Ind. Eng. Chem. Res. 1993,32,943-951
943
Spectroscopic Measurement of Local Compositions in Binary Liquid Solvents and Comparison to the NRTL Equation Daniel J. Phillips and Joan F. Brennecke’ Department of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana 46556
In this paper we compare the local compositions of solvents around a solute predicted from the nonrandom two-liquid (NRTL) equation with experimental spectroscopic measurements of the local compositions to test the ability of the thermodynamic equation to model the true local environment. Shifts in the wavelength of maximum absorption of the solvatochromic probe phenol blue are used to estimate the local compositions. Mixtures investigated include acetone/cyclohexane, triethylaminelcyclohexane, ethyl butyrate/cyclohexane, cyclohexanone/cyclohexane,toluene/cyclohexane, acetophenonelcyclohesane,acetophenone/toluene, and ethyl butyrate/cyclohexanone. Comparison with the NRTL equation requires the interaction energies between the phenol blue and each of the solvents, and these parameters are determined from the solubility of phenol blue in the pure solvents. In most cases the measured local compositions compare reasonably well with those predicted from the NRTL equation. Spectroscopic measurements such as these are very useful in testing and refining thermodynamic models.
Introduction The local composition of the solvent species around a dilute solute dissolved in a solvent mixture can be significantly different than the bulk composition. Understanding the solvation of solutes in mixed solvents is of importance in solution thermodynamics and solution chemistry. Besides influencing solubility and phase behavior, preferential solvation has been shown to affect reaction rates (Sastri et al., 1972;Langford and Tong, 1977; Kolling, 1991). Correspondingly, the idea of local compositions or preferential solvation (these two terms will be used interchangeably) has pervaded the literature in at least three areas. It is central to the development of a variety of thermodynamic models, it has been studied by simulations and related to bulk thermodynamic measurements through the Kirkwood-Buff integrals, and it has been observed in a wide variety of spectroscopic measurements. Local compositions that differ from bulk conditions are the basis of several well-accepted thermodynamicmodels, including Guggenheim’s quasi-chemical theory (Guggenheim, 1952), the Wilson equation (Wilson, 1964), the NRTL equation (Renon and Prausnitz, 1968), and the UNIQUAC equation (Abrams and Prausnitz, 1975;Maurer and Prausnitz, 1978). The basis of all these models is that the local mole fraction of one component around another is different than the bulk mole fractions and is related to the strength of the interaction energy between the species. The details of the models vary. Quasi-chemical theory is based on alattice model that relates the localmole fractions to the interaction energies and a fiied lattice coordination number. Wilson’s equation is based on loose semitheoretical arguments that local mole fractions should be related to the bulk through the Boltzmann factor and uses local volume fractions instead of local mole fractions to calculate the Gibbs free energy of mixing. The NRTL equation abandons Guggenheim’s lattice theory and introduces a nonrandomness parameter, a,essentially in the place of the lattice coordination number. Like NRTL, UNIQUAC retains the Boltzmann factor relationships but uses surface fractions and divides the molecules into segments, introducing the group contribution idea. All of
* Author to whom correspondence should be addressed.
