J . Phys. Chem. 1989, 93, 5623-5627
terminate errors in the complicated case, however, are bound to be larger since multiple measurements are often necessary to access the state of a particular exchanged ion. Consequently, deconvolution will yield poorer results, which may be improved only by improving the precision of the isotherm data obtained.
5623
Acknowledgment. We thank B. J. Travis, W. L. Earl, B. R. Erdal, D. L. Bish, and J. H. Hall for helpful discussions. This research has been supported by the Nevada Nuclear Waste Storage Investigations Project, which is managed by the Yucca Mountain Project Office of the U S . Department of Energy.
Dielectric Spectrum of Dimethyl Suifoxide/Water Mixtures as a Function of Composition U. Kaatze,* R. Pottel, and M. Schafer Drittes Physikalisches Institut, Universitat Gottingen. 0-3400 Gottingen. West Germany (Received: August 8, 1988; I n Final Form: February 14, 1989)
At 25 O C the complex dielectric spectrum between 1 MHz and 40 GHz has been measured in the whole composition range for aqueous solutions of dimethyl sulfoxide. Different relaxation spectral functions have been fitted to the measured frequency-dependent permittivity data. It was found that the unsymmetrical continuous Davidson-Cole relaxation time distribution is appropriate to describe the spectra. The width of the distribution function is remarkably small. When plotted versus the mole fraction of dimethyl sulfoxide, the principal dielectric relaxation time in correspondence with other parameter exhibits a pronounced relative maximum. The static permittivity reflects some kind of antiparallel ordering of dipole moments.
Introduction In chemistry, biology, and physiology, there is a current wide interest in the molecular properties of aqueous mixtures with low water content. Despite this interest, however, our knowledge of the molecular structure and dynamics of these systems is rather poor. An efficient approach to the problem could be the study of binary aqueous solutions, in particular, if performed as a function of concentration. Recent measurements on aqueous solutions of nearly nondipolar quinoxaline over the complete composition range revealed interesting solute association effects,’ thus indicating that dielectric spectroscopy can add useful contributions to our understanding of the solution properties of relevant liquid mixtures. In this article we present and discuss results for aqueous solutions of dimethyl sulfoxide (DMSO). The interest in this system does not only spring from its unique biological properties2s3and from the wide use of DMSO and its aqueous solutions as solvents and reaction media.4 The polyfunctional DMSO can interact strongly and specifically with water through hydrogen bonds. The methyl groups, on the other hand, may induce cooperative ordering of water molecules by hydrophobic hydration effects. In addition, dipole forces may result in self-association of DMSO molecules. Studies of the thermodynamic and transport properties of the DMSO/water system resulted in the generally accepted conclusion that in the mole fraction range xDMs0 = 0.3-0.4 the DMSO-water interactions due to hydrogen bonds are at a maximum. There (1) Kaatze, U.; Pottel, R.; Schmidt, P. J . Phys. Chem. 1988, 92, 3669. (2) Leake, C. D., Ed. Biological Actions of Dimethyl Sulfoxide; Annals of the New York Academy of Sciences; New York Academy of Sciences: New York, 1967. (3) Jacob, S. W., Rosenbaum, E. E., Wood, D. C., Eds. Dimethyl Suuoxide; Marcel Dekker: New York, 1972. (4) Fuchs, R.; McCrary, G. E.; Bloomfield, J. J. J . A m . Chem. Soc. 1961, 83, 4281. ( 5 ) Cowie, J. M. G.; Toporowski, P. M. Can. J . Chem. 1961, 39, 2240. (6) Rallo, F.; Rcdante, F.; Silvestroni, P. Thermochim. Acta 1970, I , 31 1. (7) Packer, K. J.; Tomlinson, D. J. Trans. Faraday Soc. 1971, 67, 1302. (8) Tokuhiro, T.; Menafra, L.; Szmant, H. H. J . Chem. Phys. 1974, 61, 2275. (9) Fox, M. F.; Whittingham, K. P. J . Chem. Soc., Faraday Trans. 1 1975, 71, 1407.
