and B. W. Skelton, Journal of Organometallic Chemistry 565, 159. (1998). 15. ... I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A.. Al-Laham, C. Y. ...
Journal of Computational and Theoretical Nanoscience Vol. 1, 1–15, 2005
Copyright © 2005 American Scientific Publishers All rights of reserved Printed in the United States of America
Multiscale Simulation of the Synthesis, Assembly and Properties of Nanostructured Organic/Inorganic Hybrid Materials RESEARCH ARTICLE
Clare McCabe,1 Sharon C. Glotzer,2 3 John Kieffer,3 Matthew Neurock,4 and Peter Cummings5 6 ∗ 1
Department of Chemical Engineering, Colorado School of Mines, Golden C0 80401 Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109-2136 3 Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI 48109-2136 4 Department of Chemical Engineering, University of Virginia, Charlottesville, VA 22904-4741 5 Department of Chemical Engineering, Vanderbilt University, Nashville, TN 37235-1604 6 Chemical Sciences Division and Nanomaterials Theory Institute, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6181 2
Polyhedral oligomeric silsesquioxane (POSS) molecules are unique nanometer-sized inorganic– organic hybrid structures based on a (SiO15 8 core. Depending on the functionalization of the POSS cages, the resulting systems can be solid or liquid, or, upon cross-linking, turned into a network. Although much is known experimentally about the chemical synthesis of POSS systems, very little theoretical understanding exists at the molecular level or beyond. In particular, the way in which individual POSS molecules can be assembled and manipulated at the nanoscale to form meso- and macroscale systems has not been investigated previously. The overall goal of our work is to develop a multiscale computational framework to simulate the synthesis and self- and guided-assembly of POSS systems. In this report we present an overview of the computational approach on which this framework is based, which combines simulation techniques at the electronic, atomistic, and mesoscale levels, and we provide an overview of progress in each of these areas.
Keywords: Polyhedral Oligomeric Silsequioxanes, POSS, Multiscale Simulation.
1. INTRODUCTION Polyhedral oligomeric silsesquioxane (POSS) molecules are unique nanometer-sized multifunctional molecules, with the chemical composition (RSiO15 n (n = 6 8 10 ) that is a hybrid intermediate between that of silica (SiO2 and polysiloxanes (R2 SiO)n . The most studied member of the series (n = 8) is the polyhedral octasilsesquioxane (RSiO15 8 , which is essentially a cube with Si atoms on the corners, and O atoms along the edges of the cube. In its simplest form, R is hydrogen (see Fig. 1). The polyhedral cores of the POSS molecules can be multifunctional and serve as platforms that can be synthetically modified to contain groups for ∗
Author to whom correspondence should be addressed.
J. Comput. Theor. Nanosci. Vol. 1, No. 3 2005
copolymerization, adhesion, light sensitization, binding, catalysis, and improved solubility. The ability to independently functionalize each corner of a POSS cage with organic or inorganic groups confers a nearly infinite array of possible nanostructures made of assemblies of POSS molecules. Depending on the functionalization of the POSS cages, the resulting systems can be solid or liquid, or, upon cross-linking, turned into a network, hence creating a class of organic–inorganic hybrid molecules with a wide variety of applications in areas such as liquid crystals,1–5 nanocomposites,6–10 and CVD coatings.11 POSS molecules are truly nanostructured building blocks, which, through self- and guided-assembly, can be transformed into a remarkable array of products that are just now becoming available to industry on a large scale.
© 2005 by American Scientific Publishers
1546-198X/2005/1/001/015/$17.00+.25
doi:10.1166/jctn.2005.d
1
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J. Comput. Theor. Nanosci. 1, 1–15, 2005
molecular dynamics [MD], and Monte Carlo [MC] simulation methods and mesoscale MD, Langevin (Brownian) dynamics [BD], and MC simulations using coarse-grained models. In this report we provide a brief overview of progress in each of these areas. (a)
(b)
(c)
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Fig. 1. (a) The fundamental POSS cube (HSiO15 8 . Silicon atoms are shown in blue, oxygen in red, and hydrogen in white. (b) An example of mono-alkyl-tethered POSS, in this case propyl-POSS, H7 (CH3 (CH2 2 (SiO15 8 . Carbon atoms are shown in green. (c) An example of fully functionalized octa-alkyl-tethered POSS, in this case octa-propyl-POSS, (CH3 (CH2 2 SiO15 8 .
Although much is known experimentally about the chemical synthesis of POSS derivatives12–14 and their characterization,15 16 little theoretical understanding exists at the molecular level or beyond. In particular, the way in which individual POSS molecules can be assembled and manipulated on the nanoscale level to form meso- and macroscale systems has not been investigated previously. Design and development of novel, hybrid organic–inorganic materials based on POSS technology requires a fundamental understanding of assembly processes that take place in these materials over time and length scales that span from atomistic to macroscopic scales. The investigation of directed self-assembly of POSS–polymer materials in particular requires the simulation of large, assembling systems containing thousands to hundreds of thousands of POSS cages functionalized with organic tethers, a task currently impossible using ab initio methods and even classical methods with chemically detailed force fields. Hence a multiscale modeling framework is needed, which will information gleaned at the electronic or atomistic levels to be used in mesoscopic models of the system. In working toward this goal we have studied POSS systems at the electronic, atomistic, and mesoscale levels, employing a variety of methods: ab initio quantum chemical methods (in particular, density functional theory [DFT] and molecular orbital theory [MOT] calculations BY using CASTEP, DMOL, Gaussian 98,17 and VASP18–21 ab initio molecular dynamics,18–21 atomistic
2. AB INITIO STUDIES OF POSS MOLECULES Our ab initio studies of POSS systems have focused on three major areas: structure and properties of the isolated simplest POSS cube (HSiO15 8 ; force field development and evaluation for (HSiO15 8 and alkyl-tethered POSS molecules (RSiO15 8 , where R is an alkyl group; and ab initio molecular-dynamics simulations of the erosion of POSS molecules by energetic atomic oxygen. 2.1. Structural Properties of (HSiO15 )8 We have evaluated the structural properties (bond lengths and angles) of the isolated (HSiO15 8 cube by using several different theoretical techniques: gradient corrected numerical basis (DMOL)22–25 and periodic plane wave (VASP) density functional theory methods19 26 and restricted Hartree Fock (RHF) with the cc-pVdz basis set using Gaussian 98.17 We also calculated these same quantities using molecular mechanics (MM) applied to two popular force fields, the universal force field (UFF) of Rappé and coworkers27 and the COMPASS (Condensedphase Optimized Molecular Potentials for Atomistic Simulation Studies) force field.28–30 MM calculations were also performed on a reactive force field (RFF) developed previously by Kieffer for silicates and other oxide materials.31 32 We are adapting this force field to POSS systems as part of this project. As can be seen in Table 1, all of the theoretical methods and the classical force fields predict structural properties for the isolated (HSiO15 8 cube to a high degree of accuracy. It is of interest to note that the UFF force field predicts the structural properties most accurately; however, there is little difference between the different theoretical approaches. First-principles density functional theoretical studies show that the smallest cube, (HSiO15 8 , has unique
Table I. Experimental measurements and theoretical predictions for the structure of the fundamental polyhedral oligomeric silsesquioxane (POSS) cage, (HSiO15 8 . For each theoretical method, the bottom line shows the average percentage absolute error for the four properties calculated.
