woche ihrer Winterferien freihalten, denn es warten vom 21. bis zum 23. Februar 2011 erlebnisreiche Tage auf die jungen Forscher. Prof. Dr. Thomas von Unwerth, der in der Volkswagen-Konzernforschung mehrere Jahre das Thema mobile Brennstoffzellensysteme vorantrieb und seit Juli 2010 an der TU Chemnitz die Professur Alternative Fahrzeugantriebe leitet, vermittelt den Schülern zu Beginn einen ersten Eindruck der Verwendungsvielfalt von Wasserstoff. Am zweiten Tag sind die Schüler zu Gast bei den Tüftlern des Studententeams "Fortis Saxonia". Hier sind handwerkliche Fähigkeiten gefragt. Neben dem selbstständigen Aufbau elektrischer Schaltungen und dem Löten von Bauteilen gibt es Einblicke in das futuristische Chassis des Schüler sind regelmäßig zu Gast im "Wunderland Physik" und bei "Fortis Ökomobils "Sax3" und in das selbstentwickelte preisgekrönte Saxonia": Student Oliver Böhm (v.l.) vom Schülerlabor "Wunderland Physik" und Sebastian Kratzert vom Team "Fortis Saxonia" erläutern den Urban-Konzeptfahrzeug "Nios". Die Arbeitsergebnisse dürfen am Ende mit Schülern Linda Seemann und Toni Steiger vom Chemnitzer nach Hause genommen werden. Schüler, die bereits das zweite Mal an Andre-Gymnasium, wie mit einer Brennstoffzelle ein Fahrzeug diesem Workshop teilnehmen, können sogar an der Adaptierung einer angetrieben werden kann. Foto: Bildarchiv der Pressestelle/Mario eigenen Solarzelle arbeiten. Am 23. Februar dreht sich alles um die Steinebach Speicherung von Energie. Ein Ausflug nach Markersbach in eines der größten Pumpspeicherwerke Europas ist sicher der Höhepunkt des Workshops. Anmeldungen nimmt Dr. Gunter Beddies, Leiter des Schülerlabors "Wunderland Physik", bis 14. Februar 2011 per E-Mail [email protected] oder telefonisch unter 0371 531-33114 entgegen. Maximal 30 interessierte Schüler ab der 8. Klasse können teilnehmen. Unterstützt wird der Workshop von der Robert Bosch Stiftung im Rahmen des Programms "NaT-Working". Programm des Workshops: http://www.fortis-saxonia.de/news/2011/NaT_W_2011.pdf Das Schülerlabor "Wunderland Physik" im Internet: http://www.tu-chemnitz.de/physik/S_Labor "Fortis Saxonia" im Internet: http://www.fortis-saxonia.de Mario Steinebach 23.01.2011

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Forschung

Kostengünstigere Solarzellen - bald aus Sachsen? Forscher der TU Chemnitz und vier sächsische Firmen entwickeln Dünnschicht-Solarzellen auf Silizium-Basis Massentaugliche Herstellung ist das Ziel Eine technologische Revolution in der Photovoltaik planen Wissenschaftler der Technischen Universität Chemnitz gemeinsam mit vier mittelständischen sächsischen Unternehmen. Sie wollen ein kostengünstigeres Verfahren zur Herstellung von Dünnschicht-Solarzellen auf Silizium-Basis entwickeln. Der Grund: Derzeitige Solarzellen, die Sonnenenergie umweltschonend direkt in elektrische Energie umwandeln, haben einen relativ niedrigen Wirkungsgrad und hohe Herstellungskosten. An der Professur Anorganische Chemie der TU Chemnitz werden unter Leitung von Prof. Dr. Heinrich Lang neuartige, siliziumorganische Verbindungen hergestellt. Anschließend werden sie auf entsprechende Substrate aufgebracht. Während die Chemiker dafür Sprühverfahren nutzen, verwendet die Professur Digitale Drucktechnologie und Bebilderungstechnik Dunja Grimm von der Professur Anorganische Chemie legt eine Probe in unter Leitung von Prof. Dr. Reinhard R. Baumann spezielle Druckverfahren. ein Analysegerät, mit dem die thermische Zersetzung neuartiger Diese Substrate lassen sich im Anschluss durch thermische bzw. siliziumorganischer Verbindungen für die Anwendung im photochemische Nachbehandlung in Halbleiterschichten umwandeln. Im Photovoltaik-Bereich untersucht werden kann. Foto: Uwe Meinhold Labor der Professur Halbleiterphysik werden Forscher um Prof. Dr. Dietrich R.T. Zahn die Schichten eingehend charakterisieren. Zudem befindet sich eine so genannte "In-Line Analytik" in der Entwicklung, mit der die erzeugten Schichten bereits während des Produktionsprozesses charakterisiert werden, was eine minimale Reaktionszeit zur Prozesskontrolle zulässt. Die grundlegende Erforschung dieser neuen Technik an der TU Chemnitz wird durch Bundes- und Landesmittel gefördert. So entsteht in diesem Rahmen ein neues Chemielabor im Universitätsteil Straße der Nationen 62. "Das Projekt gliedert sich hervorragend in das Forschungsschwerpunktfeld "Smart Systems and Materials" der TU Chemnitz ein", versichert Zahn. Sobald die Grundlagenforschung abgeschlossen sei, soll das neue Verfahren mit Hilfe der Industriepartner zur Marktreife gebracht werden. Zu den beteiligten Unternehmen gehören das Institut für innovative Technologien ITW e. V. Chemnitz, die SIGMA Chemnitz GmbH, die SITEC Industrietechnologie GmbH Chemnitz und die DTF Technology GmbH Dresden. "Das neue Verfahren bringt eine deutliche Zeit-, Material- und Energieeinsparung mit sich", sagt Hans Freitag, Mitglied der Geschäftsleitung der SIGMA Chemnitz GmbH. Ein wesentlicher Vorteil des Verfahrens liege in der extrem hohen Materialausbeute im Vergleich zu derzeit angewandten kostenintensive Vakuum-, Lithographie- sowie Hochtemperaturprozessen. "Dieser Effekt schlägt sich positiv in der Kostenstruktur nieder und ermöglicht aus Sicht der beteiligten Unternehmen künftig eine einfache, massentaugliche Herstellung", ergänzt Freitag. Weitere Informationen erteilen Prof. Dr. Dietrich R.T. Zahn, Telefon 0371 531-33036, E-Mail [email protected], Prof. Dr. Heinrich Lang, Telefon 0371 531-31673, E-Mail [email protected] sowie Hans Freitag, Telefon 0371 2371-102, E-Mail [email protected] Mario Steinebach 14.02.2011

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Ehrungen

Ein herausragender Fachgutachter auf Lebenszeit Prof. Dr. Michael Schreiber vom Institut für Physik der TU Chemnitz ist "Outstanding Referee 2011" der American Physical Society Die American Physical Society (APS), die weltweit 48.000 Mitglieder vereint, zeichnete Prof. Dr. Michael Schreiber, Inhaber der Professur "Theoretische Physik III - Theorie ungeordneter Systeme" der Technischen Universität Chemnitz, als hervorragenden Fachgutachter ("Outstanding Referee") aus. Dieser Ehrentitel wird auf Lebenszeit vergeben. Jährlich wählt die APS weniger als ein halbes Prozent ihrer mehr als 45.000 aktiven Gutachter der APS-Fachzeitschriften aus. Die 143 "Outstanding Referees", die im Februar 2011 ernannt wurden, stammen aus 22 Ländern, die meisten aus den USA, Deutschland, Großbritannien, Kanada und Frankreich. Basierend auf der Qualität, der Anzahl und der Zuverlässigkeit ihrer Gutachten wurden sie aus einer Datenbank ausgewählt, die seit mehr als 20 Jahren geführt wird. Alle anonym agierenden Fachgutachter spielen eine wichtige Rolle bei der Auswahl, der Überprüfung und der Verbesserung der von den Autoren eingesandten Manuskripte für die Veröffentlichung in einer wissenschaftlichen Zeitschrift der APS.Dazu zählen "The Physical Review", die "Reviews of Modern Physics" und die "Physical Review Letters". Diese Zeitschriften zählen zu den wichtigsten internationalen wissenschaftlichen Zeitschriften der Physik. Deren Gutachter müssen sich innerhalb ihres Fachbereichs sehr gut auskennen. Schreiber profitiert hierbei von seiner Arbeit als Chefredakteur der EPL, einer europäischen Fachzeitschrift auf dem Gebiet der Physik mit zunehmender internationaler Ausstrahlung. Prof. Dr. Michael Schreiber, der seit 2010 Chefredakteur der Zeitschrift EPL ist, profitiert von diesen Erfahrungen auch bei seiner Gutachtertätigkeit bei der American Physical Society. Foto: Mario Steinebach

Von der TU Chemnitz wurde bereits 2008 ein Physiker als "Outstanding Referee" geehrt: Privatdozent Dr. Wolfram Just von der Professur Komplexe Systeme und Nichtlineare Dynamik, der heute an der School of Mathematical Sciences der Queen Mary University of London tätig ist.

Homepage des "Outstanding Referees Program" der APS inklusive Übersicht aller seit 2008 ausgezeichneten Fachgutachter: http://publish.aps.org/OutstandingReferees Weitere Informationen erteilt Prof. Dr. Michael Schreiber, Telefon 0371 531-21910, E-Mail [email protected]. Mario Steinebach 27.02.2011

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Forschung

Die neue Führungskräfte-Schmiede der Zukunft Passgenau und bedarfsorientiert: Kompetenzschule der TU Chemnitz verschafft Promovierenden wichtige Führungsqualifikationen und so Wettbewerbsvorteile auf dem Arbeitsmarkt Die Technische Universität Chemnitz wird künftig ihre Doktoranden während der Promotion überfachlich noch besser qualifizieren, um sie auf die Übernahme leitender Tätigkeiten in Wirtschaft und Wissenschaft vorzubereiten. Deshalb startet im März 2011 eine Kompetenzschule im Rahmen der Forschungsakademie der Universität, an der ein bedarfsorientiertes Kursangebot entwickelt wird. "Wir wollen so unseren Promovierenden Kompetenzvorsprung sowie entscheidende Vorteile auf dem Arbeitsmarkt von morgen verschaffen", sagt Prof. Dr. Dietrich R.T. Zahn, Prorektor für Forschung der TU Chemnitz und wissenschaftlicher Leiter der Forschungsakademie. Die Angebote der Kompetenzschule sollen die wissenschaftliche bzw. fachliche Qualifikation der Promovierenden ergänzen und somit die beruflichen Optionen der Teilnehmer als Führungskraft - insbesondere auf dem sächsischen Arbeitsmarkt erweitern. "Zugleich wollen wir so die Attraktivität einer Promotion an der TU Chemnitz erhöhen und damit den Pool an Hochqualifizierten in unserer Region vergrößern", sagt Zahn.

An der Professur Halbleiterphysik der TU Chemnitz untersuchen die Doktoranden Iulia Korodi und Philipp Schäfer an einer Ultra-Hochvakuumkammer die elektrischen Eigenschaften dünner organischer Halbleiterschichten. Auch sie können künftig vom Kursangebot der Kompetenzschule profitieren. Foto: Wolfgang Thieme.

In den kommenden Monaten wird ein spezielles Kursangebot entwickelt, das weit über die Vermittlung üblicher Schlüsselkompetenzen hinausgeht. "Es soll den Promovierenden ermöglichen, sich über die Dauer von zwei Jahren parallel zur Promotion fachübergreifend wesentliche Management- und Kommunikationskompetenzen anzueignen", sagt Projektleiter Dr. Carlo Klauth. Da ein hoher Anteil der Absolventen der Kompetenzschule eine berufliche Tätigkeit in Sachsen aufnehmen werde, unterstütze das Projekt die Minimierung des Führungskräftemangels und stärke die Wettbewerbsfähigkeit der Unternehmen im Freistaat. "Insbesondere die Vermittlung von Kompetenzen zu Projektmanagement, sozialer Führung, interkultureller Kommunikation, Verhalten in Krisen- und Konfliktsituationen, sowie strategischem Management und Marketing in der Kompetenzschule der TU Chemnitz trifft genau den Bildungsbedarf der sächsischen Unternehmen, was aktuelle Umfragen belegen", versichert Klauth.

Die Pilotphase der Kompetenzschule wird bis Ende des Jahres 2013 aus Mitteln des Europäischen Sozialfonds (ESF) mit rund 700.000 Euro gefördert. "Die Universitätsleitung setzt sich dafür ein, diese Führungskräfte-Schmiede danach als feste Serviceeinrichtung an der TU Chemnitz zu etablieren", sagt Zahn. Die Qualifizierung des wissenschaftlichen Nachwuchses unter dem Dach der Forschungsakademie bleibe eine der wichtigsten Aufgaben der Universität. "Um hier ein nach außen sichtbares hohes Niveau in der Führungskräfteentwicklung zu erreichen, werden alle Kurse von Anfang an in ein umfangreiches System zur Qualitätssicherung und kontinuierlichen Weiterentwicklung eingebunden", ergänzt der Prorektor. Als Promotionsstudenten eingeschrieben sind an der TU Chemnitz derzeit 480 Promovierende, darunter ein Drittel Frauen. Hinzu kommen zahlreiche Promovierende, die ihre wissenschaftliche Arbeit im externen Verfahren absolvieren. Die meisten promovieren in den Ingenieurund Naturwissenschaften, in den Wirtschaftswissenschaften, in der Politikwissenschaft und in der Informatik. Weitere Informationen erteilt Prof. Dr. Dietrich R.T. Zahn, Telefon 0371 531-10031, E-Mail [email protected] Mario Steinebach 03.03.2011

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Schüler

Grundschüler belegen mit viel Energie vordere Plätze Viertklässler der Albert-Einstein-Grundschule sichern sich Podestplätze bei "Schüler experimentieren" - Projekte entstanden im Ganztagsangebot des Future Truck-Teams der TU Einmal pro Woche ist das Team des Future Trucks der TU zu Gast an der Chemnitzer Albert-Einstein-Grundschule. Dort gestalten die Unimitarbeiter das Ganztagsangebot "Naturwissenschaften forschend entdecken". Wenn es terminlich passt, steht auch der Future Truck mit all seinen Experimenten und Exponaten bereit; wenn er anderswo unterwegs ist, haben die Mitarbeiter einzelne Versuche im Gepäck. "Um unsere Arbeit mit der Grundschule noch nachhaltiger zu gestalten, haben wir jetzt erstmals mit drei Gruppen am Wettbewerb Schüler experimentieren teilgenommen", berichtet Veronika Mühlhausen vom Future Truck-Team. Dieser Wettbewerb ist eine Sparte von "Jugend forscht" und richtet sich an Schüler bis 14 Jahre. Beim Regionalwettbewerb Südwestsachsen von "Jugend forscht" am 5. März 2011 belegten die drei Teams der Albert-Einstein-Grundschule einen zweiten und einen dritten Platz. "Wir waren in der Kategorie Physik die einzige Grundschule, die angetreten ist. Dass sich die Kinder dann gleich gegen ältere Schüler von Gymnasien durchsetzen konnten, ist ein schöner Erfolg für alle Beteiligten", so Mühlhausen.