0022-3654/89/2093-5623$01.50/0
is, however, still some disagreement as to whether specific hydrogen-bonded complexes are formed and what the lifetime of such complexes is.1s1s The structure of aqueous solutions at low DMSO content is still in dispute. A neutron inelastic scattering and X-ray diffraction study,” for instance, indicated that small amounts of DMSO increase the molecular order of water. Infrared spectroscopy16 as well as density measurements” show that small quantities of DMSO have little effect on the water hydrogen bonding. Other even lead to the conclusion that small amounts of DMSO act as “structure breaker” in water. So far less attention has been given to DMSO solutions of low water content. If solutesolute association leads to the formation of microphases, small solvent regions might exist in which the molecular motions are as fast as in pure water. But one can also imagine that in highly concentrated solutions molecular complexes are formed, in which water molecules act as hydrogen-bonded links between DMSO molecules. Dynamic properties corresponding to the frequently discussed idea of “bound” water could be expected in this case. Complex permittivity measurements on DMSO/water mixtures have been performed previously at four frequencies in the microwave region.21 However, these data, though covering a fairly broad frequency range, are still insufficient for a detailed analysis ~~~
(10) Lindberg, J. J.; Majani, C. Acta Chem. Scand. 1963, 17, 1477. (1 1) Safford, G. J.; Schaffer, P. C.; Leung, P. S.; Doebbler, G. F.; Brady, G. W.; Lyden, E. F. X. J . Chem. Phys. 1969, 50, 2140. (12) Glasel, J. A. J . Am. Chem. Soc. 1970, 92, 372. (13) Higashigaki, Y.; Christiansen, D. H.; Wang, C. H. J . Phys. Chem. 1981,85, 2531. (14) Madigosky, W. M.; Warfield, R. W. J . Chem. Phys. 1983, 78, 1912. (15) Baker, E. S.; Jonas, J. J . Phys. Chem. 1985, 89, 1730. (16) Brink G.; Falk, M. J . Mol. Strucf. 1970, 5 , 27. (17) MacDonald, D. D.; Smith, M. D.; Hyne, J. B. Can. J . Chem. 1971, 49, 2817. (18) de Visser, C.; Henvesland, M. J. M.; Dum, L. A,; Somsen, G. J . Chem. Soc., Faraday Trans. 1 1978, 74, 1159. (19) Petrella, G.; Petrella, M.; Castagnolo, M.; Dell’Atti, A,; DeGiglio, A. J . Solution Chem. 1981, 10, 129. (20) Subbarangaiah, K.; Murthy, N. M.; Subrahmanyam, S. V . Bull. Chem. Soc. Jpn. 1981, 54, 2200. (21) Achadov, J. J. Dielectric Properties of Binary Solutions; Pergamon: Oxford. 1981.
0 1989 American Chemical Society
5624
The Journal of Physical Chemistry, Vol. 93, No. 14, 1989
of the spectra with respect to the Various questions raised. We therefore measured for various DMSO/water mixtures the complex dielectric spectrum between 1 MHz ahd 40 GHz. The results of our measurements are compared to permittivity spectra of other aqueous systems. Comparison is also made with other properties of aqueous DMSO solutions. Experimental Section Solutions. Dimethyl sulfoxide (DMSO, Fluka, 99.5%) was used without further purification. Water was distilled, additionally deionized by bed ion exchange, and sterilized by UV irradiation. The solutions were prepared by weighing appropriate amounts of solute and solvent into suitable flasks. The specific electric dc conductivity u of the samples, measured in the usual manner at 0.1, 1, 10, and 100 kHz, was smaller than 1.2 X S/m, indicating negligibly small amounts of ionic species. Complex Permittivity Measurements. Between 1 MHz and 40 GHz the complex (relative) electric permittivity t(v)
=
t'(u) -
it"(v)
Kaatze et al.
