REVIEW OF SCIENTIFIC INSTRUMENTS
VOLUME 72, NUMBER 3
MARCH 2001
Neutron confinement cell for investigating complex fluids Tonya L. Kuhla) Department of Chemical Engineering and Materials Science, University of California, Davis, Davis, California 95616
Gregory S. Smith Manuel Lujan, Jr. Neutron Scattering Center, LANSCE-12, MS H805, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
Jacob N. Israelachvili Materials Research Laboratory and Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106
Jaroslaw Majewski Manuel Lujan, Jr. Neutron Scattering Center, LANSCE-12, MS H805, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
William Hamilton Neutron Scattering Section, Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
共Received 18 September 2000; accepted for publication 20 November 2000兲 We describe an apparatus for measuring the molecular density and orientation of confined, ultrathin complex fluids under static and dynamic flow conditions. The device essentially couples the utility of the surface forces apparatus—ability to control surface separation and alignment under applied loads—with in situ structural characterization of the intervening material utilizing neutron reflectivity measurements. The apparatus is designed such that single crystal substrates of quartz or sapphire with areas up to tens of square centimeters can be kept parallel at controlled and well-defined separations from millimeters to less than 100 nm. The large substrate surface area enables direct structural measurements of the density profile of ‘‘soft’’ material placed between the aligned substrates. In addition, the cell is also designed to enable steady shear rates from 0.001 to 20 Hz to be applied in order to follow the dynamic structural response of the confined material, especially at the solid-solution interface. Faster shear rates of order 104 can be obtained using oscillatory motion. Current design specifications focus on the use of neutron reflectivity to characterize the structure of end-grafted polymer brush layers, but the device can be employed to probe the structure of any complex fluid of interest and is amenable to other characterization techniques. © 2001 American Institute of Physics. 关DOI: 10.1063/1.1347981兴
I. INTRODUCTION
single surface and under confinement. Here, we will focus on the behavior of tethered diblock polymer chains in selective solvents, where one end of the polymer block anchors the chain to the surface and the other block extends away from the interface into solution. On the experimental side, a lot of information regarding the structure of grafted polymer layers has been deduced from force measurements utilizing techniques like the surface forces apparatus 共SFA兲1 and various scanning probe microscopies.2 Such measurements are very powerful and sensitive surface probes, however, the information they provide is not molecular. As a result, in many cases our understanding and interpretation of experimental data has evolved from theoretical studies based on scaling arguments,3 mean field theories,4 and/or computer simulations.5 At the molecular level, neutron reflectivity experiments have been very successful in providing detailed density distribution profiles of polymeric materials at single interfaces 共depth profiling兲, where the structure of adsorbed diblock polymers in good, theta, and poor solvents has been investi-
Polymer molecules at solid or fluid interfaces have an enormous spectrum of applications in a wide variety of technologies. They provide a mechanism to impart colloid stabilization, they are used as protective coatings 共including mechanical protection of solids against friction and wear兲, they govern the interactions of biological cell surfaces, and through judicious design they are used to modulate dispersion properties 共such as rheology兲 under a variety of processing conditions. Knowledge of the conformations that adsorbed or terminally anchored chain molecules adopt when subjected to confinement and/or solvent flow is essential for predicting the interaction forces and rheological properties of the polymer layers involved in all of the above-mentioned applications. There exists a substantial body of theoretical literature and experimental data on the static morphologies of adsorbed polymers, grafted chains, block copolymers, etc., at a a兲
