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Langmuir 1987, 3, 598-599
Group Contribution Model for Predicting the Solubilization of Organic Solutes by Surfactant Micelles George A. Smith, Sherril D. Christian,* and Edwin E. Tu.cker Department of Chemistry and the Institute for Applied Surfactant Research, T h e University of Oklahoma, Norman, Oklahoma 73019
John F. Scamehorn School of Chemical Engineering and Materials Science and the Institute for Applied Surfactant Research, T h e University of Oklahoma, Norman, Oklahoma 73019 Received January 12, 1987. I n Final Form: April 3, 1987
By examining experimental solubilization data and aqueous solubility results for organic solutes, we have been able to develop a group contribution method to estimate free energies of transfer of solutes between the ideal gaseous state and the interior of aqueous surfactant micelles. Only the structural formula of the solute and the value of its Henry's law constant in water are required to predict the limiting equilibrium constant for transferring the solute from the infinitely dilute solution in water into the micelle. Until recently, there have been only a few detailed studies of the solubilization of organic solutes in aqueous surfactant solutions in which intramicellar mole fractions of the organic component have been varied throughout wide ranges.'+ Solubilization experiments have commonly been limited to determining the total concentrations of solutes in micellar solutions, at saturation with respect to the organic solute. In particular, there has been a paucity of information about the solubilization of solutes in the limit as the mole fraction of organic compound in the micelle approaches ~ e r o . ~ - ~ J O - ~ ~ In many applications of micellar-based separation methods (for example, micellar-enhanced ~ltrdiltration),'~ the concentrations of organic solutes in micelles may be expected to be quite small. Therefore, it is important to be able to measure or predict partition coefficients of solutes in the limit of infinite dilution. Treiner and Chattopadhyay14 have attempted to correlate partition coefficients for the solubilization of organic molecules into aqueous surfactant micelles by using the additivity scheme of Hansch and co-workers,15obtaining a reasonably good linear relation between these coefficients and partition coefficients for the same solutes determined in the water plus octanol systems. Hirose and Sepulveda have similarly correlated the transfer of aromatic solutes between water and ionic micelles by using a group contribution method.16 (1) Christian, S. D.; Smith, L. S.; Bushong, D. S.; Tucker, E. E. J . Colloid Interface Sci. 1982, 89, 514. (2) Tucker, E. E.; Christian, S. D. Faraday Symp. Chem. Soc. 1982, 17, 11.
(3) Tucker, E. E.; Christian, S. D. J . Colloid Interface Sei. 1985, 104, 562. (4) Matheson, I. B. C.; King, A. D. J . Colloid Interface Sei. 1978,66, 464. (5) Nagarajan, R.; Chaiko, M. A.; Ruckenstein, E. J. Phys. Chem. 1984, 88, 2916. (6) Stilbs, P. J . Colloid Interface Sci. 1982, 87, 385. (7) Simon, S. A.; McDaniel, R. V.; McIntosh, T. J. J . Phys. Chem. 1982,84, 1449. (8) Rehfeld, S. J. J . Phys. Chem. 1971, 75, 3905. (9) Mukerjee, P.; Cardinal, J. R. J . Phys. Chem. 1978, 82, 1620. (10) Valenzuela, E.; Abuin, E.; Lissi, E. A. J. Colloid Interface Sci. 1984, 102, 46. (11)Dougherty, S. J.; Berg, J. C. J. Colloid Interface Sci. 1974,48, 110. (12) Goto, A.; Endo, F. J . Colloid Interface Sci. 1978, 66, 26. (13) Dunn, R. 0.;Scamehorn, J. F.; Christian, S. D. Sep. Sci. Technol. 1985,20,257. Leung, P. S. In Ultrafiltration Membranes and Applications; Cooper, A. R., Ed.; Plenum: New York, 1979; p 415. Scamehorn, J. F.; Harwell, J. H. In Surfactants and Chemical Engineering; Wasan, D. T., Shah, D. O., Ginn, M. E., Eds.; Marcel-Dekker: New York, in press. (14) Treiner, C.; Chattopadhyay, A. K. J. Colloid Interface Sci. 1986, 109, 101. (15) Hansch, C.; Dunn, W. J. J . Pharm. Sci. 1972, 61, 1. (16) Hirose, C.; Sepulveda, L. J . Phys. Chem. 1981, 85, 3689.