Mit dem Vergleich von verschiedenen Dämmmaterialien erreichten die Viertklässler Florenz Förster, Tim Krause und Robert Vogel (v.l.) den zweiten Platz. Betreut wurden sie von Felix Schmieder, studentische Hilfskraft, und Veronika Mühlhausen, Wissenschaftliche Mitarbeiterin. Foto: privat

Das Hauptthema an der Albert-Einstein-Grundschule war ein Energiesparhaus. "Unter diesem Dach konnten sich die Kinder einzelne Aspekte aussuchen, die sie genauer betrachten wollten", so Mühlhausen. Drei Schüler beschäftigten sich in ihrem Projekt mit den Energiesparmöglichkeiten durch Dämmmaterialien und verglichen verschiedene solcher Materialien - der Lohn war der zweite Platz beim Regionalwettbewerb. Nur einen Platz dahinter landeten zwei Schüler, die sich mit Solarzellen befassten. Ebenfalls erfolgreich teilgenommen haben drei Schüler, die verschiedene Elektrogeräte bezüglich ihres Energieverbrauchs verglichen und Vorschläge für das Stromsparen im Haushalt erarbeiteten.

"Wir arbeiten mit den Teams noch bis Schuljahresende weiter an ihren Projekten sowie an anderen naturwissenschaftlichen Themen", sagt Mühlhausen und ergänzt: "Die Gruppe, die mit Dämmmaterialien experimentiert hat, möchte beispielsweise noch ein Modellhaus bauen, wo man die Wirkungen von verschiedenen Materialien ausprobieren kann." Nach den Sommerferien soll die Zusammenarbeit von Future Truck und Albert-Einstein-Grundschule dann ins fünfte Jahr starten. Weitere Informationen erteilt Veronika Mühlhausen, Telefon 0371 531-36728, E-Mail [email protected]. Katharina Thehos 07.03.2011

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Forschung

Magnetismus in zwei Dimensionen Die Professur Oberflächen- und Grenzflächenphysik der TU Chemnitz untersucht gemeinsam mit dem Helmholtz-Zentrum Dresden-Rossendorf die Ausrichtung von Spins in niederdimensionalen Systemen Mit der Temperatur hat es wenig zu tun, wenn Physiker von "Spin-Eis" sprechen. "Dabei geht es stattdessen um die Kuriosität der Anordnung", sagt Prof. Dr. Manfred Albrecht, Inhaber der Professur Oberflächen- und Grenzflächenphysik der TU Chemnitz. Hierbei befolgen die magnetischen Momente einzelner Bausteine in einem Gitter die gleichen Ordnungsregeln wie die Wasser-Moleküle im normalen Eis. "Spin-Eis hat in den vergangenen Jahren ein hohes Forschungsinteresse geweckt", sagt Albrecht. Denn im Spin-Eis können sich magnetische Nord- und Südpole beliebig weit voneinander entfernen. Dadurch entsteht der Eindruck als gäbe es frei bewegliche Träger von magnetischen Monopolen. Diese magnetischen Monopole widersprechen zunächst der gängigen Vorstellung, dass Magnete immer zwei Pole haben - einen Süd- und einen Nordpol. Um weitere Die Wissenschaftler um Prof. Dr. Manfred Albrecht arbeiten in ihrem Erkenntnisse über das Spin-Eis und die magnetischen Monopole zu neuen Forschungsprojekt an einer Maschine zur gewinnen, beschäftigt sich die Chemnitzer Professur Oberflächen- und Molekularstrahlepitaxie, mit der sie Magnetschichten im Nanobereich Grenzflächenphysik im Forschungsvorhaben "Nukleation von Spinordnung aufwachsen lassen. Foto: Falk Bittner in niederdimensionalen kolloidalen Partikelsystemen" mit der Ausbildung und Untersuchung von Spinsystemen in zweidimensionalen Anordnungen von Mikropartikeln. Das Projekt wird ab Februar 2011 für drei Jahre von der Deutschen Forschungsgemeinschaft mit 350.000 Euro gefördert. Im Rahmen dieses Projektes wollen die Wissenschaftler Schichten von Mikropartikeln auf regelmäßigen sowie unregelmäßigen Gittern durch Selbstanordnung herstellen. "Da diese speziellen Anordnungen zu definierten Ausrichtungen der Spins - also der Ausrichtung kleinster magnetischer Bereiche - führen, dienen sie als besonders gute Modelle zur Untersuchung der magnetischen Eigenschaften von niederdimensionalen Systemen", schätzt Albrecht ein. Durch die Projekt-Kooperation mit Dr. Artur Erbe und Dr. Sibylle Gemming vom Helmholtz-Zentrum Dresden-Rossendorf können die Chemnitzer Physiker die magnetischen Eigenschaften solcher Partikelanordnungen sichtbar machen. Mit Hilfe moderner Herstellungs- und Charakterisierungstechniken sowie Simulationen hoffen sie, neue Erkenntnisse über die magnetische Wechselwirkung zwischen Partikeln in niederdimensionalen Systemen zu gewinnen. "In diesem Projekt betreiben wir Grundlagenforschung", sagt Albrecht. Anwendung könne diese später einmal im Datentransfer haben: "Diese Forschungsrichtung könnte zentral für die Architektur zukünftiger magnetischer Datenspeicher sowie logischer Operationen sein, in denen man magnetische Monopole anstelle elektrischer Ströme nutzen würde." Weitere Informationen erteilt Prof. Dr. Manfred Albrecht, Telefon 0371 531-36831, E-Mail [email protected]. Katharina Thehos 07.03.2011

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Schüler

XII. Sächsische Physikolympiade an der Uni 154 Gymnasiasten kämpfen am 9. März 2011 um die Qualifikation zum Landesausscheid - Johannes-Kepler-Gymnasium Chemnitz ist mit 58 Schülern am stärksten vertreten - Ab Mittag schnuppern alle Uni-Luft 154 Schüler aus den Klassenstufen 6 bis 10 von 31 sächsischen Gymnasien sind am 9. März 2011 an der Technischen Universität Chemnitz zu Gast. Sie kämpfen mit Papier, Stift und pfiffigen Lösungswegen um den Einzug in den Landesausscheid der XII. Sächsischen Physikolympiade. Zu lösen sind ab 9.30 Uhr zwei theoretische Aufgaben und eine Aufgabe zu einem Experiment. Insgesamt haben die Schüler im Hörsaalgebäude an der Reichenhainer Straße 150 Minuten Zeit zur Bearbeitung. Nach dem Wettbewerb haben die Teilnehmer die Möglichkeit, spannende Einblicke in die Arbeit von Chemnitzer Wissenschaftlern zu erhalten, zum Beispiel im Hochspannungs- und im Robotiklabor der Fakultät für Elektrotechnik und Informationstechnik und in den Labors des Instituts für Physik der TU Chemnitz. Während einer Experimentalvorlesung von Dr. In der Experimentalvorlesung wird den Teilnehmern am Thomas Franke und Dr. Hans-Gottfried Hempel zum Thema "E-Feld gegen Regionalausscheid auch die Abstoßung gleichnamiger Ladungen an einem Van-de-Graaff-Generator demonstriert. Dieser Juniorhelferin der H-Feld - Elektrizitätslehre in Experimenten" steigt buchstäblich die Chemnitzer Kinder-Uni standen bei diesem Experiment die Haare Spannung im Hörsaal, bevor um 14.45 Uhr im Beisein des Rektors der TU tatsächlich zu Berge. Foto: Mario Steinebach Chemnitz das Geheimnis um die besten Nachwuchsphysiker der Region gelüftet werden. Die erfolgreichsten Teilnehmer erhalten mit ihren Urkunden eine Qualifizierung für den Landesausscheid des Freistaates Sachsen. Dieser wird am 8. und 9. April 2011 ebenfalls in Chemnitz ausgetragen. Am stärksten beim Regionalausscheid vertreten ist in diesem Jahr das Johannes-Kepler-Gymnasium Chemnitz mit 58 Schülern. Dessen vertiefte Ausbildung im mathematisch-naturwissenschaftlichen Bereich umfasst auch die Vorbereitung auf Olympiade- und Wettbewerbsteilnahmen. "Besonders freut uns das rege Interesse von Schülerinnen aus den Klassenstufensieben und acht - rund 50 Prozent der Teilnehmer dieser Klassenstufen sind naturwissenschaftlich interessierte Mädchen", sagt Thomas Scheunert, Organisator des Wettbewerbs. Unterstützt wird der Wettstreit auch in diesem Jahr vom Verein zur Förderung der Sächsischen Physikolympiade e.V., der TU Chemnitz, den Physiklehrern an den Gymnasien und den Eltern, welche die Schüler zur Teilnahme ermutigt und auch bei Fragen während der Vorbereitung auf den Wettbewerb geholfen haben. An der ersten Stufe des Wettbewerbs - einem Hausaufgabenwettbewerb - nahmen übrigens 2.000 sächsische Schüler teil, davon fast 800 aus dem Regionalbereich Chemnitz/Zwickau. Weitere Informationen erteilen Thomas Scheunert, Johannes-Kepler-Gymnasium Chemnitz, Telefon 0371 488-8500 oder 0171 4775504, E-Mail [email protected], sowie Dr. Steffen Seeger, Institut für Physik der TU Chemnitz, Telefon 0371 531-33279, E-Mail [email protected]. Mario Steinebach 08.03.2011

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Schüler

Mathe-Olympiade - die 50. Jubiläumsauflage des Schülerwettbewerbs wird am 17. März 2011 mit einer Festveranstaltung gefeiert - Prof. Dr. Albrecht Böttcher spricht über "Olympia und Marathon" - Spannende Einblicke in die Physik

"Alles Gute zum 50.!" wünscht auch Dr. Frank Göring, Wissenschaftlicher Mitarbeiter der Professur Algorithmische und Diskrete Mathematik der TU Chemnitz. Er ist ein erfahrener und erfolgreicher Mathe-Olympionike. So erreichte er beispielsweise ab der Klassenstufe 7 die ersten Preise bei Kreis- und Bezirksolympiaden und holte bei seinen drei Teilnahmen an der Internationalen Mathematik-Olympiade zwei Goldmedaillen - als bisher einziger Deutscher beide mit voller Punktzahl - sowie eine Silbermedaille. Heute ist er aktiv an der Durchführung des Schülerwettstreits beteiligt. Foto: Mario Steinebach

Die erste Olympiade Junger Mathematiker wurde im Schuljahr 1961/62 in der DDR ausgetragen. Sie hat seitdem mit jährlich 125.000 Teilnehmern, neben dem Bundeswettbewerb Mathematik oder dem "Siemens Schülerwettbewerb in Mathematik, Naturwissenschaften und Technik" nichts an ihrer Bedeutung verloren. Anlässlich des 50. Jubiläums der Mathematik-Olympiade möchten die Regionalstelle Chemnitz der Sächsischen Bildungsagentur gemeinsam mit der Chemnitzer Wirtschaftsförderungs- und Entwicklungsgesellschaft mbH und dem Bezirkskomitee Chemnitz zur Förderung mathematischnaturwissenschaftlich interessierter und begabter Schüler allen Förderern, Unterstützern und Freunden dieser Olympiade auf einer Festveranstaltung an der Technischen Universität Chemnitz danken. "Zu ihnen gehören viele Lehrerinnen und Lehrer, denen es gelingt, interessierte und begabte Kinder und Jugendliche zu einer Teilnahme an Wettbewerben zu motivieren. Sie tragen durch ihr Engagement einerseits bei der mathematischen Vorbereitung der Schüler auf den Wettbewerb als auch bei der Durchführung zahlreicher Aktivitäten rund um die Mathematik-Olympiade zum Gelingen des Wettbewerbs bei und das oft über den Rahmen ihrer schulischen Tätigkeit hinaus", sagt Heike Scherf, Pressesprecherin der Regionalstelle Chemnitz der Sächsischen Bildungsagentur.

Die Festveranstaltung beginnt am 17. März 2011 um 15 Uhr im Neuen Physikgebäude, Reichenhainer Straße 70. Prof. Dr. Albrecht Böttcher, ehemaliger Preisträger der Internationalen Mathematik-Olympiade von 1973 und heutiger Inhaber der Professur Harmonische Analysis und Operatortheorie an der TU Chemnitz, hält den Festvortrag zum Thema "Olympia und Marathon". Zudem sind im Rahmen der Festveranstaltung verschiedene Besichtigungen vorgesehen. So gewähren beispielsweise das Institut für Physik und das Schülerlabor "Wunderland für Physik" spannende Einblicke. Stichwort: Schülerwettbewerbe in Sachsen Die Palette der Schülerwettbewerbe in Sachsen ist breit gefächert. Ob mathematisch-naturwissenschaftlich, sprachlich-literarisch, künstlerisch-musisch, sportlich oder Wettbewerbe zur Gesellschaftskunde, politischen Bildung und Umwelterziehung, sie alle bereichern das Schulleben und profilieren unsere Schulen. Zahlreiche Förderer und Unterstützer tragen zum Gelingen bei. Sowohl in der Grundschule als auch an weiterführenden Schulen stärken Schülerwettbewerbe besondere Begabungen und Neigungen und fordern Schüler heraus, selbstständig oder im Team Fähigkeiten zu entwickeln und problembezogen anzuwenden. Lesen Sie auch: TU-Mathematiker fördern junge Mathe-Genies Mario Steinebach 15.03.2011