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gated as a function of grafting density.6,7 Probing the structure the tethered polymer layer adopts under confinement has proven more elusive. The difficulty here lies in the need of ultraflat surfaces of a suitably large surface area for neutron scattering measurements. Not only must these surfaces be closely opposed 共intersurface separations below a few hundred nanometers or less are required兲, but they must also be kept aligned and parallel throughout the duration of the measurement in order to confine the film of interest uniformly. Early work by Cosgrove and co-workers paved the way for the apparatus we describe here.8 In their design, large, optically polished quartz flats were forced to closely approach using a hydraulic ram. Intersurface separations of about 100 nm were attained, however it proved difficult to maintain a constant gap separation during the course of an experiment, which greatly complicated data interpretation. Although the structure of tethered polymer layers at single interfaces or confined has received much attention, for the most part the dynamic behavior of polymer layers under shear has only been inferred. Techniques such as ellipsometry or the hydrodynamic flow method enable average polymer layer thicknesses to be evaluated. However, they do not provide information on the segmental conformation or density profile of the polymer chains away from the interface. Likewise, even less known is the effect of geometric confinement imposed by a second surface although this more closely matches the conditions of colloidal processing and the many other technological situations listed previously. Recently, there has been more focus on understanding these effects. For example, dynamic shear investigations utilizing the SFA indicate that polymer brush layers extend and generate a normal force component during shearing motion,9 while a novel shear cell for neutron reflectivity measurements has been used to investigate the conformations tethered polymer chains adopt when exposed to flowing solvent at a single surface.10 In addition, a new device developed by Granick and co-workers, micrometer-gap optorheometer, should prove to be a powerful tool for probing the rheology and structure of complex fluids at the mesoscale, gaps of a few microns and larger.11 In this paper, we describe an apparatus, the neutron confinement cell, which can be used for determining 共i兲 the molecular orientations and density distributions of physically adsorbed and chemically grafted polymer chains on solid supports, 共ii兲 how these are affected by shear at a single surface, and 共iii兲 how the proximity of a second surface 共imposed confinement兲 alters the conformation, intersurface forces, and rheology of polymer layers in thin films. Current design specifications focus on the use of neutron reflectivity to characterize the structure of end-grafted polymer brush layers, but the device can be employed to probe the structure of any complex fluid of interest and is amenable to other characterization techniques. II. APPARATUS A. Overall features of the apparatus
The apparatus and a schematic are shown in Fig. 1. The frame and interior components of the neutron confinement
Kuhl et al.
FIG. 1. 共A兲 Photograph of the neutron confinement cell 共NCC兲 with the outer steel housing removed. A 12 in. ruler on the left-hand side gives an idea of the size of the apparatus. 共B兲 Cross section of the NCC. The neutron beam passes perpendicular to the view shown. The apparatus is constructed with 304 and 316 stainless steel and all inlets and outlets are sealed by Teflon o-rings or gaskets. A hydraulic ram can be used to apply high loads, which are calibrated by measuring the compression of Belleville washers of variable spring constant. The upper quartz substrate mounts into the top of the outer housing. The lower sapphire 共quartz兲 substrate mounts on a mechanical slider and can be translated 共sheared兲 relative to the upper surface using a mechanical motor drive assembly.
cell 共NCC兲 are constructed from 304 and 316 stainless steel. All inlets, outlets, and openings are sealed with Teflon™ gaskets or o-rings, enabling liquid vapor pressure to be maintained and preventing contamination from entering the chamber. Single crystal quartz windows 共1 mm thick兲 act as beam ports for the incident and reflected neutron beam. The heart of the device is the substrates used to confine the complex fluid of interest. Theoretically, the minimum gap obtainable with the device is solely a function of the smoothness 共waviness兲 of the substrates used. In other words, the gap separation is equivalent to the separation between the two substrates. In the current design, the NCC uses single crystal quartz and single crystal sapphire substrates of nominal surface waviness less than /25 and /20, respectively. Thus, the peak-to-valley height difference on each
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Rev. Sci. Instrum., Vol. 72, No. 3, March 2001
