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Langmuir 1985, 1,564-567
impinging species that is causing the values to be in error. Experiments employing a surface that is hot relative to the incident gas atoms should minimize any errors here as a consequence of the fact that sticking probabilities typically drop with an increase in the surface temperature.
Acknowledgment. We are pleased to acknowledge support of this work by the Research Corporation, the
donors of the Petroleum Research Fund, administered by the American Chemical Society, and the University of Missouri’s Weldon Spring Endowment Fund. We also would like to thank J. C. Tully for helpful comments on the surface model and C. L. Krueger for discussions concerning experimental results. Registry No. Ar, 7440-37-1;W, 7440-33-7.
Semiequilibrium Dialysis: A New Method for Measuring the Solubilization of Organic Solutes by Aqueous Surfactant Solutions Sherril D. Christian,* George A. Smith, and Edwin E. Tucker Department of Chemistry, T h e University of Oklahoma, Norman, Oklahoma 73019
John F. Scamehorn School of Chemical Engineering and Materials Science, T h e University of Oklahoma, Norman, Oklahoma 73019 Received February 25, 1985. I n Final Form: M a y 7, 1985 An experimental method is described for determining equilibrium constants for the solubilization of organic solutes by aqueous surfactant solutions. One side of an ordinary equilibrium dialysis cell is loaded with a solution containing a surfactant (largely in micellar form) and a solute that is present both as the free monomer and in solubilized form in the micelles. The other side of the cell initially contains distilled water. After approximately 1day, the permeate (dilute solution) side of the cell is analyzed to determine the concentrations of the surfactant and of the organic solute that have passed through the membrane. Although the surfactant in the permeate is not at equilibrium with that in the retentate (concentrated solution) side of the cell, the organic solute diffusesthrough the membrane rapidly enough to be in equilibrium simultaneously with the solutions on both sides of the membrane. Because the concentration of surfactant in micellar form is extremely small on the permeate side of the membrane, the concentration of organic solute in the permeate is nearly equal to that of the unbound organic solute in the retentate solution. By using information about the concentrations of organic solute and surfactant on both sides of the membrane, one may calculate the equilibrium constant for solubilization of the solute in the surfactant micelles in the concentrated solution. Results are given for aqueous solutions of the solute phenol and the cationic surfactant n-hexadecylpyridinium chloride. results have shown that solubilization equilibrium conIntroduction stants inferred at saturation may differ by at least a factor Only a few experimental techniques are capable of of 2 from those obtained when the same surfactant soluyielding reliable solubilization data for organic solutes in tions contain the organic solute a t low ~oncentrations.~-~ surfactant solutions. In systems containing solutes of Ultrafiltration and molecular sieve techniques7 have been sufficient volatility, vapor pressure methods’ have provided the most accurate and extensive results yet a ~ a i l a b l e , ~ - ~ applied to obtain solubilization data at solute concentrations less than saturation, but these methods have not but there have been few careful, systematic studies of the found extensive use. Because an understanding of solusolubilization of solutes of low volatility, throughout wide bilization phenomena is essential in many areas of colloid ranges of activity or concn. Several groups of workers have science, we sought to devlop a general experimental meused a maximum solubility (phase equilibration) method6 thod for determining solubilization constants for surfactant to determine the extent of solubilization of liquid or solid solutions containing solutes of almost any type. organic solutes at saturation. However, our vapor pressure In practical applications of solubilization, an organic solute (e.g., a contaminant) may be present in surfactant (1) Taha, A. A.; Grigsby, R. D.; Johnson, J. R.; Christian, S. D.; Affssolutions at concentrations well-belowsaturation. We have prung, H. E. J. Chem. Educ. 1966,43,432. Tucker, E. E.; Christian, S. recently reported the use of micellar-enhanced ultrafilD. J. Chem. Thermodyn. 1979,11, 1137. trations to remove a solute from an aqueous stream. A (2) Tucker, E. E.; Christian, S. D. Faraday Symp. Chem. Soc. 1982, 17, 11; J. Colloid Interface Sci. 1985, 104, 562. surfactant is added to the aqueous stream to give a final (3) Christian, S. D.; Tucker, E. E.; Lane, E. H. J. Colloid Interface Sci. concentration well above the critical micelle concentration 1981, 84, 423. (4) Christian, S. D.; Smith, L. S.; Bushong, D. S.; Tucker, E. E. J . (cmc) and the resulting solution is passed through an ul-
Colloid Interface Sci. 1982,89, 514. (5) Christian, S. D.; Scamehom, J. F., presented at the Symposium on Interfacial and Colloidal Systems, The 1984 International Chemical Congress of Pacific Basin Societies, Honolulu, HI, Dec 16-21, 1984. (6) Elworthy, P. H.; Florence, A. T.; MacFarlane, C. B. ‘Solubilization by Surface Active Agents”; Chapman and Hall: London, 1968; Chapter 2.