TABLE 1: Typical Experimental Errors in Complex Permittivity Values of DMSO/Water Mixtures u, GHz Ac'fe', % 0.001-0.1 0.1-1 1-5.3 5.3-8.4 8.4-18 26-30 30-40 40
Results and Treatment of Permittivity Data In Figure 1 a Cartesian d ' ( u ) versus t ' ( u ) plot is given for the 11.5 mol/L aqueous solution of DMSO. Also shown for reasons
k1
f2 f l f0.5 fl f2 f 4 I
I
20'
i l
f l f2 f 4 17
I
I
-
20
4,
10
0 E'(VI
Figure 1. Plot of the complex dielectric spectrum in the e",d plane for the 11.5 mol/L aqueous DMSO solution (xDMSO = 0.5, 0)and pure water (+27) at 25 "C. Open circles represent literature data2] as obtained by interpolation of c' and c" values at 0, 20, 30, and 60 " C .
of comparison are the complex permittivities for pure water. Within the limits of experimental error the latter data can be represented by a semicircle with its center located on the abscissa. The dielectric spectrum of pure water can thus be d e s ~ r i b e d ~ ~ ~ ~ ~ by a Debye functionz9given by the expression (o = 29v)
Herein tw(0) and tw(m) denote the permittivities extrapolated to low and high frequencies (Figure l), respectively, and T, is the (discrete) relaxation time. The values of these parameters at 25 OC are given in Table 11. The complex plane representation of the dielectric spectrum of the mixture is a more complicated curve, indicating that there is a distribution of relaxation times. We therefore tried to analytically describe the measured permittivity data of the solutions and of pure DMSO by the Havriliak-Negami spectral function,30 which can be expressed as (3) with a and fl denoting relaxation time distribution parameters and T~ a principal relaxation time. The Havriliak-Negami function includes the Cole-Cole (fl = 03'),Davidson-Cole ( a = 0jz), and Debye ( a = fl = 0) relaxation spectral function as limiting forms. Equation 3 has been fitted to the measured spectra by using a nonlinear least-squares regression analysis. Very small cy values were found throughout in this fitting procedure. To increase the significance of the other parameter values we also analyzed the data in terms of the Davidson-Cole relaxation spectral function (a=0 in eq 3). The results are collected in Table 11. We studied the reliability of the parameter values by generating artificial sets of permittivity data. For this purpose the original t' and 6' values have been randomly modified within their limits of experimental (27) Kaatze, U.; Uhlendorf, V. Z . Phys. Chem. (Wiesbaden) 1981, 126, 151.
(22) Muller, S. C. Dissertation, University of Gottingen, 1978. (23) Gottmann, 0.;Dittrich, A. J . Phys. E 1984, 17, 772. (24) Pottel. R. Ber. Bunsen-Ges. Phys. Chem. 1965, 69, 363. (25) Kaatze, U . Ado. Mol. Relax. Processes 1975, 7 , 71. (26) Kaatze, U . Mikrowellen Magarin 1980, 27.