these equations are engineering models or approximations that can be improved. For instance, Lambert et al. (1992) have used Monte Carlo simulations to determine true coordination numbers and obtained better representation of liquid/liquid equilibrium (LLE). Nonetheless, the local composition equations have been very successful in correlating experimental data. The UNIQUAC equation is widely used in industry and the NRTL equation has been very effective in modeling LLE, which cannot be predicted by many of the other excess Gibbs free energy models. Local compositions can result from either a significant size difference and/or a difference in the strength of interaction between the species. If the molecules are of different sizes, one type of molecule may simply pack better around a central molecule. Conversely, difference in interaction energies can result either from specific attractions like hydrogen bonding where the interaction is dependent on the angle and position of the molecules or from nonspecific interactions between the species such as dipoleldipole or van der Waals forces. Therefore, in the case of a polar solute in a liquid mixture containing similar size polar and nonpolar components, one would expect the local composition of the more polar solvent around the solute to be higher than in the bulk. Suppan (1987) describes this phenomenon as dielectric enrichment. Specific chemical forces and dielectric enrichmentare very different in terms of local compositions. While strong dipolar or dispersive forces will tend to increase the local composition of that species, this will not necessarily be the case for asolvent that can hydrogen bond with a solute. Since complexes are of fixed stoichiometry, once the required number of solvents is present there may not be any further attraction for that solvent. Molecular dynamics simulations confirm the existence of preferential solvation (Narusawaand Nakanishi, 1980; Hoheisel and Kohler, 1984). For a dilute solute dissolved in an equimolar mixture of equal size Lennard-Jones particles with different interaction energies, local compositions can be on the order of 75/25rather than 50150. Correspondingly, the first peak in the radial distribution function of the excluded species can be lower than its second peak (Narusawa and Nakanishi, 1980). In mixtures of molecules of significantly different sizes packing effects may be dominant, and may be of opposite sign to the effect
0888-5885/93/2632-0943$04.00/00 1993 American Chemical Society
944 Ind. Eng. Chem. Res., Vol. 32, No. 5, 1993
caused by the difference in attractive forces (Hoheiseland Kohler, 1984). It is possible to calculate local compositions from the Kirkwood-Buff integrals (Rubio et al., 1986; Ben-Naim, 1988) as long as one chooses a reasonable cutoff distance of the radial distribution function to be used in the definition of "local". Since the Kirkwood-Buff integrals can be calculated from macroscopic thermodynamic data, such as the compressibility, excess volumes, and excess Gibbs energies, this provides an independent method to estimate local compositions. Moreover, it provides an alternate means to test local composition models from the measurement of thermodynamic properties. A number of spectroscopic probes are sensitive to the local environment, including the local composition in a mixed solvent. These techniques include nuclear magnetic resonance (NMR) chemical shifts, NMR relaxation times, fluorescence lifetimes, and UV-vis absorption maxima. Since spectroscopicprobes measure their environment on a molecular scale, they are particularly well-suited for the measurement of local compositions. The main difficulty is the interpretation of the spectroscopic data since most of the techniques were developed based on the experimental observation that in some liquid mixtures the measured property did not vary linearly between that of the pure solvents. Conversely,in mixtures of solventsthat are similar in size, shape, and energy, the measured quantity would vary linearly. In most cases, the analysis requires some assumptions. For instance, in NMR one must assume that the magnetic coupling between agiven solvent molecule and the atom on the molecule of interest is independent of the overall composition of the solvation sphere (Frankelet al., 1970). As such, one neglects secondorder effects but this may be a reasonable assumption, especially for nonelectrolytes. The method to determine the degree of preferential solvation from NMR shifts and relaxation times was developed by Frankel et al. (1970) and has been used extensively, especially for ions in mixed aqueous solvents (Covington and Newman, 1979,1988;Remerle and Engberts, 1983; Covington and Dum, 1989). Suppan (1987) discusses how the local polarity of solvent mixtures can influence the excited-state lifetime of fluorophores. Measurement of the absorption maximum of a chromophore in mixed solvents, the method pursued in this study, was used by Kim and Johnston (1987) and Yonker and Smith (1988) to investigate the preferential solvation of a solute by a cosolvent in supercritical fluid mixtures. They found dramatically increased local compositions of the cosolvent, much greater than will be reported here for liquid solutions. In the studies most closely related to the work presented here, Bagchi and co-workers ( M d d a et al., 1988; Chatterjee and Bagchi, 1990,1991)used the probe N-alkylpyridiniumiodideto measure preferential solvation in liquid mixtures. Unfortunately, all of those mixtures contained either water or alcohols and the complications caused by the self-association of those species was not addressed. In this study we will limit ourselves to solvents that do not show any indication of hydrogen bonding with themselves or with the other solvent. Clearly, the local composition or preferential solvation measured from spectroscopy is related to those predicted by thermodynamic models and simulations, and this has been recognized by a number of authors (Marcus, 1983, 1988, 1989; Chatterjee and Bagchi, 1990; Kim and Johnston, 1987). Spectroscopicmeasurements reflect the true interactions on a molecular scale and provide an independent measure of local compositions not based on
"I
Ground State
'J
Excited State
Figure 1. Ground state and excited state of phenol blue.
