Anal. Chem. 1987, 5 9 , 674-677
674
Dielectric Characterization of Binary Solvents Containing Acetonitrile Orland
W.Kolling
Chemistry Department, Southwestern College, Winfield, Kansas 67156
For electrochemical solvents containing acetonitrile (AN) paired with a cosolvent havlng elther a lower or hlgher dleledrk constant ( E ) , the trend In E , vs. mde fractlon Is usually nonllnear at 25 'C. Maxlma or mlnlma occur In the excess function (At) among representatlve systems and the magnitude of that deviatlon with respect to pure AN Is goverened by the dlpolarlty, pdarirability, and any hydrogen bondJng tendency from the added cosolvent. The empirical patterns In didecMc behavlor for 10 solvent systems including AN-pdar aprotk and AN-hydrogen bond donor paks conform to rational correlatlon functlons for E , = t ( X , ) over the complete mole fraction range.
Even though acetonitrile (AN) has been explored as a nonaqueous solvent during only the past 35 years, it is now as important in analytical chemistry as other common Lewis-base solvents including dimethyl sulfoxide (Me2SO) and dimethylformamide. Although AN differs from the latter by a very weak hydrogen bond donor (HBD) tendency, the HBD acidity of acetonitrile is largely overshadowed by its dipolar and aprotic characteristics as exemplified by its extremely low and its dipole moment of 3.92 D autoionization (Ki (1). Contemporary applications that are representative of acetonitrile as a solvent include the evaluation of medium effects on the kinetics of solvent assisted nucleophilic substitution reactions (2) and the voltammetric behavior of alkanes at ultramicroelectrodes (3). Although ion pair association by electrolytes in AN is the norm because of an intermediate value for the dielectric constant of the solvent, several investigators have demonstrated that associative complications involving the supporting electrolyte and the electrogenerated ionic intermediates can be eliminated by the use of the ultramicroelectrodes in the presence of little or no added supporting electrolyte (4,5). Thus, there may well be potentially significant extensions of such electrochemical techniques to cosolvents containing AN that are "tunable" in terms of continuously increasing or decreasing the dielectric constant from 36.0 (pure AN) upon adding a more or less dipolar cosolvent. The static dielectric constant ( e ) remains a key descriptor of polarity in all solvent continuum models for medium effects upon electrolytic equilibria, ionic solvation and solubility, and ionic mechanisms of reaction. However, as one reviews the literature data on binary solvents, clearly the trend in c with changing composition of the mixture is rarely an exact linear function for most cosolvent systems (6, 7), and AN-cosolvent systems do not seem to be exceptions to that pattern (8-11). On the other hand, the earlier dielectric constant data sets for acetonitrile-containing solvent pairs (8-11 ) are typified by too restricted a mole fraction range for their mixtures and by being too limited in the types of cosolvents represented. Within these limitations it is not possible to identify with any certainty the sources of specific solvent-solvent interactions which give rise to such nonideal dielectric behavior for the AN mixtures. In the present report the dielectric characteristics are examined for 15 binary solvents containing acetonitrile which
cover a total t interval from 2 to 43 (at 25 "C). A full range of solvent types was included as the second component, i.e., nonpolar and polar aprotic solvents as well as strong hydrogen bond donors (HBD). As a consequence, it is now possible to estimate the magnitude of the deviation from ideal dielectric behavior for the mixed solvent by applying a general linear regression in dipolarity and HBD acidity parameters for the added component. Likewise, nonlinear correlation functions of the form reported previously (6, 7) were devised to represent the empirical trend in e, vs. solvent composition for the ten more important cosolvent systems containing acetonitrile. EXPERIMENTAL SECTION Solvents. Spectroscopic (ACS) grade acetonitrile was dried initially for 3 weeks over anhydrous