7902
J . Phys. Chem. 1989, 93, 7902-7906 P-Se system compared to the P-S system is due to a more efficient thermodynamic competition of such 3-fold units with tetrahedral Se=PSe,/, groups, as expressed by the K value near unity. This is entirely expected since the size difference of the atoms involved should lead to substantial weakening of the P-Se double bond. The N M R results presented in this contribution substantiate this prediction and provide a quantitative assessment of this effect. The excess selenium atoms not involved in P=Se double bonds then engage in chalcogen-chalcogen bonds. The trend for more effective competition of homoatomic versus heteroatomic bond formation apparent from our present study also parallels the results obtained in our previous N M R investigations of boron chalcogenide systems.52
apparent from Figure 7, Price et al. postulate a cluster model for these glasses involving P4SeSand P4Se4units surrounded by Se-rich regions.24 These clusters are assumed to contain P atoms of the type Se=P(Se2j2)(P),13, Le., tetrahedral units containing a P-P bond. We cannot rule out the possibility that such groups might have NMR chemical shifts substantially different from S-PSe3/2 units, and might therefore contribute to the downfield resonance assigned to 3-fold P atoms. This caveat needs to be borne in mind especially in view of the highly variable chemical shifts of threeand four-coordinated P atoms observed in phosphorus-chalcogen bonded environments. Conclusions The NMR data presented here provide important insights into glass formation in non-oxide chalcogenide systems. In this regard, a comparison of the two systems P-S and P-Se is highly instructive. In contrast to the exceptionally high glass-forming tendency found in the system P-Se, glasses in the system phosphorussulfur form only over a limited range of compositions (0-25 atom % P) and are easily crystallized upon annealing. In contrast to the results discussed here, the N M R spectra of P-S glasses are completely dominated by S=PS3/2 groups and indicate the absence of trigonal PS3/2 units and of any units containing P-P bonds.45 Thus, we conclude that the strong glass-forming tendency in the
Acknowledgment. Financial support of this research by the UCSB Academic Senate and the donors of the Petroleum Research Fund, administered by the American Chemical Society, is gratefully acknowledged. H.E. also thanks the University of California for a Regent’s Junior Fellowship. Registry No. P, 7723-14-0; Se, 7782-49-2; P4Se4, 56863-52-6; P4Se3, 1314-86-9. (52) Hurter, H. U.; Krebs, B.; Eckert, H.; Muller-Warmuth, W. Znorg. Chem. 1985, 24, 1288.
Rotational Relaxation and Interaction-Induced Effects in Liquid Dichloromethane T. W. Zerda Physics Department, Texas Christian University, P.O. Box 32915, Fort Worth, Texas 76129 (Received: March 21, 1989)
Raman spectra of three AI vibrational modes of CH2CI2are studied at pressures varying from 1 to 2000 bar. The rotational second moments and total intensity measurements indicate that induced effects are important for the v4 band while they may be neglected for the vI and vj bands. Rotational correlation functions are obtained from VV and VH polarized components of the v I and v3 bands. In order to find elementary correlation times T ~ T, ~ and , T,, the experimental correlation functions are compared with the theoretical functions obtained from the Fokker-Planck-Langevin model. The elementary times are used to characterize rotational relaxation.