Property Si Si Si O
O (Å) H (Å) O Si Si O
Ave. Error (%)
2
Molecular mechanics
Exp.
Plane wave (VASP)
Atomic orbital (DMOL)
RHF (cc-pVdz) (GAUSSIAN 98)
UFF
Compass
Kieffer RFF
1619 148 1475 1096
1630 1463 1467 1096
1654 1481 1459 1096
1650 1462 1487 1091
1592 1470 1468 1100
1624 1473 1469 1102
162 147 1461 1096
24
33
44
32
17
29
24
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McCabe et al./Multiscale Simulation of Organic/Inorganic Hybrid Materials
2.2. Development of Force Fields for Tethered POSS Molecules Because the targets of many of our simulations are materials composed of functionalized POSS molecules, we have embarked on developing force fields for such systems. In particular, an early focus is alkyl-tethered POSS of three varieties: single alkyl-tethered POSS, such as H7 R(SiO15 8 , tetra-tethered POSS with four alkyl groups on one side of the cube, and octatethered POSS of the form (RSiO15 8 ; in both cases, R is an alkyl group. Ideally, one would like to be able to use the same model for the cage of a tethered POSS as is used for nontethered POSS; likewise, the development of force fields would be simplified dramatically if the alkyl tether on a tethered POSS molecule behaved much like the corresponding alkane, since that would enable the use of standard force fields for alkanes in describing the alkyl chains. Let us first consider the degree to which the POSS cage is perturbed by the presence of a single tether, similar to that shown in Figure 1(b). Table 2 shows the impact of the tether on the structure of the POSS cage based on
Table II. Impact of a single tether on the structure of the bare (HSiO1.5)8 POSS cage.
(B1) Si (B2) Si (B3) Si O Si Si O
O O O O Si
POSS
ethyl-POSS
propyl-POSS
1650 1650 1650 1091 1487
1655 1647 1650 1083 1494
1656 1646 1650 1082 1498
RHF calculations using Gaussian 98 with cc-pVdz basis set.34 In the absence of a tether, all Si O bond lengths are equal, all O Si O bond angles are equal, and all Si O Si angles are equal. We report these values in the first column of values in the table (labeled POSS). The second and third columns show the same quantities for mono-ethyl-tethered and mono-propyl-tethered POSS, respectively. Three bond lengths are shown: B1 is the computed bond length for Si O bonds where the Si atom has an alkyl group attached; B2 is the next closest Si O bond (i.e., it has an O atom in common with B1); B3 is the next closest Si O bond (i.e., it shares an Si atom with B2). The O Si O bond angle is the angle that includes the Si to which the alkyl group is tethered; for the Si O Si bond angle, one of the Si atoms has an alkyl group is tether. From these results we can conclude that for the two alkyl tethers considered (propyl and butyl), the impact on the POSS cage structure is negligibly small. Given that the results in Table 2 suggest that the impact of an alkyl tether on a POSS cube is minimal, we now consider to what degree the tethering of an alkane chain to a POSS cube impacts the alkane tether. We have probed this question by examining rotation energies around bonds and partial charge distributions for various POSS molecules tethered with alkyl groups at one corner.34 The energies were calculated in the RHF approximation with the cc-pVdz basis set. A typical result is shown in Figure 2, where the torsional potentials of the alkyl portion of alkyl-tethered POSS are shown to be essentially the same as those for an alkane molecule. This and other results reported in detail elsewhere34 lead us to conclude that force fields developed for alkanes can be successfully adopted for use in alkyl-tethered POSS systems; likewise, force fields developed for inorganic materials such as the untethered POSS cage can be used successfully to represent alkyl-tethered POSS systems. These observations have provided the justification for much of our early atomistic simulation work on POSS systems using standard force fields, some of which is reported below in Section 4.
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electronic properties. The lowest unoccupied electronic states just above the last filled orbital are centered inside of the cube, thereby creating a cavity for excess electrons. At least two of these states are below the vacuum level, indicating that the potential inside the cage is lower than that of the vacuum. Any charge transfer to the cage from either other molecules or environment would reside in these states and take on characteristics of an “electron in a box.” The POSS cage (SiO15 8 (frequently referred to as T8 , therefore, can readily accept and localize an electron into the center of the cage and thus provide important luminescence properties. By using ab initio methods, we were able to show that fluorinating the corners of the cages—i.e., creating (FSiO15 8 , denoted POSS(F)8 —dramatically increases the electron affinity of the T8 cage, thereby making it energetically favorable for the POSS(F)8 to capture an extra electron inside the cube.33 Calculations indicate that this can be achieved by adding a low ionization alkali metal atom such as Na next to the POSS(F)8 cube. The alkali metal readily ionizes to produce an electron that transfers into, and is localized at the center of, the POSS cube. The POSS(F)8 system, therefore, behaves as a molecular color center. The addition of alkali promoters alters its optical properties, whereby it would absorb light of different wavelengths. By changing the nature of the POSS cube, the end-group substituents, or the specific metal atom, we can begin to tune the wavelength. These molecular color centers might be useful in the creation of optical fibers or lasers. More recent calculations are probing the effect of fluorinated alkyl tethers along with substituents with aromatic resonance structures at the cube edges in order to probe the luminescence of these structures.