calcium sulfate. This was followed by fractional distillation through a 52-cm Raschig column from which center 75% cut was retained (corrected boiling range 81.3-81.6 O C ) . Just prior to preparation of the solvent mixtures, the distilled AN was passed through a column of activated alumina to remove traces of acetic acid and water. The latter did not exceed 0.0005% in the final product, based on Karl Fischer titration, and is well below the limit of a detectable effect upon the measured dielectric constant. All other spectroscopic (ACS) grade solvents were redried and redistilled as reported previously (6),following standard procedures (12). Instrumentation. Experimental values for dielectric constants were determined from changes in dielectric cell capacitance with a Sargent Model 5 cathode-coupled oscillator. Standard values at 25 "C from the literature (12) for several of the pure liquids were used to calibrate the instrument; i.e., acetonitrile, benzene, o-dichlorobenzene, ethanol, ethyl acetate, methanol, and tetrahydrofuran. Experimental procedures have been given in detail elsewhere (13). The precision in the t values of the mixed solvents is f0.06-0.14 (standard deviation) for the lower dielectric constant range (2-36) and *0.10-0.15 for the upper range (32-43). A minimum of five replicate measurements were made for each cosolvent mixture and mean values for the more important solvent systems are summarized in Table I. RESULTS AND DISCUSSION The initial phase of this study centered on the comparison of the empirical trends in c vs. mole fraction plots for representative AN-cosolvent systems in order to identify common patterns of dielectric behavior as well as those solvent characteristics modifying such patterns. Dielectric Constants for Mixed Solvents. A suitable measure of the departure of the dielectric constant for the solvent mixture from ideal behavior has been defined by Payne and Theodorou (14) using eq 1. Here, t, is the measured dielectric constant of the mixture, el and tz are the values for the pure components, and X1 and Xzare their respective mole fractions. Although this excess function will be zero for the ideal binary mixture, real mixtures have finite values which are most often negative in sign (6, 7). Dielectric constant data from Table I were used to calculate the excess function (At,), and the plots of those deviations as a function of X z for the specific binary systems are shown in Figure 1. The hydrogen bond donor-acceptor pair, eth-
0003-2700/87/0359-0674$01.50/0@ 1987 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 59, NO. 4, FEBRUARY 15, 1987
675
Table 1. Dielectric Constants (at 25 "C)for Binary Solvents AN/acetic anhydride X2" ern 0.000
0.102 0.209 0.325 0.411 0.527 0.644 0.752 0.876 0.928 1.000
22.00 23.01 24.48 26.02 27.20 28.80 30.37 32.02 33.91 34.77 36.01b
AN/ ethyl acetate
x2
ern
0.000
6.02b 7.81 9.79 11.86 14.42 16.48 19.26 25.50 29.24 31.58 34.47
0.105 0.208 0.313 0.430 0.522 0.605 0.776 0.860 0.912 0.970
AN/ tetrahydrofuran
AN/ benzene x2
em
0.000
2.28b 5.34 8.18 11.47 14.55 18.03 21.54 25.10 28.51 32.22
0.158 0.297 0.421 0.530 0.629 0.717 0.798 0.878 0.938
AN/o-dichlorobenzene
x2 0.000
0.084 0.191 0.304 0.445 0.530 0.616 0.742 0.828 0.912
ern
10.12b 11.23 12.80 14.36 17.01 19.22 21.41 25.05 28.27 31.62
AN/dimethylacetamide
AN / sulfolane
x2
x2
0.000
0.087 0.159 0.301 0.470 0.558 0.631 0.708 0.798 0.860 0.948
ern
37.7gc 37.72 37.65 37.48 37.21 37.05 36.88 36.76 36.54 36.33 36.10
AN/ethanol
0.000
0.069 0.158 0.280 0.395 0.499 0.550 0.676 0.788 0.909 0.952
Em
43.32c 43.15 42.90 42.58 42.21 41.75 41.35 40.26 39.03 37.46 36.75
AN/methanol
x2
ern
x2
ern
x2
ern
0.000
7.54b 8.71 10.23 11.61 13.21 15.72 18.02 20.58 23.77 28.00 31.44 34.08
0.000
24.34b 25.45 26.60 27.66 28.59 30.07 32.51 33.46 34.34 35.18 35.78
0.000
32.63* 33.30 34.08 34.59 34.98 35.26 35.42 35.63 35.76 35.85 35.97
0.076 0.166 0.248 0.327 0.439 0.524 0.613 0.706 0.820 0.903 0.961
0.090 0.175 0.262 0.348 0.477 0.683 0.770 0.855 0.921 0.974
0.092 0.230 0.352 0.465 0.582 0.660 0.776 0.848 0.913 0.963