(7) Aboutaleb, A. E.; Sakr, A. M.; El-Sabbagh, H. M.; Abdelrahman, S. I. Arch. Pharn. Chemi, Sci. Ed. 1977,5, 105; Pharm. Ind. 1980,42, 940. (8) D u n , R. 0.; Scamehorn, J. F.; Christian, S. D. Sep. Sci. Technol. 1985, 20, 257.
0743-7463/85/2401-0564$01.50/0 0 1985 American Chemical Society
Langmuir, Vol. 1, No. 5, 1985 565
Semiequilibrium Dialysis i-
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0.8 0.8
0.4 0
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Figure 1. Transfer of n-hexadecylpyridinium chloride through
membrane for an initial concentration of 0.000585 M in the retentate solution. Curve corresponds to fiborder rate equation with half-life of 3.4 h. trdilter (1000-loo00 dalton molecular weight cutoff). In the case of contaminants that are effectively solubilized by the surfactant micelles, the permeate solution contains a much smaller concentration of the solute than does the original stream.8 In particular cases, this concentration has been shown to be approximately equal to that of the unsolubilized solute in the highly concentrated (retentate) s~lution.~~* Considering these results, we thought it would be worthwhile trying to use a variation of the well-known equilibrium dialysis techniquegJOto infer solubilization constants for organic compounds in aqueous surfactant solutions. The present paper indicates that a dialysis method is in fact quite convenient for studying such solubilization equilibria. We have termed the method “semiequilibrium dialysis”,8 because equilibrium can be reached with respect to the dissolved organic compound, although the surfactant continues to diffuse through the membrane so long as there is a difference in total concentration between the two chambers of the cell. Results are reported here for the solubilization of phenol in aqueous n-hexadecylpyridinium chloride solutions at 25 “C.
Experimental Section Ordinary 5-mL equilibrium dialysis cells and transparent regenerated cellulose membranes (6000 dalton molecular weight cutoff) were obtained from Fisher Scientific and used without modification. (In several preliminary experiments,the membranes were presoaked in water or dilute aqueous formaldehyde solutions, but this treatment did not significantly modify the results.) Phenol was purified as described previously;” high-quality nhexadecylpyridinium chloride monohydrate (CPC) was obtained from Hexcel Corporation and used without further purification. The surface tension vs. concentration curve for aqueous CPC solutions showed no minimum and no impurities were observed by HPLC analysis, using UV or conductivity detectors. When equilibrium dialysis experiments were performed, aqueous solutions of surfactant or of surfactant plus organic solute were placed in one compartment of the cell, and pure water was added to the other side. The cells were kept in a desiccator, submerged in a themostated bath at 25.00 OC. At various times, samples of the more dilute solution (the “permeate”)were taken and analyzed to determine the concentrationsof surfactant and/or organic solute. In several experiments, conductance measurements were made to determine the concentration of the ionic surfactant (9) Klotz, I. M.;Walker, F. M.; Pivan, R. B. J.Am. Chem. SOC.1946, 68,1486. (IO) Huang, W. M.; Ts’o,P. 0.P. J.Mol. Biol. 1966, 16,523. (11) Lin, L.-N. Ph. D. Dissertation, The University of Oklahoma,
Norman, 1975.
5
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Figure 2. Transfer of n-hexadecylpyridinium chloride through membranefor an initial concentrationof 0.2265 M in the retentate solution.
as a function of time, but in most runs, UV analysis (in the 230-280-nm region) was employed to determine the surfactant and organic solute concentrations at times 1&24 h after the start of the experiment.
