870
Anal. Chem. f988, 58, 870-873
Nonlinear Regression Model for Dielectric Constant Data of Binary Solvents Containing the Lower Alkanols Orland W. Kolling
Chemistry Department, Southwestern College, Winfield, Kansas 67156
Experimental curves showing dielectric constant ( E ) vs. solvent composltlon are usually nonlinear in the 2-36 range for cosolvents containing an alcohol as one component. Rational correlation functions for em = f ( X , ) were derived for those ROH-polar aprotic solvent pairs In which deviations from slmple linearlty appear to be governed largely by the hydrogen-bond acceptor basicity of the polar component. The precislons for the calculated E , values are slmllar to results obtained with parallel functions for other nonldeal polar-nonpolar cosolvent systems. For ROH-nonpolar solvent pairs, the rational function fits the E , vs. X , trend only in the alcohol-rich mole fraction range. The relationship between these rational functions for calculating E , and the standard form of the Pad6 approximant Is clarlfled.
Cosolvent systems containing the lower alkanols with an added aprotic component have been used for some time in analytical separation methods based upon solvent effects on solubility equilibria and the resolution of solute mixtures by TLC and liquid chromatography. For such systems, empirical measures of the influence by the solvent on the given process are often related to "solvent polarity" indexes, which may be connected ultimately to theoretical models using functions in the static dielectric constant of the medium (1, 2). Unfortunately, the literature data base for dielectric constants of specific alcoholic binary solvents is quite often incomplete, and the common trend in dielectric constant ( e ) as a function of solvent composition is nonlinear for these cosolvent systems. Since the graphic estimation of unknown t values in these instances can easily be in error by 10-20%, it is preferable to seek reliable correlation functions for e, = f(X,) as nonlinear regressions for the concise storage of dielectric constant information. In an earlier study (3) it was demonstrated that rational functions can be fitted to experimental dielectric constant data for nonpolar-polar aprotic binary solvents over the total mole fraction range. The algorithm recommended by King and Queen (4)yielded functions having adequate precision by using equations with only a first-power dependence on the composition variable. For the present investigation, the potential applications of rational regression functions to dielectric constant data for solvent pairs containing the lower alcohols were examined. Both nonpolar and polar aprotic liquids were included as the non-hydrogen-bonding component paired with the alkanols. Even though literature data are available for many of the alcohol-solvent systems, the values frequently include too few mixtures or too limited a mole fraction range to be useful in a statistical analysis of this type (5-10). Therefore, it was necessary to redetermine experimental ,E vs. composition curves for most of the solvent pairs considered in this study. Eighteen cosolvent systems containing a hydrogen-bond donor (HBD) paired with either a hydrogen-bond acceptor (HBA) or a nonpolar component were examined, and the dielectric constant ranges included fell within the interval 2.2 (CCl, and 0003-2700/86/0358-0870$01 SO10
dioxane) to 33 (methanol). For the majority of the cosolvents, the HBA species were oxobases, Le., ether, ester, or ketone.