Mole fraction of acetonitrile. Reliable literature values used as standards (12). CRedeterminedvalue for the pure solvent. anol:AN, is the only case that approximates ideal dielectric behavior. Most of the nonpolar to moderately polar aprotic cosolvents paired with AN yield deviations that are negative and their curves are similar in the magnitude of the curvature and general shape to those for aprotic pairs reported previously (6). The greatest differences in the Acm vs. X, graphs are found for the cases of AN/sulfolane, AN/Me2S0, and AN/ acetic acid (not included in Figure 1)in which clear maxima occur. For purposes of concise comparison, the values of the excess function at the minimum or maximum (At-) are listed in Table I1 for the 15 AN-containing solvent pairs considered in this study. In general Ac- lies in the mole fraction range of 0.50-0.55 in all instances, including those pairs containing a strong HBD component. Adequate em data are now available for a sufficient number of AN-solvent pairs to permit useful general rules of correspondence to be developed as a substitute for only qualitative rationalizations about particular solvent systems (14).For a starting point, one anticipates that primary interactions between two aprotic components will be dipole-dipole orientation and dipole-induced dipole interactions governed
0
i
x,
Flgure 1. Trend in the excess function (At,) with changing mole fraction X , (AN) for representative binary solvents containing acetonitrile. Cosolvents are (1) sulfolane, (2) methanol, (3) dimethylacetamide, (4) ethanol, (5) acetic anhydride, (6) acetone, (7) odichlorobenzene, (8) ethyl acetate, (9) 1,4dioxane, and (10) benzene.
Table 11. Solvent Parameters and Dielectric Constant Deviations (Ae,,) for Binary Solvents Containing Acetonitrile r*
a
At,,
Ae,,
b
(cosolv)n (cosolv) (exptl) (calcd) aprotic cosolvent acetic anhydride benzene o-dichlorobenzene dimethylacetamide dimethyl formamide dimethyl sulfoxide 1,4-dioxane ethyl acetate sulfolane tetrahydrofuran hydrogen bonding cosolvent acetic acid acetone acetonitrile ethanol methanol 1-propanol
0.76 0.59 0.67 0.88 0.88 1.00 0.55 0.55 0.98 0.58 0.64 0.71 0.75 0.54 0.60
0.08 0.19 0.83 0.93
0.52
0.78
1.12
-0.80 -5.80 -4.62 0.38 0.60 2.80 -5.23 -5.20 2.28 -4.51
-1.45 -5.90 -4.50 0.65 0.65 2.80 -5.12 -5.12 2.40 -4.59
3.55 -1.63
3.65 -1.80 -0.10 0.03 1.70
0.00
0.05 0.73 1.38c -0.70
-0.65
Kamlet-Taft parameters from the recent comprehensive summary (18). bValuescomputed from eq 4. CSecondvalue based on literature data (8). (I
largely by the molecular structure of the added component compared to acetonitrile. As was pointed out initially by Abboud, Kamlet, and Taft (15) and expanded by Brady and Carr (16), the dipolar effect of a given pure solvent is approximately proportional to its molecular dipole moment and for "select solvents" the dipole moment correlates well with the semiempirical Kamlet-Taft T* (dipolarity) parameter. When a dipolar but non-hydrogen-bonding component is mixed with the moderately polar acetonitrile, two structuremaking and structure-breaking processes will give rise to nonideal dielectric behavior for the mixed solvent: (a) a more polar additive may interact with AN to form a new dipolar pair or higher aggregate while simultaneously disrupting any dipole-dipole structure for the pure component 1and/or AN; and (b) a less polar additive may promote the dipolar selfaggregation of AN to form species of lower dipole moment through the effect of decreasing t alone. For a strong HBD additive solvent, specific donor-acceptor (AN) interactions may approximate stable stoichiometric complexes which form in competition with the simultaneous disruption of the solvent structure for the HBD component ( 1 4 ) . By using the above solvent-solvent processes, one may construct a simple semiquantitative model for the various interactive factors influencing the magnitude of the deviation Aemm corresponding to that condition of the maximum or
676
ANALYTICAL CHEMISTRY, VOL. 59, NO. 4, FEBRUARY 15, 1987
4t
J/I
0
WE
o o
i
O
_11 * 1 11 /
f z
0.4 Figure 2. Scatter diagram comparing Atm at the maximum or minimum wRh the dipolarity value (r,.) of the added solvent in binary solvents containing acetonitrile. Points refer to (0)the polar aprotic, (0)hydrogen bonding, and (X) aromatic solvents.