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Campus

Chemnitz startete mit großer Party ins Jahr der Wissenschaft 2011 Etwa 500 Besucher folgten dem Wissensparcours durch das Hauptgebäude der TU und erhielten an 30 Stationen Einblicke in viele Projekte - Freiflächenwettbewerb "Querdenken und Mitgestalten" hat begonnen Am Nachmittag des 18. März 2011 war es soweit: Mit einer großen Auftaktparty ist Chemnitz in das Jahr der Wissenschaft gestartet. 30 Projektpartner stellten sich auf einem Wissensparcours im Hauptgebäude der Technischen Universität Chemnitz vor. Etwa 500 Besucher kamen dem Motto des Jahres der Wissenschaft nach: "Ihr werdet staunen". Oberbürgermeisterin Barbara Ludwig eröffnete gemeinsam mit dem Rektor der TU, Prof. Dr. Klaus-Jürgen Matthes, die Veranstaltung. "Denken soll ins Zentrum rücken, Wissenschaft und Forschung gehören in die Mitte unserer Stadt. Der künftige Innenstadt-Campus folgt diesem Ziel ebenso wie das Jahr der Wissenschaft 2011. Die Chemnitzerinnen und Chemnitzer sind neugierig. Ohne Neugier wäre eine Industriestadt wie Chemnitz auch gar nicht denkbar. Darum lade ich die Bürgerinnen und Bürger sowie Gäste der Stadt ein: Seien Sie gerne neugierig, entdecken Sie Wissenschaft und Forschung Spannende Einblicke in die Wissenschaft vermittelte das "Wunderland für sich und staunen Sie", so Ludwig. Matthes fügte hinzu: "Was wir mit dem Physik". Foto: Mario Steinebach Jahr der Wissenschaft angepackt haben, gab es so vorher so noch nie. Dass sich nicht nur Stadt und TU zusammentun, sondern eine Vielzahl von Partnern und Projekten sich gemeinsam für die Wissenschaft engagieren, ist großartig." Die Auftaktveranstaltung war zugleich auch der Startschuss für den Freiflächenwettbewerb "Querdenken und Mitgestalten". Hierzu wurden erstmalig die Flächen im Chemnitzer Stadtgebiet vorgestellt, zu denen in den kommenden Monaten die Bürger ihre Gestaltungsideen einbringen können. Die besten Ideen werden nach Ende des Wettbewerbs umgesetzt. Die drei Flächen befinden sich in der der Straße der Nationen nahe Zöllnerstraße, in der Matthesstraße am Konkordiaplatz sowie am Fuß des Sonnenbergs in der Jakobstraße Ecke Martinstraße neben den Bunten Gärten. Ein Highlight der Auftaktveranstaltung waren die Auftritte der Show "The Drum Beat". Dahinter steht das weltweit einmalige Forschungsprojekt der TU Chemnitz zur geistigen und körperlichen Wirkung des Trommelns bzw. Schlagzeugspielens. Fünf Studentinnen der TU Chemnitz tanzten und trommelten, während die Zuschauer parallel dazu auf Leinwänden Puls und Herzfrequenz der Tänzerinnen beobachten konnten. Bei den zahlreichen kleinen Forschern besonders beliebt war die "Mathe-Insel", auf der es zehn verschiedene Knobel- und Rechenaufgaben zu lösen galt. Aber auch im "Wunderland Physik" gab es - nicht nur für die Kleinen - eine Menge zu entdecken. Die Studenten und Mitarbeiter des Instituts für Physik der TU zeigten und erklärten sehr anschaulich, warum beispielsweise eine Glühbirne leuchtet oder wie Magnetismus funktioniert. Auch die Sprechstunde von Dr. med. Dirk Sandrock, Chefarzt für Nuklearmedizin im Klinikum Chemnitz, wurde rege besucht. Wer seine Schilddrüse einmal im Ultraschall begutachten wollte, konnte sich bei ihm einer so genannten Sonografie unterziehen. Der kleine Vorgeschmack, den das Industriemuseum auf die Sonderausstellung "Vom Gänsekiel zum iPad - Schreibwerkzeuge im Wandel der Zeit" gab, stieß ebenfalls auf großes Interesse. Besonders die jüngeren Forscher konnten sich für das Schreiben mit historischen Federn oder längst ausrangierten Schreibmaschinen begeistern. Auch das Naturkundemuseum stellte Teile seines "Versteinerten Waldes" aus. Mit dem Besuch des Parcours konnten kleine Wissenschaftler zugleich auch den ersten Puzzle-Baustein für das Diplom des Jahres der Wissenschaft sammeln. Erwachsene Wissenschaftsbegeisterte erhielten Stempelkarten. Bei jedem Besuch einer Veranstaltung im Jahr der Wissenschaft gibt es einen Diplom-Puzzleteil beziehungsweise einen Stempel. Wer ein "abgeschlossenes" Diplom oder eine vollständige Stempelkarte vorweisen kann, erhält eine Einladung zur großen Wissenschaftsparty am Ende des Jahres. Das komplette Jahresprogramm und alles Wissenswerte rund um das Chemnitzer Jahr der Wissenschaft 2011 finden sich auf www.jahrderwissenschaft.de. (Quelle: Stadt Chemnitz) Weitere Berichte über den Wissensparcours gibt es nachzulesen in der Freien Presse und anzuschauen im MDR-Sachsenspiegel. Mario Steinebach 18.03.2011

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Girls´Day 2011: TU Chemnitz lockt mit spannenden Angeboten Schülerinnen stehen am 14. April sechs "TU-Specials" und ein Ausbildungs-Special zur Auswahl - Um eine Anmeldung bis zum 12. April wird gebeten Mädchen entscheiden sich in ihrer Ausbildungs- und Studienwahl immer noch häufig für nichttechnische Berufsfelder oder Studiengänge. Vielen Unternehmen fehlt auch deshalb zunehmend qualifizierter Nachwuchs in technischen und techniknahen Bereichen. Der bundesweite Girls´Day soll am 14. April 2011 dem entgegenwirken. Auch die Technische Universität Chemnitz beteiligt sich daran. Wissenschaftler sowie Studierende geben von 8 bis etwa 14.15 Uhr Einblicke in ihre Disziplinen - vom Maschinenbau und der Mathematik über die Elektro- und Informationstechnik bis zur Informatik, Physik und Chemie. Unter dem Motto "Studieren in Chemnitz - Girls gestalten die Zukunft" stehen sechs "TU-Specials" zur Auswahl, davon sind jeweils drei für Schülerinnen der 5. bis 9. Klassen und der 10. bis 13. Klassen bestimmt. Die Der Girls´Day soll Mädchen auch an der TU Chemnitz spannende Jüngeren können zum Beispiel bei "Mathematischen Spielereien" die Welt Einblicke in faszinierende Wissenschaftsgebiete ermöglichen. der Mathematik näher entdecken, die Älteren lernen dieses Themengebiet Foto: Bildarchiv der Pressestelle/Wolfgang Thieme bei der Veranstaltung "Zu Risiken und Nebenwirkungen fragen Sie Ihren Mathematiker!" kennen. Zudem gibt es noch viele weitere spannende Vorträge und Mitmach-Angebote, die von selbst gemachten 3D-Filmen bis zu chemischen Experimenten reichen. Ein weiterer Programmpunkt ist das "Ausbildungs-Special": Hier stehen die Ausbildungsberufe Druckerin, Mediengestalterin Digital und Print, Elektronikerin für Geräte und Systeme, Industriemechanikerin sowie Fachinformatikerin für Systemintegration im Mittelpunkt. Der Mädchen-Zukunftstag wird eröffnet mit einer Informationsveranstaltung zum Girls´Day und zum Studium an der TU Chemnitz, die um 8 Uhr vom Prorektor für Forschung, Prof. Dr. Dietrich R.T. Zahn, im Hörsaalgebäude an der Reichenhainer Straße 90 gehalten wird. Parallel dazu informiert Silke Meyer vom Dezernat Personal über die Berufsausbildung an der Universität. Anschließend starten die Schülerinnen mit ihrem gewählten Special entweder am Campus oder begeben sich gemeinsam mit den Uni-Scouts in den Uni-Teil Straße der Nationen 62. An beiden Standorten können sich die Schülerinnen an Infoständen auch über das komplette Studienangebot informieren. Zusätzlich bietet die Universität eine Campustour an, bei der unter anderem in das Studio von Radio UNiCC geblickt wird sowie viele weitere Eindrücke vom Uni-Leben vermittelt werden. Das ausführliche Girls´Day-Programm der TU Chemnitz findet man im Internet unter http://www.tu-chemnitz.de/tu/misc/girlsday. Hier können sich die Schülerinnen noch bis 12. April 2011 für ihr favorisiertes Veranstaltungs-Special anmelden. Der Antrag auf Freistellung vom Schulunterricht ist unter https://www.tu-chemnitz.de/tu/misc/girlsday/ erhältlich. Weitere Informationen erteilt Nadja Höhnel, Bereich Marketing/Öffentlichkeitsarbeit der TU Chemnitz, Telefon 0371 531- 38376, -11111, E-Mail [email protected]. Mario Steinebach 26.03.2011

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Physik-Olympioniken suchen in Chemnitz ihre Meister Der Landesausscheid der 12. Sächsischen Physikolympiade wird am 8. und 9. April 2011 am Johannes-Kepler-Gymnasium und an der Technischen Universität ausgetragen Die besten Nachwuchsphysiker Sachsens treffen sich am 8. und 9. April 2011 in Chemnitz. 113 Schülerinnen und Schüler der Klassenstufen 7 bis 10 kämpfen beim Landesausscheid der 12. Sächsischen Physikolympiade um Plätze und Preise. Veranstalter des Wettbewerbs ist der Verein zur Förderung der Sächsischen Physikolympiade. Unterstützt wird er von der Technischen Universität Chemnitz und vom Johannes-Kepler-Gymnasium Chemnitz. Der Landeswettbewerb beginnt am 8. April mit einem physikalisch-technischen Rahmenprogramm Die Wettbewerbsklausur startet am Folgetag um 8.30 Uhr im Johannes-Kepler-Gymnasium. Zu lösen sind zwei theoretische und eine experimentelle Aufgabe. Die feierliche Ehrung der Sieger findet am 9. April von 13.30 bis 16 Uhr in der Aula der Bereits beim Regionalwettbewerb im März rauchten die Köpfe der Technischen Universität, Erfenschlager Straße 73, Haus A, statt. Zu Beginn Nachwuchsphysiker. Foto: Frank Börner hält Prof. Dr. Christian von Borczyskowski vom Institut für Physik der TU Chemnitz einen öffentlichen Vortrag zum Thema "Über Wasser wandeln". Gegen 15 Uhr erhalten die Preisträger des Landeswettbewerbs ihre Urkunden. Weitere Informationen erteilt Thomas Scheunert vom Johannes-Kepler-Gymnasium Chemnitz, Telefon 0171 4775504, E-Mail [email protected] Mario Steinebach 04.04.2011

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Musikalische Physik - physikalische Musik Im öffentlichen Physikalischen Kolloquium an der TU Chemnitz spricht am 11. Mai 2011 der Hamburger Musikwissenschaftler Prof. Dr. Rolf Bader "Synergetik in musikalischer Akustik und Musikpsychologie" lautet das Thema des Physikalischen Kolloquiums an der TU Chemnitz am 11. Mai 2011. Referent ist Prof. Dr. Rolf Bader vom Musikwissenschaftlichen Institut der Universität Hamburg. Die öffentliche Veranstaltung beginnt um 17.15 Uhr im Raum N013 im Hörsaalgebäude, Reichenhainer Straße 90. Der Professor für Systematische Musikwissenschaft bringt in seinem Vortrag zahlreiche Klangbeispiele zu Gehör und erklärt an ihnen physikalische Grundlagen von Musikinstrumenten. Dabei greift er einige Beispiele heraus, die er näher erläutert, und erklärt grundlegende Modelle. Bei einer Geige beispielsweise bilden die Saiten und der Bogen so genannte nichtlineare Systeme. Bei Flöten oder Orgeln treten diese Systeme durch die Turbulenz in der Luft auf. Sie sind der Grund für die Selbstorganisation, die sowohl in der Physik der Musikinstrumente als auch in der Wahrnehmung von Musik auftritt. Durch Finite-Element- oder Finite-Differenz-Modelle, logistische Abbildungen, Wavelet-Transformationen und andere Modelle und Verfahren versuchen Wissenschaftler, diese Phänomene zu analysieren und durch selbstorganisierende Klangsyntheseverfahren Musik zu machen. Auch in der Rhythmusforschung, der Tonartenerkennung oder der Klangwahrnehmung werden synergetische Modelle oder neuronale Netze eingesetzt. Weitere Informationen unter http://www.tu-chemnitz.de/physik/upload/20110511_5835.pdf und bei Prof. Dr. Günter Radons, Telefon 0371 531-33205, E-Mail [email protected].

Prof. Dr. Rolf Bader präsentiert in seinem Vortrag auch Klangbeispiele. Foto: privat

Katharina Thehos 05.05.2011

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Wissenschaft im Einkaufszentrum TU Chemnitz lädt anlässlich ihres Jubiläums vom 9. bis zum 14. Mai 2011 ein zu Experimenten und Vorträgen in der Sachsen-Allee Was haben eine Seemöwe und eine Dampfmaschine gemeinsam? Computer werden kleiner und kleiner - vielleicht verschwinden sie ja irgendwann ganz? Und kann man sich gesund trommeln? Die Antworten auf diese und weitere Fragen kennen Wissenschaftler der Technischen Universität Chemnitz. Vom 9. bis zum 14. Mai 2011 lassen die TU-Forscher alle interessierten Bürger zu Mitwissern werden - dann nämlich kommt die Wissenschaft ins Einkaufszentrum. Sechs Tage lang präsentiert sich die TU in der Chemnitzer Sachsen-Allee am Thomas-Mann-Platz. Den Anlass dazu bieten das 175-jährige Jubiläum der Universität und das Chemnitzer "Jahr der Wissenschaft". In Zusammenarbeit mit der Stadt Chemnitz und der Sachsen-Allee können bei der Experimentierwerkstatt `Jahr der Wissenschaft 2011´ Jung und Alt eine Woche lang die Vielfalt der Forschung, Entwicklung und Ausbildung an der TU Chemnitz erleben.

Der Future Truck zeigt es an: Diese Woche ist die TU Chemnitz in der "Sachsen-Allee" präsent. Jeder ist eingeladen, hier zu verweilen - ob mit oder ohne Einkaufstüte. Foto: Katharina Thehos

Jeden Tag zu den Center-Öffnungszeiten - also von Montag bis Freitag von 9.30 bis 20 Uhr und am Samstag von 9 bis 20 Uhr - sind der Future Truck der TU und zahlreiche Experimente des Kreativzentrums der Uni zu Gast. Hier können die Besucher sich zum Beispiel selbst am Flaschenzug in die Höhe heben, Motoren- und Getriebemodelle in Gang setzen und in einem Fahrsimulator Kilometer machen, durch das Riesenkaleidoskop schauen, mit der Riesenseifenhaut experimentieren, den Turm von Hanoi und eine Leonardo-Brücke bauen.

