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J . Phys. Chem. 1989, 93, 6550-6552
(iii) Results on the ordering and dynamics of P probe in the reentrant nematic liquid crystal suggest that the chains are more disordered in the SA and R N phases (in the sense of chain packing) compared to the SA phase of a normal smectic, whereas they experience enhanced resistance to rotational motion in the R N phase, probably due to enhanced packing in the chain region. This is suggestive of reduced short-range chain cooperativity in ordering and dynamics as increased packing of chains from adjacent layers occurs concomittent with the loss of smectic order. (iv) In general, the nematic and SA phases in systems exhibiting reentrance are rather similar to those in structurally similar liquid
crystals where reentrance is not observed. At the molecular level, the N-SA and SA-RN transitions are very similar and the effects driving the transition are very subtle. Small changes in molecular properties can make a difference, e.g., the decrease in average chain length by the addition of 6 0 C B to 8 0 C B to produce a reentrant nematic. Previous X-ray13 and densityZoresults also demonstrate the similarities of these phase transitions with nothing dramatic occurring. Registry No. 60CB, 41424-1 1-7; SOCB, 52364-73-5; PD-Tempone, 36763-53-8; MOTA, 14691-89-5; P, 64120-21-4; CSL, 121575-16-4.
NMR Studies of Rotational Motlon at Low Viscosity R. F. Evilia, J. M. Robert,? and S. L. Whittenburg* Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148 (Received: September 26, 1988; In Final Form: April 7 , 1989)
We have measured the rotational correlation time of dilute solutions of several small molecules dissolved in supercritical fluids using I4N NMR spectroscopy. In supercritical fluids at the densities employed, the solubility is sufficiently high to obtain rapid acquisition of the spectra, while the viscosity is extremely small. Comparison of the rotational correlation times with the literature values obtained from light-scattering measurements at higher viscosity demonstrates that the StokesEinstein-Debye plot deviates from linearity as the inertial limit is approached. The measured correlation times compare favorably with the free-rotor correlation time.
Introduction Many studies of rotational motion have demonstrated the general applicability of the Stokes-Einstein-Debye equation1 T = At)/T + TO (1) where T is the effective rotational correlation time whose definition for nonspherical molecules requires analysis of anisotropic reorientation, t) is the solution viscosity, and T is the absolute temperature. A is the slope of the Stokes-Einstein-Debye plot, and so is the intercept. A and T O are relatively insensitive to temperature and pressure.2 The Stokes-Einstein-Debye equation is one form of Walden’s rule that states that the correlation time is proportional to t)/Te3 While there is an overwhelming number of studies that demonstrate the validity of the Stokes-EinsteinDebye equation, there have been several studies that show deviations from this relation~hip.~ The physical interpretation of the A parameter is fairly well understood. It is related to the shape and volume of the rotating particle and the boundary condition for interaction between the interacting particle and the adjacent solvent. The Stokes-Einstein-Debye hydrodynamic theory models the particle as a sphere and assumes a continuum solvent.s This theory predicts that the A parameter is given by A = V/[kBZ(l + l)], where I is the order of the rotational correlation function, Vis the molecular volume, and kB is Boltzmann’s constant. The order of the rotational correlation function is equal to 2 for light-scattering and N M R spectroscopy. Perrin has removed the assumption of sphericity and enabled the theory to be applied to ellipsoidal particles6 Youngren and Acrivos have further extended the approach by incorporating molecules of arbitrary shape.’ In their approach, the A parameter can be calculated from the three primary axial lengths and remains a function of the molecular volume. The Stokes-Einstein-Debye theory assumes stick boundary conditions; that is, the solvent adjacent to the rotating particle sticks to the particle. Hu and Zwanzig have extended the model to incorporate ‘Present address: Department of Chemistry, Hartwick College, Oneonta, N Y 13820.