Fixman and Riders proposed the Fokker-Planck-Langevin (FPL) model for molecular rotation in liquids. This is a frictional model in which the molecule is approximated by a solid object immersed in a viscous fluid. Angular velocity of the molecule is constantly modulated by intermolecular torques. A fluctuation in intermolecular interaction generates a torque that only slightly changes the angular momentum of the molecule. For a significant change of angular momentum a large number of fluctuations are necessary. The angular velocity correlation function is assumed to be described by the Langevin equation, and the conditional probability of the molecular reorientation and angular velocity is assumed to be governed by the reorientational Fokker-Planck equation. The FPL model calculations are quite complicated, and only approximated solutions are available. The most accurate results have been obtained by McClung? His numerical technique based on a series expansion of the angular velocity and orientational probability distribution functions allows to compute reorientational correlation functions, memory functions, correlation times, and spectral densities. Recently the FPL model has been extended to asymmetric top molecule^,'^ and general expressions for reorientational correlation functions and correlation times have been derived. This makes possible a comparison of experimental Raman band shapes with
Introduction CH2C1, is an asymmetric molecule with moments of inertia I, = 252.46 X I,, = 273.46 X and I, = 26.96 X 1040 g cm2 [ref 11. Two moments of inertia are almost equal, and most authors regard the molecule as a symmetric t ~ p ,but ~ ,this ~ assumption limits the conclusions of experimental investigations. Different models have been used to discuss reorientational motion of asymmetric molecules. Commonly used are the extended diffusion (ED) model proposed by Gordon4 and later modified by McClungS and expanded to asymmetric molecules by Bull6 and Leickman and c o - ~ o r k e r s . ~The (ED) model assumes free orientation of the molecule between collisions which are instantaneous and random. Two versions of the model have been proposed: (1) each collision changes the orientation and the magnitude of the angular momentum vector ( J diffusion); (2) only the orientation is randomized ( M diffusion). (1) Evans, M.; Evans, G. J.; Coffey, W.; Grigolini, P. Molecular Dynamics; Wiley: New York, 1982. (2) Brier, P. N.; Perry, A. Adu. Mol. Relax. Interact. Processes 1976, 13, I
(3) Rodriguez, A. A.; Schwartz, M. Spectrosc. Lett. 1987, 20, 785; J . Mol. Liq. 1988, 37, 117. (4) Gordon, R. G. J . Chem. Phys. 1966, 44, 1830. (5) McClung, R. E. D. J. Chem. Phys. 1969, 51, 3842; 1972, 57, 5478. (6) Bull, T. E.; Egan, W. J . Chem. Phys. 1984, 81, 3181. (7) Leickman, J. C.; Guissani, Y.; Bratos, S . J. Chem. Phys. 1978, 68,
(8) Fixman, M.; Rider, K. J . Chem. Phys. 1969, 51, 2425. (9) McClung, R. E. D. J . Chem. Phys. 1980, 73, 2435.
3380.
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The Journal of Physical Chemistry, Vol. 93, No. 23, 1989 7903
Rotational Relaxation in CH2Cl2 the theoretical prediction of the FPL model. Previously, such studies have been done only for spherical top, SFslo and CF4,1* and linear, N20,I2molecules. In this paper we will analyze Raman band shapes of CH2C12in order to characterize reorientational motion and frictional anisotropy in the modulation of the angular momentum of this molecule. Reorientational motion of CH2C12has been studied by using different experimental techniques including neutron scattering,2 NMR,3,14IR,15J6 Raman," dielectric relaxation,I8 and computer simulations.'* Interpretation of experimental data is quite complicated, and usually authors had to assume that dichloromethane can be approximated by a linear structure. The goal of this research is to study reorientational motion of CH2C12in the liquid phase without any assumption about its geometry. High pressure is used to study the effect of density on molecular reorientation. However, increased pressure may result in induced effects that can alter band s t r u c t ~ r e s , l ~and - ~ ~we carefully evaluate these effects by measuring second moments and total intensities for all three vibrational bands under investigation. The reorientational correlation functions are computed only from the band shapes free of induced effects and are compared with the theoretical values obtained from the FPL model. The elementary correlation times 7 x , T,,, and T ~ which , characterize components of the retarding torque, are found and discussed in terms of anisotropy of reorientational motion.
Theory Experimental Raman correlation functions are linear combinations of tensor correlation functions, Gikk(t),defined in the molecular frame23 Grot(t)
=
C@kk(t)a'k
k
(1)
where coefficients dk are Raman anisotropic polarizability components which depend on molecular polarizabilities, axxraYy,and aZr, defined in Cartesian coordinates. In Raman experiments we measure reorientational correlation functions @k. associated with Wigner functions of the second order; therefore,j = 2. Lee and McCIung showedI3 that for asymmetric molecules correlation functions G2kk(t)are related to the elementary correlation functions @2mk as follows G2kk(t)
= xcm(k)
@2mkdOooo;koOW(t)
(2)
LTU
+
angular velocity between w and w dw and orientation between fl and fl dfl at time t, given that it had angular velocity between w0 and wo d o and orientation between flo and flo dfl at time zero. Equation 3 is solved for the matrix representation of the operator 2,and the indexes ks000;ksOOO represent the row and column of the inverse of the Z matrix. The functions @ can be computed by using the numerical program developed by Lee and M c C 1 ~ n g . l The ~ functions depend on parameters T * ~ 7, * y , and T * , which represent elementary correlation times about three coordinates, and the calculations have to be done independently for each set of parameters. Asterisks denote reduced time units, T * , = 7 , (kT/Za)1/2. The details of the computational technique can be found in ref 13.