Besondere Einblicke in Forschung, Lehre und Leben an der Chemnitzer Uni gibt das Rahmenprogramm. Am 9. Mai steht zunächst die offizielle Eröffnung durch Prof. Dr. Cornelia Zanger, Prorektorin für Marketing und internationale Beziehungen, sowie Vertreter der Stadt Chemnitz und der Sachsen-Allee auf dem Programm. Hierbei erwartet die Besucher außerdem ein kulinarisches Experiment - Roland Keilholz, Chef des Chemnitzer Restaurants alexxanders, wird versuchen, die Anwesenden auf den Geschmack der Wissenschaft zu bringen. Anschließend stehen am Montag ein Vortrag aus der Fakultät für Informatik zum Thema "Rechnen in der Wolke" und Live-Musik der TU BigBand auf dem Programm. An den folgenden Tagen berichten Wissenschaftler von ihren Forschungsprojekten, Studenten erzählen von ihren Erfahrungen im Ausland und der Career Service gibt Starthilfe für die Karriere. Das genaue Programm ist zu finden unter http://www.sachsenallee.de/media/page-images/veranstaltungen/2011_1/Programm_Sachsenallee_TU_Chemnitz.pdf. "In gewisser Weise ist die Veranstaltung auch eine Experimentierwerkstatt für uns", sagt Zanger und ergänzt: "Wir haben ein abwechslungsreiches Programm zusammengestellt und möchten Einblicke geben, wie und woran die Mitarbeiter der TU Chemnitz forschen und arbeiten. Ein Einkaufszentrum ist sicher ein ungewöhnlicher Ort dafür, bietet aber eine interessante Umgebung, in der Wissenschaftler und Bürger in Dialog treten können. Und wer weiß, vielleicht entstehen aus diesem Austausch von Wissenschaftlern auch neue Ideen." Weitere Informationen erteilen Dr. Steffen Seeger, TU Chemnitz, Telefon 0371 531-33279, E-Mail [email protected], und Jens Preißler, Centermanagement der Sachsen-Allee, Telefon 0371 45 20 60. Katharina Thehos 09.05.2011

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Der Traum vom Fliegen Die Kinder-Uni Chemnitz lüftet am 15. Mai 2011 das Geheimnis des Fliegens Wer schon einmal die Welt aus der Vogelperspektive gesehen hat, wird diesen Anblick nur schwer vergessen können. Aber wie haben die Menschen es geschafft, sich auch in der Luft bewegen zu können? Am 15. Mai 2011 beschäftigt sich die Kinder-Uni Chemnitz mit dem faszinierenden Thema des Fliegens. Von den ersten, kühnen Träumen, die Vögel nachzuahmen, über die waghalsigen Flugversuche bis zur Raumfahrt war es ein weiter Weg, den Dr. Steffen Seeger vom Institut für Physik an der TU Chemnitz in seinem einstündigen Vortrag nachzeichnen wird. Dabei werden die Juniorstudenten in Experimenten erleben, welche Phänomene die Pioniere der Luftfahrt verstehen und beherrschen lernen mussten, was ein Flugzeug in der Luft hält, wie eine Rakete funktioniert und ob man eigentlich alles zum Fliegen bringen kann, was Flügel hat. Passend zum Thema erhalten die jungen Studenten am Ende der Vorlesung eine kleine Überraschungstüte. Was darin ist? Spannende Physik, mehr wird natürlich noch nicht verraten. Der Vortrag beginnt um 10.30 Uhr im Raum N 115 des Hörsaalgebäudes an der Reichenhainer Straße 90. Der Eintritt ist frei. Weitere Informationen: http://www.tu-chemnitz.de/kinderuni Kontakt: Brita Stingl, Telefon 0371 531-13300, E-Mail [email protected] Katharina Thehos 09.05.2011

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Gaudeamus igitur: Kommers nicht nur für Studierende TU beteiligt sich am 14. Mai im Industriemuseum an der Chemnitzer Museumsnacht 2011 - Hits von 1836, chemische Kabinettstückchen und eine etwas andere Festrede bereichern das Programm Es ist das berühmteste traditionelle Studentenlied der Welt: "Gaudeamus igitur". Übersetzt aus dem Lateinischen heißt es "Lasst uns also fröhlich sein!". Und mit dieser Aufforderung lädt die Technische Universität zur Chemnitzer Museumsnacht 2011 ein. Anlässlich ihres 175-jährigen Jubiläums und des Jahres der Wissenschaft werden am 14. Mai im Sächsischen Industriemuseum Chemnitz fast vergessene studentische Traditionen wieder belebt. So gibt es in der Ausstellung "Wissen, was gut ist. 175 Jahre TU Chemnitz" ab 18 Uhr literarische und musikalische Hits von 1836 - dargeboten von Studierenden der Medienkommunikation unter Leitung von Dr. Ruth Geier. Überraschende physikalische Experimente demonstriert Dr. Hans-Gottfried Hempel vom Institut für Physik. Chemische Kabinettstückchen zeigen Prof. Studierende der Medienkommunikation lassen zur Museumsnacht das Jahr 1836 im Industriemuseum Chemnitz lebendig werden. Sie schreiben Dr. Heinrich Lang, Sascha Tripke und Dieter Schaarschmidt von der zudem immer wieder neue Beiträge für "1836 - Die etwas andere Professur Anorganische Chemie. Um 20.30 Uhr und um 22.15 Uhr präsentiert Chronik" im Internet. Foto: Christian Schenk das Studentenkabarett "MehrTUerer" erstmals "Die etwas andere Festrede". Jazz statt Studentenlieder spielt um 20 Uhr die Jazz-Combo der Uni. Und die Tanzgruppe "in.takt" der TU Chemnitz zeigt um 21.30 Uhr und 23.15 Uhr, was sie unter "technica saltata" versteht. Dieser ungewöhnliche "Kommers" findet im Bereich der Jubiläumsausstellung statt, die natürlich auch durchschritten werden kann. Lohnenswert ist auch der Besuch der Ausstellung "Vom Gäneskiel zum iPad - Schreibwerkzeuge im Wandel der Zeit", die auch zeigt, mit welchen Hilfsmitteln Studenten und Professoren im 19. und 20. Jahrhundert geschrieben haben. Und wer noch mehr über die TU-Geschichte und studentische Traditionen erfahren möchte, sollte zum "etwas anderen" Jubiläumsbuch greifen, das im Museumsshop erhältlich ist. Insgesamt lockt die Chemnitzer Museumsnacht 2011 mit mehr als 90 Angeboten. An 28 Standorten beteiligen sich insgesamt 31 Museen, Galerien und Einrichtungen. Auf sechs Sonderlinien können die Besucher der Museumsnacht mit Bus und Bahn zu den nächtlichen Schauplätzen gelangen oder auf die umweltfreundliche Variante mit dem "Chemnitzer Stadtfahrrad" zurückgreifen. Museumsnacht-Tickets für Erwachsene zum Preis von acht Euro und Jugend-Tickets für drei Euro gibt es im Vorverkauf und an den Abendkassen der beteiligten Museen und Einrichtungen. Für Kinder bis einschließlich 15. Geburtstag ist der Eintritt frei. Neue Einblicke in "1836 - Die etwas andere Chronik" der Medienkommunikation sind hier möglich: http://www.tu-chemnitz.de/tu/1836/daguerrotypie.html Weitere Informationen zur Museumsnacht: www.chemnitz.de Mario Steinebach 10.05.2011

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Viel heiße Luft und leichte Flugversuche im Hörsaal Dr. Steffen Seeger vom Institut für Physik lüftete in der Kinder-Uni am 15. Mai 2011 das Geheimnis des Fliegens - Kinder erhielten Überraschungstüte mit Wasserraketen- oder Rennballonbauanleitung Ein kurzer Film beweist es: Eine Ballerina schwebt beim Tanzen förmlich durch die Luft, aber am Ende kommt sie immer wieder auf den Bühnenboden zurück. Auch jedes Kind, das in die Höhe springt, landet wieder auf dem Erdboden. "Oder auf der Nase", wie ein Zuhörer der Kinder-Uni in größten Hörsaal hineinrief. Doch wie haben es die Menschen geschafft, in der Luft zu bleiben und sich dort zielgerichtet bewegen zu können? Dr. Steffen Seeger vom Institut für Physik der TU Chemnitz nahm am 15. Mai 2011 etwa 600 Kinder sowie deren Eltern und Großeltern mit auf eine unterhaltsame Reise von den ersten, kühnen Träumen, die Vögel nachzuahmen, über waghalsige Flugversuche bis hin zur modernen Raumfahrt. Zuerst erläuterte er den Juniorstudenten, dass die uns umgebende Luft ein Der Chemnitzer Physiker Dr. Steffen Seeger begeisterte im größten Gemisch aus Gasteilchen ist. Zudem sei warme Luft leichter als kalte, was Hörsaal der TU seine Zuhörer mit vielen Experimenten. Dieser mit Helium gefüllte Ballon erhob sich bis an die Decke. Er musste jedoch man bei Schornsteinen gut beobachten könne. Ebenso übe Luft Druck aus zuvor von Ballast befreit werden. Foto: Mario Steinebach und sei träge. Um alles das zu beweisen, zeigte der Physiker zahlreiche Versuche, bei denen auch einige Kinder mit Eifer assistierten. So waren die Experimente hautnah im Hörsaal mitzuerleben. Und wenn beim ersten Mal nicht gleich alles klappte, war das auch nicht so schlimm. "Wenn etwas nicht funktioniert, dann liegt das auch an der Physik", sagte Seeger lachend. Viel Beifall erhielt er für die fliegende Mülltüte, die zuvor zwei Kinder mit heißer Luft gefüllt hatten. Jedoch flog sie völlig unkontrolliert durch den Hörsaal. Vor einem deratigen Problem stand vor 160 Jahren auch Henri Giffard, der ein steuerbares Luftschiff bauen wollte. Am 24. September 1852 hob es in Paris ab und flog etwa 27 Kilometer weit. Dies war der erste bemannte motorisierte Flug der Geschichte der Menschheit. Das Forschungsluftschiff der TU Chemnitz, das Seeger im Bild zeigte, fliegt da schon genauer. "Wer es einmal von der Nähe anschauen möchte, sollte mit seinen Eltern ins Chemnitzer Industriemuseum gehen, wo es bis zum 3. Oktober in der Jubiläumsausstellung der TU Chemnitz zu sehen ist", empfiehlt Seeger. Die Kinder erfuhren auch, von vielen gescheiterten Flugversuchen auf der Welt - zum Beispiel von gefährlichen Tests des Schneiders von Ulm oder von Otto Lilienthal. Seeger zeigte auch das wahre Prinzip der Luftfahrt, nämlich angestellte Flächen mit Vortrieb im Experiment. Passend zum Thema erhielten die Juniorstudenten am Ende der Vorlesung eine kleine Überraschungstüte. Mit den Utensilien und den Anleitungen darin können die Kinder einen Rennballon oder eine Wasserrakete bauen und zusammen mit ihren Eltern Experimente aus der Vorlesung selbst ausprobieren. Ein herzlicher Dank der Kinder-Uni geht an die Alligator Ventilfabrik GmbH Giengen/Brenz für die Unterstützung dieser Aktion. Weitere Informationen zu künftigen Veranstaltungen der Kinder-Uni an der TU Chemnitz: http://www.tu-chemnitz.de/kinderuni Kontakt: Brita Stingl, Telefon 0371 531-13300, E-Mail [email protected] Informationen zur Jubiläumsausstellung "Wissen, was gut ist. 175 Jahre TU Chemnitz", in der das Luftschiff der TU Chemnitz zu sehen ist: http://www.saechsisches-industriemuseum.de/_html/sonderausstellung/tu_chemnitz/index.htm Mario Steinebach 15.05.2011

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Campus

Der etwas andere Tag der offenen Tür Insbesondere Studieninteressenten und Absolventen der TU zog es zum "Langen Tag der Wissenschaft" an die TU - einige reisten extra aus anderen Bundesländern an Obwohl er erst 15 Jahre alt ist, weiß Lucas Vogel schon jetzt, dass er nach dem Abitur an der Technischen Universität Chemnitz studieren möchte. "Entweder Elektrotechnik oder Informatik", sagt der Schüler der 9. Klasse des Europäischen Gymnasiums Meerane, der beim "Langen Tag der Wissenschaft" der TU Chemnitz zum ersten Mal gemeinsam mit seiner Mutter den Campus besuchte. "Einer meiner Lehrer hat mich auf die Veranstaltung hingewiesen. Nun möchte ich mich unter anderem auch darüber informieren, ob und wann ich in Chemnitz ein Schülerpraktikum absolvieren kann." Einen etwas längere Anreise hatten Sina Gierig aus Berlin und ihre Begleiterin. Die 20-Jährige hatte im Internetportal www.studieren.de vom Studiengang Sensorik und kognitive Psychologie erfahren. "Genau dieser Mix aus Technikwissenschaften und Psychologie interessiert mich, deshalb bin ich heute zu diesem besonderen Tag der offenen Tür gekommen, um mehr über den Studiengang und die Uni zu erfahren." Sie steuerte auch gleich den Stand des Studentenwerkes Chemnitz-Zwickau an.

