J. Phys. Chem. 1994,98, 6835-6839
6835
High-Resolution 13C NMR Study of Liquid 2-Ethylhexyl Benzoate Confined to Porous Silica Glasses Jing Zhang and Jiri Jonas' Department of Chemistry, School of Chemical Sciences, University of Illinois, Urbana, Illinois 61801 Received: February 18, 1994; In Final Form: April 29, 1994'
The natural abundance carbon- 13 N M R spin-lattice relaxation times, TI, and spin-spin relaxation times, T2, of different carbons in the model liquid lubricant 2-ethylhexyl benzoate (EHB) confined to porous silica glasses prepared by the sol-gel process are measured as a function of pore size in the range of pore radii from 21 to 80 A at 294 K. In agreement with our earlier results for other polar liquids we find that the two-state fastexchange model is valid for the 13C spin-relaxation data for liquid EHB; Le., the 1/T1 rates scale as 1/R with the pore radius, R. The analysis of the 1/T1 data for each carbon in confined EHB in terms of the two-state fast-exchange model allows us to calculate the relaxation rates 1/Tls for each carbon of the EHB liquid in the surface layer. The comparison of 1/Tls for each carbon with the 1/T1 values for individual carbons in bulk EHB provides information on motional dynamics of EHB at the liquid/surface interface. The experimental 13C spin-spin relaxation rates 1/Tz obey the quadratic power law 1/R2 for confined EHB, confirming that at low frequency the pure geometric confinement effects dominate over surface interaction effects. Additional information on the EHB surface interactions is obtained by carrying out the N M R experiments with surfacemodified silica glasses.
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Introduction Our work dealing with the molecular dynamics of model lubricants was motivated by the needl for improved understanding of these fluids at the molecular level. In earlier reports" we have discussed the results of variable pressure and temperature studies of the diffusion and relaxation behavior of the model lubricant 2-ethylhexyl benzoate (EHB). This complex liquid has been chosen as a model synthetic hydrocarbon based elastohydrodynamic (ehd) lubricantss Understanding the motional properties of complex liquids including the lubricants close to or at solid surfaces is very important for a molecular-level picture of the lubrication process. NMR relaxation techniques represent an excellent tool for the study of dynamics in complex fluids? However, it is important to realize that the NMR measurements of relaxation of liquids in contact with the solid surfaces are difficult or impossible to perform as the NMR signal from the bulk liquid usually dominates the signal. Fortunately, the results of our systematic experiments on the behavior of liquids confined to porous silica glassesprepared by the sol-gel process offer a novel approach for the determination of the motional characteristics of complex liquids at the liquid/ solid interface. It is well-known that the dynamic behavior of a molecular liquid can be strongly affected when a fluid is confined to a very small space. Many studies have been performed using various techniques to understand the role of confined geometry in modifying the behavior of a confined In our earlier studieseI7 we have established the applicability of the two-state, fast-exchange model to analyze the spin-lattice relaxation time, T1,data for polar liquids confined to the sol-gel prepared silica glasses with a wide range of pore diameters at various temperatures and pressures, and the model was found valid for proton, deuteron, and nitrogen- 14spin-latticerelaxation times of these polar liquids. In order to understand the experiments in the present study, we give the basic expression used in this two-state fast-exchange model. The observed NMR relaxation rate for a liquid in a pore can be written as a function of a pore radius R as follows: *Abstract published in Aduance ACS Abstracts, June 1, 1994.