1
30
(1)
of the samples has been measured as a function of frequency u by spot frequency measurements. Three different methods have been used. From 1 to 100 MHz a very sensitive rf-admittance bridge (Boonton 33D/1) has been utilized in input admittance measurements on a small "reflection" cell. This cell contains the sample in a short piece of circular waveguide which is excited far below its cutoff frequency.22 Modal analysis of the transition betweem the coaxial line feeder and the waveguide-below-cutoff section shows that the cell can be represented by a simple lumped circuit element network.23 With the present liquids ( 8 > 45) this equivalent network consists of only two capacitors. One represents the actual cell, and the other one represents the piece of coaxial line. The no-load capacitance of the former capacitor slightly depends on the sample permittivity. It increases by about 1% if t' of the liquid decreases from infinity to 45.22 This effect has been carefully considered by calibration measurements using liquids of well-known permittivity. Between 1 MHz and 1 GHz a broad-band vector voltmeter (Rohde & Schwarz ZPU) has been used to determine the complex transmission coefficient of a "transmission" It essentially consists of a coaxial line, the inner conductor, however, being interrupted for a certain distance to form a small piece of circular waveguide. The waveguide, which contains the sample between two dielectric windows, is again excited below its cutoff frequency. Modal analysis of the transmission cell resulted in a 9-network representation, the lumped elements of which are capacitors t h r o ~ g h o u t .The ~ ~ capacitances of these elements have been also found by calibration measurements with reference liquids. In the frequency range from 1 to 40 G H z we applied a traveling-wave method. The wave transmitted through a liquid-filled coaxial line or circular cylindrical waveguide was balanced against a reference wave by a double-beam interferometer Variation of the sample length allows for absolute measurements. Five microwave bridges consisting of standard coaxial line components or waveguide devices were used to cover the frequency range. With all measurements the temperature of the sample liquid ( 2 5 "C) was controlled to within f0.05 K. The accuracy of the frequency was better than 10.1%. The errors A d and A€'' of the complex permittivity values depend on the frequency and on the magnitude of the t' and tf' values themselves. Typical At' and At" values are given in Table I.
,
A e"/ e", % f2 f 4 f 3
(28) Kaatze, U . Chem. Phys. Lett. 1986, 132, 291. (29) Debye, P. Polare Molekeln; Hirzel: Leipzig, 1929. (30) Havriliak, S.;Negami, S . J . Polym. Sci. 1966, C14, 99. (31) Cole, K. S.; Cole, R. H. J . Chem. Phys. 1941, 9, 341. (32) Davidson, D. W.; Cole, R. H. J . Chem. Phys. 1950, 18, 1484.
The Journal of Physical Chemistry, Vol. 93, No. 14, 1989 5625
Dielectric Spectrum of DMSO/Water Mixtures
TABLE 11: Molarity, Molality, Mole Fraction, and Volume Fraction of DMSO and Parameters of the Davidson-Cole Relaxation Spectral Function (Ep 3 with a 0) for Dimethyl Sulfoxide/Water Mixtures at 25 OC c, mol/L f 0.5%
0 1.002 3.00 5.00 7.27 9.89 11.51 12.76 13.78 14.08
0
m, mol/kg f 0.1% 0 1.079 3.785 7.560 14.34 30.77 57.26 123.81 589.7
x f 0.1%
u f 0.005
40)
4m)
Tsr PS
0 0.019 0.064 0.120 0.205 0.357 0.507 0.694 0.920 1
0 0.07 1 0.213 0.355 0.516 0.702 0.817 0.906 0.979 1
78.36 f 0.05 77.75 f 0.25 77.13 f 0.25 76.25 f 0.25 74.23 f 0.25 69.70 f 0.25 64.02 f 0.25 58.38 f 0.25 51.5 f 0.4 47.0 f 0.6
5.16 f 0.08 3.0 f 1 3.0 f 1 3.0 f 1 4.6 f 1 5.2 f 1 4.9 f 1 4.0 f 1 3.5 f 1 3.9 f 1
8.27 f 0.02 11.7 f 0.2 19.7 f 0.2 30.4 f 0.3 44.4 f 0.4 56.8 f 0.5 52.1 f 0.4 41.2 f 0.4 28.4 f 0.5 21.1 f 0.2
I
I
I
1
I
02
04
06
08
10
X
Figure 2. Relaxation time distribution parameter @ofthe Davidson-Cole
function displayed as a function of mole fraction x of the organic constituent for DMSO/water mixtures at 25 OC. uncertainty (Table I). The Davidson-Cole relaxation function has been fitted to each of these artificially generated spectra (about 20 per liquid), and the results obtained thereby have been used to estimate the uncertainties of the parameter values (Table 11). In the case of the mixtures we additionally applied spectral functions which are related to more specific solution models. In the simplest version the dielectric dispersion and loss was considered by a sum of two Debye terms. We expected that these terms could be attributed to the water and DMSO molecules, respectively. However, physically meaningless parameter values have been found, indicating that the subdivision into contributions from the different molecules does not correspond to reality.