substrate across the inner 90% of the surface is about 300 Å. The outer 10% of each substrate is rounded off to ensure that there are no edge asperities. Another critical concern is that these substrates must be kept in a parallel alignment at a constant gap separation for the duration of the reflectivity measurement 共2–12 h兲. Otherwise, contributions from different substrate separations will tend to smear out the reflectivity profile.8 In our apparatus, the substrates are mounted into recesses within the steel housing 共upper surface兲 and in the shearing mount 共lower surface兲. The steel surfaces upon which the substrates rest are machined to a lapped tolerance of less than 10 m. A Teflon gasket material of Durlon 9000 is placed along the bottom and sides of the substrate recesses to distribute the applied load evenly across the substrate surface. Moreover, the flexibility of the gasket material and the compliance of the substrate materials themselves, quartz against sapphire, enable the surfaces to conform and self align. As we shall show in Sec. III, very small gap separations were obtained using this construction. The assembled device fits on top of a piston ram, which can be used to apply large normal loads to the substrates through a series of variable spring constant Belleville washers. By measuring the deflection of the Belleville washers, the applied load can be accurately determined. A locking collar enables the applied load to be maintained if the device is removed from the piston ram assembly. B. Substrate chemistry
We found that contamination on the surfaces frequently determined the minimum separation as opposed to the physical smoothness of the substrate surface. Both bare quartz and sapphire have high surface energies. As a result, it is difficult to remove particles or contamination from these surfaces. One important aspect of our design was hydrophobizing the single crystal substrates with a molecular layer of either chemically grafted octadecyltrichlorosile 共OTS兲 or physically adsorbed octadecylphosphonic acid 共OPA兲 on the quartz and sapphire, respectively. The purpose of hydrophobizing the substrates was twofold. First, the hydrophobic layers provided a protective coating on the two ultrasmooth surfaces. Second, hydrophobic surfaces were much easier to clean and to keep clean of contaminants and particles, in particular dust. Indeed, we found that by effectively removing dust and other particles from the substrate surfaces, extremely small intersurface separations of less than 70 nm were obtainable. 1. Quartz
By virtue of its hydrolyzable functional groups, OTS molecules were covalently bound to the quartz substrate hydroxyl groups as well as cross-linked within the organosiloxane layer. As a result, a robust, chemically inert, protective monolayer was formed on the quartz substrate. The procedure was as follows. The quartz surface was first cleaned and the surface hydroxylated by immersion in a strong basic solution of 10 wt% NaOH for 10 min at 50 °C. The quartz was then rinsed in Millipore water and dried in a clean stream of nitrogen gas. Next, following the procedure of Moav and
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Sagiv,12 the quartz was immersed in a solution of 1 mM OTS in dried bicyclohexyl. The OTS monolayer was allowed to self-assemble for 1 h.13 Upon removal from solution, the monolayer coated substrate was autophobic and the quality of the formed monolayer was initially judged from the dewetting of the solution from the substrate surface. The substrate was then rinsed in clean chloroform and baked in an oven at 102 °C for 3–6 h. Baking the monolayer increased the cross-link density of the organosiloxane layer to the substrate as well as intermolecularly. The advancing contact angle of water on the now hydrophobized quartz substrate was 110° and the receding contact angle was 100°⫾5°. 2. Sapphire
Similarly, the sapphire substrate was hydrophobized with a self-assembled monolayer of OPA. OPA forms a strong physisorbed monolayer on sapphire through ionic bonds between the phosphonate group and the two negative oxygens above the aluminum ions. The neutral oxygen 共P⫽O兲 is above the vacancy site and the P–C bond is normal to the surface.14 Adapting the procedure followed by Bermann et al.,15 the sapphire substrate was first thoroughly cleaned in Helmenex solution, rinsed with copious Millipore water, and dried thoroughly in a stream of clean nitrogen. The substrate was then immersed in a solution of 0.5 mM OPA in bicyclohexyl at 60 °C for 1 h. Afterwards, the substrate was rinsed in clean chloroform to remove residual solvent and unbound surfactant. The resulting coating was homogeneous as probed by contact angle measurements with an advancing contact angle of 80° and a residing contact angle of 60°⫾5° with water. C. Shear capabilities