+ +
+
Experimental Section Spectral grade dichloromethane was purchased from Aldrich and was used without further purification. Raman experiments were done using an argon ion laser and a Spex double monochromator. The monochromater and a photon counter were interfaced with an IBM-XT connected to a VAX computer. All calculations were done on the VAX. A stainless steel high-pressure Raman cell equipped with four windows was used. Pressure was generated by an Enerpac hand pump and intensified 10 times by a Haskel intensifier. Accuracy of the pressure readings was better than 5 bar. The temperature of the cell was controlled and set to be 300 K throughout measurements. The CH2C12molecule has the point group symmetry C, with its permanent dipole moment (1.6 D) along the C2 symmetry axis.',2 The symmetry axis coincides with one of the principal axes of inertia. The Raman spectrum of CH2CI2consists of nine bands, four of which belong to the A, species. The three A, bands, u,, u3, and u4, are well isolated from neighbors, and their shapes can be accurately analyzed. The u I vibration centered at 2988 cm-' is assigned to the H-C stretching mode, the u3 band at 705 cm-I is due to the C-C1 stretching mode, and the u4 bending C1-C-C1 mode is centered at 288 cm-I; all bands are relatively intense and thus easy to measure. Because the bands are relatively narrow, the slits were open only to 1.2 cm-'. This required long counting time intervals, from 32 to 60 s at each step. The band contours were recorded at 1-cm-' intervals over the frequency region exceeding 100 cm-' on both sides of the band centers. Results The reorientational correlation functions were obtained from23
where
C,(k) = [ l
P is the conditional probability density that a molecule will have
+ 2(1/21/2 - 1/2)6k,O + (1 - 21/2)6k,01(1 + 6k,O) Grot(t)
C,,(k) = 1 / 2
=
Jan>H(U)eiW' dw
-
Functions @2mkmkbooo(t)depend on eigenvalues and eigenvectors of the matrix representation of the Liouville operator 2 used in the rotational Fokker-Planck equation aP/at = -ZP
(3)
(IO) Zerda, T. W.; Schroeder, J.; Jonas, J. J . Chem. Phys. 1981,75,1612. ( I I ) Perry, S.; Schiemann, V.; Wolfe, M.; Jonas, J. J . Phys. Chem. 1981, 85, 2805. (12) Levi, G.; Marsault, J. P.; Marsault-Herail, F.; McClung, R. E. D. J . Chem. Phys. 1980, 73, 2443. (13) Lee, D. H.; McClung, R. E. D. Chem. Phys. 1987, 112, 23. (14) Sandhu, H. S. J . Magn. Reson. 1978, 29, 563. (15) Rothschild, W. G. J . Chem. Phys. 1970, 53, 990. (16) K. Tanabe, Spectrochim. Acta 1975, 32A, 1169; 1974; 3ZA, 1611. (17) Hacura, A.; Zerda, T. W.; Kaczmarski, M. J . Raman Spectrosc. 1981, 11, 437. (18) Coffey, W.; Evans, M.; Grigolini, P. Molecular Dqfusion and Spectra; Wiley: New York, 1984. (1 9) Birnbaum, G. Phenomena Induced by Intermolecular Interactions; NATO AS1 Ser. B127; Plenum Press: New York, 1985. (20) Zerda, T. W.; Song, X.; Jonas, J.; Geiger, L.; Ladanyi, B. J . Chem. Phys. 1987.87, 840. (21) Ladanyi, B.; Geiger, L.; Zerda, T. W.; Song, X.; Jonas, J. J . Chem. Phys. 1988, 89, 660. (22) Song, X.; Jonas, J.; Zerda, T. W. J . Phys. Chem., submitted for publication. (23) Bartoli, F. J.; Litovitz, T. A. J . Chem. Phys. 1972, 56, 413.
