J. Phys. Chem. 1995, 99, 12409-12412
12409
Diffusion Ordered Spectroscopy of Room Temperature Chloroaluminate Melts Cynthia K. Larive* and Mengfen Lin Department of Chemistry, University of Kansas, Lawrence, Kansas 66045
Bernard J. Piersma Department of Chemistry, Houghton College, Houghton, New York 14744
W. Robert Carper* Department of Chemistry, Wichita State University, Wichita, Kansas 67260 Received: March 22, 1995; In Final Form: June 9, 1995@
'Hdiffusion ordered spectroscopy is used to determine diffusion coefficients for 1-ethyl-3-methylimidaolium chloride (MEICl) in 0.8:land 1:l AlCl3-MEICl melts between 20 and 45 "C. All MEI+ diffusion coefficients (ring, methyl, and ethyl protons) are virtually identical for a particular melt at a given temperature. The MEI+ diffusion coefficients are viscosity dependent and correlate with conductivities, indicating that the transport properties of these melts are determined by the molar quantities of salt and not by the properties of the individual ions. I3C NMR correlation times are used with viscosities and microviscosity factors from a "slip" model to determine the radius of MEP. Introduction A number of different methods have been used for diffusion studies of molten salts. The most recent is the NMR spin echo method employing a pulsed field gradient, as initially used by Stejskal and Tanner,' which permits a direct measurement of self-diffusion. Herdlicka et al. used this method to determine self-diffusion coefficients of Na+ in molten NaN03 over the temperature range 596-670 K.2 These results2 compared favorably for those obtained using other methods. A recent modification of the NMR method is that of DOSY (diffusion ordered spectroscopy), developed by Morris and J o h n ~ o n ,which ~ . ~ makes use of data inversion programs for the analysis of discrete or continuous distributions of diffusion coefficients. DOSY is particularly useful in the analysis of complex mixtures since the results are displayed in a twodimensional spectral format with conventional chemical shift along one axis and diffusion coefficient in the other dimension. This method makes use of the LED (longitudinal encodedecode) pulse sequence5 and actively shielded gradient coils6,' to acquire high resolution NMR spectra. A major advantage of the LED experiment relative to other NMR methods for measuring diffusion is that signal amplitudes are limited by T I ' S rather than T2's. In addition, this method has a high tolerance for gradient pulses of several hundred Glcm in a narrow bore magnet.4 Diffusion coefficients are extracted from the resonance intensities of a series of LED spectra obtained as a function of (yg6)2,where y is the magnetogyric ratio and g and 6 are the gradient pulse amplitude and duration. In this investigation we report a series of diffusion measurements which are compared with previously reported viscosity and I3C NMR relaxation data.9.10 As pointed out by Boere and Kidd," the number of studies in which viscosity data and NMR correlation times are both available for the same systems is small. By combining NMR diffusion data, NMR rotational correlation times, and viscosities, we are able to test physical models as applied to molten salt microdynamics. The systems reported herein are room temperature molten salts containing @
Abstract published in Advance ACS Abstracts, July 15, 1995.
0022-365419512099-12409$09.00/0
Figure 1. ME1 cation (positions are labeled).