0022-3654/94/2098-6835%04.50/0
Tl
TlB
2 c 1 1 ) R TS-T,,
where T I Bis the spin-lattice relaxation time for bulk liquid, T I S is the spin-lattice relaxation time for the liquid in the surface layer, and c is the surface layer thickness. If one finds that the experimental l/T1 rate scales as 1/R with the pore radius, eq 1 allows one to calculate l/Tls, the spin-lattice relaxation rate of the liquid in the surface layer. Therefore, the use of several glass samples covering a range of pore sizes enables us to determine the relaxation rate dependenceupon the pore size and to calculate the relaxation behavior of the surface layer liquid. Until the present study our NMR relaxation experiments on confined liquids in porous silica glasses did not take advantage of the high-resolution capabilities of the NMR techniques. In particular, the natural-abundance carbon-13 high-resolution nuclear magnetic relaxation technique is an established tool for the study of molecular dynamics of liquids, including complex molecules like EHB. The relatively large chemical shifts make it possible to probe the motions of different carbons in EHB at the same time.3~~The relaxation times of the naturalabundance carbon- 13 are determined mainly by intramolecular dipole interactions between the 13C and directly attached lH, providing results which are easier to interpret than those obtained from proton NMR. The general expressionsrelating the naturalabundance of carbon-I3 spin-lattice relaxation time, Tl, and spin-spin relaxation time, T2, to the spectral density function J(w) for the intramolecular dipole coupling mechanism are
where N is the number of directly attached protons, J ( o ) is the spectral density function, OH and oc are the proton and carbon 0 1994 American Chemical Society
Zhang and Jonas
6836 The Journal of Physical Chemistry, Vol. 98, No. 27, I994 resonant frequencies, YH and yc are the proton and carbon gyromagnetic ratios, and rCH is the carbon-hydrogen bond length. The particular form of J(w) depends on the model for molecular reorientation. Because of the asymmetric shape and high degree of internal mobility in EHB, the form of J(w) needed to describe the relaxation is complicated. In addition, we determined that for liquids confined to small spaces the spectral density functions are changed dramatically compared to those in bulk liquids.12-15 In the present experiments the natural-abundance carbon-13 NMR spin-lattice relaxation rates and spin-spin relaxation rates of different carbons in the model lubricant 2-ethylhexyl benzoate (EHB) confined to sol-gel porous silica glasses are measured as a function of pore size in the range from 21 to 80 A at 294 K. As already mentioned, the present study of confined EHB is part of our continuing research effort to improve the understanding of both the motional behavior of lubricants at extreme conditions and the reorientation dynamics of molecular liquids confined to porous silica glasses. There were several main goals of the study: First, by using the high-resolution natural-abundance carbon-13 spectra, to follow the relaxation behavior of each carbon of the EHB liquid confined to porous silica glasses; second, to determine whether the two-state fast-exchangemodeldescribes theI3CNMR relaxation rate dependence upon pore size for each carbon of the polar liquid of E H B third, provided that the two-state model is applicable, to determine whether the dynamics of the EHB molecule in the surface layer is different from that in bulk; fourth, in analogy with the results obtained for a number of liquids, to find out whether the spin-spin relaxation rate, T2-l. scales as 1/RZ due to purely topological effects;12.*5J6 fifth, by using the technique of surface modification of the porous silica glass, to investigate what is the relative role of surface interactions and geometric effects. As mentioned in our earlier work,13 the high internal surface area, the chemical and mechanical stability, and the narrow distribution of pore size makes the sol-gel prepared porous silica glass an ideal host for studies of liquid confinement. The sol-gel porous glass also represents an excellent material to study the surface effects at the molecular level as the surface area to volume ratio can be varied over a wide range. In addition, the surface modification techniquecan change the strength of the interaction between the glass surfaceand theconfined liquid to provide further information on the role of the liquid/surface interactions.
Experimental Section The EHB sample with purity of 99.8% was synthesized by Palmer Research Ltd. (U.K.) and used without further treatment. The proton decoupled carbon-13 spectra were obtained at 75.5688 MHz by using a commercial General Electric NMR pulse spectrometer, GN300NB. Thespin-lattice relaxation times, TI,were measured by the inversion recovery ( 18OoX-r-9O0,) method. The composite 180" pulse was used to compensate for any inhomogeneity in the H I field. The spin-spin relaxation times, T2, were measured by the Hahn spin echo (90°-t-1800) method. The magnetic field, &,was shimmed before and after each measurement so the line width broadening caused by diffusion was negligible. Porous glasseswith a narrow pore size distribution and a specific pore size prepared by the sol-gel process were used as the porous media. The preparation of porous glasses by the sol-gel process was carried out by acid (HC1) and base (NH40H) catalyzed hydrolysis of tetraethylorthosilicate (TEOS, Aldrich Co.) in ethyl alcohol solution.15 The amount of base and acid added to the solution was varied over a wide range, and the drying rate was controlled carefully in order to produce glasses with different pore sizes and to make relatively large pieces of porous glasses. The BET method was applied to measure the surfacearea, average pore radius, and the pore size distribution on an AUTOSORB-1 BET instrument (Quantachrom Corp.). The results of the BET
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0 PPM 60 40 20 Figure 1. (a) Structure formula of EHB. (b) High-resolution naturalabundance 13CNMR spectra of EHB in porous silica glasses with 21 A pore radius at 294 K.