Am Stand der Fakultät für Elektrotechnik und Informationstechnik informierte sich der Meeraner Schüler Lucas Vogel (Mitte) gemeinsam mit seiner Mutter nicht nur über Studienmöglichkeiten, sondern auch über den fliegende Mini-Helikopter mit vier Rotoren, der mit Kamera und Videofunk ausgestattet werden und so Feuerwehr, Polizei oder Technischem Hilfswerk bei ihren Einsätzen helfen und wertvolle Informationen liefern kann. Foto: Mario Steinebach

Ebenfalls aus Berlin reiste Sophie Böttinger an - gemeinsam mit ihrem Opa. "Mir gefällt, dass der lange Tag der Wissenschaft sehr schön organisiert ist und dass man vertiefte Einblicke in die einzelnen Studiengänge bekommt. Ich fand nur schade, dass Veranstaltungen zu einzelnen Studiengängen simultan gelaufen sind. Zum Beispiel gab es eine Veranstaltung zu European Studies und gleichzeitig eine zu Pädagogik. Ich hätte mir gern beide angesehen. Am besten hat mir die Einführungsveranstaltung gefallen, weil dort die ganzen Vorteile vom Master- und Bachelorstudiengang erklärt wurden und warum es sich lohnt, an einer Uni zu studieren - das hab ich so in der Form noch nie gehört", sagt die Studentin, die bereits an einer Fachhochschule eingeschrieben, aber dort nicht ganz zufrieden ist. "Ich habe dort ein sehr verschultes System und auch ein eingeschränktes Angebot. Das stört mich ein bisschen. Ich überlege, an eine große Uni zu gehen, weil es hier einfach mehr Möglichkeiten gibt", ergänzt Böttinger. Den Chemnitzer Jens Mauderer hatte "die reine Neugierde" an die Uni geführt. Gemeinsam mit seiner Begleiterin hat er sich im Hörsaalgebäude die Experimente der Mathematiker und Chemiker angesehen und bei den Physikern der Molekularküche gekostet. Danach zog es die beiden in den Universitätsteil Erfenschlager Straße, wo sie unter anderem an einer Führung durch die Experimentier- und Digitalfabrik teilnahmen. "Das wollte ich immer schon mal sehen. Bei der Museumsnacht vor ein paar Jahren haben wir das leider verpasst", erzählte der Systemadministrator der Firma Sander Fördertechnik. "Ich habe auch beruflich mit Transport und Logistik zu tun, und da mein Unternehmen zu den Kooperationspartnern der Professur Fabrikplanung und Fabrikbetrieb zählt, interessiert mich dieser Programmpunkt besonders", so Mauderer, der sich anschließend auch die Führung durch das noch im Bau befindliche Projekthaus MeTeOr nicht entgehen ließ. Ebenfalls gezielt die Erfenschlager Straße angesteuert hat Volkmar Sellge . Er war dabei nicht allein - gemeinsam mit neun seiner ehemaligen Kommilitonen besuchte er die Experimentier- und Digitalfabrik. "Wir haben von 1986 bis 1991 Technologie der metallverabeitenden Industrie studiert, das entspricht in etwa der heutigen Fabrikplanung", so der Chemnitzer, dessen Kommilitonen aus Sachsen, Thüringen und Bayern angereist waren. Seit dem Ende des Studiums trifft sich die Gruppe regelmäßig, zehn Jahre nach dem Studienabschluss war sie bereits an der Uni zu Besuch gewesen. Beim 20-jährigen Jubiläum bot nun der Tag der offenen Tür Gelegenheit, erneut an die TU zurückzukehren. "Auf dem Campus haben wir vor allem die neuen Gebäude besichtigt, wie etwa das Hörsaalgebäude. Und ein paar alte Hörsäle haben wir angeschaut", erzählte Sellge. An der Professur Fabrikplanung und Fabrikbetrieb hatten sie im Vorfeld eine kleine Führung vereinbart - und waren beeindruckt von der Entwicklung in den Labors: "Es hat sich sehr viel getan, der technische Fortschritt ist schon immens", so Sellge. Sein Studium noch vor sich hat Maximilian Krumpa . Er war aus dem Kreis Siegen-Wittgenstein in Nordrhein-Westfalen angereist, um sich über ein Maschinenbau-Studium zu informieren. "Meine Eltern stammen aus Ostdeutschland und haben beide in Chemnitz studiert,

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deshalb bin ich auf die TU aufmerksam geworden", erzählte er. Zum kommenden Wintersemester möchte er mit dem Studium beginnen. "Für Chemnitz spricht, dass es hier keinen Numerus Clausus und keine Studiengebühren gibt", so Krumpa. Auf dem Campus und am Uniteil Erfenschlager Straße nutzte er den Vortrag über das Maschinenbau-Studium, die Führungen durch Forschungshallen und individuelle Studienberatung: "Es gefällt mir richtig gut, das Angebot ist sehr vertiefend - mehr als bei einem normalen Tag der offenen Tür." Eine der jüngsten Studieninteressentinnen kam aus Oelsnitz im Erzgebirge: Katrin Vogel besucht die achte Klasse am Gymnasium in Stollberg und war mit ihren Eltern im Hörsaalgebäude der TU unterwegs. "Ich interessiere mich für ein Studium in einem naturwissenschaftlichen Fach", erzählte die Schülerin, die sich unter anderem am Infostand der Physik mit Flyern eingedeckt hat - auch über die Angebote des Instituts für Schüler. "Bisher hab ich noch keine Kontakte zur TU, die Studienorientierung fängt in der Schule auch erst in der neunten Klasse an", sagte die Oelsnitzerin, die sich ein Studium in Chemnitz gut vorstellen könnte: "Dann müsste ich auch nicht extra umziehen." Voll besetzt mit Studieninteressenten war der Seminarraum, in dem Prof. Dr. Stephan Odenwald , Inhaber der Professur Sportgerätetechnik, den Studiengang Sports Engineering sowie das neue Studienangebot Medical Engineering vorstellte. "Durch seine starke Orientierung auf den Maschinenbau ist dieser medizintechnische Studiengang deutschlandweit einzigartig", sagte Odenwald. An den Informationsständen im Foyer des Hörsaalgebäudes wurden aber auch die anderen neuen Studienangebote oft hinterfragt, etwa die Bachelor-Studiengänge Elektromobilität und Regenerative Energietechnik. In der Straße der Nationen waren leider nicht sehr viele Gäste unterwegs. Lediglich in der Chemie waren die Führungen und die Mitmachstationen gut besucht. Im "Future Campus" blickten hingegen nur wenige Kinder hinter die Geheimnisse der Mathematik und der Technik. "Vielleicht sind die Chemnitzer im Jahr der Wissenschaft auf Grund der Fülle von Veranstaltungen schon etwas gesättigt", vermutet Dr. Urs Luczak vom Wissenschaftsbüro der Stadt Chemnitz. Dies sei natürlich schade, denn viele Bereiche der Uni hatten sich speziell für diesen Tag ganz besondere Angebote ausgedacht - von der "Nischel-Produktion" bis hin zur Gabelstabler-Trickshow. "In den kommenden Jahren sollte man wieder überlegen, eine lange Nacht der Wissenschaft durchzuführen - vielleicht auch einmal wieder in Kooperation mit der Chemnitzer Museumsnacht, denn zur Premiere im Jahr 2005 strömten schließlich 4.000 Gäste an die TU", erinnert sich Luczak. Diese Zahl wurde zum langen Tag der Wissenschaft nicht erreicht, vermutlich waren es unter 1.000 Besucher. Dennoch kamen mehr Gäste als bei den bisherigen Tagen der offenen Tür im Mai bzw. Juni. Fazit: "Der mit viel Engagement vorbereitete Lange Tag der Wissenschaft hätte noch mehr Besucher verdient, jedoch waren die Gäste, die gekommen sind, sehr interessiert - einige werden wir als Studienanfänger in den kommenden Jahren begrüßen können", so Tobias Bauer von der Zentralen Studienberatung. (Autoren: Katharina Thehos, Anett Michael und Mario Steinebach) Mario Steinebach 29.05.2011

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Forschung

Damit Moleküle den richtigen Weg finden Physiker der TU Chemnitz sind an der sächsischen Forschergruppe "From Local Constraints to Macroscopic Transport" beteiligt, die die Deutsche Forschungsgemeinschaft für weitere drei Jahre fördert Mit 2,5 Millionen Euro fördert die Deutsche Forschungsgemeinschaft (DFG) in den kommenden drei Jahren ein Forschungsvorhaben, das Wissenschaftler der Technischen Universitäten Chemnitz und Dresden sowie der Universität Leipzig erarbeit haben. Sie bündeln dabei ihr Wissen zur Bewegung auf der Nanometerskala. Die Forschergruppe "From Local Constraints to Macroscopic Transport" beschäftigt sich mit Transportprozessen in komplexen Materialien und zielt auf Anwendungen unter anderem in der Medizin. Bereits seit 2007 haben sich die Wissenschaftler zusammengeschlossen. In der ersten Förderphase erhielten sie drei Millionen Euro von der DFG. In den vergangenen Jahren haben die Forscher grundlegende Informationen über die Bewegung von Molekülen in porösen Materialien und Dokorandin Daniela Täuber untersucht die Bewegungen von Molekülen in Flüssigkeiten mit einem hochempfindlichen Mikroskop. Foto: Flüssigkristallen, über die Brownsche Bewegung heißer Nanopartikel und Christian Schenk die Dynamik von Makromolekülen in biologischen Systemen gewonnen. Darauf wollen sie jetzt aufbauen. In der aktuellen Projektphase kommen diese Erkenntnisse zum Einsatz, um die Bewegung von Molekülen und Nanopartikeln durch äußere Einflüsse zu kontrollieren. "Die zwölf beteiligten Arbeitsgruppen verfolgen die Vision von einer Manipulation von Molekülen und Materialien auf der Nanometerskala", sagt Prof. Dr. Christian von Borczyskowski, Inhaber der Professur Optische Spektroskopie und Molekülphysik an der TU Chemnitz, und ergänzt: "Gerichteter Transport von Molekülen, Aggregaten und Partikeln in Flüssigkeiten kann in Zukunft eine wichtige Rolle bei der Herstellung neuer Materialien spielen." Beispielsweise könnten Medikamente im menschlichen Körper direkt dahin gelenkt werden, wo sie wirken sollen - dadurch ließen sich Krankheiten besser bekämpfen. "Bis zur Realisation dieser Vision gibt es jedoch noch viele Probleme zu lösen", so von Borczyskowski. Von der TU Chemnitz ist neben Prof. von Borczyskowski auch Prof. Dr. Günter Radons, Professur Komplexe Systeme und Nichtlineare Dynamik, beteiligt. Außerdem werden zwei Doktoranden die Chemnitzer Wissenschaftler unterstützen. Sie beschäftigen sich vor allem mit der Untersuchung von Diffusionsprozessen in Poren von Oxiden und in Flüssigkeitsfilmen. "Dazu setzen wir Farbstoffmoleküle in die Flüssigkeiten ein und beobachten mit hochempfindlichen Mikroskopen, wie sich diese Moleküle bewegen. In dünnen Flüssigkeitsfilmen läuft diese Diffusion völlig anders ab, als in größeren Flüssigkeitsvolumen", erklärt Daniela Täuber, die an der Professur Optische Spektroskopie und Molekülphysik promoviert. Die Untersuchung dieser Prozesse ermöglicht ein besseres Verständnis der Beweglichkeit von flüssigkristallinen Molekülen. Diese ist zum Beispiel für das Schaltverhalten in miniaturisierten opto-elektronischen Displays von Bedeutung. Weitere Informationen erteilen Prof. Dr. Christian von Borczyskowski, Telefon 0371 531-33035, [email protected], und Prof. Dr. Günter Radons, Telefon 0371 531-33205, [email protected]. Katharina Thehos 31.05.2011

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Campus

Überraschungsausflug zum Kindertag Vorschüler des Kindergartens "Krabbelkäfer" besuchten am 1. Juni 2011 das Schülerlabor "Wunderland Physik" an der TU Chemnitz und experimentierten mit Luft und Wasser Schöner konnte der Kindertag nicht beginnen: Die Vorschüler der Kita "Krabbelkäfer" in Chemnitz besuchten am 1. Juni 2011 das "Wunderland Physik". Dann drehte sich alles rund um das Thema "Luft und Wasser". Der Leiter des Schülerlabors, Dr. Gunter Beddies, holte die Kinder deshalb auch am kleinen Teich vor dem Studentenwohnheim Reichenhainer Straße 35/37 ab und erläuterte bei strömendem Regen, warum ein Schiff schwimmt. Danach gingen die Vorschulkinder ins Institutsgebäude für Physik am Smart Systems Campus. Hier konnten sie die Zusammenhänge und Phänomene aus Natur und Wissenschaft selbst unter die Lupe nehmen und die Geheimnisse von Luft und Wasser beim Experimentieren erkunden. Sie gingen beispielsweise den Fragen nach, warum Wasser aus einem umgestülpten Glas nicht herausläuft oder warum 16 Pferde vor etwa 350 Hört man eine Schulklingel im Vakuum? Die Kinder lernten von Dr. Jahren die so genannten "Magdeburger Halbkugeln" nicht auseinander Gunter Beddies bei diesem Versuch, dass für die Übertragung des ziehen konnten. "Wir möchten so der Beobachtungswelt der Kinder, ihrer Klingeltons die Luft verantwortlich ist. Im Vakuum gibt es nämlich Lust am Ausprobieren und ihrer natürlichen Neugierde gerecht werden und keinen Schall. Foto: Mario Steinebach spielerisch ihr Interesse für naturwissenschaftliche Zusammenhänge wecken. Zudem unterstützen wir die Erzieherinnen der Kindertagesstätte auf dem Uni-Campus in ihrer pädagogischen Arbeit", sagt Beddies. Als die Vorschüler am späten Vormittag in ihren Kindergarten an der Reichenhainer Straße 33a zurückkehrten, konnten sie dort weiter forschen. Hier wurde von den Erzieherinnen für alle Kita-Kinder ein "Versuch macht klug"-Parcours aufgebaut. "Die Kinder konnten beispielsweise mit Luft, Kugeln, Magneten, Spiegeln und Farben experimentieren", sagt die Kita-Leiterin Petra Grund. Homepage des Schülerlabors "Wunderland Physik": http://www.tu-chemnitz.de/physik/S_Labor/ Weitere Informationen erteilt Dr. Gunter Beddies, Telefon 0371 531-33114, E-Mail [email protected]. Mario Steinebach 01.06.2011

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Schüler

Phänomenal: Zum Geburtstag wird geforscht "Wunderland Physik" lädt am 10. Juni 2011 zum Experimentieren ein - Mehr als 7.200 Schüler nutzten in den letzten fünf Jahren dieses besondere Schülerlabor am Institut für Physik Die Energiewandlung untersuchen, Messungen mit Hilfe von Computern durchführen, Licht und Farbe erforschen - das Schülerlabor "Wunderland Physik" der Technischen Universität Chemnitz bietet viele Experimente für den Unterricht. Jetzt besteht es bereits seit fünf Jahren. "Rund 7.200 Schüler aller Altersgruppen und Schularten experimentierten hier. Etwa zwei Schulklassen pro Woche betreuen wir in unserem Labor", berichtet der Leiter des Schülerlabors Dr. Gunter Beddies und ergänzt: "Besonders nachgefragt sind neben den Versuchen rund um die regenerative Energiegewinnung vor allen die vielfältigen computergestützten Experimente." Zudem kamen mehr als 200 Lehrer zu Informationsveranstaltungen und Fortbildungen ins "Wunderland Physik". Die meisten Schulklassen stammen aus Gymnasien der Region. Für Schüler der Klassenstufen acht bis zwölf bietet dieses besondere Labor eine spannende Unterrichtsergänzung. "Mit unserem reichen Fundus an Versuchsaufbauten, die beispielsweise auch mit Forscherkisten aus der Industrie ergänzt werden, sorgen wir mittlerweile auch in Kindertagesstätten für jede Menge Aha-Effekte", erzählt Beddies. Dr. Gunter Beddies vom "Wunderland Physik" lädt zum Experimentieren ein. Foto: Bildarchiv der Pressestelle/Uwe Meinhold

Anlässlich des fünften Geburtstages lädt das "Wunderland Physik" Jung und Alt am 10. Juni 2011 von 15 bis 18 Uhr in den Neubau des Instituts für Physik, Reichenhainer Straße 70, ein. Hier können insbesondere Kinder und Schüler den physikalischen Phänomenen auf den Grund gehen. So kann unter anderem ein Sonnenstundenzähler oder ein Elektromotor gebaut werden. Und ein Parcours mit verschiedenen Stationen lädt zum Mitmachen und Experimentieren ein. Das Schülerlabor "Wunderland Physik": http://www.tu-chemnitz.de/physik/S_Labor/ Weitere Informationen erteilt Dr. Gunter Beddies, Telefon 0371 531-33114, E-Mail [email protected]. Mario Steinebach 07.06.2011