1-ethyl-3-methylimidazoliumchloride (MEICl) and AlC13. Of particular interest is the 1:1 (mole ratio) of MEICl and AlC13 which exists as a mixture of MEI+ (Figure 1) and AlCL-.12-14
Experimental Section Materials. The 1-ethyl-3-methylimidazoliumchloride and chloroaluminate molten salts were prepared as previously des~ribed.'~ All materials were stored under anhydrous helium gas atmosphere in a drybox. All molten salt preparations and manipulations were performed in the drybox. Samples were loaded into 5 mm sample tubes, capped in the drybox, removed, and sealed immediately with a torch. Diffusion Coefficient Measurements. Diffusion coefficients were measured by pulsed-field gradient NMR spectroscopy using the LED pulse sequence, which can by viewed as an enhanced stimulated echo experiment.6 In this experiment, a longitudinal eddy current delay, Te, is used to minimize spectral artifacts resulting from residual eddy currents. In these experiments, a Te of 26 ms was used. The normal LED sequence was modified slightly, replacing the 90" read pulse immediately prior to acquisition with a 30' pulse to avoid overloading the receiver with the intense signals from the concentrated molten salt samples. The spectra were measured using a Bruker 500 MHz AM spectrometer specially modified to accommodate pulsed field gradient experiments. Details of the gradient instrumentation have been described previously.I6 A 5 mm Bruker inverse probe with an actively shielded z gradient coil was used. The coil constant was calibrated with P-cyclodextrin, octanol, and decanol, which have diffusion coefficients close to those of molten salts (3.2 x 1.4 x and 7.5 x io-' cm2 s-I, respectively). 0 1995 American Chemical Society
12410 J. Phys. Chem., Vol. 99, No. 33, 1995
Larive et al.
In pulsed-field gradient NMR, the signal attenuation depends on gradient area as follows:
I = I, exp[-D(A - 6/3)y2g2621
(1)
where Io is the intensity of the resonance in the NMR spectrum in the absence of gradient pulses, y is the magnetogyric ratio, A is the delay period during which molecular diffusion occurs, g and 6 are the gradient amplitude and duration time, respectively, and D is the diffusion coefficient. Typically, in each pulsed field gradient NMR experiment, a series of IH spectra were collected with the modified LED pulse sequence as a function of gradient amplitude. In these experiments, the gradient duration time 6 was 3 ms, the gradient amplitude was varied from 0.021 to 0.392 T m-l, and the diffusion delay time was selected as either 0.3 or 0.4 s. The LED data were processed using the DOSY methodology (diffusion ordered spectroscopy), as described previously. 6' The individual spectra were transferred to a Silicon Graphics Indigo workstation and processed using Felix 2.30 (Biosym). Following Fourier transformation, the spectra were analyzed using computer programs generously provided by Dr. Charles S. Johnson, Jr. Diffusion coefficients were extracted using the program SPLMOD.'8x19The advantage of this method of data processing is that knowledge about the composition of the sample and the nature of the NMR experiment is used to limit the values of possible diffusion coefficients to a realistic range. The results of our experiments were fit in each case to a single diffusion coefficient. In addition, an effective multiplex data processing advantage is obtained since all the diffusion coefficients of the sample can be calculated simultaneously. The measurement of separate diffusion coefficients for each NMR resonance permits the precision of the measurement to be estimated for each component of the sample. 3343
' '
Results Diffusion Coefficients. The Stokes-Einstein equation gives the relationship between the diffusion coefficient and the radius (a) of a spherical particle moving (Brownian motion) in a continuous medium of macroscopic viscosity (17): D = kTI6nqa (2) An altemate form of eq 2 is that proposed by McLaughlin in which the 6 in eq 2 is replaced by a 4.20 Diffusion coefficients of MEIf were determined for 1: 1 and 0.8:l (mole fraction) AlC13-MEICl melts between 20 and 45 "C. The 1:l AlCl3-MEICl melt contains MEIf and AlC14-, whereas the 0.8:1 basic melt contains MEI+, AlCk-, and C1-. Figure 2 is the DOSY spectrum of the 1 :1 AlC13-MEIC1 melt at 20 "C. DOSY spectra are contour maps with NMR chemical shift and negative log diffusion coefficient along the two axes. There is a third dimension, intensity, which is shown in the projections along the NMR and diffusion dimensions. As expected, the diffusion coefficients from each MEI+ 'H resonance are equivalent within the experimental error of the measurement. The diffusion coefficient for MEI+ (1:1 AlC13MEICl melt) at 20 "C is (0.95 & 0.02) x cm2 s-l. A plot of 1/D vs q/T (viscosities reported previo~sly)~ over the temperature range 20-45 "C for both melts is shown in Figure 3. Collectively, the 1: 1 and the 0.8: 1 (mole ratio) melts have effectively a zero intercept and an average slope of 16.4 s W(cm2 cP) (Rval = 0.998). The average slope yields an a value of 1.20 A, using eq 2, and an a value of 1.80 A, using McLaughlin's modification of eq 2.*O Both of these results give a Stokes radius for MEI' that is considerably smaller than the 4.6 value suggested by MOPAC calculations of MEI+.*' Plots
6:O
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Figure 2. DOSY spectrum of AICl&IEICI melt, 1:l ratio at 35 "C. The contours in this spectrum correlate 'H chemical shift with the negative log of the diffusion coefficient. The projection plotted at the top of the contour map corresponds to the one-dimensional 'H NMR spectrum. The spectrum was calculated from 33 individual LED spectra, each composed of 2048 real data points. The number of points in the diffusion dimension of the calculated spectrum was 5 12.