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isotherm indicate that the sol-gel porous glass is characteristic of mesoporous material having pores of approximately cylindrical cross section. The narrow pore radius distribution width was discussed in detail in our earlier study.13 Glass samples with average pore radii in the range of 79.7-20.8 A were used in the experiment. The range of pore sizes was chosen by considering the dimension of the confined molecule and relative confinement effects. In order to fill the pores totally without excess liquid outside, the sample loading procedure was carried out as the follows: First, a piece of the silica porous glass was evacuated to 10-5 Torr at 300 OC for 18 h to remove water and other volatile impurities from the glass sample. Then an excess amount of EHB liquid previously degassed by several freeze-pumpthaw cycles was added to the cleaned glass sample. The glass sample was immersed into and allowed to equilibrate with the liquid for 24 h at room temperature. Finally, the filled porous glass sample was taken out from bulk EHB, and the liquid on the outside surface of the glass sample was removed. After the glass-liquid sample was loaded into a glass tube, the sample was degassed by the freezepumpthaw method again and the NMR sample sealed. The surface of the nonmodified sol-gel porous glasses has several surface silanol groups per 100 A,Z which can interact strongly with the confined liquid through hydrogen bonding. In order to change the strength of the surface interactions, the polar - O H groupson the glass surface were replaced with the less polar -OSi-(CH3)3 groups, resulting in a more hydrophobic surface. The chemical treatment was carried out according to the procedure outlined in the literature.'* First the sol-gel porous glass was dried to 1 V Torr at 300 "C for 18 h, and then the cleaned glass wasplacedintoa toluene (Fisher Scientific) solutionof 1,1,1,3,3,3hexamethyldisilazane (HMDS, Eastman Kodak Co.) at room temperature for 24 h. The excess solution was dried at 110 OC under lo-$ Torr vacuum. The experimental data for the carbon-13 relaxation times of the confined model lubricant EHB are accurate within 12%; the temperature is accurate to f0.5 K.
Results and Discussion The structural formulaof EHB and the high-resolution naturalabundance 13C NMR spectra of EHB confined to a glass with 20.8 A pores at 294 K are shown in Figure 1 (the carbonyl resonance is not included). The high-resolutioncapability permits relaxation time measurements for individual carbons in confined EHB. As expected,one can find that the line widths of individual resonances of confined EHB are much broader than those for the bulk liquid EHB.
Liquid EHB Confined to Porous Silica Glasses
The Journal of Physical Chemistry, Vol. 98, No. 27, 1994 6831
The nuclear magnetic relaxation rates of molecular liquids confined to porous media are greatly enhanced in comparison to those of bulk liquids. As pointed out earlier,I5J6the confinement effects on the relaxation rates have contributions which originate from two different mechanisms: one is from the surface interactions of molecules at the liquid-solid interface; the other is from pure topological confinement of the liquid molecules. The first mechanism has been well interpreted in terms of the twostate fast-exchange mbdel.19 In the two-state model the liquid in the pore is assumed to have two distinct phases: a bulk phase, which has the same relaxation properties as the bulk liquid, and the surface-affected phase, for which the relaxation rate is greatly enhanced. If the diffusion between the two phases is much faster than the relaxation rate, the relaxation behavior is characterized by a single-exponential decay rate. The second mechanism15J6 reflects the enhancement of the probability of molecular collisions in a confined low-dimensionalsystem due to the molecular motions in a restricted geometry. The topological confinement dominates over surface interaction at low frequency and for small pores. Theoretically, the overall relaxation rate 1/T, (i = 1, 2, or lp) of the confined liquid can be generally writtenI6 as a linear combinationof bulk, confinement,and surface interaction effects:
