2702
J . Phys. Chem. 1990, 94. 2702-2705
ref 3 for a charged cylinder with a radius b = 10 h;, cell radius a = 12.2 A, surface charge density (r = -0.15 C m-*, temperature T = 298 K, and dielectric constant t = 79 or 35 (to mimic a 80% ethanollwater solution) in the bath. The excess LiCl concentration in the PB cell was obtained as in ref 10 for an ordered DNA phase in equilibrium with a bath of 0.25 M LiCI. This yields a salt concentration of 0.014 M LiCl in the ordered DNA phase which is used in the solution of the PB-Smoluchowski equation with t = 79. The salt concentration corresponds to a LiCl to DNA phosphate ratio of 0.067. This value is nearly 2 orders of magnitude less than the LiCl content found experimentally by Rupprecht and Forslind2' for Li-DNA fibers at a similar salt content. The discrepancy could partly be due to the LiCl absorbed in the void between fibrils, which would contribute to the experimental LiCl c~ncentration~~ but not to the calculated. However, it seems more likely that the continuum PB model completely fails for the present very compact system. This is also supported by the value of the diffusion quotient calculated from the PB-Smoluchowski model, D , / D o = 0.64, which should be compared with D , / D o 0.01 for the apparent transverse diffusion given in Table 11. Recent Brownian dynamics simulations4*on ordered DNA systems give lower diffusion coefficients than the PB model but indicate that the molecular nature of the water and DNA double helix is of importance for dense ordered DNA systems. The salt dependence observed in Table I11 is consistent with the interpretation of the splittings (performed on the same samples) given above. If added LiCl is hydrated and mainly associated with the grooves of and between the DNA, it is expected that the average mean square displacement and diffusion coefficient will increase with increasing LiCI. The hydration dependence is also expected, since adding water makes the volume that is not taken by the DNA more fluidlike and this should increase the mobility. The considerable increase in the diffusion quotient between 75 and 84% R H is interesting. At 84% R H it is likely that the void space between the fibrils has been filled with water. This should start to remove the restriction barriersz1and thus increase the diffusion coefficients. Finally, it should be noted that it has been pointed that a &dependence of the diffusion can also be due to an inhomogeneous magnetic susceptibility, which can be induced by the macroscopic heterogeneity of the sample. Due to the macroscopic property of our samples (see Experimental Section), we cannot rule out that this contributes to the observed A-dependence in our
-
(48) Guldbrand, L. Mol. Phys. 1989, 67, 217. (49) Packer, K.J. J . Magn. Reson. 1973, 9, 438. (50) Majunder. S.; Gore, J. C. J . Magn. Reson. 1988, 78, 4 1
system. The presence of such a contribution, however, could not explain the axial dependence of the diffusion on A. Summary and Conclusions
'Li quadrupolar splittings in macroscopically oriented Li(B)DNA fibers have been found to decrease with increasing salt and/or water content. Apparent Li+ self-diffusion coefficients parallel and perpendicular to the fiber axis exhibit restriction effects and a small anisotropy. D,,and D , increase with increasing salt and water content. The salt and hydration dependence can be explained by considering lithium ions dynamically averaged over many different environments in the microscopically very heterogeneous system. Increasing the content of water and salt makes the environment more hydrated and the ions more mobile. The continuum model Poisson-Boltzmann theory is not applicable to describe the DNA-counterion association in the present compact and water-scarce systems. The restriction in the diffusion in the direction perpendicular to the fiber axis is due to the radial extension of the fibrils. The restriction in the parallel direction, on the other hand, has not been satisfactorily explained but can be tentatively attributed to an unexpected large spread in the orientation of the microcrystallite axes or to a heterogeneity in the fiber structure in the long axis direction. The results of high relative humidity (84%) give some indications that restriction effects start to disappear at higher water content. The diffusion data give, however, a good estimate (particularly of the trends) of the intrinsic unrestricted diffusion, which is considerably slower than for lithium ions in dilute isotropic DNA solutions but still show that the ions are highly mobile around and along the DNA molecule. In order to obtain a better understanding of the above issues and to continue this study, it would be fruitful to investigate more thoroughly the behavior at higher humidities when the ordered DNA fibers have a considerably higher water content than in the present work. This is also motivated by the fact that more water-rich oriented DNA systems probably have more biological relevance as models for DNA in living systems. Such studies are currently in progress at our laboratories. Acknowledgment. Valuable help from Peter Stilbs at the beginning of this project is highly appreciated. We are indebted to Jozef Kowalewski for many valuable discussions and suggestions. Discussions with Rolf Brandes and Gojmir Lahajnar are acknowledged. This work has been supported by the Swedish Natural Science Research Council (NFR) and by the Knut and Alice Wallenberg foundation. Registry No. Li, 7439-93-2.