Lateral motion 共shear兲 is accomplished using a variablespeed motor-driven screw, which presses or pulls the lower substrate holder relative to the stationary upper substrate. The lower substrate holder is mounted on a low friction slider rail, which ensures smooth motion even when the substrates are under a high applied load. To maintain parallel motion, the motor driven screw is aligned with the interface between the two substrates. Thus, the substrates are neither driven apart nor toward each other during the shearing motion. Depending on the gap separation between the two substrates and the time of the neutron reflectivity measurement, shear rates spanning over 4 orders of magnitude are attainable, 0.001–20 Hz. Faster shear rates can be used, but the limitation of data collection time requires that an oscillating—back-and-forth—motion must be used. Higher shear rates would be desirable for some experiments involving polymer brush layers. Indeed, previous work by Baker et al. has shown little change in polymer brush structure in a good solvent at shear rates above 10 000 Hz.10 In those experiments, shear was accomplished by solvent flow, whereby the solvent was pumped at relatively high rates but still under laminar flow conditions past an adsorbed polymer layer. In our case, the substrates slide laterally past one another. As a result, the shear is at the substrate interface as opposed to the outermost portion of the
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layer exposed to the solvent flow. It will be interesting to compare our results with those reported previously with more conventional solvent flow shear cells as well as to investigate the effects of oscillatory shear motion.10,16 D. Neutron reflectivity measurements
The NCC was tested on the MIRROR17 neutron reflectometer on the HB-3A beam line of the High Flux Isotope Reactor at Oak Ridge National Laboratory. This reflectometer is set up for vertical sample geometry. Although the cell was originally designed for horizontal sample geometry, we found it operated well in vertical geometry. In the measurements presented here, a perpendicular scattering vector Q z 共⫽4 sin /兲 range from 0.004 to about 0.05 Å⫺1 was covered at MIRROR’s operating neutron wavelength ⫽2.59 Å, which corresponds to reflection angles, , between 0.05° and 0.6°. Reflected neutrons were counted using an Ordela model 1150N linear position sensitive 3 He detector with ⬃1 mm 共rms兲 resolution at a sample to detector distance of 3.37 m, giving the instrument a limit resolution of Q ⬃0.0005 Å⫺1 . To avoid reflections from the rounded surfaces at the edges of the substrates, a slit just upstream of the sample was varied according to the angle of incidence to maintain a constant 20 mm illumination length 共footprint兲 near the center of the sample interface. Depending on the instrument configuration, the reflectometer resolution varied from 0.0005 to 0.001 Å⫺1 共⬃2/7000 Å兲 during the course of a measurement. Assuming a minimum sampling of about four points per period, the instrument could therefore resolve interference fringes between the reflections from sufficiently parallel quartz and sapphire surfaces for separations less than about 3000 Å. Thus, the visibility of interference fringes in our data is a sensitive indication of well-controlled intersubstrate separations below this limit, as shown in Sec. III. Initial tests were performed without material between the two substrates 共an air gap兲 to determine the intersubstrate separation obtainable with the device. Subsequently, the reflectivity profile was measured when a mixture of hydrogenated and deuterated toluene was placed between the substrates at a ratio chosen for good neutron contrast relative to both the quartz and sapphire substrates. In our initial measurements we restricted the beam height to 1.5 mm to better ensure sample uniformity over the illuminated region. With this restriction, runs obtaining good statistics and signal to background ratios for reflectivities down to 10⫺3 required about 12 h 关Fig. 2共a兲兴. Larger area illumination with a beam height of 5 mm 共interfacial area of 20 mm⫻5 mm⫽100 mm2兲 required significantly shorter data collection times of about 4 hours 关Figs. 2共b兲 and 3兴. The reduced data are plotted as R * Q z4 versus the perpendicular scattering vector, Q z 共this compensates for the ⬃1/Q z4 decrease of the reflectivity due to the Fresnel’s law兲. The vertical error bars on the data represent the statistical errors in the measurements after background subtraction 共standard deviation, R 兲. The horizontal error bars represent the rms instrument Q z resolution calculated on a point-bypoint basis 共with no allowance made for sample irregularity
FIG. 2. Neutron reflectivity data for air gaps of 共a兲 1925 Å and 共b兲 874 Å between a single crystal quartz and sapphire substrate mounted in the NCC. The solid curves are fits to the data using the model described in the text. Parameters are tabulated in Table I.