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where R is the average pore radius, Ai(w) represents the pure topological effect depending on the spin density, diffusion coefficient, molecular size, and frequency w , and 6, represents the surface effects. For the high-frequency spin-lattice relaxation times, our earlier studies9-'7 show that the surface interaction effects at the liquidsolid interface dominate the reduction of the overall spin-lattice relaxation time, TI, of confined polar liquids such as pyridine, nitrobenzene, acetonitrile, and toluene. Therefore, for the spinlattice relaxation rate, 1/ TI,of confined polar liquids, the general equation eq 4 can be simplified to eq 1. As already mentioned, eq 1 is the result of the two-state fast-exchange model, and it predicts that the spin-lattice relaxation rateof polar liquids, l/Tl, should linearly depend on the inverse of pore radius, 1/R. In Figure 2 the I3C spin-lattice relaxation rates, l/NTl, for the different carbons of confined EHB at 294 K are plotted as a function of the inverse pore radius, 1/R, for both the surface nonmodified (Figure 2a) and modified (Figure 2b) porous glasses. It is interesting to find in this study that the linear dependence of 13C spin-lattice relaxation rates, 1INTI, on 1/Ris well obeyed for the range of pore diameters used in the experiment, and the two-state fast-exchange model can describe well the 13C spinlattice relaxation times of all carbons in the model lubricant EHB confined to the sol-gel porous glasses with or without surface modification. The applicability of the two-state fast-exchange model to the observed 13Cspin-lattice relaxation times confirms that surface interactions dominate the l3C spin-lattice relaxation time, NTI, of the individual carbons in the confined EHB molecules. The surface modification techniqueof porous glasses represents a very useful approach to study the relative role of surface interactionsand pure topologicaleffects on the dynamicsof liquids in confinedgeometries.13 In this experiment the glass silica surface was modified by replacing polar - O H groups with less polar -0Si-(CH3)3 groups which cannot form a hydrogen bond to the EHB molecules. The OH concentrations on the sol-gel silica glass surface and the ratio of -OH groups replaced by -04(CH3)3 groups on the glass surface after the surface modification were calculated from the experimental data obtained by the 29Si CP MAS NMR technique. The results20 indicated that the surface of the nonmodified porous glasses contains approximately
1 /R
( k l )
Figure 2. (a) I3C spin-lattice relaxation rates (l/NTl) of EHB as a in the nonmodified porous glasses at 294 function of pore radius (R1) K 0 ,ring;0 ,C-8;m, C-9;V, C- 10 and C- 1 1; V,C- 12 and C- 14;0,C- 13; A, C-15. (b) I3C spin-lattice relaxation rates (1/NT1) of EHB as a in the modified porous glassa at 294 K: function of pore radius (R1) 0 , ring; 0, (2-8; 4 (2-9; V, C-10 and C-11; V, (2-12 and (2-14; 0, C-13; A, C-15.
TABLE 1: l)C Spin-Lattice Relaxtion Times for Bulk EHB, WID, and the EHB on the Sol-Cel Surfaces, WIS, at 294 K carbon no. ring 8 9 10 and 1 1 12 and 14 13 15
bulk liquid NTIB,s 0.730 0.621 0.602 1.23 1.47 9.09 7.14
modified surface NTls, s 0.383 0.373 0.337 0.713 1.03 6.98 5.03
nonmodified surface NTl,, s 0.438 0.325 0.270 0.593 0.777 5.02 3.99
two -OH groups per 100 A2 and the ratio of the polar -OH group replaced by the less polar-OSi-(CH3)3 group is between 47% and 61%. About half of the polar -OH groups on the glass surface still remain on the glass surface after the chemical treatment, and the strength of the surface interaction is therefore only partially reduced. Therefore, it is not surprising that even after surface modification the surface effect still dominates over the pure topological effect as shown in part b of Figure 2. With the assumption that the thickness of the surface-affected liquid layer is approximately two molecular diameters, the spinlattice relaxation rates of the surface phase liquid, 1INTIS, were obtained by eq 1 from the experimental data. The results of the spin-lattice relaxation times of EHB in the surface/liquid layer both for the nonmodified and modified porous glasses, NTls, are summarized in Table 1, where the hard-sphere radius of EHB, r = 3.7 A, at temperature 294 K was determined from the selfdiffusion data by using the fluidity analysis method.2 Clearly, the spin-lattice relaxation times of EHB in the surface layer are much shorter than those for bulk EHB for both the nonmodified surface and the modified surface cases. In order to follow qualitatively the effect of confinement on the motional dynamics of EHB, the spin-lattice relaxation rates of EHB in the surface layer, l/NTls, at the different carbon
6838 The Journal of Physical Chemistry, Vol. 98, No. 27, 1994 5.08
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Figure 3. Dependence of the I3C spin-lattice rleaxation rates of EHB in the surface/liquid layer, 1/NTls, on carbon number (A,nonmodified glass; 0 ,modified glass) compared to those for bulk liquid, I/NT~B (0, bulk) at 294 K.