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Viscosi ty/T (c P/K) Figure 3. Plot of Udiffusion coefficient (s/cm2) vs viscositylT (cP/K) for 1:l and 0.8:l AlCl3NEICl melts from 20 to 45 "C.
of In D vs reciprocal temperature (not shown) give identical E, values of 5.9 kcal for both the 1:l and 0.8: 1 (mole ratio) AlC13MEICl melts. A study of tetraalkylammonium tetraalkylborides (R3R'N+-R3R'B-) reports self-diffusion coefficients for a series of salts that are identical for cations and anions over the temperature range 25-65 "C using the pulsed-field gradient method.22 The authors point out that both Coulomb forces and repulsive interactions between hydrocarbons exist in these melts (as is the case to a limited extent with these melts). Furthermore, they conclude that the transport properties of a given salt are
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J. Phys. Chem., Vol. 99, No. 33, 1995 12411
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Conductivity Figure 4. Diffusion coefficients x lo6 (cm2/s) vs conductivity (cm2/ (equiv ohm)) for 1:l and 0.8:l AlC13iMEICl melts from 20 to 45 "C.
uniquely determined by the molar quantities of that salt and not by individual properties of the ions in the melt.22 This suggests that similar results should be obtained for the self diffusion coefficients of MEI+ and C1- in the 1:l MEICl-AlCl3 and similar melts. The only reported values for an MEI+ and C1- diffusion coefficients in MEIC1-AlC13 melts are values of 1.02 and 6.1 x lo-' cm2 s-) obtained for MEI+ and C1- in a 0.8:l melt using pulse voltammetry at 26 0C.23 The value of 1.02 x lo-' cm2 s-l for MEI+ is considerably smaller than the DOSY value of 5.4 x cm2 s-] obtained at 25 "C in this study and values of 3.9 and 11.5 x cm2 s-l reported for the N-butylpyridinium cation in 0.6:l and 1:l (mole fraction) AlC13-N-butylpyridinium chloride melts at 30 0C.24 The diffusion coefficient for C1- in the 0.6:l AlCl3-N-butylpyridinium chloride melt was initially reported as 9.6 x cm2 s-l and then corrected to a value of 5.2 x cm2 s-1.25 The value23 obtained for C1- (6.1 x cm2 s-l) in the 0.8:l AlCl3-MEICl melt is reasonably close to the value obtained for MEI+ in this study and may be correct for both species,23provided that the transport properties of these salts are a function of their molar quantities and not of their individual ionic properties. The direct relationship between diffusion coefficients and bulk viscosities9 shown in Figure 3 supports this concept. Another test of this concept is the relationship between difusion coefficients and conductivity9between 20 and 45 "C contained in Figure 4. The slopes for the two melts in Figure 4 are 0.32 x equiv o h d s for both the 0.8:l and 1:l MEICl-AlC13 melts (Rval = 0.999 and 0.992, respectively). The linear relationship (with the exception of the 45 "C data for conductivity in the 1:l MEICl-AlCl3 melt) between the diffusion coefficients and the conductivity supports the theory that the transport properties of a chloroaluminate melt (within a specified temperature range) are determined by the molar quantities of the salts present and not by individual properties of the ions in the melt.22 NMR Correlation Times. In classical mechanics, the correlation time, tc,of a spherical particle undergoing isotropic rotation is
zC= 4 n a 3 ~ / 3 k = T Vq/kT
(3) Comparison of experimental data with correlation times calculated from eq 3 is generally unsuccessful as the theoretical correlation times are generally too large by a factor of 10.26327 For correlation times determined by NMR, the relationship between tc and temperature in the viscosity dependent region
10 x Viscosity/T (cP/K) Figure 5. I3C C2 and (C4
+
C5)/2 correlation times (ps) vs 10 x Viscosity/T (cP/K) for 1:l AlCl&lEICl melt from 20 to 45 "C.