2.3. Development of Reactive Force Field The disparate chemistries of the inorganic POSS cage and polymeric tethers pose a particular challenge for the description of the interactions in a POSS-polymer hybrid material using semi-empirical potentials. Owing to the 3
McCabe et al./Multiscale Simulation of Organic/Inorganic Hybrid Materials
T-propyl 7
n-butane
6
T-butyl
5
J. Comput. Theor. Nanosci. 1, 1–15, 2005
breaking of chemical bonds. This latter aspect is accomplished by using a charge-transfer term ij . The functional form of this potential is,35 N qj q i qj q i 1 = + 3 j · rij + 3 · r 4 0 j=i rij rij rij i ji
4 3 2
+
1 0 0
30
60
90
120
150
180
Rotation Angle
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Fig. 2. Torsional potential energy associated with dihedral angles for several tethered POSS molecules and for n-butane. The energies are calculated as single-point energies by using the restricted HartreeFock approximation and Gaussian 98 with the cc-pVdz basis set. The diamonds are torsional potential energies for the Si C C C dihedral angle in mono-propyl-POSS [H7 (SiO15 )8 ]CH2 CH2 CH3 ]; the triangles are for the C C C C dihedral angle in mono-butylPOSS [H7 (SiO15 8 ]CH2 CH2 CH2 CH3 ]; and the squares are for a butane molecule (i.e., not tethered to a POSS cube). Clearly, the torsional energies of the butyl POSS are almost indistinguishable from that of a butane molecule, suggesting that the impact of the POSS cube on the alkyl tether is minimal. Furthermore, the similarity between the torsional energies of the Si C C C and C C C C dihedral angles suggest that a good approximation for the Si C C C torsional energy is the alkane C C C C torsional potential from a typical high-quality alkane force field.
difference in the nature of atomic interactions and the need to emphasize different aspects of chemical bonding, simulations of inorganic and polymeric materials have traditionally been carried out using force fields described by different functional forms. For example, charge polarity constitutes a prominent component of the bonding character in silicon dioxide, whereas in many hydrocarbons these effects are negligible. On the other hand, in polymers, torsional interactions play a more significant role. In the modeling of POSS systems, it is necessary to not only represent the interactions within each type of material, but to also accurately account for the interplay between organic and inorganic structures as well as for the effect that the interspersion of different chemical characters at the molecular scale has on such interactions. Ultimately, in studying the assembly of tethered POSS cages into networks, we need to allow for chemical reactions to take place, such as cross-linking between polymers; therefore, we require the capability to perform explicit-atom large-scale reactive MD simulations. For this purpose, we have developed a charge-transfer potential designed for systems that exhibit mixed covalent-ionic interactions.31 35 This potential includes directional terms to constrain the orientations of covalent bonds caused by electronic hybridization, and torsional terms to control the dihedral angles in polymer chains. In addition to centralforce Coulomb interactions, the force field is capable of simulating dynamical polarization of electronic configuration as well as charge redistribution upon formation and 4
+ −
NC j=1
j i · 3 j · rij i · rji − 3 5 rij rij
Aij ei +j −rij ij +
NC Cij 6 j=1 rij
+
NC NC−1 j=1 k=j+1
¯
2
ij +ik e−ijk −ijk
B1 1+cosljkn
i∈ljkn
+B2 1−cos2ljkn +B3 1+cos3ljkn +B4 where qi = qi − 2
NC j=1
ij ij
and
ij = −Aij
ij
!ij
ij e"ij e−rij !ij
The charge transfer is evaluated according to ij = erij −ab + 1−1 . The dipoles i associated with individual atoms are determined in a self-consistent manner according to i = %i E, where E is the electric field at the location of atom i and %i its polarizability. The design of this potential is based on input from experiments and ab initio density functional calculations. In particular, we determined the parameters that control the charge distribution, i.e., the reference charge qi , the amount of charge transferred by forming a bond ij , and the empirical parameters a and b, by comparing the pertinent interaction energies between density functional theory calculations and molecular mechanics (MM) simulations. Rather than using Mulliken charges or similar measures to attribute a certain amount of charge to a given atom, we mapped out the potential energy experienced by a point charge and a charge dipole positioned at a variable distance and orientation relative to a hydrogen-terminated POSS cage. By using a nonlinear least-squares fitting procedure, we then optimized the aforementioned parameters until the charge distribution in our semi-empirical force field yielded the best agreement with the two calculation approaches. Figure 3 illustrates the computational procedure. As shown in Figure 3 (a), a POSS cube terminated with hydrogen is placed with its center at the origin of the coordinate system, each coordinate axis perpendicularly piercing one of the cubes faces. A charge dipole represented by a Na+ and Cl− ion pair (or a proton) is placed at a position relative to the cube as described by the distance r from the cube’s center and the two angles and , measured relative to the positive x-axis in the x-y-plane and relative to the positive z-axis in the plane perpendicular to the x- and y-axes. The position and orientation of the dipole was varied and the energy of these
J. Comput. Theor. Nanosci. 1, 1–15, 2005
McCabe et al./Multiscale Simulation of Organic/Inorganic Hybrid Materials
(a)
z θ
y φ x
(b)
(c)
LUMO θ = 45, = 0 Na+ at 5.19 Å
0.568
0.568
–0.301 –0.287
–0.807
– 0.307 – 0.900
1.558
–0.810–0.287
–0.807
– 0.287
– 0.301
– 0.287 – 0.810
1.558
– 0.307
1.558
1.521 –0.810
– 0.810
–0.810
– 0.810
–0.810
– 0.810 – 0.810
–0.810 1.521
1.521 1.525
1.521
–0.287
–0.810
–0.810 1.525
–0.294
– 0.301
– 0.900
– 0.307
1.521
1.525
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– 0.676
–0.810
– 0.294
–0.287
– 0.810 – 0.810 1.525
– 0.287
1.521
– 0.810
– 0.287
– 0.294
–0.294
(d)
(e) – 0.670
–0.812
0.574
0.574
–0.347
–0.290
– 0.347
– 0.290 – 0.812
–0.812
–0.295
1.572 –0.812 –0.290
1.521 –0.810 –0.811 1.523–0.811
–0.811
1.523
–0.295 –0.811 1.521
1.521
1.521 – 0.810 – 0.295
–0.813
–0.810 1.521 –0.810 –0.811
– 0.811 –0.290
1.523 –0.811
–0.295
– 0.812 – 0.290
– 0.811 1.523– 0.811
1.523
– 0.295 – 0.811 1.521
1.521
– 0.813
– 0.810 1.521 – 0.810 – 0.811 1.523
– 0.290
– 0.811 –0.295
– 0.295
– 0.295
Fig. 3. The highest and lowest molecular orbitals for the interaction between NaCl with POSS. These results were subsequently used in the parameterization of the reactive force field. (See text for details.)
configurations was evaluated as a function of these variables. DFT calculations explicitly yield the spatial configuration of electronic orbitals and the corresponding charge distribution, as shown in Figures 3 (b) through (e), and the POSS-cube dipole (or proton) interaction energies are a direct consequence of this charge distribution. To reproduce these energies using classical MM calculations, only the fractional charge attributed to the center of each atom and the polarization of this charge (i.e., the separation between center of charge and center of mass) were adjusted. In Figure 4, the potential energy
surfaces for the two calculation approaches are compared. Comparison shows that an excellent agreement can be achieved. By using this procedure, we determined the optimal assignment of partial charges to be +0.73725 for silicon, −0.3795 for oxygen, and −0.168 for hydrogen. In addition, we have used experimentally observed structures and properties of POSS materials to optimize potential parameters. For example, POSS cubes symmetrically functionalized with hydrogen (T8 or small hydrocarbons on all eight corners crystallize in the R3 space group, which has three POSS cubes per unit cell.15 16 36 5
–0.04 –0.05
δ(O-Si-O) 566
–0.03
ν(Si-O) 465
–0.02
E (eV)
J. Comput. Theor. Nanosci. 1, 1–15, 2005
δ(Si-O-Si) 399
McCabe et al./Multiscale Simulation of Organic/Inorganic Hybrid Materials
–0.06
–0.09 90
75
60
45
30
15
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Theta
0
0
15
30 45
60
75
90
Phi
0.08 0.06 0.04 0.02 0 – 0.02 – 0.04 – 0.06 – 0.08 – 0.1 – 0.12 100
Fig. 5. Infra-red spectra for the POSS crystal from experiment (black line) and from simulation using the reactive force field.