0743-7463/S7/2403-0598$01.50/0
Table I. Experimental and Predicted Values of Partition Coefficients for the Transfer of Organic Solutes from the Ideal Gas Phase into Aqueous Surfactant Micelles" l-hexadecylpyridinium chloride In K' In K'* exptl calcd 6.14 6.26 7.10 7.07 15.15 15.16 16.01 16.18 ~~
solute benzene toluene phenol p-cresol benzyl alcohc31 ethane pentane hexane cyclohexane methanol 1-propanol 1-butanol 1-pentanol
2.66' 4.18 4.97
2.92 3.77 5.06
11.01 11.66
10.99 11.83
sodium dodecyl sulfate In K' In K' exptl calcd 5.86 5.75 7.03d 6.60 14.02 14.32 14.94 0.14' 2.62' 3.93 4.91 7.91d 10.03d 10.64 11.91
15.17 0.42 2.98 3.83 5.12 8.14 9.85 10.70 11.55
"Aqueous solutions of surfactants at 0.10 M, temperature 25 O C . Partition coefficient, K', is molarity of organic solute within the micelle, divided by molarity in the ideal gas phase, extrapolated to infinite dilution. Results from this work unless otherwise noted. 'From: Abuin, E. B.; Valenzuela, E.; Lissi, E. A. J . Colloid Interface Sci. 1984,101,401. dFrom: Stilbs, P. J. Colloid Interface Sci. 1982, 87, 385. eFrom: Matheson, I. B. C.; King, A. D. J . Colloid Interface Sei. 1978, 66, 464.
Recently, we have used vapor pressure and semiequilibrium dialysis methods to infer accurate and detailed solubilization isotherms for numerous organic soluteaqueous surfactant s y ~ t e m s . l - ~ J ~One - ~ ~result of this research has been the determination of limiting parition or solubilization equilibrium constants for many solutes, with transfer from the dilute aqueous phases into micelles of sodium dodecyl sulfate (SDS), hexadecylpyridinium chloride (CPC), and several other surfactants.20 Although the analyses of Treiner and Chattopadhyay and of Hirose and Sepulveda give fair correlations of the new data, at least for limited groups of solutes, we present here a more successful alternative method for predicting solubilization (17) Christian, S. D.; Tucker, E. E.; Smith, G. A,; Bushong, D. S. J. Colloid Interface Sci. 1986, 113, 439. (18) Christian, S. D.; Smith, G. A.; Tucker, E. E.; Scamehorn, J. F. Langmuir 1985, 1, 564. (19) Smith, G. A,; Christian, S. D.; Tucker, E. E.; Scamehorn, J. F. J . Solution Chem. 1986, 15, 519. (20) Smith, G. A. Ph.D. Dissertation, The University of Oklahoma, Norman, 1986.
0 1987 American Chemical Society
Langmuir, Vol. 3, No. 4, 1987 599
Letters results. The method uses group free energies of transfer for species from the ideal gaseous phase into the intramicellar “solution”. A related scheme developed previously has been shown to be useful for predicting the effect of solvents on thermodynamic properties of solutes that are involved in molecular complex equilibria.21 Table I includes information about experimental and calculated values of the logarithms of partition coefficients for solutes distributed between the ideal gaseous phase (at unit molarity) and the ideal dilute intramicellar solution phase (unit molarity). In calculating the molarities of organic solutes within the micelles, we have used partial molar volumes of 0.250 L mol-l for SDS and 0.375 L mol-’ for CPC in micellar form. The dimensionless partition coefficients are defiied as K’ = [ ~ o l u t e ] ~ ~solute],,,^ ~,/ Thus, by analogy with the dimensionless partition coefficients relating the concentrations of solutes in two immiscible phases, values of K’ represent ratios of the equilibrium molar concentration of a solute in the intramicellar solution to the molar concentration of the solute in the gas phase. Values of In K’are correlated by eq 1, where n, represents the number of groups of a particular type and bi represents the contribution to In K’ of the i-th type of group. The average deviations in In K’for the SDS and In K ’ = Cnibi
(1)
drocarbon moieties (which reflect the effects of hydrophobic hydration or ~olvation~*,*~ do not influence values of the free energies of transfer into micelles. Hence, if we assume that given chemical groups tend to solubilize preferentially in particular regions within the micelle, it is plausible to predict that Gibbs free energies of solubilization from the gas phase will be nearly additive, barring the existence of specific conformational effects. One may anticipate, and indeed we that positional effects will cause compounds such as 0-,m-, and p-chlorophenol to have somewhat different values of K‘, although the group method will of course lead to the same predicted values. Moreover, the branching of hydrocarbon chains must also influence the thermodynamics of solubilization; we find, for example, the tert-butyl alcohol is solubilized to a lesser extent than 1-butanol by either SDS or CPC micelles.20 By using predictions of K’from the group contribution method, together with readily available values of the limiting Henry’s law for individual solutes in water (defined as ratios of solute partial pressures divided by mole fraction in the limit of infinite dilution), it is possible to predict values of partition or equilibrium constants for the transfer of organic solutes from dilute aqueous solution into the surfactant micelles. Thus, reference to the diagram below indicates that the free energy solute