Reorientational Diffusion and Internal Rotation in Trichloroethane S. P.Wangt and M. Schwartz* Department of Chemistry, University of North Texas, Denton, Texas 76203 (Received: August 12, 1989)
The Raman band shapes of the v l (CH, symmetric stretch), v5 (CCl, symmetric deformation), and v7 (CH, antisymmetric stretch) vibrations in 1,l,l-trichloroethane have been studied as a function of temperature in the liquid phase. Perpendicular NMR relaxation times. and parallel diffusion coefficients, D, and D,,,were determined from v7 together with published 35CI The two coefficients were similar both in magnitude and dependence on temperature, implying that the reorientation is nearly isotropic in the neat liquid. Values of the parameter, R,characterizing the methyl group internal rotation jump rate as determined from band-shape analysis of the degenerate v, mode were in qualitative agreement with results from I3C NMR dipole-dipole relaxation time data and yielded estimates of approximately 2 kcalfmol for the barrier to internal rotation. Introduction
Recently, we have been interested in analysis of the Raman band shapes of degenerate vibrational modes to investigate the 'Robert A. Welch Predoctoral Fellow. *To whom correspondence should be addressed.
0022-3654/90/2094-2702$02.50/0
parallel, "spinning", rotation in molecules of C,, symmetry in the liquid When applied to the methyl rotors, iodomethane',2 (1) Wang, S. P.; Yuan, P.; Schwartz, M. J . Raman Spectrosc. 1989, 20,
339.
0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 6, 1990 2703
Diffusion and Rotation in Trichloroethane
TABLE I: Temperature Dependence of Raman Bandwidths and Rotational Diffusion Coefficients in TrichloroethaneO
296 31 1 326 343
(0.01) 3.56 (0.08) 3.67 (0.30) 3.51 (0.02) 3.98 (0.02)
(0.05) 9.52 (0.04) 10.37 (0.23) 11.01 (0.12)
(0.01) 3.58 (0.09) 3.66 (0.07) 3.48
12.50
3.61 (0.04)
(0.19)
(1.9) 28.8 (5.0) 35.0 (2.9) 44.5 (13.3)
(0.01)
50.1 (2.6)
OQuantities in parentheses represent the standard deviation of the three runs. *Temperature (K). coefficients (1 0"W).
and acetonitrile,j it was observed that the calculated values of Dl, and their dependence on temperature, Ea(D,,),were in excellent agreement with coefficients predicted by the free-rotor model of molecular reorientation. In contrast to CH31and CH3CN, it is well established that the methyl group reorientation in 1 ,l,l-trichloroethane (TCE) is restricted by a 3-fold barrier to rotation about the C-C bond."9 In order to further explore the utility of Raman line-shape analysis to characterize the reorientational dynamics in C,,molecules, we have studied the Raman spectra of the following vibrations in T C E u l ( A l ) CH, , symmetric stretch (2943 cm-I); ~5(A1),CCl, symmetric deformation (345 cm-I); u7(E), CH3 antisymmetric stretch (3010 cm-I). The results, together with published j5Cl N M R relaxation time results,IO are used to determine D,, Dll,and R (the internal rotation jump rate) as a function of temperature in the liquid phase.