thermodynamic measurements. However, only in the case of Kim and Johnston (1987) for an equation of state with density-dependent local composition mixing rules for supercritical fluid mixtures has a comprehensive comparison been made between the spectroscopic measurements and a practical thermodynamic model. Therefore, the purpose of this work is to measure local compositions in binary liquid solutions using absorption spectroscopy and compare those values to ones predicted by the NRTL equation. Liquid solvents will be limited to those that do not self-associateor combinewith the other solvent through hydrogen bonding and to mixtures that are roughly similar in size. Experimental Section
Materials and Equipment. The solvatmhromic probe, phenol blue (N&-dimethylindoaniline, -97 % 1, was used as received from Aldrich Chemical Company. It matched the melting point of the pure solid within 1 "C. The solvents obtained from Aldrich (triethylamine, acetophenone, and ethyl butyrate) and those from Fisher Chemical (cyclohexane, cyclohexanone, toluene, and acetone) were all certified ACS reagents (>99% ) and used without further purification. The UV spectrophotometer used was a Cary 1by Varian. The wavelengths measured fell in the visible region between 450and 750 nm, and points were taken at intervals of 0.5 nm. The sample cell was a clear glass cell with path length of 1cm. All mass measurements were performed on a Mettler AE50 digital analytical balance and were accurate within 0.0001 g. Procedure. The determination of the local composition of the two solvents around phenol blue in various mixtures was based on the wavelength of maximum absorption of the probe. A trace amount (1 X 106 to 3 X 106 mole fraction) of phenol blue was dissolved in mixtures in which the concentrations of the cosolvents were varied. Since the solute is so dilute, one can effectivelyneglect any solute/ solute interactions and only be concerned with the distribution of the two solvents around the solute probe. At room temperature (26.0 & 1.0 OC) and atmospheric pressure, the solutions (each with a different concentration of the two cosolvents) were analyzed in the spectrophotometer. Experiments scanned the entire composition range, typically with nine different concentrations of the binary solvent mixtures. The wavelength of maximum absorption was taken as the average of several readings (typically between 5 and 16). It was observed that the wavelength of the peak in the solutionsdiffered nonlinearly between each of the pure solvents, as will be discussed in detail below. The physical significance of the wavelength shift between the two cosolvents can be explained by examining the difference between the dipole moment of the excited state and that of the ground state. (SeeFigure 1.) The dipole moment of the excited state is approximately 2.6 D greater than that of the ground state. A more polar solvent would therefore support the excited state to a greater degree, slightly lowering the energy of that state. This leads to a smaller transition energy gap between the ground state and excited state of phenol blue in the more polar solvent. Since the transition energy is related to the wavelength by ET = hc/X, the more polar
Ind. Eng. Chem. Res., Vol. 32, No. 5, 1993 946 solvent results in a longer wavelength of maximum absorption (Kim and Johnston, 1987). Predicting the local composition using the NRTL equation requires the solubility limit of phenol blue in the various pure solvents in order to determine the interaction energies. The solubility was determined for each solvent at 25.0 f 1.0 "C by contacting the liquid with an excess of the solid phenol blue and stirring vigorously. The saturated liquid was diluted and analyzed by UV-vis absorption spectroscopy. The absorption was used in conjunction with an independently determined Beer's law plot to calculate the maximum solubility of phenol blue in that solvent. Solubilities were determined in this fashion in each solvent two or more times to ensure reasonable reproducibility (&lo%1.
NRTL Equation The local compositions measured with UV-vis spectroscopy will be compared to those predicted from the nonrandom two-liquid equation (NRTL) developed by Renon and Prausnitz (1968). The NRTL equation was chosen simply as an example of one of the localcomposition models and because it has been relatively successful in reproducing liquid-liquid equilibrium, which is a more stringent test than vapor-liquid equilibrium of an excess Gibbs free energy model. In a simple binary mixture the ratio of the probability of finding a molecule 2 around a central molecule 1to the probability of finding a molecule 1 around central molecule 1 can be defined in terms of bulk mole fractions and interaction energies between 2-1 and 1-1 pairs of molecules (g21 and g d :
--- ~2 ex~(-a1&21lRT) ~ 2 1
(1)
x11 x1 exp(-algll/RT) The term aij is a constant that is characteristic of the nonrandomness of the mixture, and in this study is taken to be 0.3, as suggested by Prausnitz and Renon for mixtures of polar liquids (Renon and Prausnitz, 1968). In addition, the local mole fractions must sum to unity so that one can obtain explicit expressions of the local mole fractions:
When the above two equations are coupled with the twoliquid theory of R. L. Scott, the following expression for the excess Gibbs energy of a binary mixture is obtained (Renon and Prausnitz, 1968):
&
721G21
= x14,,
+ r2G2,
+
+
x 2712G12 xlG,,
1
yields the following expressionsfor the activity coefficients (Renon and Prausnitz, 1968):
In the systems that will be presented, the interaction occurs between three components-phenol blue (the solute), cosolvent A, and cosolvent B. This requires a multicomponent variation of the NRTL equation given above. Since these interactions can be taken as multiple binary interactions, multicomponent mixtures can be generalized by using only binary parameters. In keeping with the notation given previously, the local mole fraction of component j around a molecule i is given by xji. In this case, phenol blue is taken as component 2, while the two liquid solvents are labeled 1and 3. Since the amount of phenol blue dissolved in the mixtures was less than about 1X mole fraction, it was assumed that the phenol blue mole fraction was negligible. This leads to the following equations established for the three-component mixture (with phenol blue as component 2).