Discussion Relaxation Time Distribution. Similar to the quinoxaline/ water mixtures1 a tendency toward the unsymmetrical Davidson-Cole relaxation time distribution is found. It is interesting to note that in the framework of a free-volume an unsymmetrical relaxation time distribution results if the rates of molecular reorientation and local density fluctuations have comparable values. Other than with the aqueous solutions of nearly nondipolar quinoxaline, however, the spread in relaxation times is comparatively small with all DMSO/water mixtures ( p 5 0.2). As shown by Figure 2, the p values depend on the composition of the mixtures in a characteristic manner. If small amounts of DMSO are added to water or small amounts of H20are added to DMSO, the width of the relaxation time distribution distinctly increases up to a maximum value of about 0.2 at around x D M S O = 0.1 and 0.8, respectively. The increase in the p values when going from the pure liquid to a mixture may be due to two effects, the perturbation of the molecular order by the foreign molecules and the contributions to the dielectric spectrum from the latter molecules themselves. (33) Anderson, J. E.; Ullmann, R. J . Chem. Phys. 1967, 47, 2178.
B EO 0.142 0.192 0.191 0.131 0.1 13 0.154 0.196 0.198 0.122
f 0.020 f 0.024 f 0.040 f 0.006
f 0.006 f 0.006 f 0.014
f 0.020 f 0.009
In the intermediate region (0.1 5 x D M S O 5 0.8) the width of the distribution function is remarkably small with a relative minimum of /3 = 0.1 1 at X D M S O = 0.33. At compositions around this minimum the mixtures, with respect to their molecular motions, appear to be almost homogeneous liquids. This finding confirms our above result, that a subdivision of the dielectric spectra into two discrete Debye-type relaxation processes is less appropriate. As already briefly mentioned in the Introduction, most studies on aqueous dimethyl sulfoxide solutions point at strong solutesolvent interactions. The existence of stoichiometrically welldefined hydrogen-bonded DMSO/water aggregates is suggested thereby. Such aggregates are expected to add well-separable contributions to the dielectric spectrum provided the radii of the rotating entities differ by a sufficient amount from one another. The reorientation time T~ of each species, assumed to be spherically shaped, will follow the generalized Debye relation34 ( k = 1.38 X 10-23 v A s K-I) (4)
where Q* is the dynamic coefficient called “microviscosity” and a* an effective radius of the entity the motion of which is considered. At the present accuracy of the permittivity data a superposition of two Debye-type relaxation processes can be discriminated from a process with continuous relaxation time distribution if the discrete relaxation times differ from one another by a factor of at least 3. Thus our above finding means that the radii of different aggregates in a solution do not differ distinctly more than by a factor of 3’13 = 1.5, provided the aggregates are sufficiently stable. If, however, their lifetimes are comparable with the reorientation times, the dielectric spectrum reflects not only reorientational motions but also association/dissociation processes. A clear separation of the various contributions is impossible in this case.35 Principal Dielectric Relaxation Time. A plot of the principal dielectric relaxation time T~ as a function of the composition of solutions is given in Figure 3 . At small DMSO content the T~ values increase with xDMSO, reach a relative maximum at x D M S O = 0.33, and decrease to the pure DMSO value, which is 21.1 ps = 2.55,. The viscosity Q and the rotational correlation time T~ of water show a similar concentration dependence. The latter quantity was derived from N M R measurement^.^' The relative maximum of the viscosity and the rotational correlation time has a smaller value ( ~ ( 0 . 3 3 ) / ~ (=0 )~ , ( 0 . 3 3 ) / ~ , ( 0 = ) 4.2) than that ) of the principal dielectric relaxation time ( ~ , ( 0 . 3 3 ) / ~ , ( 0= ~ , ( 0 . 3 3 ) / ~=, 6.9). The T , values reflect contributions from the reorientational motions of both the dipolar water and DMSO molecules. Surprisingly, at low DMSO concentration where ~ ( xC) Q( l ) , the ~~~