0022-365418912093-6550$01.50/0
slip boundary conditionsS8 Thus, it is now possible to model the rotation of molecules of arbitrary shape in solution in the limits of stick and slip boundary conditions. For most small molecular fluids, slip boundary conditions are in good agreement with the experimental slopes: while several examples of nonslip boundary conditions have been measured.IO The physical meaning of the intercept term in eq 1, T O , is less clear. It can be obtained in two ways: By one method, it can be obtained by extrapolation of the Stokes-Einstein-Debye plot obtained from measurements carried out as a function of temperature. In this approach, the measurements are performed at high solvent viscosity and the data are extrapolated to t)/T 0. Thus, the intercept is not related to the inertial limit, that is, to the free-rotor correlation time. Indeed, experiments have reported negative intercepts.2*3g11Kivelson and Evans have derived expressions that relate the T O term to cross-correlation functions between torquelike terms and kinetic variables.Iz The other method for obtaining the intercept is to measure the rotational correlation time as a function of viscosity at sufficiently low
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(1) Berne, B. J.; Pecora, R. Dynamic Light Scattering, Wiley: New York, 1976. (2) Wolfe, M.; Jonas, J. J. Chem. Phys. 1979, 72, 3252. Herring, F. G.; Phillips, P. S. J. Chem. Phys. 1980, 73, 2603. (3) Dote, J. L.; Kivelson, D.; Schwartz, R. N. J. Phys. Chem. 1981, 85, 2169. (4) Kivelson, D.; Madden, P. A. Annu. Reu. Phys. Chem. 1980, 32, 523. (5) Debye, P. Polar Molecules; Dover: New York, 1929. (6) Perrin, F. J. Phys. Radium 1934, 5, 497. (7) Youngren, G.; Acrivos, A. J. Chem. Phys. 1975, 63, 3846; J. Fluid Mech. 1975, 69, 371. (8) Hu, C.; Zwanzig, R. J. Chem. Phys. 1970, 52, 6353. (9) Cheung, C. K.; Jones, D. R.; Wang, C. H. J. Chem. Phys. 1976, 64, 3576. (10) Higashigaki, Y.; Whittenburg, S. L.; Wang, C. H. J. Chem. Phys. 1978.69, 3297. Whittenburg, S. L.; Wang, C. H. J. Chem. Phys. 1979, 70, 2035. (11) Fury, M.; Jonas, J. J. Chem. Phys. 1976,65,2206. Patterson, G . D.; Lindsey, C. P.; Alms, G. R. J. Chem. Phys. 1978, 69, 3250. (12) Evans, G. T.; Kivelson, D. J. Chem. Phys. 1986, 84, 385.
0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 1 7 , 1989 6551
N M R Studies of Rotational Motion at Low Viscosity viscosities that the extrapolation is meaningful. In this inertial limit, the correlation time is that for a rotating particle with a vanishingly small interaction with adjacent solvent. The extrapolated correlation time should be directly related to the free-rotor correlation time, T~ = (2?rI/9kB7')'/*, where I is the moment of inertia of the rotating axis. In this article, we report measurements of the effective rotational correlation time of several small molecules under supercritical fluid conditions where the solvent viscosity is exceedingly small. The correlation times are measured by N M R spectroscopy. The rotational correlation times will be compared with the relaxation times available in the literature. Most of these literature values are the result of light scattering measurements of optical anisotropy. There are two important differences between the correlation times obtained from N M R and light scattering. First, for many molecules, N M R can yield relaxation times for motion about each of the rotational symmetry axes, whereas, light scattering provides only an average value for rotation about all three axes. Second, N M R yields the single-particle reorientation relaxation time, while depolarized Rayleigh light scattering includes the effect of reorientational pair correlation. The depo, larized Rayleigh light-scattering relaxation time, T ~is related , to the single-particle reorientation time, T ~ vial3 TLS
=
k2/J2)7S
= FLsTs
(2)
where g2 is the static orientational pair correlation factor, J2 is the corresponding dynamic quantity, and FLs is the orientational pair correlation factor obtain from light scattering. An orientational pair correlation factor enters into dielectric relaxation measurements and is not necessarily equal to the light scattering value.i4 It should be recognized, however, that the advantages of N M R measurements are somewhat offset by the need for independent estimates of various interactions, such as the quadrupole coupling constant in this work.
