Perfluorinated solvents as nonpolar test systems ... - ACS Publications

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Anal. Chem. 1982, 54, 1751-1757

1751

Perfluorinated Solvents as Nonpolar Test Systems for Generalized ;Models of Solvatochromic Measures of Solvent Strength James E. Brady and Peter W. Carr" Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455

The ?r* values of perfluorodlmethyldecalln, perfluorotrlbutylamine, perfluoroheptancs, and perfluorooctane have been found to be -0.33, -0.:38, -0.39, and -0.41, respectlvely. These values lndlcate that solvent polarlrablllty provldes a major contrlbutlon to thie ?r" scale of solvent dlpolarlty/polarlzablllty. A three-parmeter equatlon Is shown to provide reasonable correlatlon far 76 solvents of solvent 7" values for a varlety of solvent types including polychlorlnated and aromatlc solvents whlch are conventionally excluded from the so-called select solvent set. The utlllty of perfluorinated solvents as Ilquld-llquld extractlon reference phase Is assessed and shown to bo strongly dependent upon the lndicator solute belng studied.

At present a major limitation of chromatographic theory is the inability to quantatively predict the effect of solvent on the retention characte!ristics of solutes. An understanding of the thermodynamics of solute-solvent interactions in pure solvent systems at the miolecular level should provide needed insight into the elucidation of solute/solvent interactions in chromatographicallyimportant mixed solvent systems. Many approaches to this problem proceed through the use of a model system and the assumption of a linear free energy relationship between the process involved in the model system and the system of interest. Thus the model system serves as the basis for a solvent polarity scale!. A number of solvent polarity scales have been developed as a means of predicting the effect of solvent on a variety of chemical phenomena (e.g., reaction rates and equilibria, phase equilibria, spectral characteristics, etc.) (1-4). Chromatographi~~ally important scales of solvent strength include the well-known eo and P'scales of Snyder ( 5 , 6 ) as well as the solubility parameter approach of Karger et al. (7-9).The a* solvatochromic scale of solvent dipolarity/polarizability, developed by Kamlet, Taft, and their coworkers (10-20),is one of the more significant scales developed in view of the range of solvents whose 7r* value has been determined, the large number of test solutes employed, as well as the successful develolpment of a theoretical, qualitative model of the experimentally derived a* parameters. The theoretical analysis as well as experimental realization of the a* and the companion isolvatochromic a. and 0 scales (of solvent proton donating and accepting ability, respectively) has been succinctly summarized in a recent review (21). Our interest in the a* !male is based on the role played by solute/solvent dipolarity--]polarizabilityin the phase transfer equilibria of solutes. In the Kamlet-Taft formalism, a solvent's a* value is a direct, measure of the ability of a solvent to interact with a non-hydrogen-bonding solute through dipolar interactions. It should therefore represent part of the overall energetics of dissollving such a solute in a solvent. The a* scale has only minimal contributions from the energy of cavity formation which results from the disruption of solvent-solvent interactiona. The strength of solvent-solvent interactions is conventioriallyrelated to the Hildebrand sol0003-2700/82/0354-1751$01.25/0

ubility parameter (22-25) or to microscopic surface tensions (26-29). Although solute-solvent interactions as measured by the solubility parameter approach have been questioned, we believe that it may be possible to ultimately estimate both gas-liquid and liquid-liquid partition coefficients (and therefore chromatographiccapacity factors) by use of a model in which solvent-solvent interactions are represented in terms of solubility parameters and solute-solvent interactions are represented in terms of solvatochromic parameters such as a*,a , and 0. Ultimately we wish to attempt a direct comparison of solvent a* values (obtained from spectroscopic measurements)with liquid-liquid phase equilibria of the same indicator solutes. It must be recognized that there are many fundamental physical differences between solvatochromic and phase partitioning scales o€solvent strength. At the most fundamental level, the solvatochromicmethodology involves changing the solute dipole moment collinear with the reaction field (12). The reaction field can be viewed as the electric field resulting from the polarization and orientation of solvent molecules by the solute molecule. Both types of experiments involve changing the dipole moment of a given molecule surrounded by solvent molecules. In general, a phase equilibrium experiment also involves changing the size of the cavity occupied by the solvent as well as changing its polarizability, hydrogen bonding characteristics, and configurationalfree energy from solvent to solvent. In contrast, the spectroscopicexperiment is able to selectively probe the effect of variations in the solute's dipole moment with only minor contribytions from cavity processes, etc. However, a fundamental difference between the two types of experiments is that phase equilibria are not subject to the Franck-Condon principle. That is, the solute molecule in a phase equilibrium experiment is always in electrostatic equilibrium with the surrounding medium while the excited-state solute molecule in a spectroscopic experiment is not. It is difficult to assess a priori how similar the two types of solvent scales are. However, previous results indicate that dipolar effects in phase equilibrium are very strongly correlated with spectroscopic results (30, 31). The importance of solvatochromic scales of solvent strength lies in the possibility that they may allow empirical deconvolution of the various components of the total free energy involved in phase transfer processes. Future experiments in this laboratory will be directed to this end. The present work is concerned both with the suitability of perfluorinated solvents as immiscible reference phases in liquid-liquid extraction studies of Kamlet's a* indicator solutes and with the more general question of the determination'and rationalization of the a* values of a wide variety of monofunctional aprotic solvents. Two criteria govern the general suitability of a solvent as a reference phase for partitioning studies. The most obvious requirement is that the indicator probe be sufficiently soluble in the reference phase to allow its detection. Preliminary results have demonstrated that exremely low levels of the a* indicator solutes can be determined by high-pressure liquid 0 1982 American Chemical Society