(34) 7, 689. (35) (36) Solvent (37)
~~
~~
~
Weingartner, H.; Holz, M.; Hertz, H. G. J . Solution Chem. 1978, Kaatze, U.; Giese, K. J . Mol. Liquids 1987, 36, 15. Covington, A. K., Dickinson, T., Eds. Physical Chemistry of Organic Systems; Plenum: New York, 1973. Gordalla, B. C.; Zeidler, M. D. Mol. Phys. 1986, 59, 817
5626
The Journal of Physical Chemistry, Vol. 93, No. 14, 1989
Kaatze et al. 1
6
5
-
4
1
c
c"
3
2
1
0
02
04
06
08
10
X
Figure 3. Ratio Y(x)/Y(O)of the solution to pure water value of some dynamic quantities plotted versus mole fraction x of D M S O for DMSO/water mixtures a t 25 "C. Shown are the data for the principal dielectric relaxation time T ~ the , viscosity q , j 6 and the rotational correlation time T~ of water3' derived from N M R measurements.
0 0
I
I
1
I
I
02
04
06
08
10
X
Figure 4. Relaxation time ratio
T , / T ~ shown
as a function of mole fraction for aqueous solutions of DMSO at 25 "C ( O ) ,of quinoxaline at 25 and 35 'C (XI), and of acetone at 30 'C (A*').
T ~ ( X ) / T , ( O )values are smaller than the T ~ ( x ) / T , ( O ) values. This
finding seems to be in contradiction to the fact that the dielectric relaxation time of pure DMSO has a distinctly higher value than that of pure water ( ~ , ( 1 ) / ~ , ( 0=) 2.5). Note, however, that the reorientation time of the aprotic DMSO molecule in the pure liquid is unexpectedly high. The corresponding value for pure acetone, for instance, is 2.8 ps = 0.387, (30 O C Z 1 ) . Likewise high is the viscosity of DMSO ( q = 1.96 mPa s) as compared to that of acetone (7 = 0.3 mPa s). These data have been discussed34to indicate that self-association effects are important in pure dimethyl sulfoxide. The finding of T,(x)/T,(O) < ~ ~ ( x ) / r , (atO x) < 0.1, which points at fast orientational motions of the DMSO molecules, may thus be taken to reflect a reduction of the DMSO-DMSO interactions in dilute aqueous solutions. The strong increase in the 7, values when going from pure water to dilute aqueous solutions seems thus to be predominantly due to hydrophobic hydration effects3840 as usually found around organic solutes. We do not known the concentration dependence in the evaluation of the relative molal shift of the principal dielectric relaxation time at c C 1 mol/L. Frequently, however, the plot of r, versus solute molality m is a straight line that can be extrapolated back to pass through the pure water value r , at m = 0. We therefore assume a linear concentration dependence in the evaluation of the relative molal shift of the principal dielectric relaxation time, Bd, defined by
Bd = (0.39 f 0.02) mol kg-' results for the DMSO/water system at 25 O C . This is one of the highest Bd values ever found with aqueous solutions of organic molecules. The nondipolar 1,4diazabicyclo[2.2.2]octane has a similar value (Bd = (0.36 f 0.02) mol kg-' at 25 OC41). Even higher values seem to be characteristic for large organic ions.42 We therefore conclude that the DMSO molecules are particularly effective in promoting the water structure around them. Factors that are important in influencing the principle dielectric relaxation time may be the size of the solute molecule, its overall shape, and the combined action of hydrophobic hydration effects and the hydrogen-bonding interactions. (38) Frank, H. S.; Evans, M . W. J . Chem. Phys. 1945, 13, 507. (39) Hertz, H. G.Ber. Bunsen-Ges. Phys. Chem. 1964, 68, 907. (40) Ben-Naim, A. Hydrophobic Inreracrions; Plenum: New York, 1980. (41) Kaatze, U.; Wen, W.-Y. J . Phys. Chem. 1978, 82, 109. (42) Wen, W.-Y.; Kaatze, U. J . Phys. Chem. 1977, 81, 177.