minimum. As an approximation, one may assume an additivity for the contributions of the major perturbing influences, Le., simple dipolar At,, induced dipolar Ati, and hydrogen bonding Ath. Then, eq 2 follows with the expectation that the Atmm = At, + Ati Ath At0 (2)
+
+
real signs for each of the terms will not necessarily be positive and that the net deviation is relative to AN as component 2. Since the deviation At,, is expressed in terms of the static bulk dielectric constant, the individual contributions to that sum can be substituted by specific solvent parameters measuring those particular effects. The Kamlet-Taft parameters conform to the requirements for the isolated terms (17): rl* dipolarity (At,); a1 polarizability effect (Ati); and a1 HBD acidity (Ath). The resulting general form of a linear regression in Atmm is given by eq 3 in which the weighting
Atmm = sal* + d6,
+ acyl + Ae0
(3) coefficients and intercept Ato are included. The scatter diagram in Figure 2 showing the pattern of At- (exptl) vs. rl* clearly indicates that separate polarizability and HBD acidity influences coming from component 1 are present in these cosolvent systems. The final regression expressed in the Kamlet-Taft parameters is given by eq 4 and is based on the data summary in At,, = 1 7 . 5 ( ~ 1 *- 0.08561) 6.42 CY^ - 14.74 (4)
+
Table I1 and the most recent literature values for the parameters (18). Here, the small negative d6 term is actually zero (6, = 0) for all cases except the aromatic and polyhalide solvents for which 61 is unity, and the ratio s / a = 2.7 indicates that dipolarity is the dominant effect for even the stronger HBD solvents (ROH and HOAc). The uncertainties in the coefficients are s f 0.1, d f 0.005, a f 0.02, and intercept AcO f 0.01. Calculated values for At- listed in Table I1 have an overall precision of f0.22 (SD) and the correlation coefficient ( r ) is 0.961 when all values are included. Since this r value is lower than usual for such regressions, it must be emphasized that eq 4 is suitable for only approximate estimates of the deviation in dielectric constant at t,, and has been verified for a n interval of 0.5-1.0 in rl*. Nevertheless, the relationship is useful in that it allows one to predict whether a given or unknown AN-cosolvent pair will exhibit a positive or negative deviation from ideal behavior for t, vs. X 2 plots. Among “select solvents”, the condition of At,,,, = 0 corresponds to a rl* 0.84 which is close to the values for propylene carbonate (PC) and tetramethylurea (18). When eq 4 is applied to pure acetonitrile itself (see Table 11),an assumed HBD acidity of 0.25 is necessary for At- to be zero; however, even though the literature mean N value is
Table 111. Constants for the Rational Regression Functions for the Calculations of cma e(ca1cd) SD cosolvent with AN
a1
b,
(n = 10-14)
acetic anhydride acetoneb
-0.259
benzene‘ o-dichlorobenzene dimethylacetamide 1,4-dioxaneb ethyl acetate methanol sulfolane tetrahydrofuran
-0.879 -0.408 0.540 -0.885 -0.689 -0.664 2.34 -0.607
0.0059 0.0146 0.0254 0.0307 0.0128 0.0244 0.0239 -0.0175 0.0493 0.0243
f0.08 f0.02 10.12 10.13 f0.03 f0.13 f0.15 10.03 f0.15 f0.16
overall uncertainties
fO.001
fO.0001
-0.122