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Forschung

Mit der Zwillingspolymerisation zu neuen Materialien Chemiker und Physiker der TU Chemnitz erhalten für die Erforschung von Hybridmaterialien mehr als eine Million Euro von der Deutschen Forschungsgemeinschaft

Tina Löschner und Prof. Dr. Stefan Spange von der Professur Polymerchemie beraten, wie eine Nanokompositprobe, hergestellt durch die Zwillingspolymerisation, für eine Festkörper-NMR-Messung präpariert werden kann. Dr. Andreas Seifert (im Hintergrund) ist der leitende Wissenschaftler für die Festkörper-NMR-Spektroskopie im Rahmen der Forschergruppe. Foto: Christian Schenk

Aus Eins mach Zwei - das ist das grundlegende Prinzip der an der Professur Polymerchemie der Technischen Universität Chemnitz entwickelten Zwillingspolymerisation. Eine speziell konstruierte Verbindung, das Zwillingsmonomer, reagiert dabei in nur einem Arbeitsschritt zu zwei unterschiedlichen Homopolymeren. Ein Monomer ist ein reaktionsfähiges Molekül - mehrere Monomere können durch eine chemische Verbindung zu einem Polymer werden. Handelt es sich um gleichartige Monomere, die sich verbinden, so entstehen Homopolymere. Die Chemnitzer Zwillingsmonomere bestehen wiederum aus zwei verschiedenen Bausteinen, die über eine Atombindung verknüpft sind. Basiert die Zwillingspolymerisation auch auf einem einfachen Grundprinzip, so handelt es sich bei genauerer Betrachtung um einen komplexen Prozess. Um ihn besser verstehen und steuern zu können, forschen Wissenschaftler von mehreren Professuren der Chemnitzer Fakultät für Naturwissenschaft nun an dem Thema "Zwillingspolymerisation von organisch-anorganischen Hybridmonomeren zu Nanokompositen". Die Forschergruppe, an der Chemiker und Physiker beteiligt sind, wird von der Deutschen Forschungsgemeinschaft (DFG) seit dem 1. Mai 2011 für drei Jahre mit mehr als einer Million Euro gefördert.

Ihr Ziel ist die Erzeugung von neuen Hybridmaterialien. Diese bestehen aus einem organischen und einem anorganischen Teil - verbinden also kohlenstoffhaltige und kohlenstofffreie Stoffe. "Die entstehenden funktionalen Hybridmaterialien können in Zukunft beispielsweise in der Katalyse oder für die Speicherung von Gasen eingesetzt werden", sagt Prof. Dr. Stefan Spange, Inhaber der Professur Polymerchemie an der TU Chemnitz und Sprecher der Forschergruppe. Bei der Katalyse werden chemische Reaktionen beschleunigt oder gesteuert. "Konkret geht es in unserer Forschergruppe um ein neues Synthesekonzept, das solche Materialien in großer Menge und mit genau definierten molekularen, strukturellen und morphologischen Eigenschaften verfügbar machen soll", so Spange weiter. Dabei wollen die Wissenschaftler sowohl die etablierten Verfahren verbessern als auch neue entwickeln. Dabei führen die Chemnitzer Chemiker und Physiker Synthese, Analyse und Theorie zusammen: "Die bisher studierten Zwillingspolymerisationen führen zu interessanten Produkten. Jedoch zeigen sie, je nach Zusammensetzung und Reaktionsdurchführung, komplexe und bislang wenig verstandene Reaktionsabläufe. Unser Forschungsschwerpunkt ist es deshalb, den Mechanismus der gekoppelten Bildungsprozesse, die zu den beiden makromolekularen Strukturen führen, zu analysieren und eine Theorie für diesen neuen Polymerisationstyp zu entwickeln", so der Sprecher der Forschergruppe. Die Wissenschaftler werden dafür neue komplexe Monomere herstellen und diese dann gezielt miteinander zur Reaktion bringen. Das übergeordnete Ziel des Forschungsvorhabens ist es, eine neue Konzeption in den Materialwissenschaften zu entwickeln. "Voraussetzung dafür ist, die grundlegenden Zusammenhänge zu verstehen. Das fängt bei der Reaktivität und elektronischen Struktur der Monomerbausteine an und geht über die Reaktionsverläufe im Polymerisationsprozess bis hin zu den Materialzusammensetzungen und -eigenschaften", so Spange. Beteiligt sind neben der Professur Polymerchemie auch die Professuren Analytik an Festkörperoberflächen (Prof. Dr. Michael Hietschold), Anorganische Chemie (Prof. Dr. Heinrich Lang), Computerphysik (Prof. Dr. Karl Heinz Hoffmann), Halbleiterphysik (Prof. Dr. Dietrich R.T. Zahn) und Koordinationschemie (Prof. Dr. Michael Mehring) sowie Honorarprofessor Dr. Alexander Auer. "Durch die Synergie der Expertisen soll ein neues Forschungsfeld aus der Taufe gehoben werden, in dem Chemnitz im Moment Alleinstellung aufweist und als Keimzelle dienen kann", sagt Spange. Die Forschergruppe im Internet: http://www.zwipo.tu-chemnitz.de

Weitere Informationen erteilt Prof. Dr. Stefan Spange, Telefon 0371 531-31714, E-Mail [email protected]. Katharina Thehos 23.06.2011

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Veranstaltungen

Mit der Enterprise durch den Hörsaal Zwischen Warp-Antrieb und Beamen: Dortmunder Experimentalphysiker Prof. Dr. Metin Tolan hält am 28. Juni 2011 einen öffentlichen Vortrag über die Physik bei Star-Trek In der Kultserie "Star-Trek" wird seit den 1960er Jahren jede Menge Physik gemacht. Mal fliegt das Raumschiff Enterprise mit einem Viertel der Lichtgeschwindigkeit, mal mit Überlichtgeschwindigkeit - dank des Warpantriebes. Und wer kennt nicht den berühmten Satz: "Beam mich hoch, Scotty"? Doch was ist davon Wunschdenken, was könnte eines Tages möglich sein? Der Dortmunder Experimentalphysiker Prof. Dr. Metin Tolan, der deutschlandweit mit seinen humoristisch-physikalischen Vorträgen seit vielen Jahren Hörsäle füllt, hinterfragt am 28. Juni 2011 ab 13.30 Uhr an der Technischen Universität Chemnitz die Physik bei Star-Trek und zeigt, inwieweit die Innovationen des 21. Jahrhunderts etwas davon Realität werden lassen. Und da noch immer die bei "Star-Trek" verpackten Technik-Visionen aus dem letzten Jahrhundert Begeisterung bei Jung und Alt wecken, rechnet das Institut für Physik der TU Chemnitz mit vielen Prof. Dr. Metin Tolan entführt seine Zuhörer mit dem Raumschiff Zuhören. Deshalb fliegt die Enterprise an diesem Tag auch durch den Enterprise in die unendlichen Weiten des Universums. Foto: TU größten Hörsaal der TU Chemnitz - nämlich den Raum N115 im Dortmund/Juergen Huhn (Wikipedia) Hörsaalgebäude an der Reichenhainer Straße 90. Im Publikum sitzen auf jeden Fall die Schüler in den ersten Hörsaalreihen, die am 27. und 28. Juni an der 18. Chemnitzer Schüler-Sommerschule Physik teilnehmen. Schon deshalb lohnt sich für interessierte Schüler eine Anmeldung. Aber auch alle anderen Physik- und "Star-Trek"-Fans sind bei diesem öffentlichen Vortrag herzlich willkommen. Weitere Informationen erteilt Dr. Steffen Seeger, Telefon 0371 531-21555, E-Mail [email protected] Homepage der 18. Chemnitzer Schülersommerschule Physik: http://www.tu-chemnitz.de/physik/Cplus/schule/index.php Mario Steinebach 24.06.2011

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Veranstaltungen

Stand und Perspektiven der Molekülspektroskopie 488. Wilhelm und Else Heraeus Seminar findet vom 12. bis 15. Juli 2011 an der TU Chemnitz statt "Single Molecule Spectroscopy: Current Status and Perspectives" ist das Thema eines öffentlichen Seminars, zu dem vom 12. bis 15. Juli 2011 an der Technischen Universität Chemnitz 40 führende Wissenschaftler und 50 Nachwuchsforscher aus 27 Hochschulen und anderen Forschungsinstituten erwartet werden. Die auf unterschiedlichen Gebieten mit der Molekülspektroskopie in Verbindung stehenden Wissenschaftler aus acht Ländern kommen im "Alten Heizhaus" der TU Chemnitz zusammen, um neueste Forschungsergebnisse auf diesem Gebiet auszutauschen. Zudem würdigen sie die Arbeit des Teams von Prof. Dr. Christian von Borczyskowski, Inhaber der Professur Optische Spektroskopie und Molekülphysik an der TU Chemnitz und ehemaliger Rektor der TU, der am 11. Juli seinen 65. Geburtstag feiert. "Allein die Möglichkeit, Moleküle einzeln zu beobachten, ist erstaunlich", sagt Prof. Dr. Michael Schreiber, Inhaber der Professur "Theoretische Physik III - Theorie ungeordneter Systeme" der Technischen Universität Chemnitz. Und in den 20 Jahren, seit dem es dieses Forschungsgebiet gibt, haben sich laut Schreiber daraus faszinierende Aspekte bei der Beobachtung zum Beispiel des Ablaufs von biologischen Prozessen und bei der Analyse von Eigenschaften neuer Materialien ergeben. "Die extrem hohe Auflösung erlaubt ganz neue Experimente am ultimativen Limit chemischer Analyse", schätzt Schreiber ein. Gefördert wird die Veranstaltung von der Wilhelm und Else Heraeus-Stiftung in Hanau. Sie ist die größte private Stiftung auf dem Gebiet der Physik. Gegründet wurde sie 1963 von Dr. Wilhelm Heinrich Heraeus und seiner Frau Else. Das kinderlose Paar besaß Anteile am Technologie-Konzern Heraeus, die es der Stiftung vermachte. Die Erträge aus diesen Anteilen werden seither für die Förderung der Grundlagenforschung in der Physik verwendet. Eines der geförderten Projekte sind die Heraeus-Ferienkurse für Physik, die seit 1991 in den neuen Bundesländern stattfinden. Sie richten sich an Studenten höherer Semester und an Doktoranden. Zudem fördert die Stiftung regelmäßig wissenschaftliche Veranstaltungen - auch an der TU Chemnitz. Weitere Informationen erteilt Prof. Dr. Michael Schreiber, Telefon 0371 531-33141, E-Mail [email protected]. Mario Steinebach 06.07.2011

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Annual Report 2011

Campus

Erfahrungsaustausch rund um die Vermittlung physikalischer Phänomene Praktikumsleiter und Vorlesungsassistenten der Physik aus ganz Deutschland treffen sich zwischen dem 19. und 23. September 2011 in Chemnitz Mehr als 100 Teilnehmer aus ganz Deutschland - von Bremerhaven bis Konstanz sowie von Saarbrücken bis Dresden - kommen Ende September zur 31. Praktikumsleitertagung sowie zum 7. Workshop für Vorlesungsassistenten nach Chemnitz. Auch aus Wien, von anderen österreichischen Hochschulen und aus Athen haben sich Gäste angekündigt. Die Leiter der Physikpraktika sind innerhalb der Arbeitsgruppe "Physikalische Praktika" (AGPP) der Deutschen Physikalischen Gesellschaft e. V. (DPG) deutschlandweit organisiert. Die Praktikumsleitertagung findet traditionsgemäß im Herbst an einem Hochschulstandort statt, abwechselnd in den westdeutschen und ostdeutschen Bundesländern. Vom 20. bis 23. September 2011 lädt nun die Technische Universität Chemnitz ein. "Ziel dieser Veranstaltung ist es, den Hochschulstandort vorzustellen und die an Zu den besonderen Praktikumsangeboten der TU Chemnitz gehört das der TU vorhandenen Physikpraktika zu präsentieren, wodurch eine rege Schülerlabor "Wunderland Physik", das bereits seit mehr als fünf Jahren Diskussion mit den Kollegen von anderen Hochschulen zur weiteren besteht. Foto: Wolfgang Thieme Gestaltung der Physikpraktika, insbesondere unter dem Aspekt der neuen Bachelor- und Masterstudiengänge angeregt werden soll", sagt der Leiter des Fortgeschrittenen- und Labor-Praktikums und einer der Organisatoren der Praktikumsleitertagung, Dr. Thomas Franke. Vom 19. bis zum 21. September 2011 treffen sich zudem die Vorlesungsassistenten der Experimentalphysik in Chemnitz zum nunmehr 7. Workshop. "Dass der Workshop für Vorlesungsassistenten und die Praktikumsleitertagung am selben Ort stattfinden und sich zeitlich überschneiden, ist bisher einmalig und bietet die Gelegenheit, dass sich die beiden Interessengruppen zu einem breiten Erfahrungsaustausch zusammenfinden können", sagt Franke und ergänzt: "Das 175-jährige Jubiläum der TU Chemnitz bot einen angemessenen Anlass, die beiden Tagungen in diesem Jahr an unsere TU zu holen. Außerdem bietet der Neubau des Instituts für Physik einen einladenden Rahmen für diese Veranstaltungen." Die Physiker der TU Chemnitz präsentieren im Verlauf der Tagungen ihre oft ganz speziellen Praktikumsangebote - vom Grund- über das Fortgeschrittenen- und Laborpraktikum bis zum Computerpraktikum. Auf dem Programm stehen außerdem unter anderem die Vorstellung des Physikhörsaales inklusive der neuen und modernen Präsentationstechnik, Besichtigungen der Vorlesungssammlung, der modernen Praktikumsräume inklusive des Schülerlabors "Wunderland Physik" und ein didaktisch und methodisch ausgerichteter Experimentalvortrag zum Thema "Eine geschlossene Darstellung der Elektrodynamik von den Feldern bis zu Maxwell mit vielen Demonstrationsexperimenten". Darüber hinaus gibt es Vorträge der Unternehmen, die sich in der Firmenausstellung im Foyer des Hörsaalgebäudes am Mittwoch präsentieren. Vertreten sind hier vor allem Firmen aus der Lehrmittelbranche, aber auch Lieferanten für den Labor- und Forschungsbedarf. Das Rahmenprogramm bietet Möglichkeiten, die Stadt Chemnitz kennen zu lernen - beispielsweise bei einer Stadtführung, einem Besuch im VW-Motorenwerk, im Museum Gunzenhauser oder dem Sächsischen Industriemuseum. Im Rahmen der Jubiläumsausstellung "175 Jahre TU Chemnitz" sind dort nämlich auch Exponate zu bewundern, die von Adolf Ferdinand Weinhold selbst konzipiert wurden, um die damals bescheidene physikalische Sammlung der Gewerbschule zu erweitern. Dass aus diesen kleinen Anfängen eine deutschlandweit beachtete Sammlung entstanden ist, geht vor allem auf das Wirken Weinholds zurück, der sein Wissen auch in vielbeachteten Büchern veröffentlicht und damit in Chemnitz eine Tradition der anschaulichen Demonstration physikalischer Phänomene begründet hat. Seine Bücher dienten vielen Physikdozenten, Vorlesungsassistenten und Praktikumsleitern nach ihm als Vorlage und Inspiration für ihre Tätigkeit. Über eines dieser Werke wird Prof. em. Dr. Manfred Wobst in seinem Vortrag "Vorschule der Experimentalphysik: Ferdinand Adolf Weinholds Wirken in Chemnitz" im Industriemuseum sprechen. Dieser Vortrag am 22. September 2011 um 18 Uhr ist öffentlich und richtet sich an alle Interessierten. Ein weiterer Vortrag im Rahmen der Tagungen zum Thema "Stilllegung und Sanierung der Hinterlassenschaften des Uranerzbergbaus in Sachsen und Thüringen durch die Wismut GmbH" verdeutlicht die enormen Leistungen der vergangenen 20 Jahre in dieser Region zur Rekultivierung einer Landschaft, die in den 40 zurückliegenden DDR-Jahren arg in Mitleidenschaft gezogen wurde, und greift damit auch ein generelles aktuelles Problem der Atomwirtschaft beim sicheren Umgang mit radioaktiven Stoffen und Materialien auf. Weitere Informationen gibt es im Internet unter http://www.tu-chemnitz.de/physik/PLT sowie von Dr. Thomas Franke, Telefon 0371 531-33051, E-Mail [email protected]. Katharina Thehos 09.09.2011

