J. Phys. Chem. 1995,99, 3889-3891
3889
A Direct Method for the Measurement of Molecular Correlation Times in Solution Thomas C. Stringfellow and Thomas C. Farrar* Department of Chemistry, University of Wisconsin-Madison, I101 University Avenue, Madison, Wisconsin 53706 Received: October 4, 1994; In Final Form: January 30, 1995@
We introduce a new NMR method for the direct determination of molecular correlation times. This method is applicable for any system in which a single relaxation mechanism predominates; it utilizes experimentally determined longitudinal and transverse relaxation times, but the relaxation coupling parameter plays no role. We demonstrate the use of this method to measure the temperature dependence of the I4N quadrupole coupling constant of isocyanomethane, CHsNC, in a solution of ethanol and ethylene glycol.
Introduction NMR relaxation measurements can provide a wealth of information about a molecule; rotational correlation times, intemuclear distances, chemical shielding anisotropy, and quadrupole coupling constants are common examples. Because it is a difficult task to separate the contributions of the dynamical and interaction components which cause relaxation, workers typically resort to making assumptions about one of the two terms. Such assumptions may be justifiable in certain instances but totally unacceptable in others. An example of the latter case is relaxation via the quadrupole interaction. The nuclear quadrupole coupling constant, = e2qQlh, is an important parameter since it provides a sensitive probe of electronic and surrounding nuclear structure near the quadrupolar nucleus of interest. The ability to accurately measure and monitor changes in the quadrupole coupling constant as a function of temperature and solvent can provide important information about intra- and intermolecular interactions. There is, however, an inherent difficulty in determining quadrupole coupling constants from NMR relaxation measurements: the relaxation equations are comprised of the product of x with a sum of spectral density functions, both of which are unknowns. In many previous studies,' workers have used quadrupole coupling constant values (obtained from microwave studies of gas-phase samples or from NMR or pure quadrupole studies of solid samples) to determine molecular correlation times in the liquid or solution phase from NMR relaxation or line width measurements. However, quadrupole coupling constant values for a given molecule typically vary by 15-20% or more between the solid and gas phases, clearly introducing uncertainty in the resulting correlationtimes. It is sometimes possible to use NMR relaxation measurements of other interactions (e.g., chemical shielding anisotropy or dipole-dipole2) to obtain molecular correlation times, but these methods are not always applicable or appropriate. The isotopic enrichment technique has also been used to obtain correlation times and thus demonstrate changes in quadrupole coupling constants as a function of concentration3 and temperat~re.~It follows, then, that it would be desirable to have at one's disposal a direct and inexpensive method for determining molecular correlation times. We present here a new NMR spectroscopic method which does exactly that for molecules in the solution phase. Consequently, one can then determine the quadrupole coupling (or other interaction) constant.
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* To whom correspondence should be addressed. 'Abstract published in Advance ACS Abstracts, March 1, 1995.