where Zvv and ZVH are polarized and depolarized band shapes, respectively. This procedure removes from the correlation function contributions arising due to vibrational dephasing and energy transfer, leaving only the contributions due to orientational and collision-induced polarizability relaxation. When pressure increases, the experimental reorientational correlation function decays at a slower rate as illustrated in Figures 1 and 2. The reorientational correlation functions were used to calculate reorientational correlation times defined as
The experimental correlation functions decay slowly in time, and in order to reduce the error we calculated the experimental reorientational correlation times from
where T i s an arbitrary division between the short and long time
7904
The Journal of Physical Chemistry, Vol. 93, No. 23, 1989
Zerda I .0
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,
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,
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,
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I
I
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i 0.0
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,
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,
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i
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Figure 2. Experimental (dashed line) and the FPL theoretical (solid line) correlation functions for the v3 band of CH2C12at a temperature of 300 O C and 1 bar (a) and 2000 bar (b).
P r e v i o ~ s l y ,we ~ ~have ~ ~ shown . ~ ~ that collision-induced effects may affect molecular polarizability and thus contribute to the band shapes and band intensities. These contributions to the IVH components become more important with increasing pressure, and thus they may affect experimentally determined correlation functions and angular correlation times. The best way to detect the presence of the induced effects is to analyze the density dependence of the rotational second moment M2defined as
TABLE I: Experimental Relaxation Times Calculated from the Bandwidths, Eq 7, and from the Correlation Functions, Eq 6
u, band
v3 band
v, band
press., bar 1 500 1000 2000
Trot,
7
=
SGrot(0df,
PS 1.5 1.9 2.6 3.8
PS 2.8 3.6 4.1 4.9
1000 2000
1.5 2.0 2.8 4.0
1.5 2.1 3.0
1 500 1000 2000
2.0 2.2 2.4
1 500
1.7
Mrot(2) = M v H ( ~-) Miso(2) Ju2IvH(w) dw
S w 2 I i S a ( ~dw ) -
S I V H C ~ dw )
4.0
1.2 1.6 1.8 2.1
(8) JIiso(w)
dw
and to analyze the density of the total normalized intensity
I",, =
dependence of Groc(t),chosen in such a way that the long time portion is approximately exponential. The long time portion was approximated by an exponentially decaying function, and the second component in eq 6 was solved analytically. The results are listed in Table I. The reorientational correlation times can also be approximated from the bandwidths
(7) where A Y ~is the ~ half-width ~ , ~ ~at half-height of the VH component of the band and Avl/2qiso is the half-width at half-height of the isotropic band computed by the usual method of Ii,(w) = Iw(w) - (4/3)1vH(w). The accuracy is better than 5%. The results are listed in Table I.
SI(4dw P
(9)
where p is the density. The calculated second moments and total intensities are listed in Table 11. We estimate the error in determining M(2)to be less than 12% and that the total intensity data are accurate within 7%. The errors were estimated from three independent runs. Due to lack of data on pressure dependence of the index of refraction for CH2C12,the normalized intensity has not been corrected for geometrical factors, l / n 2 , and local fields, ((d+ 2)/3j4, which have to be taken into account to obtain the absolute scattered intensity per one molecule.20 The index of refraction for dichloromethane is quite large, n = 1.4242, and even a small increase in its value at increased pressure may have (24) Zerda, T. W.; Perry, S.; Jonas, J. Chem. Phys. Lett. 1981, 83, 600.