positions are shown in Figure 3 both for the nonmodified and modified porous glasses and compared to the spin-lattice relaxation rates of the bulk liquid, l/NTle. It can be seen that the surface modification has a significant effect on the 13Cspinlattice relaxation rates of EHB in the surface layer since the modification results in a more hydrophobic surface and reduces the strengthof surface interactions. Compared to the nonmodified surface case, the spin-lattice relaxation rates of EHB for the modified glasses, 1/NTls, are reduced for most carbons,suggesting that the mobility of EHB in the surface/liquid layer increases with thedecreasingstrengthofsurfaceinteractions.At thepresent time, we have no explanation for the finding that 1/TIS for the ring protons is greater for modified than nonmodified glasses. It has been pointed out in the earlier study3 of bulk EHB that the mobility of carbon nuclei along the chain increases as one moves away from the methine carbon (carbon 9) toward the methyl groups (carbon 13and carbon 1 9 , and a linear dependence of NTl vs carbon number along the chain of bulk EHB indicates equal rotational diffusion constants for all bonds in the chain. For the EHB molecules in the surface/liquid layer, the mobility of carbons also increases along the ethylhexyl chain as shown in Figure 3. In a qualitative sense, Figure 3 shows that the general trend in relaxation rates for individual carbons of EHB observed for bulkliquids persists even for EHB in the surface/liquid layer. Namely, the relaxationrates increasefrom ring carbons to carbons 8 and 9 and then start to decrease along the ethylhexyl chain. In the case of the l3C spin-spin relaxation times, T2, one would expect13J5J6that eq 4 has to be used to interpret the experimental data as the confinement contribution, A2(o)/Rz,may dominate over the surface effects contribution of bz/R. Therefore, it is of interest to determine whether the low-frequency I3C spin-spin relaxation rates, 1/T2, will follow the quadratic pore size dependence(llR2). Figure4gives theplotof 1/NT2vs 1/Rfor EHB confined to porous silica glasses at 294 K and clearly shows that thesimple l/Rdependenceisnolongerobeyedforthe l/NT2 relaxation rates. Within the error of our experiments, the quadratic power law is obeyed and agrea with the results obtained for proton and deuteron spin-spin relaxation rates for other molecular liquids.lSJ6 These results confirm that the 13C spinlattice relaxation rate is more sensitive to liquid+urface interactions whereas the 13C spin-spin relaxation rate reflects more the pure topological confinement effects due to logarithmic enhancements of spectral density function at low freq~encies.~~J5 This work, as well as our previous studies,'I7 shows that the relaxation behavior of liquid molecules in the surface layer is much different from that of bulk molecules. The structure of the surface layer is a very important factor in determining the molecular relaxation. However, the detailed structure of the surface layer is not clear. The molecular dynamics simulation of a liquid in the pore slit model indicates that, due to the presence of the surface and surface-liquid interactions, the liquid molecules
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1IR (A-I) Figure4. (a) 13Cspin-spin relaxation rates ( l/NT2) of EHB as a function of pore radius (&I) in the nonmodified porous glasses at 294 K 0 ,ring; 0,C-8; m, C-9; V, C-10 and C-11; V,C-12 and C-14; 0 , C-13; A, C-15. (b) 1% spin-spin relaxation rates (1/NT2) of EHB as a function of pore radius (PIin )the modified porous glasses at 294 K 0 , ring; 0, C-8; a, C-9; v, C-10 and C-11; T, C-12 and C-14; 0, C-13; A, C-15.