80
100 80
60
60
40
40
20
Theta
20 0
0
Phi
Fig. 4. Electrostatic interactions between a hydrogen-terminated POSS cube and dipole as a function of the azimuthal (theta) and polar (phi) angles, obtained from (a) ab initio calculations and (b) classical calculations using our reactive force field. The dipole is orientated in the direction pointing toward the center of the cube at all positions. The positive pole is closest to the cube and located 6.5 Å from the center of the cube; the negative pole is about 1 Å farther from the center.
In this structure, nearest-neighbor POSS cages are not positioned so as to minimize energy between each neighbor pair. Between isolated POSS cubes, the optimal orientation is when the first cage is rotated 45 with respect to the orientation of the second cage, so as to juxtapose oxygen atoms of one cube with silicon atoms of the other. Instead, the balance in this crystal is achieved through a delicate combination of long-range attractive electrostatic forces and short-range repulsive forces between atoms at the extremities of neighboring POSS cages. Several of the aforementioned force fields, including our charge-transfer potential, reproduce these structures. In fact, the quality of our force field is exemplified by the fact that a configuration of POSS cubes placed initially in cubic geometry quickly relaxes into the correct trigonal structure. An important advantage of our interaction potential is its accuracy in terms of the dynamic properties of POSS systems. As shown in Figure 5, our force field reproduces the infrared spectra of the POSS T8 crystal.37 38 Note that for the experimental spectrum used for comparison37 data from two different spectrometers have been combined, so 6
ν(Si-H) 2276
–0.08
ν(Si-O) 1140
δ(O-Si-H) 881
–0.07
that a comparison of peak intensities between near and mid infrared regions cannot be made. All simulated IR peaks appear at the correct frequencies and within each spectral range. The relative intensities are also in good agreement with experiment. Based on these findings, we are confident that our reactive force field provides an accurate description of the structure and dynamic properties of POSS systems.
3. AB INITIO MOLECULAR DYNAMICS SIMULATIONS OF POSS MOLECULE DEGRADATION BY COLLISION WITH ATOMIC OXYGEN A range of different polymers including polyamides, polyimides, polyterephthalate, Kapton® , Mylar® , polyvinylchloride, polyethylene, polymethylacrylate, polycarbonate, polysulfone, polytetrafluoroethylene, polyvinylfluoride, and PEEK have been used at the surface of spacecraft vehicles to provide electrostatic as well as thermal isolation.39–42 Although these materials offer low weight and provide excellent absorbtivity and reflectivity properties, they can readily degrade under the harsh conditions of the low earth orbit (LEO). Degradation can occur via the collisions with highly energetic and erosive atomic oxygen species in the ionosphere, and via damaging ultraviolet (UV) radiation, thermal cycling, and exposure to proton and electron radiation. Erosion by direct collision with highly energetic atomic oxygen is probably the most damaging. Hyperthermal oxygen atoms collide with the spacecraft at velocities on the order of 8 km/s, which corresponds to collisions that are equivalent to 4 to 5 eV in energy.39–44 This leads to the evolution of a significant amount of light gases as well as to a damaged polymer
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McCabe et al./Multiscale Simulation of Organic/Inorganic Hybrid Materials
Me Si
R
O Me
Si
Si
O
Me
O
R O Si
Si
O
O
Si R
Si Me
O
Si
O R
Me
Si
O
O
Me
O*
R
Si
Me
O
Me O
R
Si
O
O R
N Fig. 6. Schematic for the POSS-polydimethylsiloxane copolymer used in the in-situ erosion studies performed by Gonzalez, Phillips, and Hoflund.43
This was thought to result from to the formation of a protective silica surface layer.43 Hofland et al. also examined the effects of the flux of hypothermal oxygen atoms on the composition of thin POSS-polyurethane copolymer films and found very similar trends, in that the both the oxygen and silicon surface concentrations increased, whereas the carbon concentration decreased upon increasing oxygen exposures.44 The results also suggest the formation of CO2 , water, and small concentrations of alcohols, aldehydes, and organic acids at the surface. Previous experimental results indicate that the exposure of these POSS-polymer films to highly energetic atomic oxygen leads to the conversion of the hydrocarbon substitutes into CO2 and water.43 44 Little, however, is known about the elementary mechanism on how these steps proceed. Ab initio calculations were performed by Troya et al.46 and Gindulyte et al.,47 48 and results indicate that atomic O (3 P) is involved in a mechanism for simple alkane decomposition, whereby oxygen is thought to abstract hydrogen from the alkane chain and/or aid in the direct activation of the C C bond. The presence of oxygen ultimately is responsible for hydrocarbon degradation and the formation of CO2 and water. In order to provide a more detailed understanding of the likely reaction paths of the POSS-polymer structure with energetic atomic oxygen, we carried out a series of ab initio molecular dynamics simulations. More explicitly we examined the effects of the incidence angle as well as the kinetic energy of the incoming atomic oxygen (O 3 P). Constant energy microcannonical ensemble simulations were carried out by using the VASP program49 50 to examine the impact of atomic oxygen (O 3 P) on model alkyl substituted POSS RH7 Si8 O8 cages. The POSS-PDMS and POSS-polyurethane films described by Gonzalez et al.43 are currently intractable for CPU-intensive ab initio MD simulations. Instead we examined the impact of atomic oxygen atoms with initial kinetic energies of 4 eV and 7 eV on a singly substituted RH7 Si8 O8 cage (where R = C2 H5 model system in order to probe low and high energy impact collisions. We also explored the effect of the specific impact region on the POSS cage along with oxygen’s specific angle of incidence. This includes the attack of energetic oxygen at the oxygen atoms in the cage that bridge the Si atoms, at the Si H substituents, and at the Si Cx Hy substituents. All simulations were carried out by using nonlocal-gradient corrected density functional theory for up to 2 ps in terms of simulation time. The Hellmann-Feynman forces are calculated upon converging of the electronic structure and used to accelerate the ions according to a Verlet algorithm to integrate Newton’s equation of motion. The total energy in the simulation is conserved. This includes the electronic energy, the kinetic energy of the ions, and the Madelung energy. The forces are recalculated after each ion step by converging of the electronic structure for the new ionic