Results Figure 1 is a plot of permeate concentration vs. time, obtained in an experiment in which a binary aqueous solution of CPC (0.000 585 M) was present initially in the retentate compartment and pure water was placed on the permeate side. During the experiment, the concentration of CPC on both sides of the membrane remained well below the critical micelle concentration (cmc),so that the surfactant presumably esisted throughout the cell primarily as monomers. The solid line in Figure l represents the least-squares fit of data to a first-order rate equation, with a half-life of 3.4 h. Figure 2 shows data for the transfer of CPC from a solution having a concentration always well above the cmc. The binary aqueous solution of CPC in the retentate compartment had an initial concentration of 0.2265 M. After several hours, the rate of transfer of CPC through the membrane has slowed considerably, although a gradual increase in the CPC concentration in the permeate solution occurs even when the cmc, O.OO0 88 M:2 has been exceeded. Concentrations of CPC in the permeate solution (determined conductimetrically) are plotted for times varying from 0 to 24 h. At times longer than 24 h, the concentration of CPC in the permeate continues to increase (at a rate of about 10% per day) because the thermodynamic activity of CPC in the retentate always exceeds that in the permeate.13 However, because the total concentration of CPC in the permeate does not greatly exceed the cmc, the surfactant may be assumed to consist of monomeric CPC (at a concentration of approximately 0.00088 M) and micellar CPC, at a concentration equal to the total molarity of CPC in the permeate less 0.00088 Mal3 In Figure 3 are plotted data obtained from seven separate dialysis experiments, each cell containing phenol at an initial concentration of 0.0122 M in the retentate compartment and pure water in the permeate. The permeate compartment of each cell is analyzed at a selected time, and the solution remaining in that cell is discarded. The small extent of scatter of the points from the fitted line indicates the reproducibility of the several experiments, (12) Rathman,J. F.; Scamehorn,J. F. J. Phys. Chem. 1984,88,5807. Bushong, D. S., unpublished research; Ph. D. Dissertation in preparation. (13)
566 Langmuir, Vol. 1, No. 5, 1985
Christian et al.
Table I. Semiequilibrium Dialysis Data for the Ternary initial permeate [CPC],' M [PI, M [CPCI,M 0.2020 0.0411 0.001 22 0.2020 0.0411 0.001 23 0.2020 0.0411 0.001 34 0.001 23 0.2020 0.0411 0.001 09 0.1468 0.0299 0.1468 0.0299 0.001 07 0.00101 0.1468 0.0299 0.0299 0.001 39 0.1468 0.000 91 0.0986 0.0201 0.0201 0.000 99 0.0986 0.0201 0.001 05 0.0986 0.000 90 0.0491 0.0100 0.000 86 0.0491 0.0100 0.0100 0.000 88 0.0491
System n -Hexadecylpyridinium Chloride/Phenol/Water at 25 "C
retentate [CPCI, M [PI, M
[PI, M 0.003 24 0.003 15 0.003 16 0.003 14 0.00301 0.002 96 0.002 94 0.003 06 0.002 76 0.002 66 0.002 73 0.002 24 0.002 13 0.001 96
0.2008 0.2008 0.2007 0.2008 0.01457 0.1457 0.1458 0.1458 0.0977 0.0976 0.0976 0.0482 0.0482 0.0482
0.0379 0.0379 0.0379 0.0379 0.0269 0.0269 0.0270 0.0268 0.0173 0.0174 0.0173 0.0078 0.0079 0.0080
K,b L mol-' 54.2 56.1 56.3 56.5 55.2 56.2 56.4 55.0 54.1 57.3 55.4 51.0 59.7 64.1
Molarity of n-hexadecylpyridinium chloride. Equilibrium constant, defined as K = [solubilized phenol]/([monomericphenol] [micellar surfactant]).