EXPERIMENTAL SECTION Reagents. All non-hydrogen-bonding liquids were spectroscopic (ACS) grade and were first dried for 1week over anhydrous calcium sulfate followed by a final drying using a single pass through a column of activated alumina. The anhydrous reagent grade (ACS) alcohols were similarly redried and redistilled by using standard procedures (11). Only the center 60% cut of distillate was retained, and the water content was monitored by Karl Fischer titration. Solvent mixtures were prepared by volume and recalculated to mole fraction using liquid densities for the pure components. Instrumentation. Dielectric constants were measured as reported previously using reliable values for pure solvents as calibration standards (3,12). The summary of data for the t values of binary solvents given in Table I is limited to the revised and expanded seta subjected to regression analysis. Usable values for the l-butanol-1,4-dioxanesystem were published earlier (12). The overall precision in dielectric constant values for all of the alcoholic binary solvents does not exceed k0.14 (standard deviation). For notation purposes, the cosolvent with the lower c value is identified as solvent 1 (with mole fraction XI),and the higher is designated by mole fraction X 2 in order to be consistent with the previous investigation. RESULTS AND DISCUSSION Any interpretation of the dielectric characteristics of alcoholic media must be consistent with the highly self-associated and structured model for the pure liquids themselves, and the usual description for these hydroxylic solvents assumes a multistep monomer-linear multimer equilibrium represented by the total process in eq 1 (13). At low stoichiometric
ROH
+ (ROH),-,
+ (ROH),
(1)
concentrations of the alcohol in hydrocarbon solvents the dominant process appears to be a monomer-dimer equilbrium; however, based on NMR dilution shifts and Kirkwood g factors a greater degree of linear association occurs as the concentration increases with x = 3 , 4 ...,etc., as the size of R increases as well (13, 14). For the pure liquid, the overall association constant, K,, is greater than for solutions of ROH in nonpolar solvents (15). Dielectric Constants for Mixed Solvents. Although not included herein, the experimental t, vs. X I graphs for alcohol-nonpolar cosolvent systems are similar in form to the plots obtained for the non-hydrogen-bonding polar-nonpolar pairs examined earlier (3) showing moderate concave curvature. Comparable curves are observed for many alcohol-oxobase binary solvents as well, suggesting the likelihood that correlation functions of the same form for ,E = f ( X J should apply to a number of these hydrogen-bond donor-acceptor pairs. However, rather than dealing with these plots as a set of empirical curve-fitting problems, it is more useful to seek to identify some of the structural factors that determine common subgroups within the wide range of alcohol-nonpolar and alcohol-polar cosolvent systems. The excess function in dielectric constant (Ae,) will again be used in such preliminary comparisons (3). 0 1986 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 58, NO. 4, APRIL 1986 871 Table I. Dielectric Constants (at 25 "C) for Cosolvents Containing Alkanols ethanol:1,2-dichloroethane XZ 'rn
ethanol:CC14 XZ' em 0.000 0.075 0.182 0.272 0.360 0.451 0.544 0.618 0.714 0.809 0.903
2.23b 2.58 3.27 4.35 5.68 7.75 9.80 11.64 14.15 17.02 20.11
ethanol:1,4-dioxane 0.000 0.101 0.212 0.334 0.408 0.547 0.671 0.766 0.861 0.904 0.958
2.21' 3.60 5.52 7.66 9.20 12.15 15.13 17.50 20.06 21.32 22.96
methanol:1,4dioxane XZa em 0.083 0.162 0.244 0.320 0.437 0.546 0.608 0.699 0.780 0.850 0.907 0.958 0.979
2.94 3.66 4.58 5.51 7.46 9.67 11.12 14.00 17.33 21.05 24.57 28.54 30.58
0.000 0.073 0.196 0.311 0.406 0.521 0.644 0.735 0.816 0.902 0.963
10.36' 10.57 12.02 13.37 14.64 16.18 18.03 19.50 20.89 22.40 23.58
ethano1:diethyl ether x2
em
0.000 0.152 0.287 0.408 0.518 0.617 0.707 0.790 0.866 0.913 1.000
4.356 5.91 7.46 9.43 11.25 13.24 15.31 17.45 19.70 21.19 24.34'
ethanokethyl acetate
methanolCCL
x2
' m
xz
em
0.000 0.061 0.118 0.209 0.320 0.404 0.541 0.613 0.738 0.810 0.932
6.02b 6.68 7.30 8.41 9.85 11.02 13.28 14.69 17.31 19.07 22.27
0.083 0.131 0.194 0.282 0.349 0.423 0.508 0.613 0.702 0.825 0.886 0.913 0.960 1.000
2.67 3.02 3.40 4.71 5.88 7.36 10.73 13.87 16.93 22.14 25.42 26.94 29.85 32.66b
methano1:ethyl acetate
XZ
' m
0.112 0.247 0.334 0.408 0.539 0.615 0.737 0.805 0.902 0.970
6.91 8.31 9.42 10.56 12.95 14.61 17.89 20.66 25.60 30.34
methanoktetrahydrofuran XZ ' m 0.000 0.050 0.101 0.140 0.201 0.260 0.372 0.461 0.553 0.670 0.750 0.850 0.913
7.54c 8.08 8.75 9.30 10.11 11.08 13.12 14.88 16.89 20.20 22.50 26.01 29.46
'Mole fraction of the alcohol. Reliable literature values used as standards (11). 'Redetermined value for the pure solvent. 1
-1
t
I
0
A%
Flgure 1. Shift in the excess function (At,,,) with mole fraction (X,)
for binary solvents: (1) 1,2dichloroethane:ethanol; and CCI, with (2) 1-butanol, (3) 2-butanol, (4) 1-propanol, (5) ethanol, and (6) methanol.