There has been an extraordinary variation in quadrupole coupling constants reported for isocyanomethane. The best gasphase value appears to be 489.4 kHz as reported by K ~ k o l i c h . ~ NMR measurements have been used to obtain quadrupole coupling constant values of 30O6and 270 kHz7 for the neat liquid and 272 kHz8 in a liquid crystal solvent. Barbara9 has shown an approximately linear temperature dependence from 168 to 205 kHz over a 50 OC range for the I4N quadrupole coupling constant of isocyanomethane in liquid crystals. A value of 26.3 kHz has been observed by solid state NMR for the neat solid.I0
Theory The longitudinal or transverse relaxation rate for a nuclear spin relaxed by a single mechanism can be generally expressed by
Here i = 1 or 2, % represents the interaction term and multiplicative constant that are characteristic for a particular mechanism, and the J(nw) are spectral density functions that describe the molecular motions. %and ZnJ(no)are different for longitudinal and transverse relaxation. For quadrupole relaxation of spin 1 nuclei, the longitudinal relaxation is single exponential with rate"
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Here = (e2qQ)/his the quadrupole coupling constant expressed in s-l, eQ is the electric quadrupole moment, eq = V , = a2Vl az2 is the electric field gradient at the nucleus, q is the asymmetry parameter, J(nw) = re/(1 n2w2ze2)is the spectral density function for small-step, rotational diffusion,l' w o is the Larmor frequency in s-l, z, is the correlation time, and h is Planck's constant divided by 2n. The transverse relaxation rate is given by"
+
(3) It has been shown by BlicharskiI2that the longitudinalrelaxation rate in the rotating frame can be expressed by
0022-365419512099-3889$09.00/0 0 1995 American Chemical Society
3890 J. Phys. Chem., Vol. 99, No. 12, 1995
where w1 is the angular frequency of the spin-locking radiofrequency field. It can be seen that when W I zc > 1. Therefore, one must be able to make reliable measurements of T I and T2 or T I , throughout the dispersion region, where cootc x 1. This can be an experimental difficulty for quadrupolar nuclei having coupling constants greater than a few megahertz, as the relaxation times can then be so short as to present practical, experimental difficulties. It has been shown that molecular rotational motion is an activated process and can often be described by an Arrhenius function which relates the motions to temperature and an activation energy:
Letters
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?.C 3.5 4.5 4.5 5.0 5.5 6.0 6.5 'CgCIK/T Figure 1. Experimental T ~ I Tvalues I with the curve fit to eqs 5 and 6. The best-fit parameters are E, = 25.1 kJ/mol and 50 = 3.66 x s.
preparation of the final NMR sample was cleaned with nitric acid and then treated with EDTA solution to remove paramagnetic impurities. The sample (in a 10 mm tube) was degassed via 11 freeze-pump-thaw cycles and then sealed off under a pressure of 3 pTorr. Data Acquisition and Analysis. All spectra were recorded on a Varian Unity 300 NMR spectrometer using a Cryomagnet Systems "-band 10 mm probe. The standard Varian temperature controller setup was modified to improve the temperature stability, which was estimated to be f 0 . 2 OC. Longitudinal and transverse relaxation times were measured using inversion-recovery and Carr-Purcell-Meiboom-Gill pulse sequences, respectively. Values for T I , were also measured in the dispersion region; they were in agreement with the T2 values. The I4N spectra were acquired with continuous wave 'H decoupling during acquisition. The relaxation time constants were obtained by fitting the spectral intensity versus time data to three parameter, exponential functions using nonlinear, least-squares methods.
Results and Discussion z, = toexp(;) where E, is the activation energy and to is a preexponential factor. We, too, use this model and further assume that the molecular motions obey this function throughout the entire temperature range of interest. The T2/T1 data taken from the dispersion region can be fit to eqs 5 and 6, to obtain values for E, and to,from which correlation times can then be calculated for temperatures outside the dispersion region. Given accurate values for zc and T I at any temperature, one can use eq 2 to calculate values for at that temperature, thereby monitoring its temperature dependence.