The Journal of Physical Chemistry, Vol. 93, No. 23, 1989 7905
Rotational Relaxation in CH2C12 TABLE 11: Second Moments and Normalized Intensities for Vibrational Bands of CH2C12 press., density? M(2)9cm-2 IlP . bar g/cm3 u1 v3 u4 uI u3 1
500 1000 2000
1.308 1.367 1.414 1.487
62 68 56 65
204 208 210 203
74 68 59 51
1.00 1.02 1.02 0.99
1.00 1.02 1.01 1.03
TABLE III: Elementary Correlation Times in Picoseconds;i,, and in Reduced Units. i * , u4
1.00 1.03 1.09 1.19
“Taken from ref 32.
a large effect on the correction factors. Therefore, we will limit the discussion to a comparison of normalized intensities (9) obtained for different vibrational bands. Raman bands under consideration are observed at 495.0, 505.0, and 571.3 pm, and because the dispersion of dichloromethane is small, the index of refraction for these three wavelengths varies by less than 0.4%.33 Consequently, at normal conditions, the correction factor for the 288-cm-l band is greater by only 2% than the corresponding factor for the 2988-cm-’ band. One may assume that the correction factors will be similar also at increased pressures and any difference in I,,, for the three bands may be attributed to different contributions of the induced effects to these bands.
Discussion As seen from Table 11, the experimental second moments for two bands of CH2CI2,ul and u3, are pressure independent, while the u4 band second moment decreases with increasing density. These changes are accompanied by the changes in the total intensities. These findings suggest that the interaction-induced effects are important for the u4 band and may be neglected for the other bands. Induced Effects. In the theory on interaction-induced effects on spectral band shapes, introduced by Ladanyi and Keyes,25the total intensity of a Raman band is composed of two components l I ( w ) dw = l P R ( w ) dw
+ll”(w)
dw
(10)
where P R ( w ) denotes orientational component and F 1 ( w ) is the collision-induced term. In the dipole-induced-dipole model, the integrated intensity of the allowed component changes with density as
where A is a constant and y6ff, the effective anisotropic polarizability, is the sum of the molecular, y’,and the induced AT‘, anisotropic polarizabilities. In most cases Tleffdecreases with growing pressure.Ig Total intensity, SPR(w)dw, may either decrease or increase depending which parameter, p or 7’4changes faster with increasing pressure. The pure induced intensity, JF1(w) dw, can be roughly estimated from l l ” ( w ) dw =
B[a’a/(r’~~)]~
where B is a constant, CY is isotropic molecular polarizability, u is the intermolecular distance, and primes denote Raman polarizability components. Both components are density dependent, but this dependence can be evaluated analytically only for low at higher pressures, only molecular dynamics calculations can be used to find PRand IC’. The second moment can be separated into three parts: Mr,,(2) = MOR(2)
+ Mc’(2) + MfR(2)
(13) where f l R ( 2 ) is due to symmetry-allowed reorientation, Mc1(2) is caused by pure induced effects, and f l R ( 2 ) represents the coupling between rotational and induced terms. f l R ( 2 ) is slightly dependent on density because of the increased role of pair correlation,” but to a first approximation this effect may be ignored. The Mc1(2) and f l R ( 2 ) terms have been studied theoretically21,26*27 and e ~ p e r i m e n t a l l y ~only ~ + ~for~ -linear ~ ~ molecules, but ( 2 5 ) Ladanyi, B.; Keyes, T. Mol. Phys. 1977, 33, 1063.