Table 11. Dielectric Constant Deviations (Ae,) at the Minimum for HBD:Aprotic Pairs at 25 "C alcohol cosolvent with CC14 no. Ae,,, 1-butanol 2-butanol ethanol methanol 1-propanol other cosolvents diethyl ether with CC14 acetonitrile with sulfolane
Kamlet-Taft no.' T* P a
1 2 3 4 5
-2.98 -3.65 -4.67 -6.70 -3.81
0.47 0.51' 0.54 0.60 0.52
6 7
-0.05 2.82
0.27 0.75
0.88
0.79
0.77 0.62
0.83 0.98 0.78
0.47 0.00 0.31 0.19
Most recent literature values from the summary of Kamlet et al. (16). Redetermined value based on I5N NMR results (20).
-10
"
0
Flgure 2. Comparisons of
"
;
"
"
P I
Aem at the minimum or maximum in em vs.
X , curves with the K m t - T a f t parameters: (A) CC1,:alcohol systems (rI* of the alcohol); (B) methanokoxobase (6 of the HBA); (C) ethanol:oxobase (6 of the HBA). Numbered points refer to cosolvents in Table 11.
In Figure 1plots of Aem vs. X2(ROH) are given for the lower alkanols paired with carbon tetrachloride. It is obvious that At,,, at the minimum becomes less negative as the formula weight of the alcohol increases; however, by contrast to the non-HBD-nonpolar cases (3),the curves in Figure 1 are not perfectly symmetrical with respect to the minimum even though all of the minima occur between 0.46 and 0.50 mole fraction. The systematic and negative trend in Atm for all of these ROH-CC1, pairs is consistent with the repression of the fraction of ROH monomer in eq 1 by the added CC14 in alcohol-rich mixtures. If one uses the specific cases of ethanol-CC1, and ethanol-benzene, the Aemln values of -4.7 and -3.3, respectively, parallel the overall association constants (K, = 5.5 and 2.3) for ethanol in these two nonpolar solvents (13). Additional support for the argument that the magnitude of the influence of C C 4 in the mixtures is governed by dipolar interactions can be found from the scatter diagrams of AtmIn vs. the Kamlet-Taft 11*dipolarity number (16) using data from Table 11. In Figure 2A the negative shift in the deviation is clearly correlated with the increasing dipolarity of the alcohol. It is noteworthy that the extrapolated intercept (Aemm = 0) occurs at II* = 0.33, and this compares well with the experimental point for the isopolar pair, CC1,-diethyl ether, having Atmin = -0.05 and II* = 0.28 (16). As anticipated no significant correlation exists between A€,,,,,, and the hydrogen-bond donor or acceptor characteristics of the alcohols. In a like manner comparisons can be made between the Aemmvalues in Table I11 and Kamlet-Taft parameters of the cosolvents containing various HBA bases with a given alcohol. Such correlations with the HBA basicities ( p numbers) for the
872
ANALYTICAL CHEMISTRY, VOL. 58, NO. 4, APRIL 1986
of exactly unity for u p This assumption significantly reduces the number of computational steps. Other advantages accrue from the modified first-power function given in eq 3. Since it is not uncommon to use the e,,, = (1.000 U1X1)/(bo b,X1) (3)
Table 111. Solvent Parameters and Dielectric Constant Deviations for Cosolvents Containing Alcohols (at 25 "C)
Ac, (max or min)
cosolvent
ethanol
acetone acetonitrile benzene carbon tetrachloride 1,2-dichloroethane 1,4-dioxane diethyl ether ethyl acetate sulfolane tetrahydrofuran
-1.83
0.04
methanol
KamletTaft parametern T* fl 0.71
0.11
0.75 0.59
-7.90
0.28
-3.31
-4.76 -1.55 -2.25 -2.59 -2.65 0.75
-9.78
-1.62
-4.35
-7.82 3.00
0.81 0.55 0.27 0.55 0.98 0.58
+
0.48 0.31 0.10 0.00 0.00
0.37 0.47
0.45 0.77* 0.55
'Literature values (16). New experimental but tentative value. component solvents added to methanol or ethanol as the common ROH are shown by the plots in parts B and C of Figure 2, respectively. Beyond the seemingly linear correlations between Ae and /3 values it will be noted that the greater positive slope occurs with the stronger and more dipolar hydrogen-bond donor. It is also significant that the intercept a t Ae = 0 is approximately the same as the /3 value of the alcohol as the common HBD, i.e., curve 2B intercept 0.67 = 0.62) and curve 2C intercept 0.75 (&OH = 0.77). Thus, for those HBA cosolvents that are less basic than the alcohol, Aemin is negative and nearly all of the oxobases included in this study are placed in this group. (Acetonitrile is outlying with respect to both curves B and C of Figure 2. On the other hand, stronger HBA components like sulfolane with /3 greater than that of the alcohol exhibit positive