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ANALYTICAL CHEMISTRY, VOL. 54, NO. 11, SEPTEMBER 1982

Table I. Solvatochromic Data for Perfluorinated Solvent Systems solute 1 4 7 9 13 14

17A 19

20 21 23 28 32 33 35 39 45

solvent typesa NHB, HBA, HBD NHB, HBA, HBD NHB, HBA NHB, HBA NHB, HBA NHB NHB NHB, HBA NHB NHB NHB NHB NHB, HBA, HBD NHB NHB NHB, HBA NHB, HBA, HBD

- sa 2.343 2.133 2.013 1.407 3.436 3.138 3.364 1.682 1.261 1.682 1.621 1.664 1.593 1.536 1.596 1.852 2.428

v o , ~103

cm-'

n*FC-43

n*FC-4s/CH3CNb

n*FC-43/CH30HC

"*FC-m

"*FC-s4

34.12 37.60 30.41 33.31 28.10 31.10 29.37 30.98 36.85 33.09 25.72 28.87 24.59 26.55 24.33 25.39 32.56

-0.38 -0.35 -0.39 -0.82 -0.31 -0.49 -0.37 -0.61 -0.79 -1.38 -0.36 -0.38 -0.36 -0.40 -0.28 -0.62 -0.28

- 0.01

-0.01 0.00 0.22 0.00 0.00 - 0.54 0.05 0.03 0.19 0.14 0.05 -0.06 0.03 0.07 0.03 0.03 -0.01

-0.44 -0.42 -0.43 -0.92 -0.33 -0.38 -0.36 -0.66 -0.82 -3.21 -0.40 -0.48 -0.39 -0.45 -0.43 -0.67 -0.36

-0.44 -0.40 -0.48 -0.94 -0.35 -0.38 -0.36 -0.66 -0.93 -3.49 -0.35 -0.46 -0.36 -0.44 -0.36 -0.67 -0.33

chromatography. A second, more fundamental, consideration is that the reference phase must remain an effectively pure phase when equilibrated with a wide variety of test solvents. Most common organic solvents show substantial miscibility with a variety of solvents ranging in polarity from benzene to acetonitrile whereas perfluorinated solvents show very limited miscibility with virtually all (excluding highly halogenated) solvents, including the hydrocarbons.. In this respect it is somewhat surprising that perfluorinated solvents have not been exploited as liquid-liquid extraction reference phases. However, it must be understood that the perfluorinated solvents are so nonpolar and nonpolarizable that there may be some effect of cosolvent, even at very low concentrations of cosolvent, on the spectroscopic properties and chemical potential of a dissolved indicator solute due to solvent sorting (Le., multipolar complexation). By this we mean that the composition of the solvent, in a mixture of two or more solvents, in the immediate vicinity of a solute, i.e., the cybotactic region, may have a composition very different from the bulk average composition. Naturally this effect will strongly depend on the particular solute and cosolvent under investigation. A more general aspect of this work is the experimental determination of A* values for four perfluorinated solvents and their use in assessing the polarizability contributions to the A* scale. A major problem with many solvent strength scales, and therefore the linear free energy relationships based on them, is the limited range of solvents which comprise the scale. Due to their extremely low polarizability, perfluorinated solvents provide a means of extending the experimentally determined A* range by approximately 30%. The significance of this is 2-fold first, any general theoretical model used to described A* must accommodate the extremely negative A* values of perfluorinated Solvents; second, since perfluorinated solvents and hydrocarbons are both nonpolar but differ appreciably in polarizability, an otherwise difficult assessment of solvent polarizability contributions to the A* scale can be obtained. EXPERIMENTAL SECTION The T* indicator solutes used in this study were (numbers following the ?r* indicators are those used by Taft et al. and will be retained here) p-nitroanisole (l), 4-ethylnitrobenzene (4), 4-(dimethy1amino)benzophenone (7), ethyl p-dimethylamino(13),p-nitroaniline(14), benzoate (9), NjV-dimethyl-p-nitroaniline N-methyl-p-nitroaniline (17A), 4-(dimethylamino)benzaldehyde (19), ethyl p-aminobenzoate (20), 4-aminobenzophenone (21), 2-nitro-p-toluidine (23), m-nitroaniline (28), N-methyl-o-nitroaniline (32), o-nitroaniline (33), 2-nitro-p-anisidine (35), NjVdimethyl-4-nitrosoaniline (39), and o-nitroanisole (45). Sources

0.02 0.28 0.01 0.07 0.00 0.17 0.04 0.21 0.55 0.12 0.13 0.05 0.13 0.07 0.26 0.06

n*FC-48

-0.35 -0.37 -0.37 -0.82 -0.27 -0.35 -0.35 -0.56 -0.71 -3.15 -0.34 -0.27 -0.32 -0.36 -0.36 -0.58 -0.27

Table 11. Physical and Solvatochromic Parameters of Perfluorinated Solvents dielectric refractive b solvent constanta indexa n * exptl FC-48 FC-43 FC-84 FC-104