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coating. Silica offers outstanding resistance to oxygen and has been used to strengthen a number of these polymeric coatings. Silica alone, however, desorbs as volatile cyclic species, which can then condense on and damage external optical components. Organic functionalized POSS polymers are actively being pursued as potential coatings, since they provide both the stability of silica and the light weight characteristics and thermal insolating properties of the polymer.43–45 Experimental results suggest that a polymer that comprises organic substituents on the POSS cage degrades releasing CO2 and water, and the surface forms a more-dense silica-like over layer, which is more rich with Si and O. Recent in-situ experimental efforts by Gonzalez et al. examined the effects of the exposure of polyhedral oligomeric silsesquioxane-polydimethylsiloxane copolymer films to hyperthermal atomic oxygen fluences via in-situ X-ray photoelectron spectroscopy.43 A schematic of the basic POSS-PDMS structure is shown in Figure 6, which provides a detailed breakdown of how the surface composition of the film changes as a function of oxygen fluence. Their results indicate that the atomic oxygen preferentially attacks the cyclohexyl-ring substituents attached to the POSS cage rather than the terminal methyl groups attached to the siloxane features. This results in the primary formation of CO, CO2 and water. In addition, small peaks at the higher C (1S) binding energies suggest the formation of small levels of alcohols, formaldehydes, and organic esters. The flux of atomic oxygen in these experiments was 2 × 1013 atoms/(cm2 -s). The oxygen content in the film continuously increased from 18.5% atomic initially to 49.1% and 55.7% for exposures at 24 and 63 hours, respectively. The carbon content of these films, however, was reduced from an initial value of 65% to 16% after 63 hours. The silicon content of the initial film was increased from 16.6% atomic to 28% as the oxygen exposure increased. The rates of oxygen and silicon concentration increase at higher exposures were quite slow.
7
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positions. The simulation, therefore, directly follows the Born-Oppenheimer surface. The simulations proceed by continuously repeating DFT calculations along with traditional MD steps. The typical time-step used in updating the dynamics was 1 femtosecond. 3.1. High Energy Impact
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The structural integrity of the cage and organic substituents were examined by carrying out high energy impact simulations whereby an atomic oxygen atom (O 3 P state) with 7 eV of kinetic energy was directed at the bridging oxygen atoms in the cage (Si O Si), the terminal Si H groups and the Si C bonds of the model POSS-ethyl system examined here. The simulation results are depicted in Figures 7–11. The results demonstrate that the POSS cage itself is remarkably stable against high-energy oxygen attack. The results in Figure 7 show snapshots from a dynamic simulation for atomic oxygen directed at the terminal Si H bond. Oxygen initially inserts into the Si H bond leading to a local structural relaxation. It has sufficient kinetic energy, however, to
Fig. 8. Snapshots from ab initio MD for the attack of 7 eV atomic oxygen directed head-on to a bridging oxygen atom in the POSS cage. The atom colors as in Figure 6.
break the Si H bond and for the OH radical to scatter away from the cage as a gas phase hydroxyl intermediate, as seen in the final three snapshots in Figure 7. The kinetic energy transferred by oxygen atoms that are directed at the bridging oxygen in the Si O Si bonds of the cage or at the Si atoms of the cage causes substantial structural changes in the cage, as seen in images 3 to 6 of Figure 8. The cage ultimately relaxes back to its original form leaving the oxygen atom inserted in the Si H bond to form the stable terminal Si OH group. This uptake of oxygen by silicon is the result of very strong Si O bonds, which are on the order of nearly 8 eV. This is consistent with the experimental results by Gonzalez et al.43 who show a significant increase in the uptake of oxygen in the POSS films with increasing exposure to oxygen. In general, the POSS cage remains in tact, regardless of the approach of atomic oxygen. This suggests that the POSS cage is quite stable in the context of a oxygen attack. 3.2. Lower Energy Impact
Fig. 7. Snapshots taken from ab initio MD simulation for the attack of 7 eV atomic oxygen directed head-on to a terminal corner hydrogen atom on the POSS cage. The atom colors are silicon (orange), oxygen (red), carbon (gray), and hydrogen (white).
8
The kinetic energy for atomic oxygen in the simulations was decreased from 7 eV to 4 eV in order to examine the influence of the kinetic energy on potential reaction paths. Ab initio molecular dynamics (AIMD) simulations were carried out once again for up to 2 ps. Atomic oxygen (O 3 P) with 4 eV of kinetic energy was directed at the terminal Si H bond of the cage. The results, which are shown in Figure 9, indicate that oxygen at 4 eV can insert into the Si H bond. The Si OH bond that forms, however, remains in tact and results in the formation of
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RESEARCH ARTICLE Fig. 10. Snapshots from ab initio MD for the attack of 4 eV atomic oxygen directed head on to a bridging oxygen atom in the POSS cage. The atom colors are the same as for Figure 8.
Fig. 9. Snapshots from ab initio MD for the attack of 4 eV atomic oxygen directed at a terminal corner hydrogen atom on the POSS cage. The atom colors are silicon (orange), oxygen (red), carbon (green), and hydrogen (white).
a terminal hydroxyl intermediate. The resulting kinetic energy produced upon impact can be carried away via local vibrational modes. The impact to the structure of the cage appears to be considerably weaker than that seen for oxygen at 7 eV. Oxygen, which is directed at the bridging Si O Si atoms or at the O Si bond, results in a different final state for 4 eV oxygen as opposed to that seen for 7 eV oxygen. The attack of atomic oxygen at 4 eV leads the formation of a peroxide-like structure within the cage framework. This is a metastable state that may transform into a more stable energy state under different conditions. The conditions of the simulation, however, indicate that the kinetic energy of oxygen is dissipated into the cage, thereby resulting in the formation of a peroxide SiO OSi bond, as is seen in the latter two images shown in Figure 10. This would further enhance the uptake of oxygen into the cage structure. In the presence of other POSS cages these “peroxo” species might open up and
more preferentially form bridging Si O Si groups that would connect two POSS cages. The hydrocarbon substituent groups were found to be the most labile fragments of the cage. Energetic atomic oxygen directed at the Si C bond readily insert to form an Si O bond. This is clearly seen in the first five images of Figure 11. The O C2 H5 and the OCH2 -CH3 bonds become significantly weaker. For simulations with atomic oxygen at 4 eV, oxygen inserts into the Si C2 H5 bond to form the SiO C2 H5 intermediate, thereby leading to the formation of both Si O and C O bonds at the expense of the Si C bond. The relaxation of the cage helps to dissipate excess kinetic energy. The excess kinetic energy also goes into weakening the C C bond of the ethyl fragment as well as the O C bonds, which could lead to the formation of C1 fragments. Simulations at subsequent times lead to structural fluctuations in both the O C2 H5 bond as well as the OCH2 CH3 bonds. At lower energies the entire chain structure remains in tact for over 2 ps. The end result is the formation of an alkoxy intermediate that can subsequently lead to the formation of alcohol or aldehyde products. At higher energies and higher fluences of oxygen, the C C bond would likely break, thereby leading to the formation of CHx Oy product states. The most likely states would be the formation of CO2 , CO, 9
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or hydrocarbon neighbors can dramatically influence the likelihood of the formation of cage-opened intermediates that are stabilized by bonding to neighboring groups. These ring-opened intermediates are far less likely, since they are unstable structures. Our more recent simulations show that the collision with oxygen can induce the reaction between two cages to begin to coalesce.