These equations can be written more simply in terms of the 7's (see eqs 5 and 6): x12 =
x1 exp(-a21(712- 732))
x3 + x1 exp(-a21(712- 732)) x22 = 0
(14) (15)
Therefore, if one knows the binary interaction energies, 712 and 732, as well as the bulk mole fractions, one can predict the local compositions of the two solvents around the dilute phenol blue probe. Since eqs 14-16 require only binary interaction parameters between the phenol blue and each of the pure solvents, they will be determined from the solubility of the solid phenol blue in each of the solvents. The expression for solid/liquid equilibrium is as follows (Prausnitz et al., 1986):
(4)
where (5) 721
g21- g11 =RT
and
Differentiation of the above excess Gibbs energy equation
where we are concerned only with a binary solution of solid solute component 2 and liquid solvent component j. The solubility of the solvent in the solid is negligible, so the solid is pure phenol blue. It is common practice to simplify this expression by neglecting the terms that contain Acp since those terms are of opposite sign and are generally small relative to the first term (Prausnitz et al., 1986). This is important because the heat capacities of solid and liquid phenol blue are not available. Another assumption that was made involves the common practice of replacing the triple point temperature with the melting temperature since the numbers are generally very close
946 Ind. Eng. Chem. Res., Vol. 32, No. 5, 1993 50/50
-
mixture
8
350
390
430 470 wavelength (nm)
510
550
Figure 2. Absorption spectrum of phenol blue in cyclohexane, acetone, and a 50/50mixture of the two solvents.
for high molecular weight compounds such ai phenol blue. In addition, at equilibrium the enthalpy of fusion term, Ahf/Tt,can be replaced by the entropy of fusion. These assumptions lead to the following expression (Prausnitz et al., 1986):
The x 2 is the solubility of phenol blue in the pure solvent and is found experimentally. The entropy of fusion for phenol blue is independent of the solvent and was estimated using the group contribution method developed by Chickos et al. (1991). Using this method the Asf for phenol blue is estimated as 41.7 J/(mol-K). The melting point of phenol blue is 133 "C, and T was taken as room temperature (25.0 "C). With these values and the measured solubility, one can determine the activity coefficient of the phenol blue in the liquid (72). The activity coefficient of the solvent (7,) can be set equal to unity. This is valid since the system is relatively dilute (approximately mole fraction or less of phenol blue) so the mole fraction of solvent is essentially unity. By definition, yj 1.0 as x, 1.0 (Prausnitz et al., 1986). The two activity coefficients, 7 2 from eq 18 and y, = 1.0, can be used in eqs 9 and 10 to determine 712 and 721 by simply solvingthe two coupled nonlinear equations (where the solventj is labeled component 1). Note that G2l and G12 are functions of 712 and 7 2 1 (eqs 7 and 8). This procedure was performed for each of the cosolvents, and the resulting 7's were used to calculate the local mole fraction of the solvents around the phenol blue in binary mixtures of the solvents from eqs 14 and 16.