1.94 1.90 1.765 1.85

1.312 1.291 1.258 1.271

-0.33 -0.36 -0.39 -0.41

(k0.04) (i0.05) (k0.05) (i0.04)

a Data supplied by 3M Co., St. Paul, MN. Determined by using results from solutes 1, 4, 7, 13, 14, 17A, 23, 28, 32, 33, 35, and 45.

of the indicator solutes were Aldrich Chemical Co. (1,4, 7,9,14, 19,21,32,39,45),Eastman Chemical Co. (13,17A, 20,28), MCB (23, 35), and J. T. Baker Chemical Co. (33). The solutes were purified by dissolvingthem in dichloromethane (MCB),passing the solution over activated silica gel (J.T. Baker),and evaporating the dichloromethane followed by recrystallization from hot isopropyl alcohol. The purity of the final product was checked by reversed-phase HPLC analysis. The perfluorinated solvents, FC-43 (perfluorotributylamine), FC-104 (perfluorooctane),FC-84 (perfluoroheptane), and FC-48 (perfluorodimethyldecalin) (all perfluoro solvents were provided by the 3M Co.) were purified by passing them over activated silica gel . Samples for spectrophotometry were prepared by equilibrating 10 mL of the perfluorinated solvent with approximately10 mg of the desired solute followed by dilution as necessary. Where possible, a series of concentrationswere prepared by successive dilution. Spectra were obtained on a GCA/McPherson EU-700 spectrophotometer&0.4 nm bandwidth). The concentration range covered was to lo4 M. In some instances,limited solubilityestablished the maximum solute concentration. Samples for the perfluorinated solvent/polar solvent studies were prepared as above except that the samples were saturated with a cosolvent (methanol or acetonitrile as appropriate). The solvent to be used for dilution was prepared in a similar manner. All samples were allowed to equilibrate for at least 1week in the dark (to forestall possible photochemical degradation). The solubility of methanol and acetonitrile in FC-43 was determined by GLC (10% Fluorolube HG1200 on Chromosorb W-HP) using flame ionization detection (Perkin-ElmerSigma 3B gas chromatograph). The results of all the spectroscopic measurements are shown in Table I and appropriately averaged results are summarized in Table 11. The most obvious feature of the data set is the extremely low values of the T* values in comparison to the nalkanes. Experimental T* values were calculated according to previous work (IO) from the equation (1) **exptl = (Vrnax - VO) /S where urn, is the frequency of maximum absorbance for an in-

ANALYTICAL CHEMISTRY, VOL. 54, NO. 11, SEPTEMBER 1982

-

Table 111. Regression Analysis of Solvatochromic Parameter n * case modela regression equation

A B

I IIb

CC

a

D I1 E I11 F IV See Table IV.

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n

r

76 n* = -0.04 + 2.230(e) 76 n * = -1.50 + 2.068(e) t 7.27F(n2) 30 n* = -2.80 t. 7.5Oe(e)+ 13.28F(n2)- 26.560(e)F(n2) 76 .*= -2.54 t 6.790(e)+ 12.41F(n2)-23.160(e)F(n2) n* = 0.51 t 1.19e(e,ec)+ 6.92F(n2,ec) - 16.12e(~,e,)F(n~,~,) 76 n* = 0.49 + 1.12e’(e,ec) + 6.89F’(nZ,ec) - 13.900’(~,e~)FI(n~,e~)76 D, assumed equal to zero (see Table IV). See ref 20.

0.783 0.939 0.966 0.957 0.947 0.951

~~

Table IV. Model Equation for Regression Analysis case model I I1 I11

IV

unmodified Block and Walker (25) series expansion/nonpolarizable dipole/ unit cavity permittivity series expansion/nonpolarizable dipole/ cavity permittivity e C series expansion/polarizable dipole/ cavity permittivity e C

dicator solute in the sohrent in question, vo is nominally the frequency of maximum absorbance for the same indicator in cyclohexane,and s is a memure of the sensitivity of the electronic transition to a changing dielectric environment. Typically, vm= values are reproducible to f0.05 X lo3cm-’. Values for vo and s were taken from a compilation given by Taft et al. (10). A plot of a*erpu against r*dd aa obtained from the model used in this work is shown in Figure 1.

RESULTS .AND DISCUSSION Since the perfluorinat,e!d solvents used in this study have physical properties vastly different from the solvents previously studied by Kamlet, et al. (21), we decided to use all readily available solutes in this study. The occurrence of solutArsolute interactions was discounted since no concentration efifects on a*expu were observed for any solute. A complication in the determination of spectral band position for solutes in these very inert solvents is the presence of vibrational fine structure in the spectra of certain solutes. As in previous work (IO),,A was determined as the midpoint of the line joining the 09.4., points on each side of the band. In some instances, the presence of well-defined fine structure or band asymmetry made this a rather tenuous procedure. In these cases, positions lower on the band were used. One anticipates that d l solutes should yield the same value of a* and that the a* values of all the perfluorinated solvents should be similar since they are nonpolar and non hydrogen bonding. Plots of a*erptlv13. solute number are shown in Figure 2. In pure FC-43, the extremely negative values for solutes 9, 19, 20, 21, and 39 are immediately apparent. We should emphasize that the difference between the ~ * ~ r p values tJ between this group and tlhe remaining solutes is well beyond experimental error. The main feature that distinguishes this group of solutes from the remaining solutes is the presence of a double bonded oxygein group in either carbonyl or nitroao functionalities. Note that solute 7 is the only carbonyl containing solute not displaying anomalous behavior. At this time it is difficult to assess whether this clustering with respect to functional group is real or happenstance. All solutes displaying obvious fine striicture (9,19,20,39) or asymmetry (21) belong to this class. We have been informed that this peculiar behavior of carboinyl and nitroso compounds does not take place in more polar solvents (M. J. Kamlet, personal communication). It is unfortunate that such a common functional group as the carbonyl moiety behaves in such peculiar fashion. A definitive explanation eludes us. The extremely negative values for a* for perfluorinated solvents relative to the a* values of hydrocarbons (a*hexane = -0.08) are quite consistent with conventional chromato-

