10868
J . Phys. Chem. 1993, 97, 10868-10871
A Modified Semiequilibrium Dialysis Method for Studying Solubilization in Surfactant Micelles: Testing the Semiequilibrium Assumption Hirotaka Ucbiyama, Sherril D. Christian,’*tEdwin E. Tucker,+and John F. Scamehoms Institute for Applied Surfactant Research, The University of Oklahoma, Norman, Oklahoma 73019 Received: May 6, 1993; In Final Form: August 9, 1993”
Thedetailed analysis of data obtained with the semiequilibrium dialysis (SED) method for studying solubilization in surfactant micelles requires accounting for the formation of micelles in the permeate compartment and for the presence of solubilized organic solute in these micelles. An extension of the SED method is proposed here, in which the concentration of surfactant is maintained well above the critical micelle concentration (cmc) in both compartments of the dialysis cell. Under these conditions, it is shown that the validity of the ‘semiequilibrium” assumption, viz., that the organic solute reaches equilibrium simultaneously with both surfactant solutions, can be demonstrated for solutions of small organic molecules and typical ionic surfactants. Agreement of the new results with those obtained in conventional SED results (obtained using a concentrated surfactant solution on one side of the dialysis membrane and pure water on the other) implies that semiequilibrium is ordinarily attained in SED studies of low molecular weight solutes such as phenol and its derivatives. It is also suggested that the new modification of the SED method has important mathematical and experimental advantages over conventional SED in inferring equilibrium solubilization results.
Introduction Equilibrium dialysis has been used for many decades in studies of the binding of low molecular weight solutes to macrom0lecules.~-3 However, the utility of equilibrium dialysis as a technique for studying the solubilization of organic solutes by aqueous surfactant micelles is complicated by the gradual transfer of surfactant from the retentate into the permeate compartment, resulting in the solubilization of significant quantities of the organic solute in micelles that form in the permeate.“* Ignoring the presence of micelles in the permeate compartment can lead to quite large errors in inferred values of partition constants for transfer of solutes from the “bulk aqueous solution” into the
micelle^.^-*^ Recent articles from our laboratory describe the use of a technique called semiequilibrium dialysis (SED),9-23in which the extent of solubilizationof organic solutes in micellar solutions is inferred from analytical determinations of the concentrations of surfactant and solubilizate in both compartments of the cell; an equilibration period of approximately 20-24 h is commonly employed. Allowance is made for the presence of micelles in both compartments, and in the mathematical analysis of data the basic assumption is made that the organic solute is able to attain equilibrium with the surfactant solutions on both sides of the membrane. This implies that the thermodynamic activity of the organic solute will be the same in both compartments, and in the absence of large differences in ionic strength it is ordinarily assumed that the monomer concentration of the organic is the same in the retentate as in the permeate. It should be obvious, of course, that the surfactant cannot reach equilibrium in an SED experiment in any reasonable period of time, and in fact true equilibrium would be a state in which there is no difference between the concentrations of either the surfactant or the organic solute in the two compartments of the dialysis cell. It should also be apparent that attempts to use dialysis to *measure” the concentration of surfactant monomers in equilibrium with micelles will be unsuccessful because the surfactant continues to diffuse through the dialysis membrane at Department of Chemistry and Biochemistry, The University of Oklahoma, Norman, OK 73019. 3 School of Chemical Engineering and Materials Science, the University of Oklahoma, Norman, OK 73019. Abstract published in Aduance ACS Abstracts. September 15, 1993.