press., bar
TX
TY
7,
7*x
TSY
7*,
1 500 1000 2000
0.13 0.10 0.06 0.01
0.12 0.09 0.06 0.01
1.17 0.98 0.78 0.78
0.10 0.08 0.05
0.10 0.08 0.05 0.01
0.30 0.25 0.20 0.20
0.01
it is now well established that both terms are very sensitive to intermolecular interactions and intermolecular distances. It is also known20-22that the contributions due to these two terms increase with the magnitude of the anisotropy of the polarizability tensor. Because the ratio of anisotropic to isotropic components for the u4 band is 0.38, whereas for the u1 and u3 band it is 0.037 and 0.072, it is expected that the induced effects are more pronounced for the u4 band than for the ul and u3 modes. Indeed, the data listed in Table I1 indicate that the observed second moment for the u4 band is pressure dependent. Since the total intensity for this band has a different pressure dependence than for the other two bands, we conclude that the induced effects are important and cannot be neglected. Because the u4 band is affected by the induced effects, it will not be used to calculate the correlation function, and further discussion will be limited to the u1 and u3 bands. Rotational Relaxation. The theoretical functions (1) were calculated for both vibrational modes, u1 and u3, using CH2Cl2 polarizability data published by Escribano and other^.^' Because the induced effects were small, we assumed that the polarizability components a,,, aYY,and a,, were not affected by the increased pressure. The best fit between theoretical and experimental , T*,. The functions provided information on times T * ~ T, * ~ and examples of the fitting routine are shown in Figures 1 and 2, and the found correlation times are listed in Table 111. Theoretical correlation functions for dichloromethane depend primarily on the T * , and to a smaller extent on the T * , and T * parameters. ~ Consequently, T*, has been estimated with a greater accuracy than T * , and T * ~ . The fitting routine is very accurate at low pressures where experimental functions decay rapidly in time and even small changes in T* values can modify theoretical functions. At higher pressures, experimental functions decay at a slower rate and the fitting routine is less sensitive to the changes in T*,, T* and T*,. We estimate that at the normal conditions the error f‘dr the pa~ less than lo%, and for T * , it is 570, and rameters r*, and T * is that at the highest pressure the error increases to 50% and 20%, respectively. The theoretical elementary correlation functions are essentially exponential when times T*,, T*,,, and T*, are all less than 0.1. Only when the times are greater than 0.1 do the correlation functions show an initial Gaussian time dependence which later converts into an exponential decay. Since the experimental correlation functions for the u I and the v 3 bands were all exponential in character, we concluded that the elementary times were all small and probably less than 0.1. These expectations were confirmed by the fitting r o u t i n e t h e elementary times were all smaller than 1.0 in reduced units. The reciprocals of elementary correlation times are proportional to the frictional coefficients. Of course, the frictional coefficient increases with density, and this effect explains the density dependence of times T* listed in Table 111, as well as the slower decay (26) Keyes, T.; Kivelson, D.; McTague, J. P. J . Chem. Phys. 1971, 55, 4096. (27) DeSantis, A.; Sampoli, M. Mol. Phys. 1984, 51, 97. (28) Cox, T. I.; Bataglia, M. R.; Madden, P. A. Mol. Phys. 1879,38, 1539; 1980, 39, 1497; 1981, 43, 287, 307. (29) Zerda, T. W.; Song, X.; Jonas, J. J . Phys. Chem. 1986, 90, 771. (30) Versmold, H.; Zimmermann, U. J . Chem. SOC.,Faraday Trans. 2 1987, 83, 1815. (31) Escribano, R.; Orza, J. M.; Montero, S.; Domingo, C. Mol. Phys. 1979, 37, 361. (32) Schormak, A.; Echert, P. J . Phys. Chem. 1970, 74, 3014. (33) Landolt-Bornstein Physikalisch Chemisrhe Tabellen; Verlag Springer: Berlin, 1935; Supplement 3, Part 2, p 1684.
J. Phys. Chem. 1989, 93, 7906-7912
7906
of the reorientational functions. The magnitudes of times T* expressed in reduced units reflect only the anisotropy in the modulation of angular velocity components, whereas the same times T but measured in seconds reflect both the anisotropy in the moments of inertia and the anisotropy in the modulation of the angular velocity components. For CHzClz the z axis was chosen to be perpendicular to the H-C-H plane and the x axis to lie along the dipole moment. As seen from Table 111, there is no difference in parameters T * , and T*,, expressed in the reduced time units. This means the electrostatic interactions do not affect reorientational motion. If the interactions due to the dipole moment are more important than moments of inertia, then T,, which measures rotations around the x axis, should be longer than T,,, which detects the reorientation of the dipole moment. The fact that the time T~ is much longer than either 7, and T,, also can be explained in terms of molecular shape. The spinning motion around the z axis involves changes in the direction of the dipole moment, and if electrostatic interactions dominate then T~ should be very short. Because this time in not a short one, we conclude that the reorientation of dichloromethane is governed primarily by inertial properties and steric hindrance effects, and not by electrostatic interactions. This result agrees well with the data obtained by Schwartz and his students3 From N M R relaxation measurements they found that the rotational motion of CHzClzwas highly anisotropic and that the rotation about the z axis could be treated as a free spinning motion. They estimated that the spinning motion was 10 times faster than the tumbling motion, a result corresponding nicely to
our findings. Reorientation about the z axis, although not a completely free spinning motion, is relatively fast and does not depend on the pressure applied to the system. On the other hand, the times T,, and T , are density dependent and decrease by a factor of I O when density is increased by 10%.