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Veranstaltungen

Die Vorschule der Experimentalphysik Prof. Dr. Manfred Wobst und Dr. Hans-Gottfried Hempel referieren am 22. September 2011 im Industriemuseum im Rahmen der Sonderausstellung "Wissen, was gut ist. 175 Jahre TU Chemnitz" Das "duo infernale" Prof. em. Dr. Manfred Wobst und Dr. Hans-Gottfried Hempel präsentieren am 22. September 2011 um 18 Uhr im Industriemuseum Chemnitz im Rahmen des letzten Abendvortrages der Jubiläumsausstellung alte Experimente nach Adolf Ferdinand Weinhold in neuer Form. Zum Universitätsball 2008 traten beide zum letzten Mal gemeinsam mit einem Experimentalvortrag auf. Mit Ballkleid und Anzug saßen damals die begeisterten Gäste in den Hörsaalbänken, als der 81-jährige Physikprofessor Manfred Wobst und sein Assistent Dr. Hans-Gottfried Hempel durch den Raum wirbelten und dabei sehr anschaulich zeigten, welchen Einfluss Drehkräfte ausüben können. Prof. Wobst ist seitdem zwar etwas älter geworden, aber keineswegs weniger aktiv. Adolf Ferdinand Weinhold veröffentlichte 1872 die erste Auflage der Beim physikalischen Vortrag während des Universitätsballs 2008 standen Prof. Dr. Manfred Wobst auch schonmal die Haare zu Berge "Vorschule der Experimentalphysik - Naturlehre in elementarer Darstellung eine Neuauflage des Experimentalvortrages gibt es nun im nebst Anleitung zur Ausfertigung der Apparate". Der ersten folgten vier Industriemuseum. Foto: Heiko Kießling weitere Auflagen. In diesem Werk beschreibt Weinhold außerordentlich anschaulich physikalische Experimente zum Nachmachen. An der Chemnitzer Königlichen Gewerbschule hatte Weinhold die Experimentalphysik bereits in den Unterricht eingeführt. Bereits mit seiner Berufung kam es zum Bruch mit der "Kreide-Physik". Weinhold entwarf selbst eine Vielzahl von Geräten und Versuchsanordnungen. Prof. Wobst und Dr. Hempel nutzen nun dieses Werk, um anlässlich des in diesem Jahr begangenen 175-jährigen Jubiläums der Gründung der Königlichen Gewerbschule in Chemnitz mit einem Feuerwerk nachgestellter Experimente die Bedeutung Weinholds für die Chemnitzer Physikausbildung einem interessierten Besucher nahe zu bringen.

(Autor: Stephan Luther) Weitere Informationen zur Sonderausstellung , die noch bis zum 3. Oktober 2011 im Sächsischen Industriemuseum Chemnitz an der Zwickauer Straße 119 zu sehen ist: http://www.tu-chemnitz.de/uni-archiv/info/projekte/175jahre/175.php Katharina Thehos 20.09.2011

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Veranstaltungen

Erfolgreicher Erfahrungsaustausch zwischen Vorlesungsassistenten und Praktikumsleitern 31. Praktikumsleitertagung und 7. Workshop für Vorlesungsassistenten lockte rund 100 Konferenzbesucher an die TU Chemnitz Vom 19. bis 23. September 2011 trafen sich etwa 65 Praktikumsleiter und 35 Vorlesungsassistenten der Physik aus ganz Deutschland sowie aus Wien und Athen an der Technischen Universität Chemnitz. Erstmalig entschieden sich die Organisatoren, den Workshop für Vorlesungsassistenten und die Praktikumsleitertagung mit zeitlicher Überschneidung stattfinden zu lassen und so zu einer großen gemeinsamen Veranstaltung zu verbinden. "Wie die Tagung gezeigt hat, bleibt dieser Versuch, Praktikumsleiter und Vorlesungsassistenten zusammenzubringen, nicht einmalig. Das soll in den kommenden Jahren bei Bedarf wieder so stattfinden", sagt Dr. Thomas Franke, einer der Hauptorganisatoren der Konferenz, der selbst als Vorlesungsassistent und Praktikumsleiter an der TU Chemnitz tätig ist. So entstanden vor allem am Mittwochabend beim gemeinsamen Konferenzdinner anregende Diskussionen zwischen beiden Arbeitsgruppen. Dr. Thomas Franke (r.) und Dr. Hans-Gottfried Hempel vom Chemnitzer Institut für Physik zeigten ihren Kollegen einen didaktisch und methodisch ausgerichteten Experimentalvortrag zum Thema "Eine geschlossene Darstellung der Elektrodynamik von den Feldern bis zu Maxwell mit Demonstrationsexperimenten". Foto: Dr. Sascha Gruner

Das Veranstaltungsprogramm sowie die Rede des Rektors wurden von den Tagungsteilnehmern sehr positiv aufgenommen. "Die Veranstaltung hier in Chemnitz ist sehr gut organisiert und umgesetzt", lobt Jürgen Durst von der Friedrich-Alexander Universität Erlangen-Nürnberg. Der Praktikumsleiter besuchte die Konferenz, um sich ein Bild von der Vielfalt der Praktika-Umsetzungen an der TU zu machen und sich Inspirationen für das eigene Praktikum zu holen. Für sein persönliches Highlight der Veranstaltung, die Experimentalvorlesung von Dr. Hans-Gottfried Hempel und Dr. Franke am Dienstagabend, die sich hauptsächlich an die Vorlesungsassistenten richtete, reiste Durst - wie andere Praktikumsleiter auch - extra einen Tag früher an. Physikalischer Inhalt und methodische Gestaltung des Vortrages stießen bei den Zuhörern auf Resonanz und Erstaunen. Auch die Firmenausstellung am Mittwoch fand großen Anklang. "Es ist wichtig, dass die Lehrenden an der Hochschule mit den Firmenvertretern sprechen, damit die Firmen keine Entwicklungen ins Blaue machen, sondern wissen, was gebraucht wird", erklärt Franke. Katrin Groth von der Universität Hamburg nahm diese Möglichkeit, mit den Firmenvertretern ins Gespräch zu kommen, gern war: "Gut, viele Firmen kennt man schon, aber mit den Vertretern in Kontakt zu kommen, erleichtert es auch, sie später einfach mal anzurufen oder einzuladen. Ich finde es immer sehr gut, den persönlichen Kontakt zu pflegen." An ihrer Heimatuniversität finden die Praktika an verschiedenen Standorten statt, wodurch es nur selten zum Austausch zwischen den einzelnen Praktikumsleitern kommt. "Hier auf der Tagung hat man mal die Möglichkeit, mit anderen zu sprechen, die mit denselben Schwierigkeiten zu kämpfen haben oder auch ähnliche Erfolge einfahren. Das ist immer wieder sehr erbaulich und motivierend", so Groth. Nachdem die Physiker der TU Chemnitz am Donnerstag ihre Praktika und Studiengänge vorgestellt hatten, herrschte am Freitag reger Andrang während der Besichtigung der Praktikumsräume sowie des Schülerlabors. "Viele beneiden uns jetzt. Das gibt Ansporn für zukünftige Lehraufgaben", so Franke. Der Organisator ist mit dem Verlauf der Veranstaltung sehr zufrieden. Er dankt allen, die an der Planung und Durchführung des Workshops für Vorlesungsassistenten sowie der Praktikumsleitertagung mitgewirkt haben. "Mir liegt wirklich sehr viel an der Außendarstellung unserer Uni. Durch unser Wirken, mit dem neuen Physikgebäude und der Orangerie im Hintergrund, haben wir einen äußerst positiven und vor allem nachhaltigen Eindruck hinterlassen, das haben alle bestätigt." (Autorin: Anett Michael) Katharina Thehos 26.09.2011

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Forschung

Kostengünstige Dünnschicht-Solarzellen sind das Ziel 1,7 Millionen Euro investierten Bund und Land an der TU Chemnitz in ein neues Chemielabor für Photovoltaik und eine umfangreiche Beschichtungs-Ausstattung Derzeitige Solarzellen, die Sonnenenergie umweltschonend direkt in elektrische Energie umwandeln, haben einen relativ niedrigen Wirkungsgrad und hohe Herstellungskosten. Wissenschaftler der Technischen Universität Chemnitz wollen deshalb gemeinsam mit vier mittelständischen sächsischen Unternehmen ein kostengünstiges Verfahren zur Herstellung von Dünnschicht-Solarzellen auf Silizium-Basis entwickeln. Dafür stehen an der TU künftig ein neues Labor für die Photovoltaik-Chemie und eine moderne Beschichtungsausstattung zur Verfügung. "In den Laborausbau und in die gerätetechnische Ausstattung wurden etwa 1,7 Millionen Euro investiert", sagt Prof. Dr. Heinrich Lang, Inhaber der Professur Anorganische Chemie der TU Chemnitz. Im neuen Chemielabor werden künftig neuartige, siliziumorganische Verbindungen hergestellt und analysiert. Für deren Weiterverarbeitung David Adner, wissenschaftlicher Mitarbeiter der Professur Anorganische nutzt die Professur Anorganische Chemie der TU Chemnitz ein innovatives Chemie, arbeitet an einem Rotationsverdampfer Vorstufen für die Ultraschall-Sprühverfahren. Die ebenfalls am Projekt beteiligte Professur Synthese siliziumorganischer Verbindungen auf. Foto: Mario Steinebach Digitale Drucktechnologie und Bebilderungstechnik unter Leitung von Prof. Dr. Reinhard R. Baumann verwendet alternativ dazu spezielle Druckverfahren zur Strukturierung der Schichten. Die dafür notwendige Technik ist in großen "Gloveboxen" integriert. Dies sind so genannte Handschuhkästen, die hermetisch von der Arbeitsumgebung abgeschlossen sind. Innerhalb der mit einer im Bedienfeld durchsichtigen Scheibe ausgestatteten Box kann eine spezielle Atmosphäre zur Bearbeitung empfindlicher Stoffe bei der Solarzellenfertigung erzeugt werden. Die so hergestellten Schichtsysteme lassen sich im Anschluss durch thermische bzw. photochemische Nachbehandlung in Halbleiterschichten umwandeln. Forscher der Professur Halbleiterphysik werden unter Leitung von Prof. Dr. Dietrich R.T. Zahn die Schichten eingehend charakterisieren. Zudem befindet sich eine so genannte "In-Line Analytik" in der Entwicklung, mit der die erzeugten Schichten bereits während des Produktionsprozesses charakterisiert werden, was eine minimale Reaktionszeit zur Prozesskontrolle zulässt. Die grundlegende Erforschung dieser neuen Technik an der TU Chemnitz wird durch Bundes- und Landesmittel gefördert. Das Projekt gliedert sich in das Forschungsschwerpunktfeld "Smart Systems and Materials" der TU Chemnitz ein. Sobald die Grundlagenforschung abgeschlossen ist, soll das neue Verfahren mit Hilfe der Industriepartner zur Marktreife gebracht werden. Zu den beteiligten Unternehmen gehören das Institut für innovative Technologien ITW e. V. Chemnitz, die SIGMA Chemnitz GmbH, die SITEC Industrietechnologie GmbH Chemnitz und die DTF Technology GmbH Dresden. Weitere Informationen erteilt Prof. Dr. Heinrich Lang, Telefon 0371 531-31673, E-Mail [email protected] Mario Steinebach 06.10.2011