The fact that the T, values increase when water is added to neat DMSO is in agreement with conclusions derived from N M R measurements.s The binary liquid is more "rigidified" than the pure liquid. It is generally accepted that the interactions between water and DMSO molecules make an important contribution to the reduction in the molecular mobility. Obviously, these solute-solvent interactions exceed the self-association effects of pure DMSO. It seems to be likely that hydrogen-bonded DMSOH,O-DMSO complexes are formed in the mixtures of low water content. Since both components enhance each other's relaxation time, a relative maximum must exist at some value of x. As shown by Figure 4, such a maximum is also found with aqueous solutions of nearly nondipolar quinoxaline and of acetone. However, the mole fraction at which the maximum T , / T , value is reached is different (x = 0.2 with acetone, x = 0.4 with quinoxaline solutions). It is only briefly mentioned here that the principal dielectric relaxation time of binary liquid mixtures may show different behavior. For instance, the 7, versus x relation of 2-propanol/ watefi3 and 2-propanol/DMSOU mixtures decreases monotonously from the value of the pure alcohol to that of the other constituent. It is a self-evident attempt to relate the x, value of the relative maximum in the concentration dependence of 7, to stoichiometrically well-defined molecular complexes. In view of the two hydrogen bond accepting abilities of the DMSO oxygen atom, the H,O-DMSO-H20 species following thereby seem to be a reasonable configuration. Let us assume these complexes to rotate as a whole. The generalized Debye relation (eq 4) can be rewritten to apply for the orientational motions of the molecular species under consideration: a*3(DMS0.2H20) =--7,(xmaX) qw* a*3(~2~) 7, 7*(&"
(6)
Since we do not known the microviscosity ratio, we simply use the macroscopically determined viscosities (Figure 3) in this estimation. a*3(DMS0.2H20)/a*3(H20) = 1.6 follows. In contrast, the ratio of molar values is (4ADMSO) + 24AH20))/ 6Y(H2O) = 6.4, indicating that the Debye theory is insufficient here. Again it should be recognized that, depending on the lifetimes of molecular complexes, the principal dielectric relaxation (43) Kaatze, U.; Schafer, M.; Pottel, R. Z . Phys. Chem. (Munchen), in press. (44) Unpublished results of this laboratory.
The Journal of Physical Chemistry, Vol. 93, No. 14, I989 5627
Dielectric Spectrum of DMSO/ Water Mixtures 10 0.9
1
9
08
a"
07
-0
06
0
01
02
03
04
05
06 0 7
08
09
10
X
Figure 6. Ratio D,/D,, displayed as a function of mole fraction x of D M S O for the dimethyl sulfoxide/water system at 25 O C .