Experimental Section The samples, usually reagent grade or better, were redistilled according to standard procedures prior to their use. Most liquids were used in pure form and dissolved in supercritical ethylene. Formamide was prepared by dissolving a measured volume in an equal volume or less of absolute ethanol. The formamide-ethanol mixture was then dissolved in ethylene to prepare the supercritical sample. The sapphire sample tubes and titanium valves used in this study were similar to those reported by D. C. Roe for highpressure N M R studies of CO exchangei5 and were slightly modified as previously reportedSi6 The tubes were annealed by the manufacturer. The measured volume of the sapphire tubes, determined both geometrically and gravimetrically, was approximately 0.7 cm3. Sapphire tubes were fitted and sealed to various titanium mounting flanges and valve assemblies. Thermosetting epoxy was used to secure the sapphire tubes to the titanium assemblies. All N M R spectra were obtained on a JOEL FX90Q Fourier transform N M R spectrometer that operates at a proton frequency of 89.56 MHz. Both 5- and 10-mm probe inserts were employed in the study, as required by each particular sample container. The magnetic field was maintained at a constant value by either an internal or an external deuterium lock signal. The internal lock signal came from D 2 0 or CD3CN held in the outer chamber of a system of concentric tubes comprised of a IO-" thin-walled N M R tube and the supercritical sample container. An NM-VTS variable-temperature controller, applicable in the range of sample temperatures from -170 to +200 "C, was utilized for controlled-temperature studies. The control unit was calibrated from the proton resonance positions of methanol for the lower tem(13) Keyes, R.; Kivelson, D. J. Chem. Phys. 1972, 56, 1057. (14) Madden, P.; Kivelson, D. In Aduances in Chemical Physics; Prigogine, I., Rice, S., Eds.; Wiley: New York, 1984; Vol. LVI. Whittenburg, S. L.; McKinnon, S. J.; Jain, V. K.; Evilia, R. F. J . Phys. Chem. 1988, 92,4236. (15) Roe, D. C. J. Magn. Reson. 1985,63, 388. (16) Robert, J. M.; Evilia, R. F. Anal. Chem., in press.
"I m
.
0 0
2
4 r)/rx
IO
6 CP/K
Figure 1. Single-particle reorientation time of formamide versus q / T obtained from corrected light-scattering data (m), 75% formamide/25% acetone (e),and supercritical fluid NMR spectroscopy (0).
TABLE I: Stokes-Einstein-Debye (SED) Parameters formamide
acetonitrile
benzonitrile
exptl slope exptl intercept S E D slope (slip) S E D slope (stick) exptl slope exptl intercept S E D slope (slip) S E D slope (stick) exptl slope exptl intercept S E D slope (slip) SED slope (stick)
(1.36 0.12) x 103 ~ ~ K / C P 0.5 f 0.2 ps (0.5 f 0.5) X lo3 ps.K/cP (3 1) x 103 p s . ~ / c ~ (0.96 f 0.04) X lo3 ps.K/cP 0.1 f 0.1 ps (2 1) x 103 ps K / ~ P (9 2) x 103 ~ ~ K / C P (1.9 f 0.04) X IO3 ps.K/cP 0.7 f 0.2 ps (1.4 f 0.5) X lo3 ps.K/cP (6 1) X lo3 ps.K/cP
* *
perature range (C30 "C) and ethylene glycol for higher temperatures (>30 "C). Instrumental parameters typically employed for spectra of the quadrupolar nuclei included a 90" pulse width appropriate to the nuclear observation frequency, a short pulse delay (