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Ehrungen

Leistung zahlt sich aus Vergabe der Universitätspreise der TU Chemnitz sowie des Preises des Deutschen Akademischen Austauschdienstes erfolgte im Rahmen der Immatrikulationsfeier Die feierliche Immatrikulation in der Stadthalle am 10. Oktober 2011 bedeutete für viele den Start eines neuen Lebensabschnittes, des Studiums. Doch für ein paar stand sie auch für das Ende ihres Studiums oder ihrer Promotion - acht Absolventen wurden im Rahmen der Veranstaltung mit Universitätspreisen für ihre herausragenden Abschlussarbeiten ausgezeichnet. Außerdem wurde der Preis des Deutschen Akademischen Austauschdienstes überreicht. Mit den von der Gesellschaft der Freunde der TU Chemnitz vergebenen und jeweils mit 1.000 Euro dotierten Universitätspreisen werden bereits seit vielen Jahren die jeweilig besten Abschlussarbeiten aller Fakultäten ausgezeichnet. Preisträgerin der Fakultät für Naturwissenschaften ist in diesem Jahr Dr. Janett Prehl, die für ihre Doktorarbeit auf dem Gebiet der Die Universitätspreisträger 2011: Dr. Günther Schlee, Dr. Janett Prehl, Dr. statistischen Physik ausgezeichnet wurde. Sponsor des Preises ist die envia Thomas Risch, Michael Teichmann, Marco Porsch (hinten v.l.) sowie Mitteldeutsche Energie AG. Die Auszeichnung an der Fakultät für Sarah Zönnchen, Dr. Irina Ochirova und Dr. David Wenzel (vorne v.l.). Mathematik geht an Dr. David Wenzel für seine Dissertation über ein Thema Foto: Christian Schenk der Operatortheorie. Gesponsert wird dieser Preis von der eins energie in sachsen GmbH & Co. KG. Dr. Thomas Risch erhält den Universitätspreis an der Fakultät für Maschinenbau. Die Auszeichnung für seine Dissertation im Fachgebiet der Förder- und Handhabetechnik sponsert Niles Simmons Chemnitz. An der Fakultät für Elektrotechnik und Informationstechnik geht die Auszeichnung an Marco Porsch. Die Siemens AG Erlangen ist Sponsor des Preises, der für seine Diplomarbeit auf dem Gebiet der Kommunikationstechnik vergeben wird. Mit seiner Diplomarbeit über Modellierung und visuelle Objekterkennung gewann Michael Teichmann den Universitätspreis an der Fakultät für Informatik. Sponsor dieses Preises ist die Voith Engineering Services GmbH Road and Rail. Mit der wirtschaftlichen Bewertung technologischer Prozessketten beschäftigte sich Sarah Zönnchen in ihrer Masterarbeit und erhielt dafür die Auszeichnung an der Fakultät für Wirtschaftswissenschaften. Sponsor ist die C & E Consulting und Engineering GmbH. Preisträger an der Philosophischen Fakultät ist Dr. Irina Ochirova. Die Auszeichnung ihrer Dissertation mit einem Thema zur Europäischen Integration sponsert die Oberbürgermeisterin der Stadt Chemnitz. Dr. Günther Schlee wurde an der Fakultät für Human- und Sozialwissenschaften mit einer Arbeit zur Sensorikforschung in der Bewegungswissenschaft promoviert. Dafür erhält er den Preis, den die Deutsche Bank AG Chemnitz sponsert. Ebenfalls im Rahmen der Immatrikulationsfeier wurde der beste ausländische Student ausgezeichnet. Der mit 1.000 Euro dotierte Preis des Deutschen Akademischen Austauschdienstes (DAAD) ging in diesem Jahr an Vince Kolozsvari aus der ungarischen Hauptstadt Budapest. Er studiert im fünften Semester Europastudien mit sozialwissenschaftlicher Ausrichtung, im anschließenden Masterstudium möchte er sich in Richtung Europarecht weiterbilden. Katharina Thehos 10.10.2011

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Studium

Einblicke in die Praxis, Ausblicke auf Berufsmöglichkeiten Mit dem Fachschaftsrat Physik nach Hamburg: Studierende zwischen Teilchenbeschleuniger, Kernkraftwerk und Flugzeugbau Ein Montag Ende September, 6.30 Uhr: Am Hauptbahnhof treffen sich 19 (Wahl-) Chemnitzer und starten eine Reise nach Hamburg. Gegen 15 Uhr werden sie rund 500 Kilometer weiter nördlich mit einem freundlichen: "Hallo und Herzlich willkommen im DESY" begrüßt. Das Deutsche Elektronen-Synchrotron (DESY) war der erste Programmpunkt dieser Reise vom 26. bis zum 28. September 2011, die der Fachschaftsrat Physik organisiert hatte. Beim DESY besichtigten die Studierenden unter anderem den Beschleunigerring HERA, der zwar zurzeit nicht aktiv ist, aber dennoch Erstaunen und Respekt hervorrief. Am nächsten Morgen teilte sich die Gruppe: Sieben Teilnehmer machten sich auf den Weg ins Kernkraftwerk Krümmel. Dort wurden sie mit Kaffee und Plätzchen empfangen und in die Geschichte sowie Technik des Kernkraftwerks eingeweiht. Nach dem Mittagessen in der werkseigenen Obwohl auf dem Gelände der Lufthansa striktes Fotografierverbot Kantine erfuhren sie bei einem Rundgang durch die Anlage noch mehr über herrscht, wurde bei den TU-Studierenden eine Ausnahme gemacht - für Geschichten hinter den Kulissen der Anlage. Einer der Höhepunkte war die ein Gruppenfoto der Chemnitzern vor dem Airbus "Chemnitz". Foto: Besichtigung der eingelagerten Brennstäben und des Reaktorkerns. Die Martin Dehnert anderen zwölf Teilnehmer besichtigten in der Zwischenzeit die Liegenschaften der Lufthansa. Höhepunkt der Rundtour war ein Airbus mit dem Namen "Chemnitz". Dieses Flugzeug lag auf dem Gelände, weil neue Sitze eingebaut wurden. Die TU-Studierenden konnten von ihrer Exkursion die Nachricht mitnehmen, dass sowohl die Forschungseinrichtung DESY als auch die Lufthansa händeringend nach Physikern suchen. Bei der Lufthansa bietet sich zudem ein breites Spektrum für Studierende des Studienganges Sensorik und kognitive Psychologie. Der Fachschaftsrat Physik vermittelt Kontakte für Praktika, Bachelor-, Master- und Doktorarbeiten bei den besuchten Unternehmen. Als kulturelles Highlight schloss am dritten Tag eine Hafenrundfahrt die Exkursion ab. Finanziell unterstützt wurde die Reise vom Institut für Physik, der Gesellschaft der Freunde der TU Chemnitz e.V. und dem Chemnitzer Förderverein für Physik e.V. Weitere Informationen erteilt der Fachschaftsrat Physik: http://www.tu-chemnitz.de/fsphysik Katharina Thehos 14.10.2011

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Veranstaltungen

Von gebündeltem Licht und völliger Leere Das Jubiläumsjahr der TU Chemnitz geht auf die Zielgerade: Im Dezember 2011 lädt das Institut für Physik zu öffentlichen Vorträgen ein, die auch für Laien verständlich sind Am 10. und am 17. Dezember 2011 lädt das Institut für Physik im Rahmen des 175-jährigen Uni-Jubiläums jeweils um 10 Uhr zu öffentlichen Vorträgen ein. Diese finden im Hörsaalgebäude der TU Chemnitz an der Reichenhainer Straße 90, Raum N013, statt. Prof. Dr. Günter Huber vom Institut für Laserphysik der Universität Hamburg spricht am Samstag, den 10. Dezember 2011, zum Thema "Laser - Geschichte, Anwendungen und Ausblick". Als Albert Einstein 1916 in seinen Überlegungen "zur Quantentheorie der Strahlung" erstmals die stimulierte Emission von Strahlung postulierte, war noch nicht abzusehen, welche Revolution dieses heute im Laser angewendete Prinzip bewirken würde. Zum Einsatz kommen Laser heute zur schnellen Informationsübertragung über Hunderte von Kilometern in Glasfasern, in DVD- und CD-Spielern, für Am 17. Dezember spricht Prof. Dr. Frank Richter über "Das Vakuum wozu ist das Nichts nütze?". Der Inhaber der Professur Physik fester die Materialbearbeitung, in der Mess- und Medizintechnik. Auch viele Körper erforscht mit seinen Mitarbeitern tagtäglich den luftleeren Raum. moderne Forschungsmethoden wären ohne Laser nicht mehr denkbar. Aber Foto: Christian Schenk wie funktionieren Laser? Welche Forschungsergebnisse haben zu den heutigen Anwendungen geführt? Was ist Stand der Technik und wie werden Laser in der täglichen Forschung eingesetzt? In seinem Vortrag gibt Prof. Huber einen Abriss über Laser, ihre Geschichte und heutige Anwendungen. Im Anschluss an den Vortrag stellt Prof. Dr. Rudolf Bratschitsch, Inhaber der Professur Dynamik nanoskopischer und mesoskopischer Strukturen an der TU Chemnitz, vor, welche Forschungsfragen mit ultrakurzen Laserimpulsen am Institut für Physik der Chemnitzer Universität untersucht werden. Am Samstag, den 17. Dezember 2011, geht dann Prof. Dr. Frank Richter, Inhaber der Professur Physik fester Körper der TU Chemnitz der Frage nach "Das Vakuum - wozu ist das Nichts nütze?". Wenn die Luft aus einem Behälter mehr oder weniger vollständig herausgepumpt ist, spricht man davon, dass sich in diesem Behälter ein Vakuum befindet. Technisch gelang das erstmals im 17. Jahrhundert. Mittlerweile ist das Vakuum ein unverzichtbares Instrument, ohne das viele alltägliche Dinge wie Fernsehbildröhren oder Glühlampen nicht funktionieren. Die größten Vakuumanlagen stellen Teilchenbeschleuniger dar, wie sie zum Beispiel bei CERN in Genf stehen, aber auch Versuchsanlagen zur Kernfusion oder Weltraumsimulationsanlagen. Auch in den Labors des Instituts für Physik der TU Chemnitz ist das Vakuum ein wichtiges Hilfsmittel für die Forschung. Einige dieser Vakuumanwendungen stellt Prof. Richter im Vortrag vor. Abschließend geht er darauf ein, dass das Vakuum für die moderne Physik doch mehr ist als nur der leere Raum. Ebenfalls schon vormerken können sich alle Physik-Begeisterten die Weihnachtsvorlesung von Dr. Hans-Gottfried Hempel und Dr. Wolfgang-Hartmut Lißner. Am 21. Dezember laden sie um 15 Uhr und um 17 Uhr jeweils im Raum N012 des Hörsaalgebäudes ein zum Thema "Alles muss raus - Experimente, die uns schon immer gefallen haben". Weitere Informationen erteilt Dr. Steffen Seeger, Telefon 0371 531-33279, E-Mail [email protected]. Katharina Thehos 06.12.2011

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Annual Report 2011

Ehrungen

Glückwünsche nach Baden-Württemberg Elf Forscher erhalten Leibniz-Preise 2012, darunter Prof. Dr. Jörg Wrachtrup von der Universität Stuttgart, der sich 1998 an der TU Chemnitz habilitierte "Als ich erfuhr, dass Professor Jörg Wrachtrup, dem Leiter des 3. Physikalischen Instituts der Universität Stuttgart, gestern der hoch dotierte Gottfried-Wilhelm-Leibniz- Preis zuerkannt wurde, habe ich mich sehr gefreut", sagt Prof. Dr. Christian von Borczyskowski, Inhaber der Professur Optische Spektroskopie und Molekülphysik an der TU Chemnitz. Der Grund: Wrachtrup forschte nach seiner Promotion an der FU Berlin vier Jahre an dieser Professur und habilitierte sich 1998 am Institut für Physik der TU Chemnitz mit einer Arbeit über Optische Spektroskopie an einzelnen Quantensystemen im Festkörper. Während dieser Zeit wurden die wissenschaftlichen Grundlagen für die Auszeichnung an der Chemnitzer Professur gemeinsam mit Prof. von Borczyskowski gelegt und in den führenden wissenschaftlichen Zeitschriften "Nature" und "Science" veröffentlicht. Die mit 2,5 Millionen Euro dotierte Auszeichnung gilt als der bedeutendste Forschungspreis in Deutschland und wird auch als "deutscher Nobelpreis" gehandelt. Wrachtrup erhält die Auszeichnung, da er ein völlig neuartiges und sehr erfolgreiches Forschungsgebiet an der Schnittstelle zwischen Festkörperphysik und Quantenoptik erschlossen hat. Als Meilenstein gilt vor allem die Detektion einzelner paramagnetischer Stickstoff-Fehlstellen in Diamant, den so genannten NV-Zentren, die sich durch eine außergewöhnliche Fotostabilität auszeichnen. Wrachtrup erkannte als erster Wissenschaftler die Bedeutung von NV-Zentren für die Quanteninformationstechnologie und die Messtechnik. Das damit von ihm wesentlich begründete Forschungsfeld strahlt jedoch weit über die Festkörperphysik und die Quantenoptik hinaus bis in die Material- und Lebenswissenschaften hinein. Prof. Dr. Jörg Wrachtrup Foto: Universität Stuttgart

Mario Steinebach 09.12.2011

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Annual Report 2011

Veranstaltungen

Weihnachten ganz nach dem Geschmack des Publikums Am 21. Dezember 2011 gibt es die besten Experimente aus 35 Jahren Physik-Weihnachtsvorlesung Damit auch jeder auf seine Kosten kommt in der Adventszeit, haben sich die Physiker der TU Chemnitz in diesem Jahr etwas ganz Besonderes überlegt. Unter dem Motto "Alles muss raus - Experimente, die uns schon immer gefallen haben" widmen sich Wolfgang-Hartmut Lißner und Dr. Hans-Gottfried Hempel den Experimenten, "die wir besonders attraktiv finden und die auch beim Publikum gut angekommen sind". Am Mittwoch, den 21. Dezember 2011, werden ab 15 Uhr im Physikhörsaal N012 im Hörsaalgebäude an der Reichenhainer Straße 90 unter anderem Drehschemel gedreht, Schwingungen erzeugt und elektrische Effekte veranschaulicht. "Uns gefällt neben unseren Versuchen besonders, dass wir so lange ein Das beliebteste aus 35 Jahren: Wolfgang-Hartmut Lißner (l.) und Dr. solch zahlreiches, interessiertes und treues Publikum haben", so Hempel. Hans-Gottfried Hempel laden dieses Jahr ein zur Weihnachtsvorlesung Um diese Treue entsprechend zu würdigen, wird es zur Weihnachtszeit nur unter dem Motto "Experimente, die uns schon immer gefallen haben." Foto: Christian Schenk das Beste aus 35 Jahren geben. Es werden um die 50 Versuche aus allen Gebieten der klassischen Physik gezeigt. "Im Umgang mit Experimenten habe ich gemerkt, dass trotz abstrakter Modelle Spannung erzeugt werden kann", sagt Hempel. Die Vorlesung ist öffentlich, der Eintritt ist frei. Da die Weihnachtsvorlesung sehr beliebt ist, findet ab 17 Uhr eine Wiederholung statt. Außerdem werden beide Veranstaltungen dieses Jahr auch in den Hörsaal N115 in Echtzeit auf Großleinwand übertragen. Auskunft zur Weihnachtsvorlesung geben Dr. Hans-Gottfried Hempel, Telefon 0371 531-34333, E-Mail [email protected], und Wolfgang-Hartmut Lißner, E-Mail [email protected]. (Autorin: Maria Lange) Katharina Thehos 15.12.2011

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Annual Report 2011

How to reach us

Chemnitz University of Technology Institute of Physics Reichenhainer Strasse 70 09126 Chemnitz Germany GPS-coordinates: 50°48’55.16N 12°50’34.48O

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Chemnitz University of Technology

Institute of Physics Reichenhainer Staße 70 D-09126 Chemnitz Phone: ++49/371/531-21500 Fax: ++49/371/531-21509 www.tu-chemnitz.de/physik [email protected]