equation T * = A , + B1e(E) n* = A , + B , e ( e ) +

cp(n2)+ D 2 e ( e ) F ( n 2 ) n* = A , + B 3 t I ( e , e C+ ) C 3 E ( n 2 , e C+) D,e ( e , E c ) F ( n 2 , e c ) II*= A , + B4e’(e,eC)+ C4Fl(nZ,ec)+ D4e’(e,e,)r(n21eC)

c

/

/

c 1.00

-

.eo

-

2 0

-

d

*f*

t

A

aprolic aromallc

x polychlorinated -.20

0

r

Pnrfluorlnalnd

Flgure 1. Plot of a*axptl agalnst a*calcd (case D, Table 111).

- 0O. 2 0

.

O

O

S O L U T E NUMBER

Flgure 2. Plot of a*exptl agalnst solute number for perfluorinated solvents studled.

graphic scales of solvent strength such as the solubility parameter (6) and Snyder adsorption (to) scales. That is, fluorocarbons are extremely nonpolar. These experimental results of the a* values are important since they clearly indicate the extent to which the original single parameter correlation of a* against @(e) (12) is inadequate (see Table 111,case A) not only as a general correlation equation (as has been indicated by Taft et al. (20))but more importantly as an indicator of the experimental range of a*.

~

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ANALYTICAL CHEMISTRY, VOL. 54, NO. 11, SEPTEMBER 1982

0.00

-

-0.20

-

-0.40

-

0.20

* *)

+

-0.20

* +* + +

o.zol

:**+11:+

0.00 -0.20

I

0.20t

I

I

I

I

-0.20

I

I

I

I

I

I

0.20

I 'I

o.eo

(El

I

I

1

I

I

I

f

1.00

l-r:xP..

Flgure 3. Plots of AT* (= a*,lcd against a*exptl for the varlous models studied. The y axis Is centered at the average a*,#, value for the data set used (a*ewt,,tl,av = 0.58): (A) case A, Table I11 [crosses denote nonpolar solvents (e = 1.765 to 2.42) while the remaining solvents are represented by open clrcles]; (B) case B, Table 111; (C) case D, Table 111; (D) case D, Table 111, polychlorinated solvents only; (E) case D, Table 111, aromatic solvents only.

The minimum A* value predicted by the correlation of a* against @(e) is -0.04, this corresponds to 0 ( e ) = 0, Le., the gas phase. Clearly, polarizability must be a major contribution to a* to explain the very negative values of the fluorocarbon solvents. The necessity of including solvent polarizability is most clearly seen in a plot of 7r*dd against a*exptl for the nonpolar solvents, as shown in Figure 3 (curve a) in which a*,.dd were obtained from Table 111, case A, wherein solvent polarizability is ignored. In contrast, the residuals (see Figure 3, curve C), i.e., plot of a*dd - ~*~lrptl, are much better behaved (randomly distributed) when ?T*c&d is obtained from the equation given in Table 111,case D, where solvent Polarizability is included in the model. Recently, Taft, Abboud, and Kamlet (20)presented an "all solvent" correlation equation for a* in terms of b (molecular dipole moment), the function F(n2)(see the Appendix), and a cross term in these two variables. Using their results, we compute a* to be -0.28, -0.38, -0.46, and -0.52 for FC-48, FC-43, FC-104, and FC-84, respectively. These values should be compared to the results listed in Table 11. This agreement is surprisingly good in view of the significantly more positive a* values encompassed by their data set. Since a correlation of e(€) with p has been previously noted for the select solvent set (12),a multiple parameter correlation of a* against e(€), F(n2),and 8(e)F(n2)as used by us might be formally equivalent to that presented above. In fact, if the two correlation equations are compared by substituting the correlation of b against e(€),obtained for the select solvent set (I2),into the equation presented by Taft et al. (20)the result is as given in Table 111, case C. Note also, Table 111, case D, the result of a general least squares obtained by us.