Summary Reorientational motion of CHzClz appears to be highly anisotropic and consistent with the Fokker-Planck-Langevin model for rotational Brownian motion. Reorientational motion about the x and y axes is slow and decreases further with increasing pressure. Reorientation about the z axis is practically unperturbed by intermolecular interactions, and when pressure increases 7, decreases by 30%. The inertial properties and steric effects appear to be more important than electrostatic interactions. The pressure dependence of the second moments and normalized intensities for the v4 band indicate the presence of collision-induced effects. The v 1 and vj bands which have a low depolarization ratio appear free of induced effects. It is suggested that induced effects are important for bands of large depolarization ratio. Further studies are necessary to identify interactions responsible for the interaction-induced contribution. Acknowledgment. This study was supported by the Texas Christian University Research Fund. The author thanks Dr.R. E. D. McClung for a copy of his program to compute correlation functions for asymmetric molecules. Registry No. CH2CI,, 75-09-2.
Structure of Cu2+-Cu2+ Dimers in Nafion Swollen by Water, Methanol, DMF, and THF. ESR Results and Theoretical Simulations Shulamith Schlick,* M. G. Alonso-Amigo, Department of Chemistry, University of Detroit, Detroit, Michigan 48221
and Sandra S. Eaton Department of Chemistry, University of Colorado, Denver, Colorado 80204 (Received: January 6, 1989; In Final Form: March 28, 1989)
Cu2+-Cuz+dimers in Nafion membranes swollen by water, methanol, N,N-dimethylformamide (DMF), tetrahydrofuran
(THF), and water/methanol mixtures have been detected by ESR spectroscopy. Characterization of the dimers was on the basis of measuring the half-field spin-forbidden & = 2 transition at a.1600 G and by computer simulations. The intercation distance in the dimers, r, was deduced from the intensity ratio of the Ams = 2 and Ams = 1 transitions. The value of r = 5.0 f 0.2 A; this value was deduced by deconvoluting the experimental spectrum into contributions from the isolated cations and from the dimers. The relative orientations of the principal axes for the two cations in the dimer and the interspin vector were deduced by simulating the line shape of the half-field transition, which is independent of the value of the isotropic exchange integral J and of the intercation distance r. The best agreement with experimental line shapes was obtained for an angle of about 60° between the symmetry axes of the two cations, in Nafion swollen by water. The experimental results obtained in this study and in our previous studies of Nafion can be explained by assuming that in the dimer the cations are ligated to the sulfonic groups of the Nafion network. Experimental results support the proposal that clustering is due to an increase in the dimer concentration and a decrease in the interdimer distance. In addition, it appears that the intercation distance in clusters is equal to or larger than the intercation distance in the dimers.
Introduction The properties of ionomers, which contain an organic polymer backbone and about 10 mol% of ionic groups, can be rationalized by assuming a morphology consisting of polar and nonpolar regions and clustering of ionic charges in the polar regions. In many of the ionomers investigated, the polymer contains pendant acid groups, mostly sulfonic and carboxylic, which can be neutralized by addition of metal cations. The structure of the ionic cluster and its dependence on the swelling solvent, temperature, cation 0022-365418912093-7906$01.50/0
concentration, and cation charge have been investigated by a variety of spectroscopic and diffraction methods; the results have been summarized in several recent books.'-3 (1) Ions in Polymers; Eisenberg, A., Ed.; American Chemical Society: Washington, DC, 1980. (2) Perfuorinated Ionomer Membranes; Eisenberg, A., Yeager, H. L., Eds.; American Chemical Society: Washington, DC, 1982. (3) Structure and Properties of Ionomers; Pineri, M . , Eisenberg, A., Eds.; NATO AS1 Series; Reidel: Dordrecht, The Netherlands, 1987.
0 1989 American Chemical Society