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4. ATOMISTIC SIMULATIONS OF POSS SYSTEMS
Fig. 11. Snapshots from ab initio MD for the attack of 4 eV atomic oxygen directed perpendicular to the Si C corner bond. The atom colors are silicon (orange), oxygen (red), carbon (gray), and hydrogen (white).
H2 O, methanol, and formaldehyde. This is consistent with the experimental results presented by Gonzalez et al.43 who showed that increasing exposure of POSS-PDMS and POSS-polyurethane films leads to the formation of CO, CO2 , water, alcohol, aldehyde, and organic acid products. The general implications from the AIMD simulations presented here are that the base POSS cage is remarkably stable even when exposed to higher kinetic energy atomic oxygen. This is because of the high oxophillicity of silicon–silica. The POSS cube will readily uptake oxygen at each of the eight corners, provided that these sites are substituted with either hydrogen or hydrocarbons. This will, therefore, increase the oxygen composition as a function of oxygen fluence. The stability of the POSS system along with increasing oxygen uptake with oxygen fluence agrees quite well with the experimental results by Gonzalez et al.43 Hydrocarbon chains react with oxygen to either form oxygenate substituents or combust to form CO, CO2 and water. Oxygen acts to facilitate hydrogen abstraction from either the hydrocarbon chain or from the terminal Si H groups. All of the simulations reported herein were carried out by using a single POSS cube. The stability of the cube can largely be a function of the reaction environment. In the presence of other POSS cubes or polymer matrix, the POSS cube itself may decompose and form metastable ring-opened structures. The presence of other POSS cages 10
The success of UFF, COMPASS, and Kieffer force fields in predicting the structural properties of individual POSS (HSiO15 8 cages led us to perform molecular dynamics simulations of POSS solids and fluids by using these force fields. The simulations were performed in several different ways, depending on the force field. For UFF, the public domain DL_POLY code51 and the commercial Cerius2 code from Accelrys were used, providing cross-checks on the accuracy of the implementation in both codes. With DL_POLY, the intra- and intermolecular force constants for POSS molecules must be input for use in the calculation, whereas for Cerius2, UFF is one of the standard force field options implemented within the code. For the calculations using COMPASS, the commercial Materials Studio code marketed by Accelrys was utilized, and for the reactive force field described earlier in Section 2, simulations were performed by using FLX, an in-house code developed by Kieffer. Within DL_POLY, we also used a simplified version of COMPASS, which we refer to as the hybrid COMPASS force field.28 30 This force field is functionally equivalent to the COMPASS force field, but does not include some of the higher-order forces (i.e., cross-coupling and out-of-plane bending terms). Molecular dynamics simulations have been performed on POSS(H8 at 300 K to study the solid phase behavior of the POSS cages. The X-ray diffraction pattern and radial distribution function have been determined, and comparisons have been made between the predictions from different force fields and experiments where possible. The simulations were performed in the isothermalisobaric ensemble (NPT) by using the Rahman-Parrinello barostat. Figure 12 compares the simulation results at 300 K from the UFF and hybrid COMPASS force fields with the simulation result obtained from experimental data.16 We see that both atomistic force fields are in very good agreement with the experimental data, although the hybrid COMPASS force field appears to be more accurate, suggesting that the hybrid COMPASS force field correctly describes the solid state structure of plain POSS. In Figure 13 we present a comparison of the total (all atom) radial distribution function gr for plain POSS at 300 K obtained from Kieffer reactive force field, UFF, and COMPASS. We note excellent agreement among the different force fields. (Note the regions for which gr
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0.4
a) Larsson 1960
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Fig. 12. X-ray diffraction pattern for POSS (H8 obtained with the hybrid COMPASS and UFF force fields compared to experimental data at 300 K.
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goes to zero beyond the first peak, as is typical for a crystalline phase.) We have also studied the PVT behavior of plain and monotethered POSS fluids. As an example of our results, we present in Figure 14 a plot of the pressure-density (P-) at 300 K for decyl monotethered POSS obtained by using the COMPASS force field; in addition, a snapshot obtained at 1.4 g/cm3 after 500 ps of simulation is presented in Figure 15. From the figure we note some evidence of the formation of POSS-rich and alkane-rich domains. Similar results were obtained by using our reactive force field.52 Such a porous nanostructured material could find important uses in sensing applications such as gas absorption and detection. As described in Section 5 to follow, in order to explore this on a larger scale, we have performed simulations of this system by using a minimal model, which allows the study of larger temporal and spatial scales.
0
ρ/gcm–3 Fig. 14. Pressure versus density for monotethered decyl-POSS at 300 K obtained with the COMPASS force field. Similar results are obtained with our reactive force field.
5. MESOSCOPIC AND COARSE-GRAINED MOLECULAR SIMULATIONS OF POSS SYSTEMS We have developed a minimal model of tethered POSS cubes to expedite simulation of POSS–polymer assembly processes and to enable rapid prototyping of phase diagrams and ordered structures.53–55 The model is constructed to retain the essential geometrical and energetic features of the tethered cubes and consequently the topological characteristics of the assembled structures. We have implemented the model in MD, BD, and
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r() Fig. 13. Radial distribution function for the Kieffer reactive force field, UFF obtained with DL_POLY, UFF obtained with Cerius2, and the hybrid COMPASS force field (from bottom to top).
Fig. 15. Snapshot of monotethered decyl-POSS at a density of 1.4 g/cm3 and 300 K obtained from Materials Studio using the COMPASS force field. Similar results are obtained with our reactive force field.