A plot of a*,xptlagainst T*c&d, where a*&d as obtained from case D, is shown in Figure 1. The similarity of cases C and D is reasonable when one allows for the difference in data sets used to determine the two equations. For the purposes of correlation, either equation appears suitable. Note that both equations predict a gas-phase a* value in the range -2.5 to -3.0. This is much more negative than the value of -0.54 previously suggested by Bekarek (32,33)and does seem more reasonable in light of the a* values the perfluorinated solvents presented here. It is most interesting to note that both aromatic and polychlorinated solvents are rather evenly distributed about the correlation line shown in Figure 1. This behavior of chlorinated and aromatic solvents is never seen to be the case in correlations of rate and equilibriumprocesses against a*. Taft and co-workers have found it necessary to introduce a second ad hoc parameter to fit such solvents. This is not the case with the present work and is an encouraging observation indicating that solvent polarizability contributions to n* are well represented via the Onsager reaction field. We hasten to point out that while plots of the residuals (?r*,&d - a*exptl) against (Figure 3) display no correlation for aromatic solvents, some correlation is noted for polychlorinated solvents. Moreover, the actual magnitude of the scatter is much greater for polychlorinated solvents. A reasonable concern is whether the quality of the correlation obtained can be improved by eliminating the assumption that the solute dipole is nonpolarizable. This issue has been mentioned by Taft et al. (12). They maintain that the effect is small; however, they have not presented an "all solvent" correlation to support their contention. The two additional correlations corresponding to cases I11 and IV of Table I were run. As noted in the Appendix, a cavity permittivity of 2.25 and dipole polarizability of 0 . 2 9 4 ~were ~ ~ used. The results of these correlations are given by equations E and F in Table 111. We should mention that in all cases dioxane was excluded from correlations (see below). The marginal change in correlation coefficient for the three cases indicates that none of the models is demonstrably superior. In fact, plots of against a*&d for the three cases are virtually superimposable. Both the polychlorinated solvents and dioxane are not well fitted to the model equation. We believe that this is a consequence of their polyfunctionality. In essence, the parameter t is a bulk property whereas what matters is the dielectric constant local to the solute. In the case of polyfunctional solvents we believe that the local electrostatic environment and the bulk dielectric constant are not necessarily well correlated. This is a direct consequence of the solute's ability to disturb the statistical averaging of the various conformers (e.g., chair-boat, gauche-anti). The preservation of this averaging of conformers and orientations is implicit if bulk parameters are to be used as input to the model equations. A prime example of this effect is the a* behavior of dioxane. On the basis of dioxane's bulk dielectric constant and refractive index, a a* value of 0.26 would be calculated from case D of Table I11 while a value of 0.55 is observed experimentally (compared with a* = 0.58 for tetrahydrofuran). Clearly, in the vicinity of the polar solute, the conformational equilibria is shifted from the nonpolar chain form to the polar boat form (IO). This effect has also been noted for vicinal dihalo compounds (32). As a final point on the adequacy of the present model, one should note that the model assumes that the dependence of dielectric constant on distance from the solute cavity is independent of the size of the solvent molecule. Intuitively the rate of increase in dielectric constant outside the solute cavity should depend to some extent on the dipole density outside

ANALYTICAL CHEMISTRY, VOL. 54, NO. 11, SEPTEMBER 1982

the cavity, which is in turn related to the molecular volume of the solvent molecule. The Block and Walker reaction field has also been critized ($4)as being too slowly varying to be a real reflection of what i~ioccurring in the immediate vicinity of the solute. This critiicism is probably quite valid. Mixed Solvent Behavior. The data pertaining to the FC-43, FC-43/acetonitrile9and the FC-43/methanol systems contain a number of interesting points relating to solute behavior. In both mixed solvent systems, if a shift in a*exptl occurred, it was generally toward more positive values (solute 14 in FC-43/methanol being a notable and significant exception). This is the expected direction if the cybotactic region about the solute were more polar due to an increased local concentration of polar cosolvent. The greater positive shift seen with acetonitrile as cosolvent is presumably a reflection of its larger dipole moment, 3.44 D vs. 2.87 D for methanol. The solubilities of methiinol and acetonitrile in FC-43 are of comparable magnitude, 0.012 and 0.018 mole fraction, respectively, and in large excess compared to the solute concentration. For this reason, the enhanced positive shift with acetonitrile relative to mlethanol as cosolvent does not appear to be due to the concentration of the cosolvent. Convolved with gross dielectric effects on the cybotactic region is the possibility of hydrogen bonding. Methanol, and to a much more limited degree acetonitrile, can participate in hydrogen bonding (CYCH,CN= 0.15, OCH~CN= 0.31, ~ C H ~ O=H0.98, PCH,OH = 0.62, CY and P being solvatochromicallydetermined proton donating and accepting ability, respectively). Solutes 1,4,32, and 45 have been shown1 to be minimally influenced by hydrogen bonding. All the remaining solutes can act as acceptors while solutes 14, 17A, 20, 21, 23,33, and 35 also have appreciable donor characteristics. If hydrogen bonding plays a significant role in the solvatochromic shifts, the a* values of FC-43/methanol would be shifted positive relative to those for FC-43/acetonitri1ea This does not appear to be the case, thus the mixed solvent systems appear to be dominated by dipolar effects. An interesting exception to this trend is shown by solute 14, p-nitroaniline. The large hypsochromic shift suggests that hydrogen bonding occurs. The band for solute 14 in FC-43/CH30H is noticeably broadened relative to the band seen in either FC-43 or FC-43/CH3CN. The meta and ortho isomers of solute 14 (28 and 33, respectively) display similar behavior but to a lemer extent. The meta isomer shows a much smaller hypsochromic shift in FC-43/methanol relative to FC-43 while the ortho isomer has a bathochromic shift. It is evident that smaill amounts of both methanol and acetonitrile have a great effect on some of the indicators; yet these indicators show no sign of self-association, i.e., a* is independent of solute concentration. Both acetonitrile and methanol are much smalleir than either perfluorinated solvent molecules or the a* indicator solute molecules. A recent study of oxygen solubility in perfluorinated solvents (35) emphasizes that the bulky nature of perfluorinated molecules may be a major factor in the abilig of these solvents to dissolve large quantities of gases. The bulky structure leads to looser molecular packing, hence larger “holes”which can accommodate the solute without displacement of the solvent. It is reasonable that the solute cavity of a single indicator molecule surrounded by lbulky perfluorinated solvent molecules may be able to accommodate a small polar molecule without significant restructuring of the cavity while accommodation of a large molecule, such as another indicator solute molecule, may require a restructuring of the cavity. We should note that the extreme nonlpolar nature of the perfluorinated solvent environment favors the energetics of this type of interaction. Treatment of all FC-43, FC-Q3/acetonitrile, and FC-43/ methanol data by analy& of variance indicates that real