-
-
Experimental Results Local Composition Measurements. The local composition measurements for the liquid mixtures were determined from UV-vis absorption spectroscopy. The resulting absorption band shapes did not change throughout the different mixture concentrations, as shown in Figure 2. Since the absorption band is rather broad, it was important that the wavelength of maximum absorption shift appreciably from one solvent to the other. Typically, the shifts were from 15 to 30 nm. Moreover, the band shape did not change over the small solute concentration range used in these experiments. In all the results reported here the more polar solvent is listed first (e.g., acetone/cyclohexane; acetone is more polar). As discussed above, the phenol blue absorbs at a longer wavelength in the more polar solvent. In addition,
the more polar solvent was always the preferred solvent around the phenol blue. In the absence of large size differences, this is the expected result since the strength of interaction of the polar solute would be greater with a polar solvent than a nonpolar one. Wavelength shifts were measured for a total of eight solvent systems: acetone/cyclohexane, cyclohexanone/ triethylamine, toluene/cyclohexane, cyclohexanone/cyclohexane, acetophenone/cyclohexane,ethyl butyrate/ cyclohexane, acetophenone/toluene, and cyclohexanone/ ethyl butyrate. Table I contains the experimental data and pointedly illustratesthe wavelength shiftsin numerical terms. The wavelength shifts of the absorption maximum determined through the spectroscopicmeasurements were then used to calculate the local compositions of the various solvent mixtures around phenol blue. The method of calculation, used by Yonker and Smith (1988) and Chatterjee and Bagchi (1990, 1991), assumes a linear contribution of the local mole fraction of each solvent to the total transition energy
u g i X= X ~ ~ A E &+ ~
(19) where AET is actually the difference in the measured transition energy and the transition energy observed in an ideal gas, as given by Kim and Johnston (1987) for phenol blue. h ~ =, ET- E;!
3
2
~
;
(20) Therefore, the observed transition energy is that of the free molecule plus the stabilization from each molecule of each type in its solvent shell. This implicitly assumes that the contribution to the transition energy from a solvent molecule of type 1or type 3 is independent of the overall composition of the solvent shell. This is a common and, hopefully, reasonable assumption, as discussed above. The transition energies, ET, for the pure solvents and the mixtures were computed directly from the maximum wavelengths by the definition ET = hc/Am=, where h is Planck's constant, c is the speed of light, and Am, is the wavelength of maximum absorption. The ideal gas transition energy is an experimental value and the same used by Kim and Johnston (1987). This analysis does not include any corrections for the difference in the size of the two solvents and, subsequently, any changes in coordination number a t the different compositions, as used by Kim and Johnston (1987) for the supercritical fluid mixtures. This was neglected because the solvent molecules are all of somewhat similar size, as shown by the molar volumes in Table 11. However, this refinement could, in principle, be included in future studies. Once the transition energies are calculated, the fact that the local compositions in eq 19 must sum to unity leads to the values for the local mole fractions of each solvent around phenol blue (x12 and X 3 2 ) . The difference is taken between the local and bulk compositions of the more polar solvent and is plotted versus bulk mole fraction of the more polar solvent. As mentioned previously, in these experiments the local composition around the phenol blue is always enriched with the more polar solvent. This is not a requirement since size effects can also influence local compositions. Since the more polar solvent is preferred in these studies, the plots always show that the calculated local compositions are greater than the bulk compositions. The data points take on a parabolic shape in which the greatest difference occurs at the middle concentrations. The data for the eight different systems studied are shown as the large open circles in Figures 3-10. The larger the
Ind. Eng. Chem. Res., Vol. 32, No. 5,1993 947 Table I. Wavelength of Absorption Maximum bulk mol % of first solvent 0 5 10 20 40 50 60 80 90 95 100
acetone/ cyclohexane
cyclohexanone/ triethylaminea
toluene/ cyclohexane
cyclohexanone/ cyclohexane
551.60 552.88 557.14 563.60
554.64
550.32
550.55
561.31 567.12 575.31 576.69 579.25 583.39 584.77
552.08 554.36 558.80 560.99 562.27 566.45 568.48
562.30 568.50 575.25 579.00 580.05 584.40
588.43
569.79
588.25
574.75 578.24 579.52 579.21 581.23
bulk mol % of first solvent 0 10 20 40 50 60 80 90 100
ethyl acetophenone/ butyrate/ acetophenone/ cyclohexane cyclohexane toluene 550.30 550.95 569.60 562.40 555.40 577.10 572.00 559.10 580.50 580.50 563.10 584.80 583.10 563.90 587.80 584.90 565.10 589.80 590.80 566.20 592.90 594.80 568.20 594.80 595.70 569.70 595.20 The actual bulk mol % for this run were as follows: 0, 8.9, 18.0, 36.8, 46.7, 56.8, 77.9, 88.8, 100. 0.3
0
I
o
experimental
cyclohexanone/ ethyl butyrate 569.10 572.30 574.00 577.10 579.90 582.00 584.80 586.30 588.30
I
bulk mole fraction of acetone Figure 3. Difference between local and bulk composition around phenol blue of acetone in cyclohexane.
bulk mole fraction of cyclohexanone Figure 4. Difference between local and bulk composition around phenol blue of cyclohexanone in triethylamine.