0
01
02 03 04 05 06 07
08 0 9
10
X
Figure 5. Static permittivity ratio c(0)/cw(O) plotted versus the mole fraction x of the organic constituent for aqueous solutions of DMSO ( 0 ) and acetone (A*')at 25 O C and of quinoxaline ( X I ) a t 25 and 35 O C .
time may reflect the kinetics of association and dissociation rather than orientational motions. The idea of almost rigid rotating molecular entities with definite stoichiometric composition may be questioned for other reasons. For instance, the x,, values of other aqueous systems, if correspondingly treated, yield rather unlikely results, like acetone.4H20 complexes or even more unrealistic acetonitrile.9H20 complexes.*' Static Permittivity. In Figure 5 the ratio t(O)/t,(O) of the static permittivity of the binary mixtures and of pure water is shown as a function of the mole fraction x of the organic constituent for aqueous solutions of DMSO, acetone, and quinoxaline. At given x > 0 the c(O)/c,(O) values increase with the magnitude of the electric dipole moment p which the organic molecule would adopt in the gaseous state (quinoxaline, p = 0.51 D;45acetone, p = 2.87 D;46 DMSO, = 3.91 D4'). The static permittivity of the DMSO/water mixtures decreases montonously from the value for pure water (c,(O) = 78.36, 25 "C) to that of pure DMSO (t(0) = 47.0, 25 "C; Table 11). A complete theory relating the static permittivity of water/ DMSO mixtures to the dipole moments pw and MDMSO of the constituents should include various possibilities of dipole orientation correlations. Let us consider, for example, a solvation model of dilute solutions of water in DMSO. In the framework of this model a solute molecule (w) is assumed to be surrounded by a solvation shell (s), the dielectric properties of which may be different from that of the pure solvent. The solvated solute molecules are embedded in undistributed solvent (DMSO) with (45) Lumbroso, H.; Palarnidessi, G. Bull. SOC.Chim. Fr. 1965, 3150. (46) Budenstein, P. P., Ed. Digest of Literature on Dielectrics; National
Academy of Sciences: Washington, DC, 1973; Vol. 35, p 33. (47) Wertheimer, M. R., Yelon, A., Eds. Digest of Literature on Dielectrics; National Academy of Sciences: Washington, DC, 1979; Vol. 41, p 57.
the permittivity of pure dimethyl sulfoxide. Due to the large distances between solute molecules the water/water interactions may be neglected. Nevertheless, there are still four nontrivial dipole orientation correlation factors left, namely, gw,s,g,,, &DMSO, and gDMS0,DMSO. Since we are unable to determine the different g factors separately, the static permittivity data have been evaluated disregarding, for the present, possible dipole orientation correlations. For this reason we calculated the quantity ( N A = 6.02 X 2023 A s V-I m-I; k = 1.38 X VAs mol-'; to = 8.854 X K-1)
using the above values for the molecular dipole moments. We also utilized the experimental static permittivity data to calculate the quantity (40) - t,)(240)
D, =
+4
40)
(8)
For reasons of simplicity t, = 4.3 has been used here instead of the extrapolated t ( m ) values (Table 11). In the case of aqueous solutions and also of pure DMSO t, = 4.3 represents the e ( = ) data within the limits of experimental uncertainty. For water it had been shown previously4* that this t, value allows the static ) O C to be described with a value for the permittivity ~ ~ ( at0 25 orientation correlation factor g,,, close to zero. If indeed dipole orientation correlation effects could be neglected in the dimethyl sulfoxide/water mixtures, too, D, = D,, should hold. As shown by Figure 6, however, the D,/D,, ratio of the solutions is smaller than 1. It decreases monotonously with x and reaches a value of 0.5 with pure DMSO. Theoretically D J D , = 1 C(gij) should hold (the usual Kirkwood correlation factor49 is defined by 1 gi,J. In the case of the pure organic liquid G can be identified with the gDMwaMsqorientationcorrelation factor. Thus from gDMSO,DMSO = 0.5 a distinct effect of antiparallel ordering of the molecular dipoles emerges. Obviously, antiparallel ordering is also important in the DMSO/water mixtures. But, as already mentioned above, the relative importance of the various possible orientation correlations in causing D,/D, C 1 is not known.
+
+
Registry No. DMSO, 67-68-5. (48) Hill, N. E. J . Phys. C 1970, 3, 238. (49) Kirkwood, J. G. J . Chem. Phys. 1939, 7, 911.