1755

differences exist between both solutes and solvents when all solutes are considered. When the solute set is restricted to solutes 1, 4, 13, 23, 32, 33, and 45, there appears to be no statistical difference between the solvents though a statistical difference between solutes still exists. In fact, the a* values obtained with both pure solvents and those obtained with solvent mixtures correlated with one another as the test solute is varied. The practical implication of this is that for the set of a* indicators investigated here, phase equilibria experiments using a perfluorinated reference phase must use solutes from the set 1, 4, 13, 23, 32, 33, 45. Solutes not in this set (7, 9, 14,17A, 19,20,21,35,39)are subject to preferential solvation in the presence of small amounts of polar cosolvent. This would clearly have an effect on the measured partition coefficients and is unacceptable for the purposes of liquidliquid equilibria experiments.

SUMMARY The a* values of four perfluorinated solvents, FC-48, FC-43, FC-84, and FC-104 have been determined to be -0.33, -0.36, -0.39, and -0.41, respectively. Comparison of a* values obtained for hydrocarbon solvents and perfluorinated solvents indicates solvent polarizability, Le., inductive interaction, comprises a major portion of a*. For the purposes of liquid-liquid extraction experiments, solutes 1, 4, 13, 23, 28, 32, 33, and 45 are not subject to preferential solvation in perfluoro/polar mixed solvent systems. ACKNOWLEDGMENT We wish to acknowledge the 3M Co. of St. Paul, MN, and Larry Winter of 3M for their gift of the various fluorocarbon solvents used in this work. We also wish to acknowledge the Graduate School of the University of Minnesota for a graduate research fellowship and DuPont for a summer fellowship to James E. Brady, as well as the National Science Foundation for a grant (CHE-8205187)in support of this work. APPENDIX Model I (Nonpolarizable Solute, Cavity Dielectric = 1.0). The model used by Taft et al. (12) is based on the following assumptions (1) The solute dipole is a nonpolarizablepoint dipole. The dipole moment of a point dipole comprised of charges q+ and q- can be represented as

where 1 is the distance between the equal but opposite charges. (2) The solute dipole is situated at the center of a spherical cavity of radius a and dielectric constant unity. (3) The solute cavity is present in a dielectric continuum, i.e., unstructured media, of bulk dielectric constant e. (4) Due to dielectric saturation the dielectric constant outside the cavity varies with distance r , as measured from the center of the cavity, and asymptotically approaches the bulk value in accord with the Block and Walker equation (36) t(r) = t exp(-(a In e)/r) r >a (3) Under these assumptions Block and Walker found that the reaction field (i.e., electrostatic potential field) will be given by 6

- -- 2 1

(4)

Kirkwood (37) has shown that the work of charging a dipole under the influence of the potential due to a reaction field will be

W = -(1/2)pER’

(5)

1756

ANALYTICAL CHEMISTRY, VOL. 54, NO. 11, SEPTEMBER 1982

Note that a dot product is used since both p and ER’ are vector quantities. Thus combining eq 4 and 5 leads to ..2 LEL

. I

W = ---e(€)

This corresponds to Block and Walker model I11 (see above). Note also that if the dipole is polarizable eq 16 becomes

2 a3

e(€)is defined

e(€)

3~ In E 6 e l n ~ - e + l 1nE

2

(7)

Thus according to the Block and Walker model the only solvent-dependent parameter involved in establishing the energy of a dipole-dipole solute-solvent interaction is the function €)(e) provided that one assumes that the cavity size (a) is determined solely by the solute size and not the solvent size. We have previously used eq 12 to predict solvent orientation solubility parameters (30) with fair success. Model I1 (Polarizable Solutes). Several of the above assumptions can be eliminated quite easily. If the solute is allowed to have an average electronic polarizability, a,and the polarizability is estimated from the well-known LorenzLorentz function

then the resulting reaction field will be

The derivation of eq 9 requires the assumption that CY is a scalar. This will only be true for a spherical molecule. Model I11 (Cavity Dielectric > 1.0). If the assumption of a nonpolarizable solute is retained but the solute cavity is assumed to have a dielectric constant E, > 1.0 the relevant mathematical problem can be solved. The resultant reaction field will be

E”’R =

P a3

(10)

with

Model IV (PolarizableSolute, Cavity Dielectric > 1.0). If both of the above complexities are allowed to occur si-