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off-lattice and on-lattice MC simulations. The model consists of rigid POSS cubes comprising interaction sites at the eight cube corners and, for certain studies, at the center of the cube. The ab initio calculations and explicit atom MD simulations of the POSS cubes described previously were used to parameterize the strength and range of POSSPOSS interactions. Hydrocarbon tethers on the cube corners are modeled as bead-spring chains, for which each bead represents roughly three CH2 units. We have carried out simulations of self-assembly of mono- and tetratethered POSS cubes, whereby immiscibility between cubes and tethers, either in the neat system or mediated via solvent, drives microphase ordering of the tethered POSS cubes.53 56 We have also studied the structures formed by cross-linking octafunctional POSS cubes, for which the cross-linking interactions between linker ends are achieved via thermoreversible, attractive interactions between terminal beads on the linkers.55 Our studies are described in brief in subsequent text. 5.1. Cross-linked Networks of Octafunctional POSS Experiments by Laine and coworkers on networked octafunctional POSS cubes inspired this study.57 58 In those works, octavinylsilsesquioxane, [CH2 CHSiO15 ]8 was reacted with octahydridosilsesquioxane [HSiO15 ]8 to form a network of cubic silsesquioxanes connected at the corners by tethers with two-atom backbones. Additional networks were made by reacting octa(vinyldimethylsiloxyl)silsesquioxane, [CH2 CHSi(CH3 2 OSiO15 ]8 with octahydridosilsesquioxane [HSiO15 ]8 , and octa(hydridodimethylsiloxyl)silsesquioxane, [HSi(CH3 2 OSiO15 ]8 with octavinylsilsesquioxane, [CH2 CHSiO15 ]8 to form cubic silsesquioxane networks connected by tethers with four-atom backbones, and octa(hydridodimethylsiloxyl)silsesquioxane [HSi(CH3 2 OSiO15 ]8 with octa(vinyldimethylsiloxyl)silsesquioxane [CH2 CHSi(CH3 2 O · SiO15 ]8 , to form cubic silsesquioxane networks connected by tethers with six-atom backbones. Characterization of the networks with nitrogen sorption, positron annihilation lifetime spectroscopy (PALS), and small angle X-ray scattering (SAXS) revealed that the specific surface area and pore volume decreased as the length of the linkers increased. The network formed from two-atom tethers had a broad distribution of pore diameters (10–200 Å),58 whereas the network with six-atom tethers had a narrow distribution of pore diameters (10–40 Å).57 Wide angle X-ray scattering (WAXS) curves58 exhibited low angle scattering peaks corresponding to correlation lengths of 8 Å for the network with two-atom tethers and 13 Å for the network with six-atom tethers. Solid-state nuclear magnetic resonance (NMR) analysis showed that the degree of cross-linking and the extent of reaction increased as the length of the tethers increased. To reproduce these results as a validation of the minimal model, we simulated network formation in octafunctional POSS by using lattice Monte Carlo with a slightly 12
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Fig. 16. Coarse-grained model for octafunctionalized POSS mapped to octa(hexyl)-POSS [CH3 (CH2 5 SiO15 ]8 . The stick model on the left shows the rigid POSS cage composed of Si (orange) and O (red) atoms and the organic linkers, where the backbone atoms of each linker are drawn with different colors to distinguish the otherwise identical linkers. The schematic on the right shows the coarse-grained model (cubes) superimposed on the atomistic model. For clarity, only selected linkers are “coarsened” in this schematic. From Ref. 55.
modified version of the bond fluctuation (BF) model and algorithm.55 The BF lattice algorithm has been widely adopted for the simulation of polymer network formation. We modeled a POSS cube as a rigid cube occupying 3 × 3 × 3 vertices on a cubic lattice (Fig. 16). Attached to each corner of the cube was a flexible, short-chain linker, each of which is modeled by L connected “beads,” where each bead occupies 2 × 2 × 2 lattice vertices, and where the terminal bead is capable of forming a thermoreversible cross-link with the terminal bead of another linker. Two cross-linked linkers form a single tether that can be compared with the experimental tether lengths described previously. In this model, an L = 1 linker corresponds to approximately three backbone atoms. In this work we consider POSS cubes functionalized with linkers capable of forming tethers of length LT = 2, 4, 6, and 8. Therefore, the shortest model tether considered here is analogous to the longest tether studied in the experiments. The networks were prepared as follows. Prior to the simulation, N = 4500 octafunctionalized POSS cubes are randomly placed on a cubic lattice at a volume fraction = 005. The total number of tether beads and cube vertices ranged from 40,500 in the LT = 2 system to 148,500 in the LT = 8 system. The systems were relaxed athermally without attractive interactions between linkers for 6 − 10 × 105 MC steps. A linker segment or cube was selected at random and displaced one lattice unit in a randomly chosen direction. The displacement move is accepted if the neighboring sites in the direction of the move were unoccupied and if the resulting bond vector(s) were in the set of allowed bond vectors. Once the configuration was relaxed, cross-linking interactions were introduced between nearest-neighbor linker terminal beads to form tethers between the cubes. Our simulations predicted that the degree of porosity and average spacing between POSS cubes in the networks
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5.2. Self-Assembly of Monotethered and Tetratethered POSS Non-cross-linkable POSS systems are receiving a great deal of interest in the POSS community. Recent experiments by several groups suggest that solvent-mediated and non-solvent-mediated interactions between POSS cubes functionalized with organic substituents such as methyl, isobutyl, phenyl, cyclopentyl, and cyclohexyl groups can drive self-assembly of ordered mesophases when the decorated cubes and tethers are immiscible with each other.59–62 Examples of tethers studied experimentally include poly-ethylene-oxide and poly-ethyleneglycol. As in surfactant and block copolymer systems, immiscibility between head (functionalized cube) and tail (tether) or between blocks of the copolymer leads to organized microphases when the system, to achieve equilibrium, attempts to minimize its free energy subject to the
topological constraint that tethers and cubes are permanently bonded to one another. For example, spherical60 and cylindrical61 micelles have been reported under certain conditions. A major obstacle in the experimental characterization of these systems is the difficulty in monitoring the assembly process during microphase ordering. Consequently, few if any systematic investigations of the types of ordered structures possible for a given tetheredPOSS architecture and the manner in which they form have been carried out. We have conducted detailed simulation studies of monotethered POSS,53 tetratethered POSS,56 and POSS telechelics56 via Brownian molecular dynamics by using a minimal model of tethered POSS cubes. Of primary interest in these studies is the prediction of equilibriumordered structures as a function of temperature, volume fraction, tether length and rigidity, number of tethers, and solvent quality. In several cases, we have mapped partial or complete phase diagrams that may be used to guide experimental investigations. Our model of a tethered POSS cube consists of a rigid cage composed of eight beads permanently bonded into a cube (Fig. 17). Ab initio and atomistic MD simulations, as described previously, show that the POSS cage is indeed relatively rigid, regardless of the presence of attached tethers and functional groups and in the proximity of neighboring cubes and tethers, justifying our use of a rigid cube to expedite our simulations. To each cube is attached between one and four tethers, each comprising beads bonded together with finitely extensible, nonlinear elastic (FENE) springs. Tethers are attached to the cube via a FENE spring. Miscibility and immiscibility between cubes and tethers arising from van der Waals interactions (which may be mediated by solvent) between organic functional groups and/or the POSS cages themselves is achieved through a combination of Lennard– Jones (van der Waals) and Weeks-Chandler-Anderson (excluded volume) interaction potentials that act pair-wise between beads. Attractive interactions at low temperature, for example, are modeled via an LJ potential, and nonattractive good solvent interactions are modeled via WCA. Both potentials are parameterized by using input from the