Table 11. Physical Properties of Solvents at 25 OC pure solvent cyclohexane toluene triethylamine ethyl butyrate acetone cyclohexanone acetophenone
dipole moment (D) 0.0 0.45 0.77 1.74 2.88 3.01 3.02
molar volume (cm3/mol) 108.1 106.3 139.1 132.3 73.5 103.5 116.9
value on the y-axis the greater the preferential solvation in that system. For instance, in the acetone/cyclohexane system the difference at a bulk 50/50 mixture is 0.29. Therefore, when the bulk mole fractions are 0.50 acetone and 0.50 cyclohexane, the local mole fractions are 0.79 acetone and only 0.21 cyclohexane. A t higher temperatures, the preferential solvationshould be less and, therefore, the difference between the local and bulk mole fractions should be less significant. We attempted to demonstrate this decrease with the cyclohexanone/cyclohexane system. Unfortunately, the volatility of the liquids limited the increase to 50 OC. The solubilities were measured at this temperature to determine the T'S for the NRTL equation. The decrease in the
t m
,
,
Q
,
012
,
*
1
0.4
0.6
I
018
bulk mole fraction of toluene Figure 5. Difference between local and bulk composition around phenol blue of toluene in cyclohexane.
preferentialsolvation between 25 and 50 OC was predicted to be less than 0.01 mole fraction. The experimentally determined local compositions confirmed this result, showing no significant difference from the measurementa at 25 OC. A larger temperature increase with a higher
948 Ind. Eng. Chem. Res., Vol. 32, No. 5, 1993
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---.-.
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L
O! 8
016
0!4
012
l
c
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014
O! 6
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018
bulk mole fraction of cyclohexanone Figure 6. Difference between local and bulk composition around phenol blue of cyclohexanone in cyclohexane.
r o
experimentall e
w
0.25--
0 experimental ----NRTL
Q Q
" ' " ' " " ' ~ " ' f " ' @ 014
012
0.6
0.8
1
bulk mole fraction of acetophenone
Figure 7. Difference between local and bulk composition around phenol blue of acetophenone in cyclohexane.
I
0.3
'
1
1
1
012
'
1
1
1
"
014
1
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1
O! 6
o
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experimental
'
0: 8
bulk mole fraction of ethyl butyrate
Figure 8. Difference between local and bulk composition around phenol blue of ethyl butyrate in cyclohexane.
boiling point liquid mixture would be required to see a significant decrease in the preferential solvation. The trends shown in Figures 3-10 were generally as expected. The intermolecular forces that could account for the preferential solvation include dipoleldipole, dipole/ induced dipole, and van der Waals forces. Therefore, the important properties of the solvent are their dipole moments and polarizabilities. The dipole moments of all the solvents are shown in Table 11. It is also possible for specific chemical interactions to occur, resulting in the formation of an actual compound or complex between the solute and one of the solvents. Examples would be the formation of a hydrogen bond or an electron donor/
bulk mole fraction of cyclohexanone Figure 10. Difference between local and bulk composition around phenol blue of cyclohexanone in ethyl butyrate.