This corresponds to Block and Walker model IV (see above). One should also note that the introduction of solute dipole polarizability and a cavity permittivity greater than unity result in opposing effects. In real molecules both forces are operative and will serve to counteract each other. A final important point relates to the location of the point dipole which is assumed to be at the center of the spherical cavity. Bottcher (39),using the Onsager approach, has shown that the position of the dipole has a large influence on the reaction field. However, the effect is only slightly dependent on the solvent’s dielectric constant. The total dielectric constant of a fluid arises from two processes: polarization of the electronic structure of the material and orientation of the molecular dipoles. The first component is often referred to as the optical dielectric constant or the high-frequency dielectric constant and is equal to the square of the refractive index (n2). Electronic polarization should not be as subject to saturation effects, as are orientation processes, near moderate dipoles (1-14 D) and therefore should be very well described by the Onsager reaction field. In contrast dipole-dipole orientation interactions will be subject to saturation and therefore should be described by the Block and Walker reaction field. Since we anticipate some interaction between the dependence of n* on e(€) and F(n2),e.g., as shown in eq 4, we have adopted an approach used by Buckingham (40) in his treatment of reaction field parameters in infrared spectroscopy. In essence the reaction field will be represented as a weighted linear sum of e(€), F(n2) and a cross term in these two functions. Recent work by Ehrenson (41) has criticized this approach when used by others (20) since it neglects terms such as @(e) but retains a cross term. As a first approximation let the dependence of R* on @(e) and F(n2)be represented as

multaneously then the resultant field will be

n* = AO(e)

Model V (Classical Onsager Model and Modifications). For sake of completeness, later correlations, and our belief that the Onsager reaction field (38) is a more accurate representation of the effect of solvent polarizability on inductive interactions than is the Block and Walker approach, we will treat this situation. Note that premises 1-3 &rethe same, premise 4 is modified so that the bulk dielectric constant is achieved at the cavity surface. For a cavity permittivity of unity the Onsager reaction field is given by

ER,O= ( p / a 3 ) F ( e )

(14)

This corresponds to Block and Walker model I (see above) while that for a cavity permittivity of e, is

+ BF(n2)

(19)

Now let us recognize that the ability of the solute dipole to interact with the electronic polarizability of the solvent (i.e., dipole-induced dipole interactions) will depend upon the orientation of the solvent with respect to the solute. Under this condition it is reasonable to expect that B will depend upon e(€).This dependence is written as B = B’+ B’w(e) (20) Insertion of eq 20 into 19 results in g*

= A0(e)

+ B’F(n2)+ B”O(e)F(n2)

(21)

Since the n* indicator solutes typically have a refractive index of the order of 1.5 (42),e, will be estimated as 2.25 (i.e., n2),while the average dipole polarizability, a,will be given by 0 . 2 9 4 ~(see ~ eq 8). These are clearly very crude order of magnitude estimates; however, they should give some insight into the adequacy of the simplest formulations.

LITERATURE CITED (1) Grifflths, T. R.; Pugh, D. C. Coord. Chem. Rev. 1979, 29, 129-211. (2) Koppel, I . A.; Palm, V. A. “Advances in Linear Free Energy Relationships”; Chapman, N. B., Shorter, J., Eds.; Plenum Press: New York, 1972; Chapter 5.

Anal. Chem. 1982, 54, 1757-1764 (3) Relchardt. C. "Solvent Effects in Oraanlc Chemistry"; Verlag Chemie: Welnhelm, 1979. Grifflths, T. R.; Pugh, D. C. J . Solutlon Chem. 1979, 8 , 247-258. Snyder. L. R. "Prlnclples of Adsorption Chromatography"; Marcel Dekker: New York, 1968. Snyder, L. R. J . Chronripfogr. 1974, 92,223-230. Keller, R. A.; Karger, E. L.; Snyder, L. R. "Gas Chromatography 1970"; Stock, R., Ed.; Institute of Petroleum, London, 1971. Karger. B. L.; Snyder, L. R.; Eon. C. J . Chromafogr. 1978, 125, 71-88. Karger, B. L.; Snyder, L. R.; Eon, C. Anal. Chem. 1978, 50, 2 126-2 136. Kamlet, M. J.; Abboud, J. L.; Taft, R. W. J . Am. Chem. SOC. 1977, 99,6027-6038. Abboud, J. L.; Kamlet, M. J.; Taft, R. W. J . Am. Chem. SOC. 1977, 99,8325-8327. Abboud, J. L.; Taft, R. VV. J . Phys. Chem. 1979, 83,412-419. Kamlet, M. J.; Taft, R . W. J. Chem. Soc., Perkin Trans. 2 1979, 337-341. Kamlet, M. J.; Jones, M. E.; Taft, R. W.; Abboud, J. L. J. Chem. SOC., Perkin Trans. 2 1979. 342-348. Kamlet, M. J.; Jones, M. E.; Taft, R. W.; Abboud, J. L. J . Chem. Soc., Perkin Trans. 2 1979, 349-356. Taft, R. W.; Kamlet, U. J. J. Chem. Soc., Perkin Trans. 2 1979, 1723-1729. Kamlet, M. J.; Solomonovlcl, A.; Taft, R. W. J . Am. Chem. SOC. 1979, 101, 3734-37311. Kamlet, M. J.; Hall, T. hi.; Boykln, J.; Taft, R. W. J . Org. Chem. 1979, 44, 2599-2604. Taft, R. W.; Plenta, N. J.; Kamlet. M. J.; Arnett, E. M. J . Org. Chem. 1981, 4 8 , 661-667. Taft. R. W.; Abboud, J. L.; Kamlet, M. J. J . Am. ChSm. SOC. 1981, 103, 1080-1086. Kamlet, M. J.; Abboud,, J. L.; Taft, R. W. Prog. Phys. Org. Chem. 1980, 13, 485-630.