deviations for Ae as a maximum in e,, vs. X2plots. It is unlikely that this regular negative shift in Atmin is a hidden major dipolarity effect originating with the oxobase, since trial correlations between Aemh and the II* values in Table I11 were rather poor (r = 0.7); however, a minor dipole-dipole contribution as was identified for some strong HBD-HBA complexes by Kamlet et al. (17,18) cannot be fully excluded. Correlation Equations for e,. The generalized rational correlation function (eq 2) developed for the polar-nonpolar cosolvents (3) was applied to the alkanol-non-HBD binary solvents with only minor modifications in the computational methods employed. In the preceding study (3) iterative
procedures were used to optimize the values of the constants in the e,, = f(Xl). Based upon the eight cases in the earlier investigation as well as several other aprotic polar-nonpolar pairs examined more recently, one may now assign a value
+
Born factor to represent the dipolar effect of the medium on electrolytic association and electron transfer kinetics (18,19), the values for 1/cm can be directly obtained from eq 3 without further algebraic steps. Also it will be noted that this form of the correlation function becomes the reciprocal of the standard Pad6 approximant ( 4 ) . Thus, the number of empirical coefficients required to reproduce the data set within the given experimental precision in e,, is reduced to three. (The value of bo is characteristic for each alcohol and is numerically equal to l / e 2 for for the pure alcohol.) The initial empirical test of eq 3 was made with the acetonitrile-acetone system as a representative weak HBDnon-hydrogen-bonding pair. The rationale for this choice was based on these characteristics of the pure components: (a) as very weak hydrogen-bonding solvents, neither is highly self-associated as a pure solvent; (b) the II* dipolarity numbers of the components are nearly the same (0.71 and 0.75), so dipolar interactions in their mixtures should differ little from those within the pure liquids; (c) from the substantial difference in hydrogen-bond basicities for the components ( p = 0.48 and 0.31 for acetone and acetonitrile, respectively) the dominant behavior for acetone will be as the HBA, and likewise, from the greater a value for acetonitrile (0.19) compared to acetone (0.08), one would expect that the predominant role for acetonitrile should be as the polar but weak HBD in the solvent mixtures. Thus, a t the molecular scale the modest deviation (Ae,,, = -1.63) at X1 = 0.5 must arise largely from weak hydrogen-bond donor-acceptor interactions rather than from any major alteration of the solvent structures themselves through dipole-dipole reorganization taking place upon mixing. The results given in Table IV and the high precision in e (calculated) over the total mole fraction range verified that the overall trend in dielectric constant for the acetonitrile-acetone system is indeed similar to the rational regressions found for the purely aprotic cosolvents (3). For the alcohol-non-hydrogen-bonding binary systems, whether or not the em data can be fitted to the rational function in eq 3 is determined to a large extent by the structural characteristics of the non-hydrogen-bonding component. As is apparent in Table IV, statistically satisfactory regressions can be established for the lower alcohols paired with weak to moderately strong oxobases (ethers and esters) over the complete mole fraction range. For these cases, intermediate but negative Ae,,,,, values are found for the mixed solvents, and the uncertainties in e (calculated) for these systems are quite similar to the precisions obtained for the
Table IV. Constants for Regression Functionsn solvent pair
acetonitri1e:acetone l-butanol:1,4-dioxane ethanokCC1, ethanok1,2-dichloroethane ethano1:diethyl ether ethanok1,4-dioxane ethano1:ethyl acetate methanokCC14
methanok1,I-dioxane methano1:ethylacetate methanoktetrahydrofuran overall uncertainties
nem
bo
bl
XI range
a1
0-1.0 0-0.5 0-0.6 0-0.6 0-1.0 0-1.0 0-1.0 0-0.5 0-1.0 0-1.0 0-1.0
-0.122 -0.692 -0.797 -0.367 -0.640 -0.865 -0.563 -0.831 -0.751 -0.372 -0.514
0.0278 0.0595 0.0411 0.0412 0.0411 0.0411 0.0411 0.0306 0.0306 0.0306 0.0306
0.0146 0.0811 0.0500 0.0199 0.0419 0.0202 0.0315 0.0454 0.0814 0.0738 0.0339
fO.001
fO.0001
f0.0002
= f(X,), a. = I.OOO. *Correlation coefficient = 0.991.