C
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Figure 3. Transfer of phenol through membrane for an initial concentration of 0.0122 M in the retentate solution. Curve represents first-order rate equation with half-life of 2.1 h. which are performed with different cells and different membranes. The analytical uncertainty in the measured phenol concentrations, determined by UV analysis a t 270 nm, is about 1%. It appears that phenol transfers through the membrane with a half-life of only 2.1 h, so that after 1 day, virtually complete equilibrium is reached. The fact that a typical organic solute such as phenol transfers so rapidly through the dialysis membrane is a crucial result, strengthening our belief that the semiequilibrium dialysis method can be used to obtain accurate solubilization data. During the 18-24-h time period of the SED experiments, the CPC concentration reaches a value only a few tenthousandths molar greater than the cmc; therefore, the phenol molecules are able to "keep up" with the slow transfer of CPC through the dialysis membrane and come to equilibrium with both the retentate and the permeate solutions. Semiequilibrium dialysis results for solutions containing both phenol and CPC are shown in Table I. Initial concentrations of phenol and CPC (in a 1:5 mol ratio) are reported along with values of the concentrations of phenol and CPC in the permeate solution approximately 18 h after the start of the experiment. The concentrations of phenol and CPC in the retentate at 18 h have been calculated by material balances.
Data Analysis and Discussion The concentration vs. time curves in Figures 1-3 indicate that uncomplexed molecular or ionic species transfer rapidly through the dialysis membrane. Several previous
studies, including our own investigation of the ultrafiltration of CPC solutions containing solubilized tert-butylphenol, indicate that micelles of CPC and similar surfactants do not pass through membranes (with appropriate pore sizes) in significant amounts and that organic solubilizate molecules transfer as uncomplexed molecular ~pecies.~J"" Once the surfactant monomers have passed into the permeate solution, these molecules will almost instantaneously reequilibrate to form small concentrations of micellar aggregates. However, the data in Table I indicate that after approximately 18 h, there is so little CPC present in the permeate in the micellar forms that corrections for the amount of phenol solubilized in micelles on that side of the cell are almost negligible. (In fact, the very small amount of organic compound solubilized in micelles in the permeate solution is accounted for in the analysis of data that follows.) We describe here the derivation of a simple equation for processing data like those in Table I to infer the average or apparent solubilization constant for the equilibrium monomeric phenol + micellar CPC = solubilized phenol K = [solubilized phenol]/(cp[micellar CPC]) (1) where cp represents the concentration of monomeric phenol. We assume that the total or analytical concentration of phenol, [PI, and of surfactant, [CPC], in the two compartments can be related to cp and to the concentration of CPC monomer, ccpc, by the equations [PI, = cp + [solubilized phenol], (2) [PI, = cp + [solubilized phenol], (3) [CPC], = c C ~ C ,+~ [micellar CPC],
(4)
[CPC], = ccpc,, + [micellar CPC],
(5)
and where the subscripts "r" and "p" refer to the retentate and the permeate, respectively. The concentration of monomeric phenol is taken to be the same in the retentate as in the permeate. This is the key t o the analysis of semiequilibrium dialysis data-we assume that the activity coefficient of phenol is the same on both sides of the membrane and consequently that the (14) Hutchinson, E.,Shaffer, M. 2.Phys. Chem. (Munich) 1955, 5, 344. (15) Hutchinson, E. 2.Phys. Chem. (Munich) 1959, 21, 38 (1959). (16)Osborne-Lee, 1. W.; Schechter, R. S.; Wade, W. H. J. Colloid Interface Sci. 1983, 94, 179. (17) Abu-Hamdiyyah, M.; Mysels, K. J. J. Phys. Chem. 1967, 71,418. Mysels, K. J. Ado. Chem. Ser. 1969, N . 86, Chapter 4.