Experimental Section l,l,l-Trichloroethane was obtained commercially and purified by fractional distillation prior to use. Most details of the Raman spectral data acquisition and analysis have been presented and will not be repeated. All spectra were acquired two or three times at each temperature. The results presented in Table I represent the average of the runs. Polarized and depolarized spectra of u1 were obtained with a spectral slit width, SW = 3.0 cm-I, and frequency increment, Au = 0.3 cm-I/point. Following base-line subtraction, isotropic spectra were calculated via the standard relationship." The line width, Aiso(ul), was calculated from a fit of the experimental intensities by a model consisting of a Lorentzian line shape convoluted with a triangular slit function. Spectra of the doubly degenerate u7 vibration were recorded with SW =: 5.5 cm-' and Au = 0.6 cm-'/point. The intensities were fit by a model incorporating two Lorentzians with the same peak center but differing bandwidths (Ai2) and Ai2)) and peak maxima, convoluted with the slit function. Tsai and BaglinI2 determined the perpendicular diffusion coefficient in TCE from the line widths of the ul vibration. Due to the low depolarization ratio ( p < 0.02, as measured in our (2) Wang, S.P.; Hu, W. P.; Schwartz, M. Raman Bandshape Analysis of the Degenerate vd Vibration and Parallel Rotational Diffusion in CDJ. Mol. Phys., submitted for publication. (3) Yuan, P.; Schwartz, M. Molecular Reorientation in Acetonitrile: A Comparison of Diffusion Coefficients from Raman Bandshapes and NMR Relaxation Times. J. Chem. Soc., Faraday Trans. 2, submitted for publication. (4) Holm, R.; Mitzlaff, M.; Hartmann, H. 2.Naturforsch. 1968, 23A, 307. (5) Rubin, T. R.; Levedahl, B. H.; Yost, D. M. J. Am. Chem. SOC.1944, 66, 279. (6) Allen, G.; Brier, P. N.; Lane, G. Trans. Faraday SOC.1967,63, 824. (7) Pitzer, K. S.;Hollenberg, J. L. J . Am. Chem. SOC.1953, 75, 2219. (8) Durig, J. R.; Chen, M. M.; Li, Y. S.J . Mol. Srrucr. 1973, 15, 37. (9) Rush, J. J. J . Chem. Phys. 1967, 46, 2285. (10) Hogenboom, D. L.; OReilly, D. E.; Peterson, E. M. J . Chem. Phys. 1970, 52, 2793. (11) Bartoli, F. J.; Litovitz, T. A. J . Chem. Phys. 1972, 56, 404, 413. (12) Tsai, N. H.; Baglin, F. G. J . Raman Specrrosc. 1981, 1 I , 496.
Bandwidths (fwhm) (cm-I). dDiffusion
Depolarized
-
'oat c
1000
A
n
Isotropic
600
IO FREQUENCY (a")
Figure 1. Experimental (dotted curves) and calculated (solid curves) spectra of the wS vibration in TCE: T = 278 K.
laboratory) and the fact that the depolarized spectrum lies on the wing of u7, we chose instead to analyze u5, the CCI3 symmetric bending vibration, to determine D, as a function of temperature. Polarized and depolarized spectra were recorded with S W = 5.1 cm-' and Au = 0.5 cm-'/point. Rothschild et aLi3 demonstrated in an investigation of the equivalent vibration in chloroform that the contribution of chlorine isotope splittings to the vibrational bandwidth may be accounted for provided one knows the relative displacements of the four component peaks, j5C13 (42.9%), 35C1,'7Cl (42.0%), 35C137C12 (13.7%), and 37C13(1.5%); quantities in parentheses represent the relative abundances and, hence, intensities. Using peak separations reported by King14 (1.5, 1.7, and 1.7 cm-I), we have fit the isotropic and anisotropic spectra of u5 with a model containing four bands convoluted with the slit function to obtain the line widths, Ah(u5) and Aanis(u5). We note that since the relative intensities and displacements were fixed, the only variable parameters in the fits were the peak center and maximum intensity of the principal component and the bandwidth. A representative fit is shown in Figure 1. Results and Discussion Molecular Reorientation. Perpendicular diffusion coefficients were calculated via the standard relationship: D , = (?rc/6)[Aai, (13) Rothschild, W. G.; Rosasco, G. J.; Livingston, R. C. J. Chem. Phys.