c
(calcd) SD
f0.02 ( n = 9) f0.05 (n = 7) f0.16 ( n = 7) f0.08 ( n = 7) fO.09 ( n = 9) f0.09 (n = 10) f0.05 ( n = 10) f0.12 (n = 8) 10.12 ( n = 12) f0.08 (n = 9) f0.09 ( n = 11)
b
873
Anal. Chem. 1986, 58,873-881
aprotic polar-nonpolar cosolvent systems (3). By contrast, the dielectric constants for the alkanol-haloalkane pairs can be represented by simple rational regression equations only for alcohol-rich mixtures, i.e., mixtures in which the minor aprotic component begins to shift the structural equilibrium in the self-associated alcohol toward less polar species. At the other extreme, the e, values for those binary solvents in which the strong HBD is added to a highly polar HBA base conform to simple linear functions in X1,and the methanol-acetonitrile and ethanol-acetonitrile pairs illustrate that condition (Table 11) where the monomer of the alcohol forms a single and very stable hydrogen-bonded complex with the nitrile. For the latter cases, the structure breaking of the alcohol by the added highly polar HBA decreases the value of x in eq 1 (14). In summary, rational functions for E, = f ( X l ) can be extended to a number of alcohol-oxobase acceptor cosolvents even though the nonideal dielectric behavior of such solvent systems appears to be dominanted at the molecular level by basicity factors rather than dipolarity effects alone. The composition range for which rational functions are applicable is more restricted for the alcohol-nonpolar cosolvent where dipolar effects are the major determinants influencing the degree of self-association of the alcohol in solvent mixtures. Registry No. CC4, 56-23-5; 1,2-C2H4C12, 107-06-2;Et,O, 6029-7; EtOAc, 141-78-6;THF, 109-99-9;MeOH, 67-56-1; EtOH, 64-17-5; PrOH, 71-23-8; BuOH, 71-36-3; 2-BuOH, 78-92-2;
CH3COCH3,67-64-1; CH3CN, 75-05-8; CsHs, 71-43-2; dioxane, 123-91-1;sulfolane, 126-33-0.