or curvature兲. Reflectivities were normalized to illuminated sample area and scaled to unity below the critical edge for total reflection. The fits to the reflectivity 共calculated using the iterative, dynamical method6 as described in the following兲 included an additional parameter to normalize the calculated reflectivity to the data. However, this parameter did not vary more than 5% from unity—a value comparable to the normalization error due to the scatter of data points in the R⫽1 region below the critical angle. III. EXPERIMENTAL RESULTS
Results from two reflectivity measurements with an air gap separating the quartz and sapphire in the NCC are shown in Fig. 2. A clear series of interference fringes is visible for both, indicative of the small intersurface separations attainable with the NCC. The coherent neutron scattering length densities 共兲 of the materials used in this work and the modeling are shown in Table I.18 To calculate the reflectivity profile R(Q z ,t), the key structural components of the investigated system 关the octadecyltrichlorosiloxane 共OTS兲, the octadecylphosphonic acid 共OPA兲, and the gap between the quartz and sapphire crystals兴 were described by boxes of a constant thickness and scattering length density  (z). The reflectivity R(Q z ,t) was calculated using the optical matrix 共or dynamical兲 method.6,19 To obtain good model fits to the experimental reflectivity data, it was necessary to account for sample irregularities across the illuminated beam footprint due to, for example, substrate waviness. One possible way to account for the sample spacing irregularities would be to add a ‘‘sample curvature resolution’’ term in quadrature to the instrument reso-
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Rev. Sci. Instrum., Vol. 72, No. 3, March 2001
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TABLE I. Model fitting parameters.
Parametera
Large air gap
Small air gap
Intrasubstrate separation 共Å兲 Quartz  (10⫺6 Å⫺2 ) Sapphire  (10⫺6 Å⫺2 ) Air gap  (10⫺6 Å⫺2 ) Toluene  (10⫺6 Å⫺2 ) OTS on quartz  (10⫺6 Å⫺2 ) OTS on quartz thickness 共Å兲 OPA on sapphire  (10⫺6 Å⫺2 ) OPA on sapphire thickness 共Å兲 Gap variation- w (Å)
1925⫾4 4.17b 5.70b 0.00b NA ⫺0.4b 24b ⫺0.4b 15b 66⫾3
874⫾3 4.17b 5.70b 0.00b NA ⫺0.4b 24b ⫺0.4b 15b 47⫾5
Toluene gap 1211⫾6 4.17b 5.70b NA 1.94⫾0.02 0.9⫾0.2c 24b 0.9⫾0.2c 15b 89⫾4
a
Errors are estimated conventionally as parameter variation which changes 2 by unity multiplied by a 2 /(n⫺p) correction factor, where n⫽number of data points and p⫽number of fit parameters, i.e., square root of the reduced chi squared. b These parameters were kept fixed during the refinement of the calculated reflectivity profiles. c These scattering length density parameters were held to equal values during fitting.
lution. Adding a term of this sort did reduce the calculated fringe visibility to values near those observed in our data. However, this treatment gives a uniform reduction over Q z , while in our data a definite weakening of the fringe visibility is evident as Q z increases. A surface roughness parameter has a similar effect, but also dramatically reduces the overall reflectivity. Using these descriptions, we were unable to produce statistically satisfactory fits without using either unphysical neutron scattering length densities or modifying the resolution beyond limits consistent with the experimentally observed spread of the specularly reflected beam. Instead, we accounted for deviations in the average substrate separation t 0 by assuming that there was a Gaussian distribution of thicknesses 共gaps兲 between the two crystals of standard deviation w . The reflectivity of each constant thickness region t was described by a function R t (Q z ,t) ⫽ 兩 r t (Q z ,t) 兩 2 , where r t (Q z ) is a complex function which characterizes the reflectance of a domain of thickness t. For the case of macroscopically large domains of differing thicknesses, one would expect that the domains would reflect the neutron beam independently of one another and thus the measured reflectivity is the 共incoherent兲 average of the intensities: R 共 Q z ,t 0 兲 ⫽
冕 冑 1
w
2
⬁
⫺⬁
exp
冉
⫺ 共 t 0 ⫺t 兲 2 2 w2
冊
R 共 Q z ,t 兲 dt,
where t 0 is the average thickness of the gap between two crystals and t is the thickness of each individual domain. The standard deviation w then describes the distribution of thickness around the average value t 0 due to waviness or curvature of the crystals and resulting variation in the gap separation. Averaging incoherently assumes that the lateral size of the reflecting regions with different separations exceeds the coherence length of the neutron beam projected on the reflecting surface 共⬃10–100 m兲 and that their angles to one another are less than the instrument’s angular resolution. Reflecting facets of a smaller length scale or at larger angles would produce beam scattering or broadening effects that
FIG. 3. Neutron reflectivity data for a deuterated-hydrogenated mixture of toluene  ⬇2⫻10⫺6 Å⫺2 confined between a single crystal quartz and sapphire substrate. The solid curves are fits to the data using the model described in the text. The inset shows the mean scattering length density profile 共before incoherent averaging兲. Parameters are tabulated in Table I.