Semiequilibrium Dialysis phenol activity (on the ideal dilute solution basis) equals the concentration of the phenol monomer. With this assumption, eq 1-3 can be combined to obtain a general relation for inferring solubilization constants from SED data: K = ([PI, - [P],)/([P],[micellar CPC], [P],[micellar CPC],) (6)
[This equation is readily derived by taking the ratio of the expressions for [PI, and [PI (eq 2 and 3), dividing the numerator and denominator $y cp, replacing the terms for [solubilized phenol] /cp (in retentate and permeate) by K[micellar CPC], and solving for K.] Although eq 6 is quite general, specific assumptions may be made to convert it into a form more convenient for analyzing experimental results. Considering the fact that the total concentration of CPC in the permeate differs from the CMC by less than 1 mM, we feel justified in equating cm in the permeate solution with the cmc value, O.OO0 88'M. On the other hand, vapor pressure osmometry experiments13indicate that ccpc in the retentate solutions, at molarities in the range 0.05-0.20, is quite small compared to the total CPC concentration And even compared to the cmc. (Note that the concentration of free chloride ion increases nearly in direct proportion to the total concentration of CPC, suppressing the formation of the free surfactant cation.) Therefore, to a good approximation, the molarity of micellar CPC in the retentate can be equated to the total concentration of CPC in that compartment, and the (small) concentration of micellar CPC in the permeate compartment is taken to be equal to the molarity of CPC in the permeate less 0.000 88 M. Using these approximations, we obtain an equation that can be used to calculate K directly from the measured quantities listed in Table I: K = ([PI, - [Pl,)/([Pl,[CPCl, - [Pl,([CPCl, - 0.00088 M)) (7) The last column in Table I lists values of the solubilization constant, K, for each of the SED experiments, calculated with eq 7. The values of K for the individual data sets (see Table I) do not appear to vary significantly throughout the range of phenol and CPC concentrations, and these values may simply be averaged to obtain a solubilization constant pertaining to the entire collection of data. Alternatively, nonlinear least-squares analysis18can be used to fit all of the data in Table I to eq 7. This procedure is probably preferable with regard to the weighting of the individual concentration measurements; it involves predicting the values of the concentration of phenol in the permeate ([PI,) from eq 7 and comparing these values with the experimental values. Assuming negligible errors in the measured concentration of phenol in the retentate and the concentrations of CPC in the retentate and permeate, we infer a value of the single fitting parameter, K = 55.8 f 0.5 L/mol, and a root mean square deviation in the con(18)Christian, S.D.;Tucker, E.E.Am. Lab. (Fairfield, Conn.) 1982, 14, 31.
Langmuir, Vol. 1, No. 5, 1985 567 centration of phenol in the permeate of 0.000066 M. Our previous vapor pressure studies of solubilization isotherms for organic solute/ionic surfactant systems have provided many example^^-^ in which solubilization constants (K values) change by large percentages as the concentrations of surfactant and organic solute change. Therefore, the lack of such a trend in the data in Table I may seem surprising. It should be noted that all the data in Table I pertain to retentate solutions in which the loading ratio (i.e., moles of phenol/moles of CPC) is approximately constant and equal to 1 5 ; therefore, although the concentrations of phenol and CPC are different in the different experiments, the individual thermodynamic activities of phenol and of CPC vary relatively little. Consequently, the micelle-solubilizate species should not vary greatly in stoichiometry throughout the range of experimental conditions represented in Table I. In more recent studies (not reported here), we have in fact found that the solubilization constant ( K ) does change as the phenolCPC ratio is varied at constant concentration of CPC. These studies will be the subject of a later report. Although the use of eq 7 in analyzing SED data appears to be justified in the present case (where the phenol and CPC concentrations are both in the 1-3 mM concentration range), the assumptions made in deriving the equation from the more nearly exact eq 6 will need to be examined critically in other applications of the method. Adding an organic compound to an aqueous micellar solution will in general lower the activity of the surfactant-that is, decrease the concentration of monomeric or unbound surfactant. Therefore, the value of [micellar CPC] inferred by subtracting the original value of the cmc will be somewhat too small. For organic solutes that are quite effectively solubilized by the surfactant micelles; this error will not be significant. The experimental technique and the analysis of SED data are simple and apparently quite general in application. With other surfactants and different classes of organic solutes, it will of course be necessary to ascertain whether the solute is transported across the membrane rapidly enough 80 that equilibrium is established with both the retentate and permeate solutions. The only experimental difficulties we have encountered are that at quite large CPC concentrations (greater than about 0.3 M), large pressure differences develop between the two sides of the cell, causing the membrane to bow from the concentrated to the dilute side and sometimes causing leakage from the retentate solution. These problems undoubtedly owe to the large osmotic pressure that develops in the concentrated surfactant solutions. If one wishes to employ the semiequilibrium dialysis method with quite concentrated surfactant solutions, it will probably be necessary to build special cells, perhaps similar to those employed by Mysels and Abu-Hamdiyyah."
Acknowledgment. Support for this research was provided by the Office of Basic Energy Sciences of the Department of Energy, Contract DEAS05-84ER13175, the University of Oklahoma Energy Resources Institute, and the Oklahoma Mining and Minerals Resources Research Institute. Registry No. CPC,123-03-5;phenol, 108-95-2.