1
CPS systems, respectively, are 0.26 and 0.14, corresponding to deviations in K’ of approximately 30% and 15%. Considering the wide range of K’values represented in the table, we believe that the correlation is quite encouraging, and we are at present attempting to apply it to other types of systems. The values of the group factors (the b values) are quite similar for the two surfactants. Parameters used in the correlation are as follows: SDS for each carbon atom for each aryl group for each hydrogen atom for each hydroxyl group
2.14 -3.22 -0.64 8.57
f f f f
0.30 1.12 0.13 0.22
CPC 2.14 f 0.30 -2.68 f 1.06 -0.65 f 0.13 8.91 f 0.18
By examining the values of the group parameters for the
SDS and CPC systems, one may infer that the goodness of fit will not be greatly worsened by fitting all of the results (for both surfactants) with the same set of four constants. However, the effect of hydroxyl groups or of aryl groups appears to be somewhat greater (more positive) for the solubilization of solutes in CPC micelles than in SDS micelles. It may be useful to speculate about the reasons why the group parameter correlation of partition coefficients (between the gas phase and the intramicellar “phase”) works as well as it does. In contrast to previous corre1ations,l4J6 the group method introduced here avoids using as a reference phase the dilute aqueous solution (organic solute a t infinite dilution in water). Terms in eq 1 are only included to account for the transfer of solutes from the ideal gaseous phase, in which there are no molecular interactions, directly into the micelle. The important advantage of the group contribution method proposed here is that the unusual thermodynamic properties of aqueous solutions of solutes containing hy(21) Christian, S. D.; Lane, E. H. In Solutions and Solubilities; Dack, M. R. J., Ed.; Wiley: New York, 1975; Vol. 8, p 327.
[ u n i t molarity, ideal gas1
solute [unit molarity, ideal dilute aqueous solution, standard statel
solute molarity, ideal dily!e intramicellar solution , standard state]
Cu,;it
of transfer of a gaseous solute into the micellar interior (viz., AG = -RT In K’) may be equated to the sum of the free energy of transfer of the solute from the ideal gaseous state into infinite dilution in water (which may be calculated from the value of the Henry’s law constant for the solute) and the free energy of transfer of the solute from its solution at inifinite dilution in pure water into the intramicellar solution, also at infinite dilution. Therefore, if Henry’s law constants are available for solutes in dilute aqueous solutions, the correlational method makes possible the prediction of partition coefficients (or alternatively solubilization equilibrium constants) for transferring organic solutes from the ideally dilute aqueous solution into surfactant micelles. Only a knowledge of the structural formulas of particular solutes is required in making predictions of the extent of solubilization at equilibrium. New solubilization results will be examined to determine whether the simple model described here applies to other solutes and a variety of surfactants. Methods are also being developed to predict the dependence of the transfer free energies on intramicellar composition.
Acknowledgment. We appreciate the financial support of the Office of Basic Energy Sciences, Department of Energy, Contract DE-AS05-84ER13175. (22) Frank, H. S.; Evans, M. W. J . Chem. Phys. 1945, 13, 507. (23) Kauzmann, W. Adu. Protein Chem. 1959, 14, 1. (24) Bhat, S. N.; Smith, G. A.; Tucker, E. E.; Christian, S. D.; Scamehorn, J. F.Ind. Eng. Chem. Fundam., in press. (25) Wilhelm, E.; Battino, R.; Wilcock, R. J. Chem. Reu. 1977, 77, 219. (26) Seidell, A. In Solubilities of Organic Compounds; D. Van Nostrand New York, 1941. (27) McAuliffe, C. J. Phys. Chem. 1966, 70, 1267.