1757

(22) Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. "Regular and Related Solutions"; Van Nostrand-Reinhold: Princeton, NJ, 1970. (23) Scatchard, 0.Chem. Rev. 1931, 8 ,321-333. (24) Scatchard, G. Chem. Rev. 1949, 4 4 , 7-35. (25) Hlldebrand, J. H. Proc. Nafl. Acad. Sci. 1979, 76, 6040-6041. (26) Halicloglu, T.; Sinanoglu, 0. Ann. N . Y . Acad. Sci. 1969, 158, 308-317. (27) Slnanoglu, 0. Inf. J. Quantum Chem. 1980, IS,381-392. (28) Horvath, C.; Melander, W.; Molnar, I. J. Chromafogr. 1976, 125, 129-158. (29) Melander, W.; Campbell, D. E.; Horvath, C. J. Chromatogr. 1978, 158,215-225. (30) Carr, P. W. J. Chromatogr. 1980, 194, 105-119. (31) Kamlet, M. J.; Carr, P. W.; Taft, R. W.; Abraham, M. H. J. Am. Chem. SOC. 1981, 103, 6062-6066. (32) Bekarek, V. Collect. Czech. Chem. Commun. 1980, 45,2063-2069. (33) Bekarek, V. J. Phys. Chem. 1981, 85,722-723. (34) Ehrenson, S. J. Compuf. Chem. 1981, 2 , 41-52. (35) Hamza, M. A.; Serratrice, G.; Stabe, M. J.; Delpuech, J. J. J . Am. Chem. SOC. 1981, 103, 3733-3738. (36) Block, H.; Walker, S. M. Chem. Phys. Len. 1973, 79,383-364. (37) Klrkwood, J. G. J . Chem. Phys. 1934, 2,351-361. (38) Onsager, L. J . Am. Chem. SOC. 1938, 58, 1486-1493. (39) Bottcher, C. J. F. "Theory of Electric Polarization", 2nd ed.; Elsevier: Amsterdam, 1973; Vol. I. (40) Buckingham, A. D. Proc. R . SOC. London, Ser. A 1958, A248, 169-182. (41) Ehrenson. S.J . Am. Chem. SOC. 1981, 103,6038-8043. (42) Weast, R. C., Ed. "Handbook of Chemistry and Physics", 61st ed.; CRC Press: Boca Raton, FL, 1980.

RECEIVED for review August 20, 1981. Resubmitted and accepted June 1, 1982.

Electrochemical Detection with a Regenerative Flow Cell in Liquid chromatography Stephen 0. Weber" Department of Chemlstty, ildniversi@ of Pittsburgh, Pittsburgh, Pennsylvania

15260

William C. Purdy Department of Chemlstty, McGiIl Unlversl& 80 I Sherbrooke Street, West, Montreal, Quebec, H3A 2K6 Canada

The regenerative detector studied has two worklng electrodes, one an anode arid one a cathode, placed parallel to one another and close to each other. Solution containing depolarizer flows In the thln channel between them. I n such a detector the product of the electrode reaction at one electrode can dlffuse to the1 opposlte electrode where starting material may be recreated. Thls leads to a current ampllflcation with respect to a coulometric detector. A simple theory allows the derivation of equatlons relating current to system variables; for example, for current measured at an anode and a reduced deiaolarizer, i = nFCo(AD/b 4- 0.278) where A Is electrode area, D is dlffusion coefflclent, b is the distance between the electrodes, and U is the volume flow rate. The equatlons expllaln observed data well. To use the cell It Is required that the large nolse current generated by the low cell impedance be defeated. Thls Is possible by swltchlng the worklng electrodes In and out of the current to voltage conversion circuit. A duty cycle of a few percent yields picogram detection limits; for 2,4-toluenedlamlne following chromatography in an aqueous methanol solvent.

In any system of detection it is desirable to increase sensitivity if one can do so with less than a concomitant increase in noise. Expressions for the signal intensity are known for the various sorts of electrochemicaldetectors, the channel (I, 2), the tubular ( 3 , 4 ) ,and the wall-jet (5), and for hydrody-

namic electrode detectors in general (6). Far less is known about the noise. In the absence of specifics it has become custom to assume that the noise is proportional to electrode area (7). Qualitatively, at least, this relationship seems to be followed, although certainly many more variables enter into the relationship. Thus if one can increase the sensitivity of an electrochemical detector without increasing the electrode area, one will likely have a device with improved limits of detection. Regenerative flow cells satisfy this criterion. In a regenerative flow cell one converts analyte which has reacted at a working electrode back to its original form using physical (8, 9) or chemical (IO)methods. The latter cells involve the "catalytic" reaction (11)in which analyte A is regenerated using reagent C

A

B

+C

-

-+ k2

A

B (electrode)

products

(homogeneous)

The current to be expected from this system in a flow cell has been determined by Aoki et al. (12).The physical regeneration occurs because of a second electrode placed parallel and opposite to the first electrode so that one has the following scheme A

B

--

B (electrode 1)

A (electrode 2)

0003-2700/82/0354-1757$01.25/00 1982 American Chemical Society