were not observed. Moreover, this calculation method satisfactorily reproduced the measured weakening of fringe visibility with increasing Q z and no correction to the instrument resolution was necessary. An additional ‘‘Gaussian’’ roughness at the surface 共by modifying the interfacial reflectance by the so-called Ne´vot–Croce factor, roughness parameters兲 was not used here since in all cases the values were small 共rms ⬍5 Å兲 and their inclusion had negligible effect on the fit quality over the Q z range covered in these measurements. The solid curves are fits to the data based on the model parameters listed in Table I. Fits to these measurements gave average intersubstrate separations t 0 of 1925 Å 共a兲 and 874 Å 共b兲, with respective values for w of 66 and 47 Å. As can be seen by the quality of the fits, this model using only the scattering length densities of the quartz and sapphire substrates, air thickness 共intersubstrate separation兲, and the incoherent average of the reflectivity over a relative flatness or parallelism parameter accurately models the system.20 The smaller value for w for smaller substrate separations 关Fig. 2共b兲兴 is consistent with a greater parallelism of the substrates under higher applied load. For consistency the contribution of the hydrocarbon monolayers to the measured reflectivity profiles, OTS and phosphonic acid on the quartz and sapphire, of thickness 24 and 15 Å, respectively, was included when calculating these fits. However, because of the weak scattering contrast (  ⬇⫺0.4⫻10⫺6 Å⫺2 ) with air adding these layers to the model did not significantly improve the quality of the fits in comparison with a simple air-gap model. In all cases, similar results were obtained when the model was refined using either nonlinear versions of Marquardt– Levenburg methods or Nelder and Mead’s downhill simplex algorithm. The measured reflectivity profile when a mixture of hydrogenated and deuterated toluene, scattering length density  ⬇2⫻10⫺6 Å⫺2 , was confined between the substrates is shown in Fig. 3. A similar model was used to fit the reflectivity profile—an inset shows scattering length density profile over the interface for the average spacing (t 0 ). However in this case, the contribution of the OTS and OPA monolayers had to be included to obtain a good fit between the cal-
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culated and measured reflectivity profiles, since the scattering length density of hydrocarbon layers was significantly different from the toluene mixture. In order to minimize the number of fitting parameters, the thicknesses of both hydrocarbon monolayers were fixed to reasonable values as listed in Table I, but their scattering length densities were allowed to vary together. A best fit was obtained for monolayer scattering length density  of 0.9⫻10⫺6 Å⫺2 . The difference from the dry scattering length density is consistent with some degree of toluene penetration within the hydrocarbon monolayers. In summary, our reflectivity results demonstrate the ability to obtain ultrathin intersubstrate separations utilizing the neutron confinement cell. Based on the success of these initial measurements, this device provides a new technology to probe the structure of complex fluids or other materials of interest under confinement in a defined geometry. We are in the process of continuing these studies to probe the static structure of adsorbed polymer diblocks of PS–PEO in toluene and water as a function of confinement. The effects of dynamic shear will also be investigated. ACKNOWLEDGMENTS
This work was supported under the auspices of the United States Department of Energy through a collaborative UC/Los Alamos Research 共CULAR兲 Grant No. 9853 and DOE PECASE Award No. 05419-0099-2K. The Manuel Lujan Jr., Neutron Scattering Center is a national user facility funded by the United States Department of Energy, Office of Basic Energy Sciences-Materials Science, under Contract No. W-7405-ENG-36 with the University of California. During this work Oak Ridge National Laboratory has been managed for DOE by Lockheed Martin Energy Research Corporation under Contract No. DE-AC05-96OR22464 and by UT-Battelle LLC under Contract No. DE-AC0500OR22725. We thank Professor Abraham Ulman, Department of Chemistry, Polytechnic University Brooklyn, NY, for recommending and providing OPA to protect and hydrophobize the sapphire substrates. 1
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