“Fixed values of a. = 1 and bo = 0.0278 apply to all binary systems containing acetonitrile. Reported previously (6, 7). Revised values based on more complete data. 0.19 (18), its range of values appears to be 0.15-0.27 and uncertainties of f20% are not uncommon for the a numbers of weak HBD liquids. Because of such uncertainties and the limited number of solvent pairs used to establish the function, no clain of exact linearity for eq 4 should be made. Likewise, an assumed equivalence between Ato and the At,, for cyclohexane may well be incorrect since eq 2-4 are deviation statements rather than integral and are untested in the 0O . h * range. Correlation Equations for t,. For any given AN-cosolvent system, dielectric constants for a minimum of 9-12 solvent mixtures were obtained before data processing was initiated, and graphic distributions of the points for ,6 vs. X, were checked for internal consistency prior to compiling the composite sets. Among important cases which repeat the work of earlier investigators (i.e., AN/sulfolane and AN/methanol (IO)),it was found that the quality and quantity of the published data were not adequate for correlation analysis. Surprisingly, this was especially so for AN:methanol as was noted some time ago by Cunningham, Vidulich, and Kay (8), and therefore, the redetermination of t, values was necessary for this solvent pair having a very narrow dielectric constant range (32.6-36.0). Because of the apparent role of the common descriptors, H* and a , as cofactors influencing nonideal dielectric behavior in the AN cosolvent systems, it was expected that the t, vs. X, curves should again conform to a single type of correlation function. The rational function in the form of the reciprocal of the Pad6 approximant (19)which has been used previously with some success on purely aprotic solvent pairs (6) was applied to the AN binary solvents in the form of eq 5. Here, ,t
=
+ alxl bo + b J 1
a0
a. = 1 by assignment and X , is the mole fraction of the component added to AN, and, since bo is 1 / c 2 (AN), only the two empirical coefficients a, and bl must be determined. The numerical values for the latter constants are listed in Table 111for 10 AN solvent pairs along with the uncertainties in the calculated results. The precisions with which the computed t, vs. X , curves reproduce the corresponding experimental trends are comparable to results obtained for the previous cases (6,7)and justify the application of the simple first-power rational function given as eq 5 . Correlation equations for the acetonitrile cosolvent systems exhibit two important differences from similar functions developed for other aprotic and HBD binaries examined earlier (6, 7). Firstly, all of the previous polar-nonpolar aprotic and HBD-polar aprotic pairs showed only negative deviations
ANALYTICAL CHEMISTRY, VOL. 59,
as Aem. On the other hand, AN cosolvent systems include the total range of possible systems from -Atm to 0 to Atm (Figure l),and thus, the rational function in eq 5 has now been found to be adequate for representing data sets having either positive or negative deviations from ideal dielectric behavior. Secondly, with AN serving as a moderately polar Lewis base in those nonideal binary solvents which are hydrogen bond donorhydrogen bond acceptor pairs (AN-alkanols), no exceptional behavior for the correlation function is observed over the total composition range. This contrasts with some other aproticHBD systems containing the lower alkanols reported earlier which were fitted by the simple rational function for only about half of the mole fraction range (7). However, the ANstrong HBD cases have moderately positive deviations from ideal dielectric behavior (Table 11) for which the magnitude of Atmm decreases with the decreasing HBD acidity. The AN-alkanol systems resemble the cyclic