1975, 62, 1253.
(14) King, S . T. J . Chem. Phys. 1968, 49, 1321.
2704
100
j D
D
A
60‘ v
E
)
I 40:
L
c
v
\ 2.6
3.0
3.4 1OOOiT
A 0
3.8
(K’)
Figure 2. Temperature dependence of diffusion coefficients in TCE: (A) D, (circles); (B) D,, (squares); (C) R(Ram) (diamonds); (D) R(NMR) (triangles).
- Aim].” The results are displayed in the seventh column of Table I and in Figure 2 (line A). The coefficients are similar in mag-
nitude to those reported from measurements on vl;Iz e.g., D, (298 K) = 9.0 X 1 O ’ O s-l. Notably, however, our activation energy, Ea(D,) = 1.6 kcal/mol is far below the earlier reported result, Ea(D,) = 2.6 kcal/mol.’* The latter value is closer to the temperature dependence predicted by hydrodynamic theories of re~rientation,’~ since Ea( T / v ) = 3.0 kcal/mol.16 On the other hand, the activation energy determined here from us is in substantially better agreement with results obtained from temperature-dependent dielectric relaxation measurements; Ea(7Die;’) = 1.5,’’ 1.7,18 1.7,19 and 2.lI7 kcal/mol. At present, the basis for the deviation in Ea(D,) from measurements on u I and v 5 is not apparent to the authors. However, one may not exclude the possibility that the disagreement results from failure of the assumption (implicit in the above calculations) of statistically independent vibrational dephasing and reorientational contributions to the anisotropic bandwidth. The coupling of vibrational and rotational coordinates has been discussed recently in the literature.20s2’ Diffusion coefficients predicted from dielectric relaxation, D,(Diel) = ( 2 ~ ~ ~ , are ) - ’ in , qualitative agreement with those from Raman spectroscopy; D,(Diel) = 12-13 X 1Olo s-l at 298 K.l7-l9 The variation between the results, with D,(Diel) > D,(Ram), may be explained if reorientation is not completely in the small-step diffusional limit since, in this case, T~~~~< 3 ~ ~ ~ The correlation time, T ~ governing , 3sCl N M R quadrupolar relaxation in TCE is a function of D,, Dll, and B (the angle between the C-CI bond and the symmetry axis; 0 = 110’ in TCEt2) and is given by the Woessner eq~ation.’~O’Reilly and co-workersI0 have measured T2(35Cl)in TCE as a function of temperature in the liquid phase and reported that rC= 2.05 ps (15) Boer& R. T.; Kidd, R. G. Annual Report on N M R Spectroscopy; Webb, G. A., Ed.; Academic Press: New York, 1982; Vol. 13, p 319. (16) Galland, R. W. Hydrocarbon Process. 1967, 46, 119. (17) Holland, R. S.; Roberts, G. N.; Smyth, C. P. J . Am. Chem. Soc. 1956,
78. 20.