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decreased with increasing linker length, owing to the presence of large voids in the small-LT networks and the absence of large voids in the large-LT networks.55 This is in accordance with the WAXS and porosity experimental results of Laine and coworkers described earlier. For the case of LT = 2 (six-atom tether), we found an average spacing of 11 Å between silsesquioxane cubes, which differs slightly from the spacing of 13 Å indicated by the WAXS data. We found that all of the assembled networks are single, cell-spanning networks comprising nearly all (>99%) the POSS cubes in the system. Although the number of cubes in the network remained constant, the fraction of unreacted linkers increased as LT increased. In addition, the elastically active fraction of network material (cubes and linkers minus network defects) decreased with increasing L. The increase in network defects as L increased is expected owing to the increased degree of steric hindrance introduced by the longer linkers. With respect to the degree of cross-linking in the network, in the real system the extent of reaction increases as tether length increases from two to six, while we found in the model system that the extent of reaction decreased as tether length was increased beyond six. Combining the experimental results with our findings suggests that the six-atom tether may be the optimum length for balancing the competition between steric hindrance (resulting from the bulkiness of the functionalized silsesquioxane) and tether flexibility. For the case of the six-atom tether, the model predicts the extent of reaction to be 90% (i.e., seven or eight corners linked per cube), which overestimates the experimental extent of reaction of 81% (i.e., six or seven corners linked per cube). This may occur because the model linker is more flexible than its experimental counterpart. Ongoing studies are investigating the role of tether flexibility in network formation.
Fig. 17. Mapping of atomistic to coarse-grained molecular model of a nonane-tethered POSS cube.
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both T and , are able to map out phase diagrams indicating the type of ordered structure predicted for a given combination of T and , determine the nature of the phase boundary between ordered phases. By monitoring the equilibrium potential energy of, for example, POSS cubes versus T on both cooling and heating, we can ascertain whether the transition from a disordered state to an ordered structure occurs via, for example, a first-order or continuous transition. Examples of ordered structures we obtain are shown in Figures 18 and 19.
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Fig. 18. (a) End and (b) side views of hexagonally ordered cylindrical micelles of tetratethered POSS cubes formed via self-assembly from the disordered state. In this example, all four tethers are attached to the same side of the cube. POSS are colored pink and tethers are colored light gray. In (b), the tethers are not shown to facilitate viewing of the POSS cylindrical micelles.53
ab initio and atomistic simulations described in the preceding text. The simulations are carried out by using the BD method, in which a stochastic thermostat comprising frictional (drag) and random (heat bath) forces are included in Newton’s equation for the conservative force between beads.54 This method is commonly used to simulate polymer melts and dilute suspensions of particles and surfactant systems. In the latter, the interactions of the solute (in this case, tethered POSS cubes) with the solvent molecules is considered implicitly through the stochastic terms and through the LJ and WCA potentials used as empirical potentials of mean force.54 Excluded volume effects of the solvent molecules are neglected in this approach. Because our POSS molecules are modeled as rigid cubes, angular as well as translation momentum must be considered. We use the method of quaternions to rotate cubes independently of the tethers.54 The simulations are conducted by initializing a given system at a chosen volume fraction , equilibrating it at high temperature T , and cooling it either instantaneously or via a cooling schedule to a lower target temperature. By systematically varying
Fig. 19. Two different equilibrium structures obtained from monotethered POSS cubes via self-assembly from the disordered state. (a) Lamellar structure obtained in neutral, poor solvent for six-bead tethers. The POSS cubes are shown in purple and the tethers are show in light gray. (b) Ordered micelles of monotethered POSS cubes with 12-bead tethers in solvent good for the POSS and poor for the tethers. The POSS are not shown to facilitate viewing of the elongated micelles.56
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6. SUMMARY In this paper, we demonstrate the initial integration of quantum, atomistic, and mesoscale methods in a multiscale effort to simulate the properties of organic–inorganic hybrid polyhedral silsesquioxane materials, including their unique electronic and geometric structures, stability toward reactive oxygen, and solid and fluid phase behavior. Our quantum mechanical studies have shown that the simplest POSS cube (T8 cube has unique electronic characteristics, which may aid in the development of luminescence properties. In addition, we found that the basic POSS cube is remarkably stable to attack by atomic oxygen, which is important in the development for potential coating materials in the spacecraft industry. Detailed comparisons between both quantum mechanical results and experiment have demonstrated that classical force fields can be used to describe the structural properties of isolated H-terminated and alkane-tethered POSS cages. As a result of this success we have been able to use these classical force fields to simulate the solid- and fluid-phase behavior of bulk POSS systems. We have also developed minimal models for the POSS cage and tethers, which have been successfully used to study network formation and POSS–polymer assembly processes. Our ongoing efforts are focused on the structure and thermodynamics of tethered POSS fluids and their solubility in polymers and water, improved ab initio calibration of force fields, use of the reactive force fields to study reactions between tethers in tethered POSS fluids, and quantitative calibration of mesoscale force fields by atomistic and ab initio calculations. Acknowledgments: We are grateful to B. Coughlin, R. Laine, J. Lichtenhan, E. Lin, P. Mather, V. Rotello, C. Soles, and B. Viers for many enlightening discussions on their experimental POSS studies. P. T. C. and C. M. C. acknowledge the Center for Computational Sciences at Oak Ridge National Laboratory and the National Energy Research Supercomputing Center at Lawrence Berkeley Laboratory for computer time. S. C. G. and J. K. acknowledge the University of Michigan Center for Advanced Computing and the NPACI program for computer time. In addition, we thank the many students (Heather Barkley, Elaine Chan, Abigail Cochran, Tudor Ionescu, Cheng-Ying Lee, Feng Qi, Eric Whitebay, Charles Zhang,
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and Jinhua Zhou) and postdoctoral researchers (Murat Durandurdu, Jean-Sébastien Filhol, Monica Lamm, and Hung-Chih Li) who have contributed to this project. This work is supported by the National Science Foundation (DMR-0103399).
References and Notes
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