is' (4) where tred = V/k. The intercept, to,may be equated with free rotation times ( t f r = [(2~~/9)(Zm/kT)"~]); however, this is an extrapolation out of the hydrodynamic region, through the kinetic region, and into the inertial limit of a completely free rotor model." Figure 5 contains a plot of 13CNMR correlation times vs v/T for the 1:1 AlCl3:MEICl melt between 20 and 70 "C. The I3C NMR correlation times obtained previouslyI0 are those of the C2, C4, and C5 carbons of MEI+ (Figure 1) and are assumed to be representative of the rotational motion of the MEI' molecular "framework". The values of tred ( = V k ) obtained from the slopes in Figure 5 (Rval = 0.994 and 0.998) are 301 and 373 ps K cP-' for C2 and (C4 C5)/2 for MEI+. These values compare favorably with values of 327 and 396 ps*K.cP-' obtained previously for C2 and (C4 C5)/2 of MEI+ in a NaCl buffered melt (neutral);21 however, they produce unrealistic values of 1.00 and 1.07 A for the radii of a spherical tumbling model of MEI+. The values of zofrom Figure 5 are 6.4 and 6.8 ps for C2 and (C4 C5)/2 of MEI+, which yield values of 9.2 and 9.7 ps for (Zm/kT)1/2 from the free rotor model. These results can be compared with 1.82 and 0.85 ps for SnL and PbCL obtained by extrapolating (Zm/kT)1'2values to infinite temperature.21 Microdynamical Analysis by NMR. By eliminating the viscosity term in eqs 2 and 4, it is possible to relate the diffusion coefficient directly to the rotational correlation time:
+ +
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(5) If one uses the McLaughlin correction factor,20the 4.5 in eq 5 is replaced by 3. Equation 5 provides the direct relationship between measurements that can both made by NMR under certain conditions as discussed below. It should be pointed out, however, that although eq 5 may prove useful, it does not solve the underlying weaknesses in the derivations of eqs 2 and 3. The results are shown in Figure 6, in which MEI+ correlation times for C2 and (C4 C5)/2 are plotted vs 1/D. The slopes are 17.7 and 22.6 x cm2, and the intercepts are 8.3 and 8.7 ps for C2 and (C4 C5)/2, respectively. The average slope of the two lines (20.2 x cm2) is used to calculate a value of 0.95 8, for a using eq 5 and 0.77 8, using McLaughlin's modification. The inherent error in the classical model that relates viscosity to correlation times (eq 3) is further amplified by simplifications in the derivation of eq 2.
+ +
12412 J. Phys. Chem., Vol. 99, No. 33, 1995
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direct correlation between self-diffusion coefficients and either viscosity or conductivity, supporting the concept that the transport properties of these chloroaluminate melts are determined by the molar quantities of the salt and not by individual properties of the ions in the melt.22 As expected, the StokesEinstein-Debye model fails to produce acceptable values for the radius of MEI;2‘$26-28 however, the use of microviscosity factor^".^^,^^ produces reasonable values for the MEI+ radius from NMR I3C correlation times.