acceptor complex. This is especially true since the phenol blue has several sites that could accept a proton, as seen in Figure 1. However, we attempted to minimize this possibility by purposely eliminating any solvents with the strong potential for proton donation. Unfortunately, we believe there may have been some specific chemical interactions with toluene, as will be discussed later. Nonetheless, the trends were generally as expected. In all cases the more polar solvent was the one preferred in the local environment around the phenol blue. The difference in the bulk and local mole fractions were as large as 0.30 in the case of cyclohexanone/cyclohexane,acetophenonel cyclohexane, and acetone/cyclohexane. In the series of solvents used with cyclohexane, which has a dipole moment of 0, the degree of preferential solvationgenerallyincreased with the increasing dipole moment of the second solvent. For acetone,cyclohexanone, and acetophenone, which have dipole momenta in the range of 2.88-3.02 D, the difference in the bulk and local mole fractions was as large as 0.30, as stated above. Ethyl butyrate ( p = 1.74 D) with cyclohexane ( p = 0.0) only reached a difference of about 0.25 mole fraction. Conversely, toluene (F = 0.45 D)with cyclohexane only showed a very small (cO.1mole fraction) difference in local and bulk. The cyclohexanone/triethylamine and acetophenone/toluene systems have large differences in their dipole momenta and, consequently, exhibit large degreesof preferential solvation. On the other hand, the cyclohexanone/ethyl butyrate system has an intermediate difference in the dipole momenta, and we observe only slight preferential solvation, the difference between local and bulk mole fractions reaching about 0.07 mole fraction, as seen in Figure 10. Clearly, one would
Ind. Eng. Chem. Res., Vol. 32, No. 5, 1993 949 Table 111. Solubility Data for Phenol Blue in Each Pure Solvent at 25 OC solubility of phenol blue pure solvent (mole fraction) cyclohexane 2.13 X 10-4 triethylamine 2.54 X 10-4 2.84 x 10-3 ethyl butyrate 4.11 X toluene acetone 3.04 X 7.98 x 10-3 cyclohexanone 1.39 X acetophenone Table IV. NRTL Interaction Parameters of Each Pure Solvent with Phenol Blue Dure solvent NRTL interaction DBT- ( 7 1 2 ) cyclohexane 6.184 5.927 triethylamine 2.861 ethyl butyrate 2.504 toluene 2.798 acetone 1.857 cyclohexanone 1.319 acetophenone
not expect the trends to follow the dipole moments exactly because other forces, including dipole/induced dipole and van der Waals forces, can make significant contributions to the intermolecular interactions. Solubilities. The solubility of phenol blue in the pure solvents was needed for the analysis with the NRTL equation. The method to determine solubilities was described in the Experimental Section above, and the results are presented in Table 111. In general, the experimental results of the solubilities followed the expected trend except toluene. Otherwise, the solubility of the polar solutephenol blue increased with the increasing polarity and polarizability of the solvent. On the basis of its dipole moment of only 0.45 D, the solubility in toluene appears to be about 1 order of magnitude higher than expected. A possible explanationis the presence of specific chemical interactions between the phenol blue and the toluene, resultingin the formation of an actual compound. It is well-known that aromatics can form electron donor/ acceptor complexea with unsaturated hydrocarbons (Prausnitz et al., 1986),which could be occurring here between the toluene and phenol blue. Although weak, it may be enough to increase the solubility significantly. The only other solvent that contains an aromatic ring is acetophenone, and it is hard to determine if it has any specific interactions with the solute because it is the most polar solvent used and one would already expect it to have the best ability to solvate phenol blue, Comparison to the NRTL Equation Once the solubilitymeasurements were taken, the NRTL parameters were needed to determine the local compositions of phenol blue around each of the solvents. These parameters represent the interaction energies between phenol blue and each of the pure solvents. They were determined through the method detailed in the NRTL Equation section and are presented in Table IV. Them parameters were used to calculate the theoretical plots contained as dashed lines in Figures 3-10. The comparison between the local compositions measured by UV-vis absorption spectroscopy and those predicted from the NRTL equation is a true comparison, with no adjutable parameters used to fit one to the other. The only information required for the NRTL predictions are bulk mole fractions and the binary interaction energy between the phenol blue and each of the pure solvents, as
determined from the solubility of the phenol blue in the neat solvent. The NRTL predictions match the experimental numbers remarkably well for all of the systems except those containing toluene. In these six cases (acetonelcyclohexane, cyclohexanone/triethylamine, cyclohexanone/cyclohexane,acetophenone/cyclohexane,ethyl butyrate/cyclohexane, and cyclohexanone/ethyl butyrate) the NRTL equation successfullypredicta the actual local compositions. As mentioned above, the poor fit with the toluene systems may be due to a weak specificchemical interaction between the phenol blue and the toluene. That weak complexation would increase the solubility of phenol blue in toluene, thus producing an essentially incorrect 7 that overpredicts the strength of the interaction with toluene. Therefore, when toluene is mixed with cyclohexane, the NRTL equation overpredicts the preferential solvation. While a chemicalcomplexbetween phenol blue and toluene may increase its solubility dramatically, it may not lead to an increase in the local composition of the toluene around the phenol blue when toluene is mixed with cyclohexane. Chemical bonds can be saturated: if it is a 1/1 complex, then as long as there is one toluene by the phenol blue there would be no further attraction of another toluene molecule based on the chemical forces. Similarly, in the acetophenone/toluene mixture the NRTL equation underpredicts the preferential solvation. This is because the 7 determined from the solubility measurements indicates that the interaction between phenol blue and toluene is almost as great as the interaction with acetophenone. However, if it is a chemical interaction, once it is satisfied (with, say, one toluene molecule) the attraction to the highly polar acetophenone is much greater. Thus, the measured local compositions indicate a significant preference for acetophenone. One would expect a complex between the phenol blue and toluene to cause a shiftor change in the absorption peak. It is possible that this was not observed because the absorption peak of phenol blue is so broad. It should be noted that the inability of the NRTL equation to match the measured local compositions in the toluene systems cannot be explained by size differences that have not been taken into account in the analysis of the spectroscopicdata. The first system that does not fit is toluene/cyclohexane. In this system the two solvents are remarkably similar in size and shape, as born out by their molar volumes shown in Table 11. The NRTL predictions of the local compositions are very sensitive to the value of a,the nonrandomness factor. However,the recommended value of 0.3for polar solvents (Renon and Prausnitz, 1968)worked remarkably well, so no attempt was made to optimize the fit with that parameter. In summary,the NRTL predictionsof local compositions of binary solvents around the dilute solute phenol blue match those measured independentlyby spectroscopywith remarkable accuracy for all cases except those with the potential for specific chemical interactions. The NRTL equation cannot predict local compositions correctly in cases where hydrogen bonding or electron donorlacceptor complexes occur, as one would expect. In fact, the combination of the local composition measurements and the solubility measurements provides significant evidence of a chemical complex between toluene and phenol blue. Interestingly, this solvatochromic probe is able to differentiate between chemical and physical forces: the thermodynamic solubility measurements are affected significantly by the chemical complexation but the spec-
950 Ind. Eng. Chem. Res., Vol. 32,No. 5, 1993
troscopic local composition measurements are not. In this way, solvatochromic probes may be useful in determining the nature, as well as the strength, of forces between molecules. In interpreting the spectra it has been necessary to be concerned with the possibility of specific chemical complexation. We have made the assumption of linear contributions to the total transition energy and have neglected size and coordination number effects. While the size and coordination effects can be dealt with more rigorously and one can exploit probes that do not form chemical complexes, issues that will be dealt with in future publications, the basic assumption of linear contributions to the energy remains. Conversely, molecular simulations do not require any such approximation but are limited to grossly simplified models of the real substances. We believe that the best way to test semiempirical models on a microscopic scalewill be a combination of solvatochromic studies, as presented here, and molecular simulations. Conclusions
In this paper we have presented spectroscopic measurements of the local compositions of binary liquid solvents around the solvatochromic probe phenol blue. These values were compared to those predicted by the NRTL equation, using parameters determined from the solubility of the phenol blue in each of the pure solvents. The following conclusions can be drawn: 1. The local solvent shell around the phenol blue was preferentially enriched with the more polar solvent in all cases. 2. The local composition of the more polar component was as much as 2.5 times the bulk mole fraction for the acetophenonelcyclohexane system. 3. For systems that do not form chemical complexes the predictions of the local compositions from the NRTL equation match those measured by spectroscopy remarkably well. 4. The solubility and local composition measurements suggest that there is a weak chemical complex between toluene and phenol blue. 5. The solvatochromic probe was able to differentiate between chemical and physical forces since local composition measurements are not necessarily affected by chemical forces as strongly as thermodynamic measurements like solubility. 6. Solvatochromic probes provide a useful way to measure properties on a molecular scale and provide a means to test thermodynamic models quantitatively. Acknowledgment is made to the National Science Foundation (Grants NSF-CTS 90-09562and NSF-CTS 91-57087)and to the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this work. Nomenclature c = speed
of light
Ac, = difference in heat capacity between liquid and solid ET = transition energy AET = difference between actual transition energy and that
in an ideal gas = interaction energy between an i-j pair of molecules gE = excess Gibbs free energy of the solution h = Planck's constant Ahf = enthalpy of fusion G = NRTL parameter defined in eqs 7 and 8 R = gas constant gij
Asf = entropy of fusion T = absolute temperature Tt= triple point temperature xi = bulk mole fraction of component i xi, = local mole fraction of component i around central molecule j a = NRTL nonrandomness factor y = activity coefficient X = wavelength 7
= NRTL energy parameter defined in eqs 5 and 6
Superscripts and Subscripts
i = component i IG = ideal gas j = component j max = maximum mix = mixture T = transition
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Received for review August 31, 1992 Accepted January 21, 1993