tend to order in layers parallel to the surface and the local liquid density in the surface layer is higher than the average density in the pore.21122 For a polar liquid, the relative density of the liquid in the surface layer increases with increasing polarity.16 As a result of the larger density of the liquid in the surface layer, the viscosity is increased, the self-diffusion is lowered, and the anisotropy of the diffusion is greater when compared to that of the bulk l i q ~ i d . ~ ~The J ~characteristics J~ of the dipole relaxation process of the surface layer liquid are more like that of the twodimensional liquid, namely, the dipole-dipole correlations are much longer as a result of the logarithmic increase of the spectral density function at low f r e q ~ e n c i e s . ~ ~This J ~ J ~results in a significant increase of the NMR relaxation rates. In a general sense, the ability of obtaining experimental informationon the motional behavior of complex liquids, including lubricants, in the surface layer represents the most important result of this study of EHB in confined geometries.
Acknowledgment. This work was supported in part by the Air Force Office for Scientific Research under Grant F49620-931-0241. References and Notes (1) Tabor, D. In New Directions in Lubrication, Materials, Wear, and Surface Interactions;Loomis, W., Ed.; Noyeshbtications: ParkRidge, 1985. (2) Walker, N. A.; Lamb, D. M.; Adamy, S.T.; Jonas, J.; DareEdwards, M. P. J. Phys. Chem. 1988.92, 3675. ( 3 ) Jonas, J.; Adamy, S.T.; Grandinetti,P. J.; Masuda, Y.;Morris,S. J.; Campbell. D. M.;Li, Y . J. Phys. Chem. 1990, 94, 1157. (4) Adamy, S. T.; Grandinetti, P. J.; Masuda, Y.;Campbell, D. M.; Jonas, J. J. Chem. Phys. 1991,94, 3568. ( 5 ) Higginson, G. R.; Dowson, D. Elastohydrodynamic Lubricant; Pergamon Press: London, 1977. (6) Wright, D. A.; Axelson, D. E.;Levy, G. C. In Topics in Carbon-13 NMR;Levy,G. C., Ed.; Wiley: New York, 1979; Vol. 3, Chapter 2. (7) Molecular Dynamics in Restricted Geometries; Klafter, J., Drake, J. M., Eds.; John Wiley & Sons: New York, 1989; and references therein.
Liquid EHB Confined to Porous Silica Glasses (8) Drake, J. M.; Klafter, J.; Kopelman, R. DynamicsinSmallCon/lning Systems; Proceedingsof Symposium M, 1990 Fall Meeting of the Materials Research Society; references therein. Liu, G.; Li, Y.;Jonas, J. J . Chem. Phys. 1989, 90,5881. Liu, G.; Mackowiak, M.;Li, Y.;Jonas, J. J . Chem. Phys. 1990,149,
Mackowiak, M.; Liu, G.; Jonas, J. J. Chem. Phys. 1990,93,2154. Liu, G.; Mackowiak, M.; Li, Y.;Jonas, J. J . Chem. Phys. 1991.94, Liu, G.; Li, Y.;Jonas, J. J . Chem. Phys. 1991, 95, 6892. Xu, S.;Zhang, J.; Jonas, J. J. Chem. Phys. 1992, 97, 4564.
The Journal of Physical Chemistry, Vol. 98, No. 27, 1994 6839 (15) Korb, J. P.;Xu,S.;Jonas, J. J . Chem. Phys. 1993, 98, 2411. (16) Korb,J.P.;Delvillc,A.;Xu,S.;Kim,Y.J.;Demculcnaere,G.;Costa,
P.;Jonas, J. J. Chem. Phys., submitted for publication. (17) (181 (19) (20) (21) (22) (23)
Zhang, J.; Jonas, J.J. Phys. Chem. 1993, 97, 8815. Sindorf, D. W.:Maclcl. G. E. 1.Phvs. Chem. 1983. 87. 5516. Brownstein, K. R.; T a i , C.E. J. Reson. 1977, 26, 17. Xu,S.; Jonas, J. Unpublished results. Abraham, F. F. J. Chem. Phvs. 1979. 68. 3713. Kjcllandcr, R.; Sarrnan, S . Mol. Phyi. 1990, 70, 215. Granick, S. Science 1991, 253, 1374.
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