carbonate-methanol pairs in this respect, and even though the carbonates have much larger dielectric constants (14) than AN, their .n* dipolarities and T * / @ratios are similar to AN (18). As one reconsiders the electrochemical characteristics of AN cosolvent systems, there is good evidence that ionic conductance and ion pair association conform to regular behavior in AN-aprotic pairs over the broad dielectric constant interval from 2 to 43 (10);however, there are slight departures from the exact linearity for In KA vs. l/tm predicted by the Fuoss-Onsager theory of ion pair association. Such minor departures from linearity as well as the slight but general asymmetry in the excess function curves as XI 0 (Figure 1)are consistent with an argument for a changing degree of dipole-dipole self-association by AN as small amounts of a polar cosolvent are added. These effects are not significant enough (10) to preclude the application of such solvent pairs to electroanalytical studies if the trend in t, as a function of solvent composition shows only minor deviation from ideal behavior and follows a correlation like that in eq 5. On the other hand, if one may generalize from cases like AN:methanol and PC:methanol, ion pair association and acid-base ionization equilibria appear to be irregular in those
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NO.4, FEBRUARY 15, 1987 677
AN mixed solvents containing a strong HBD solvent (IO,20). For the latter, electrolytic equilibria become more complex through the preferential solvation of solute species by the separate aprotic and HBD cosolvents (20) as well as by specific structure-breaking processes within the mixed solvent itself. Thus, because of the shifting degree of hydrogen bonded self-association by the lower alcohols in mixed solvents, AN/ROH systems do not appear to be solvents of choice for electrochemical studies even though their trends in dielectric constants are adequately represented by the rational regression functions. Registry No. AN, 75-05-8.
LITERATURE CITED (1) Serjeant, E. Potentiometry and Potentiometric Titrations; Why-Interscience: New York, 1984; p 386. (2) Bunton, C.; Mhala, M.; Moffatt, J. J . Org. Chem. 1984, 49, 3637. (3) Cassidy, J.; et al. J . Phys. Chem. 1985, 89, 3933. (4) Bond, A.; Fleischmann,M.; Robinson, J. J . Electroanal. Chem. 1984, 768,299. (5) Howell, J.; Wightmann, R. Anal. Chem. 1984, 56, 524. (6) Kolling, 0.W. Anal. Chem. 1985, 5 7 , 1721. (7) Kolling, 0.W. Anal. Chem. 1986, 5 8 , 870. (8) Cunningham, G.; Vidulich, G.; Kay, R. J . Chem. Eng. Data 1967, 12, 336. (9) D'Aprano, A.; Fuoss, R. J . Phys. Chem. 1969, 7 3 , 400. (IO) D'Aprano, A.; Donato, I. J . Chem. SOC., Faraday Trans. I 1973, 1685. (11) D'Aprano, A.; Goffedl, M.; Trioio, R. J . Chem. SOC.,faraday Trans. 7 1976, 79. (12) Riddick, J.; Bunger, W. Organic Solvents, 3rd ed.; Why-Interscience: New York, 1970; Chapter, 5 pp 638, 704-706, 720, 749, 836, 844, 857, 860. (13) Kolling, 0.W. Trans. Kans. Acad. Sci. 1979, 82,218. (14) Payne, R.; Theodorou, 1. J . Phys. Chem. 1972, 7 6 , 2892. (15) Abboud, J.; Kamlet, M.; Taft, R. J . Am. Chem. SOC.1977, 99, 8325. (16) Brady, J.; Carr, P. J . Phys. Chem. 1984, 88, 5796. (17) Taft, R.; Abboud, J.; Kamiet, M. J . Am. Chem. SOC. 1981, 703, 1080. (18) Kamlet, M.; et al. J . Org. Chem. 1983, 4 8 , 2877. (19) King, M.; Queen, N. J . Chem. Eng. Data 1979, 2 4 , 178. (20) Lesniewski, B.; Przybszewskl, B. J . Chem. SOC.,Faraday Trans. 7 1984, 80, 1769.
RECEIVED for review August 4,1986. Accepted November 3, 1986.