(18) Clemett, C.; Davies, M. Trans. Faraday SOC.1962, 58, 1705. Mallikarjun, S.; Hill, N. E. Trans. Faraday SOC.1965, 61, 1389. MacPhail. R. A.; Straws, H. L. J . Chem. Phys. 1985, 82, 1156. Viot, P.; Tarjus, G.; Borgis, D.; Bratos, S. J . Chem. Phys. 1989, 90,
(19) (20) (21) 7022. (22) (23)
Wang and Schwartz
The Journal of Physical Chemistry, Vol. 94, No. 6 , 1990
Coutts, J. W.; Livingston, R. L. J . A m . Chem. SOC.1953, 75, 1542. Woessner, D. E. J . Chem. Phys. 1962, 37, 647. The equation for reorientation of a rigid ellipsoid is the same as eq 3 of the text with R = 0.
at 300 K and Ea(7;’) = 1.7 kcal/mol. We have used their results to calculate correlation times at the various temperatures that, together with D, from Raman measurements, have been used to determine the parallel diffusion coefficient as a function of temperature; the results are shown in Table I and in Figure 2 (line B). One observes, not surprisingly, that unlike the methyl rotors,’-3 Dl,is of the same magnitude as D, in TCE. The coefficients’ dependence on temperature, too, is quite similar with Ea(DI1)= 1.9 kcal/mol. It has been noted that the trichloroethane molecule is close to spherical in shapeI5 (due to the similar sizes of a methyl group and a chlorine atom24). From TCE’s molecular dimensions,22we calculate that the ratio of semiaxis lengths of its volume ellipsoid is p = b / a = 0.94. Thus, the experimental results suggest that picture of a pseudospherical molecule rotating almost isotropically in the liquid phase. It must be pointed out, however, that Ea(DI1) from the NMR data is sensitively dependent upon Ea(D,). For example, if one takes our 296 K diffusion coefficient (9.4 X 1Olo SKI), but assumes, instead, that Ea(D,) = 2.6 kcal/mol, then it is found that Ea(Dll)= 0.3 kcal/mol; this latter value is substantially below the results reported for CC13CN (Ea(DiI)= 1.9 k ~ a l / m o l )and ~ ~ CDCI3 (Ea(DII)= 0.7 kcal/mo1).26 Znternal Rotation. The Raman correlation function for vibrations of E symmetry in C3, molecules is the sum of two terms:27 GEa,(t) = Ae-r/rvd2)(t)+ (1 - A)e-‘/‘vA2)(t)
(1)
where A is a function of the spherical components of the polarizability derivative tensor and 7, is the vibrational relaxation time. Woessner et aL2*have calculated the functions, g{*)(t)and gi2)(t), for a symmetric top molecule undergoing small-step diffusion with a superposed internal rotation characterized by random jumps about three equilibrium orientations at a jump rate of (2/3)R. If the axis of internal rotation is coincident with the molecule’s principal symmetry axis, then both functions are ex onential, ( 2 ) ( t )= e-‘/rj(2), with T\’) = [5D, + DiI+ R]-I and 76 ) - [2D, gj f 4011 + R1-l. Fourier transformation of eq 1 yields the Raman band shape that consists of two Lorentzians with the same peak center and widths (fwhm) given by
P-
Aj2) = A,
+ (7c)-I[5DL + DII+ R ]
(2a)
Ai2) = A,
+ ( 7 ~ ) - ~ [ 2 0+14011 + R ]
(2b)
and Av = [ T C T , ] - ~ is the contribution of vibrational relaxation to the line width. It is clear from eqs 2 that for a system such as TCE where D, = D,,, one expects that the two widths should also be of the same magnitude. Yet, one observes from Table I that A$’) >> Ai2) at all temperature^.^^ It was found also in the earlier investigations of iodomethane,’.’ acetonitrile,j and other methyl rotors30that the width of the broader component of the band shape is greater than can be explained solely on the basis of molecular reorientation and vibrational relaxation. It has been suggested30 ~ that. this may result from collision-induced scattering3’ in the wings of the spectrum. Therefore, we shall confine our analysis to the narrower band component, Ai2). A comparison with earlier results reveals that Ai’) in TCE is markedly narrower than the width of the equivalent E vibrations in CH31 (A{2)Z= 23-31 cm-l)l and CH,CN (AI’) F= 25-35 cm-I).j Thus, the restricted rotation of the methyl group about the C-C axis is manifested by a narrower bandwidth of the degenerate CH3 (24) Bondi, A. J . Phys. Chem. 1964, 68, 441. (25) Gillen, K. T.; Noggle, J. H. J . Chem. Phys. 1970, 53, 801. (26) Huntress, W. T., Jr. J . Phys. Chem. 1969, 73, 103. (27) Clarke, J. H. R. Advances in Infrared Raman Spectroscopy; Clark, R. J. H., Hester, R. E., Eds.; Heyden Press: London, 1978; Vol. 4, p 109. (28) Woessner, D. E.; Snowden, B. S., Jr.; Meyer, G. H. J . Chem. Phys. 1969, 50, 719. (29) Peak intensity ratios, ( I - A ) / A [eq I ] , typically ranged from 0.3 to 0.4. (30) Gompf, J.; Versmold, H.; Langer, H. Ber. Bunsen-Ges. Phys. Chem. 1982, 86, 1 1 14. (31) Bucaro, T. A.; Litovitz, T. A. J . Chem. Phys. 1971, 54, 3846.
Diffusion and Rotation in Trichloroethane antisymmetric stretching vibration in TCE compared to systems where there is no hindrance to rotation. The contribution of vibrational relaxation, A”, to the u7 line width may be estimated from the isotropic width of the similar CH3 symmetric stretching mode, vI, using a relation (based on the IBC model32)introduced by We have calculated R as a function of temperature from eq 2a, using the experimental results for Ai2), Aiso(v,), D,, and Dil;the results are displayed in the last column of Table I and in Figure 2 (line C). It is possible, also, to determine R from I3C-H dipole-dipole relaxation times, TlDD(13C),with an equation derived by Woessner et TC = (1/4)(3 COS’ 0 - 1 ) 2 3 sin2 0 cos2 0 + (3/4) sin4 0 5Di + Dil + R 20, + 4011 + R 60, (3)
+
N M R relaxation times and nuclear Overhauser enhancements have been reported at three temperatures in liquid TCE.3s We have used the data in these references (and the standard bond length rCH= 1.09 A) to calculate the rotational correlation times, fC. Together with diffusion coefficients interpolated from the results of this study, and 0 = 109.47’, we have obtained the following jump rates: T = 283 K, R = 71 X 1Olo s-I; T = 31 1 K, R = 49 X 1Olo s-I; T = 338 K, R = 61 X 1 O l o s-I. From the results of a second N M R we find that at T = 31 1 K, R = 43 X 1Olo s-I. Thus, internal rotation rates calculated from N M R relaxation time data are in general qualitative agreement with those determined from the Raman band shape. The somewhat erratic temperature dependence of the N M R results is most likely due to the nonlinear dependence of rCon R, which causes the latter quantity to be very sensitive to small errors in Tlobsand 7 (the Overhauser enhancement). The barrier to internal rotation in TCE has been calculated by a variety of different technique^.^-^ The resulting estimates vary widely and include 1.7 kcal/mo14 from relative microwave intensities; 2.7 kcal/mo15 from calorimetric data; 2.8: 3.0,’ 5.1 ,* and 5.89 kcal/mol from the CH3 torsional frequency, vtor. The dispersion in barrier heights calculated from utor results from the (32) Fischer, S. F.; Laubereau, A. Chem. Phys. Lett. 1975, 35, 6. (33) Tanabe, K. Chem. Phys. Left. 1979,63,43. (34) It has been reported that the vibrational bandwidths of symmetric and antisymmetric methyl vibrations can be substantially different: Cavagnat, D.; Lascombe, J . J . Chem. Phys. 1982, 76, 4336. MacPhail, R. A.; Snyder, R. G.; Strauss, H. L. J . Chem. Phys. 1982, 77, 1 1 18. However, since 4