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1/I 0’ x D (s/cm*) Figure 6. MEI+ correlation times (ps) vs 1/106 x diffusion coefficient (s cm-2) for 1:1 AICl&lEICl melt from 20 to 45 “C.
It has been previously pointed out that eq 3 is valid for large particles in a continuous medium, but not for diffusing particles. In addition, there is the questionable relationship between a translational property (viscosity) and a rotational motion (rotational correlation time).2*.29 In any case, the results in Figure 6 suggest that there is a relationship between diffusion coefficients and correlation times (in molten salts) that may ultimately be justifiable on a theoretical basis. The Nonspherical Rotational Model. In order to account for the results obtained either directly or indirectly from eqs 2-5, it is necessary to adjust the classical model of a sphere rotating in a continuous medium. MEI+ is not spherical in shape and is closer to either an oblate (a < b = c) or prolate (a = b < c) spheroid whose rotation is anisotropic. In view of the fact that solute-solvent interactions may be weak in these melts and that the radius of MEI+ is larger than either C1- or AlC14-,3093’ it is likely that the Gierer-Wirtz “slip” boundary condition32is met in this case. In the “slip” boundary condition the spherical rotating molecule has a radius approaching that of the solvent molecule and slips through the solvent provided that rotation can occur without solvent d i s p l a ~ e m e n t .This ~~ microviscosity factor is to be used with the SED equation (eq 3) to produce realistic values of correlation times.’ Assuming ionic radii of 3.2 8, for both A1C4- and MEI+,30331a “slip” microviscosity correction factor of 0.16 is obtained.32 This increases the values obtained from eq 4 to 1.84 and 1.97 8, from 1.00 and 1.07 8,. These correction^^^ are typical;” however, they assume a spherical particle (and not either an oblate or prolate spheroid as is the case with MEI+) and are not sufficiently large enough to account for reported correlation times.” Alternately, the Hu-Zwanzig allows for the existence of prolate and oblate spheroids, and both “slip” and “stick” factors have been calculated for these shapes. The ratio of the minimum:maximum axis of MEI+ is ~ 0 . 6 0 ,which produces a prolate and oblate slip microviscosity factors of 0.067 and 0.096, re~pectively.~~ This increases the values obtained from eq 4 to 2.46 and 2.63 8, for the prolate spheroid and 2.18 and 2.33 8, for the oblate spheroid (from 1.00 and 1.07 A). Both the prolate and oblate spheroids are possible models for MEI+, as rotational motion either about the axis that passes parallel to the extended methyl and ethyl groups or about an axis perpendicular to the imidazole ring may occur. In either case, however, the appropriate microviscosity factor produces a reasonable result for the “average” radius of MEI+. Summary. The DOSY results reported herein provide a