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Experimental Section Sample Preparation. Isocyanomethane was prepared in a quantity of about 8.5 g, according to the method of Schuster, Scott, and Casanova.I3 A further distillation was performed to increase the purity of the product. All reagents were obtained from the Aldrich Chemical Co. A 'H spectrum of the neat liquid indicated a purity greater than 99%. The NMR sample for this study was prepared in a mixture of ethanol46 (anhydrous, 99 atom %, from Cambridge Isotope Labs) and ethylene glycol-d6 (99.4 atom %, from MSD Isotopes) such that the final sample composition was 6.42 mol % isocyanomethane, 33.46 mol % ethylene glycol, and 60.12 mol % ethanol. This particular solvent was chosen for its ability to become viscous at very low temperatures without freezing, such that the dispersion region could be readily accessed. All glassware used in the
Longitudinal and transverse relaxation times were measured at nominal temperatures between 20 and - 110 "C. Figure 1 shows a plot of T2ITl data over this region. These experimental data were fit to eq 5, with eq 6 substituted for tc,and the theoretical (solid) curve reflects the least-squares, best-fit parameter values of E, = 25.1 kJ/mol and zo = 3.66 x s. The quadrupole coupling constant was then calculated for each temperature at which a T I value had been measured, according to eqs 2 and 6 and the optimized E, and to values. These results are shown in Figure 2 for temperatures in the relaxation dispersion region. The fact that there is a greater than 2-fold change in XN over this temperature range is significant in itself. Considering that the values in this temperature range are only about 10-25% of the gas-phase value of 489.4 ~ H zthis , ~system is clearly one for which it would be inappropriate to use the gas-phase value of the quadrupole coupling constant for determining molecular correlation times. Also shown in Figure 2 are the molecular correlation times, which were calculated from eq 5 at each T2/ T I point in the region shown. The linear fit to these data, as shown by the solid line, results in E, = 25.3 kJ/mol and to = 3.14 x s, which agree well with the values obtained from the direct fit to the T2/T1 data. The linearity of the data suggests that the Arrhenius model is appropriate for this system. We have demonstrated that the T2/T1 method is a useful technique for directly measuring the molecular correlation time for molecules in systems where the nuclear relaxation dispersion region can be accessed. This method is complementary to other
Letters
J. Phys. Chem., Vol. 99, No. 12, I995 3891 22
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Acknowledgment. We thank the National Science Foundation for the support of this research (NSFGrant CHE-9102674). ;1
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assumptions about the isotropy of the molecular motions or the role of intermolecularcontributions to the overall relaxation rate. A more detailed account of this work will follow; it will focus on quadrupole coupling constants rather than the T2IT1 method and will include results of experiments that are in progress.
6.0
6.5
IOOOK/T Figure 2. Quadrupole coupling constant (QCC) values (open circles) and molecular correlation times, tc(filled diamonds), in the temperature range corresponding approximately to the relaxation dispersion region. The QCC values were calculated from TI data using eqs 2 and 6 after determining Ea and to from TdT, data. The tcvalues were calculated from eq 5 for each measured TdTI value in the region shown and then fit to eq 6 to obtain Ea = 25.3 kJ/mol and TO = 3.12 x s as the best-fit parameters.
experimental NMR methods. It has the advantage of being less costly than the isotopic enrichment technique, which involves the preparation of a series of sometimes expensive samples. The T2IT1 method can be used directly for quadrupolar nuclei, without the necessity of first making relaxation measurements for, say, a dipole-dipole system from which one first obtains molecular correlation times; therefore, it is not necessary to make
References and Notes (1) See, for example: Moniz, W. B.; Gutowsky, H. S. J . Chem. Phys. 1963, 38, 1155. Bopp, T. T. J. Chem. Phys. 1967, 47, 3621. Woessner, D. E.; Snowden, B. S., Jr.; Strom, E. T. Mol. Phys. 1968,14, 265. Stark, R. E.; Vold, R. L.; Vold, R. R. Chem. Phys. 1977, 20, 337. (2) See, for example: Assink, R. A,; Jonas, J. J . Magn. Reson. 1971, 4, 347. Vold, R. R.; Sparks, S. W.; Vold, R. L. J . Magn. Reson. 1978,30, 497. (3) Gordalla, B. C.; Zeidler, M. D. Mol. Phys. 1986, 59, 817. (4) Ludwig, R.; Gill, D. S.; Zeidler, M. D. Z. Nutu@orsch. 1991, 46A, 89. (5) Kukolich, S. G . J . Chem. Phys. 1972, 57, 869. (6) Loewenstein, A.; Margalit, Y. J . Phys. Chem. 1965, 69, 4152. (7) Moniz, W. B.; Poranski, C. F., Jr. J . Phys. Chem. 1969, 73, 4145. (8) Yannoni, C. S. J . Chem. Phys. 1972, 52, 2005. (9) Barbara, T. M. Mol. Phys. 1985, 54, 651. (10) Unpublished result of work performed in our laboratory. (1 1) Abragam, A. The Principles of Nuclear Magnetism; Clarendon Press: Oxford, 1961; Chapter 8. (12) Blincharski, J. S. Acta Phys. Pol. 1972, A41, 223. (13) Schuster, R. E.; Scott, J. E.; Casanova, J., Jr. Org. Synfh. 1973, Collective Volume 5, 772. JP942669W