LITERATURE CITED (1) Majors, R.; Barth, H.; Lochmuller, C. Anal. Chem. 1984, 5 6 , 300R349R. (2) Chastrette, M.; Rajzmann, M.; Chanon, M.; Purcell, K. J . Am. Chem. Soc. 1985, 107, 1. (3) Kolling, 0 . W. Anal. Chem. 1985, 57, 1721. (4) King, M.; Queen, N. J . Chem. Eng. Data 1979, 2 4 , 178. (5) Gold, P.; Perrlne, R. J . Chem. Eng. Data 1967, 12, 4. (6) Nicolas, M.; Relch, R. J . Phys. Chem. 1979, 8 3 , 749. (7) Nicolas, M.; Relch, R. J . fhys. Chem. 1981, 8 5 , 2843. (8) D'Aprano, A,; Fuoss, R. J . fhys. Chem. 1989, 7 3 , 400. (9) Pistoia, G.; Pecci, G. J . fhys. Chem. 1970. 74, 1450. ( I O ) D'Aprano, A,; Donato, I. J . Chem. Soc., Faraday Trans. 7 1973, 1685. (1 1) Riddlck, J.; Bunger, W. "Organic Solvents", 3rd ed.; Wiley-lnterscience: New York, 1970; Chapter 5, pp 636-655. (12) Kolling, 0. W. Trans. Kans. Acad. Sci. 1979, 8 2 , 218. (13) Fujiwara. H.; Ikenoue, T. J . Chem. Soc., Faraday Trans. 1 1976, 2375. (14) Grunwald, E.;Pan, K.; Efflo, A. J . fhys. Chem. 1976, 80, 2937. (15) Gold, P.; Perrlne, R. J . Phys. Chem. 1967, 71, 4218. (16) Kamlet, M.; Abboud, J.; Abraham, M.; Taft, R. J . Org. Chem. 1983. 48, 2877. (17) Kamlet, M.; Dicklnson, C.; Gramstad, T.; Taft, R. J . Org. Chem. 1982, 47, 4971. (18) Gilkerson, W.; Kendrick, K. J . Phys. Chem. 1984, 8 8 , 5352. (19) Hupp, J.; Weaver, M. J . fhys. Chem. 1985, 8 9 , 1601. (20) Kolling, 0. W. Anal. Chem. 1984, 56, 430.
RECEIVED for review September 9,1985. Accepted December 2, 1985.
Chemical Ionization Mass Spectrometry of Carbamate Pesticides: A Major Dissociation Pathway John J. Stamp, Emil G. Siegmund, and Thomas Cairns* Department of Health and H u m a n Services, Food and Drug Administration, Office of Regulatory Affairs, 1521 West Pic0 Boulevard, Los Angeles, California 90015 Kenneth K. Chan School of Pharmacy, University of Southern California, Los Angeles, California 90033 The ammonia and methane chemical lonlzatlon mass spectra of 20 carbamate pesticldes have been examlned to determine the analytical usefulness of selected ions In pesticide resldue analysis. Transfer of the amide hydrogen to the alcohol portlon of the carbamate to form a protonated alcohol Is supported by deuterated reagent gas studies and the blocklng effect of methylation at the amlde hydrogen slte. A major dlssoclation mechanism of even electron Ions Involving the concept of a proton bound bimolecular complex has been postulated lo occur where the partlclpallng neutral molecules In the complex can rotate about the bound proton In the selection process of a suitable basic slte for cation formation. Thls mechanism now permits valuable structural Information via observance of both protonated alcohols and protonated Isocyanates. Fragmentation of protonated molecular Ions Increased upon changlng from methane to ammonia reagent gas and It was concluded that the judlclous choke of reagent gas can provide both molecular weight Information and highly slgnlflcant structural information for residue conflrmatlon.
With the dramatic increase in usage patterns of carbamate pesticides as popular agrochemicals, an urgent need has arisen to develop analytical protocols to assist in both confirmation
and screening for such compounds in the food supply. A comprehensive understanding of the major fragmentation behavior of these molecules under chemical ionization could aid in this task. Preliminary analytical data on the employment of liquid chromatography mass spectrometry (LC/MS) to analyze two representative N-phenylcarbamates demonstrated (1)a successful approach in dealing with the previously encountered difficulties due to thermal lability (2). Molecular weight information was observed by using the moving belt interface (MBI) as well as displacement reactions where the side chain was expelled as a neutral olefin via a hydrogen rearrangement process. More recently, the use of thermospray (TSP) using postcolumn addition of buffer has also indicated (3)that molecular weight information on some representative carbamates can be obtained. These authors, however, have argued that TSP is superior to the MBI because it offers greater sensitivity and highly favors formation of protonated molecular ions. Although the increased sensitivity is real for the TSP method, it was obtained at the expense of loss of potentially important spectral data due to the severe limits placed on the lower scan range ( m / z 180) because of the presence of solvent-buffer cluster ions. In the arena of environmental analysis, the presence of only one ion at the correct retention time cannot be viewed as unambiguous proof of the presence of a particular contaminant (4). While one ion might well represent the molecular weight of the com-
This article not subject to U.S. Copyright. Published 1986 by the American Chemical Society