Acknowledgment. C.K.L. and M.L. thank the National Science Foundation EPSCOR, NSF EHR 92-552223, and the Petroleum Research Fund for financial support. We also thank Dr. Charles S . Johnson, Jr., for the computer programs used in processing the DOSY data. References and Notes (1) Stejskal, E. 0.;Tanner, J. E. J. Chem. Phys. 1964, 42, 288-292. (2) Herdlicka, C.; Richter, J.; Zeidler, M. D. 2.Naturforsch. 1988, 43, 1075-1082. (3) Moms, K. F.; Johnson, C. S., Jr. J. Am. Chem. Soc. 1992, 114, 3139-3141. (4) Moms, K. F.; Johnson, C. S., Jr. J. Am. Chem. Soc. 1993, 115, 4291-4299. (5) Stilbs, P. Prog. NMR Spectrosc. 1987, 19, 1-45. (6) Gibbs, S. J.; Johnson, C. S., Jr. J. Magn. Reson. 1991, 93, 395402. (7) Mansfield, P.; Chapman, B. J. Magn. Reson. 1986, 66, 573-576. (8) Gibbs, S. J.; Morris, K. F.; Johnson, C. S., Jr. J. Magn. Reson. 1991, 94, 165-169. (9) Fannin, A. A.; Floreani, D. A,; King, L. A.; Landers, L. S.; Piersma, B. J.; Stech, D. J.; Vaughn, R. L.; Wilkes, J. S.; Williams, J. L. J. Phys. Chem. 1984, 88, 2614-2621. (10) Carper, W. R.; Pflug, J. L.; Wilkes, J. S. Inorg. Chim. Acta 1992, 202, 89-93. (1 1) Boere, R. T.; Kidd, R. G. In Annual Reports on NMR Spectroscopy; Webb, G. A., Ed.; Academic Press: New York, 1982; Vol. 13, pp 319385. (12) Lipsztajn, M.; Osteryoung, R. A. J. Electrochem. Soc. 1983, 130, 1968-1969. (13) Wilkes, J. S.; Frye, J. S.; Reynolds, G. F. Inorg. Chem. 1983, 22, 3870-3872. (14) Dieter, K. M.; Dymek, C. J.; Heimer, N. E.; Rovang, J. W.; Wilkes, J. S. J. Am. Chem. Soc. 1988, 110, 2722-2726. (15) Wilkes, J. S.; Levisky, J. A.; Wilson, R. A,; Hussey, C. L. Inorg. Chem. 1982, 21, 1263-1264. (16) Lin, M; Jayawickrama, D. A.; Rose, R. A,; DelViscio, J. A,; Larive, C. K. Anal. Chim. Acta 1995, 307, 449-457. (17) Morris, K. F.; Stilbs, P.; Johnson, C. S., Jr. Anal. Chem. 1994, 66, 211-215. (18) Provencher, S. W.; Vogel, R. H. In Numerical Treatment of Inverse Problems in Differential and Integral Equations, Dueflhard, P., Hairer, E., Eds.; Birkhauser: Boston, 1983; pp 304-319. (19) Vogel, R. H. SPLMOD Users Manual Technical Report DA06; European Molecular Biology Laboratory, Heidelberg, 1983. (20) McLaughlin, E. Trans. Faraday Soc. 1959, 55. 28-38. (21) Carper,-W. R.; Pflug, J. L.; Eiias, A. M.; Wilkes, J. S . J. Phys. Chem. 1992, 96, 3828-3833. (22) Weiden, N.; Wittekopf, B.; Weil, K. G. Ber. Bunsen-Ges. Phys. Chem. 1990, 94, 353-358. (23) Carlin, R. T.; Osteryoung, R. A. J. Electroanal, Chem. 1988, 252, 81-89. (24) Lipsztajn, M.; Osteryoung, R. A. Electrochim. Acta 1984, 29, 1349-1352. (25) Carlin, R. T.; Osteryoung, R. A. J. Electrochem. Soc. 1989, 136, 1409-1415. (26) Mitchell, R. W.; Eisner, J. J. Chem. Phys. 1960, 33, 86-91. (27) Mitchell, R. W.; Eisner, J. J. Chem. Phys. 1961, 34, 651-654. (28) Waylishen, R. E.; Pettitt, B. A.; Danchura, W. Can. J. Chem. 1977, 55, 3602-3608. (29) Kivelson, D.; Kivelson, M. G.; Oppenheim, I. J. Chem. Phys. 1970, 52, 1810-1821. (30) Dymek, C. J., Jr.; Grossie, D. A.; Fratini, A. V.; Adams, W. W. J. Mol. Struct. 1989, 213, 25-34. (31) Bock, C.; Trachtman, M.; Mains, G. J. J. Phys. Chem. 1994, 98, 478-485. (32) Gierer, A.; Wirtz, K. Z. Natui$orsch. 1953, 8A, 522-532. (33) Hu, C. M.; Zwanzig, R. J. Chem. Phys., 1974, 60, 4354-4357. JP9508113