0022-3654/93/2097- 10868$04.00/0
a significant rate even after the critical micelle concentration (cmc) is exceeded in the permeate ~ompartment.~Similar difficulties are inherent in attempts to infer monomer concentrations from ultrafiltration experiments, although the permeate concentrations of an organic solute and the mean ionic concentration of an ionic surfactant often approximate equilibrium values.24-26 In determining whether the SED method can provide accurate results in a wide variety of solubilization studies, with numerous types of surfactants and solubilizates, it will be important to examine in detail the key assumption of the method, viz., that the organicsolutesimultaneouslyreaches thermodynamicequilibrium with both of the surfactant solutions in the dialysis cell, after a suitable equilibrationperiod. The good agreementbetween results obtained by SED and other reliable experimental methods has already provided circumstantial evidence that the “semiequilibrium” assumption is valid for many types of systems, but it will be useful to develop a protocol for determining whether or not limitations on the SED method may make its use questionable for certain types of systems. Mathematical modeling, using assumed values of diffusion coefficients and effective mass-transfer coefficients, could help define the conditionsunder which the semiequilibriumassumption does or does not apply. However, the use of an experimental procedure maintaining conditions typical of actual SED experiments may be preferable in testing the semiequilibrium assumption. We describehere an approach for studying the transfer of the organic solutes and surfactants between the two compartments of the dialysiscell, in which the surfactant concentration is maintained well above the cmc both in the retentate and in the permeate. Under these conditions, the transfer of surfactant is demonstrably quite slow, reflecting the small difference in thermodynamic activity of the surfactant between the two compartments. The transfer of organic solute, however, occurs relatively rapidly during the first few hours of equilibration,under conditions quite similar to those in the usual SED experiments, where the permeate initially containsonly pure water or electrolyte solution. By measuring the change in theorganic (and surfactant) concentrations in the two compartments during a period of several days, it is possible to determine experimentally whether the semiequilibriumassumptionsare tenable for any given surfactant and organic solute. 0 1993 American Chemical Society
The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10869
Solubilization in Surfactant Micelles TABLE I: Concentrations of Phenol and CPC in Permeate and Retentate Sides after 24, 48, and 72 h permeate" retentateb time, h phenol (M) CPC (M) phenol (M) CPC (M) 24
48
72
0.001 96 0.003 89 0.005 83 0.008 06 0.010 23 0.012 56 0.015 44 0.016 85 0.001 71 0.003 67 0.005 85 0.007 82 0.010 14 0.012 78 0.014 84 0.001 94 0.003 94 0.006 15 0.008 26 0.010 35 0.012 86 0.015 19
0.01 1 38 0.010 78 0.010 52 0.010 26 0.010 89 0.010 69 0.010 73 0,010 59 0.010 54 0.011 05 0.01 1 85 0.01 1 41 0.01 1 07 0,010 97 0,010 77 0.011 99 0.01 1 58 0.011 84 0.011 74 0.01 1 5 5 0.01 1 45 0.011 17
0.007 35 0.015 63 0.022 84 0.031 92 0.036 78 0.044 65 0.053 46 0.058 20 0.006 08 0.013 70 0.020 64 0.025 87 0.034 40 0.043 68 0.049 94 0.007 23 0.014 72 0.021 52 0.029 08 0.035 23 0.043 45 0.05045
0.080 79 0.087 28 0.085 97 0.089 61 0.084 72 0.083 19 0.083 83 0.085 85 0.083 64 0.086 15 0.077 79 0.081 34 0.082 97 0.086 79 0.085 40 0.085 73 0.083 74 0.081 34 0.083 04 0.082 19 0.084 20 0.084 19
Initial concentration of CPC 0.01 mol/L. b Initial concentration of CPC 0.1 mol/L. Experimental Method Conventional two-compartment dialysis cells have been used for all of the experiments; each compartment contains approximately 5 mL of solution, and the two sidesof the cell are separated by a regenerated cellulose membrane (6000 molecular weight cutoff membrane). A relatively concentrated solution of the surfactant and an organic solute [e.g., 0.100 M hexadecylpyridinium chloride (cetylpyridinium chloride or CPC) and 0.0050.07 M phenol] is placed in the retentate compartment, and a less concentrated surfactant solution [e.g., 0.010 or 0.020 M hexadecylpyridinium chloride (CPC) J is placed in the permeate. At least three cells are assembled and loaded with the same retentate and permeate solutions so that results can be obtained for replicate samples after different equilibration periods: typically 1, 2, and 3 days. In most of the experiments, pieces of glass tubing cut in half lengthwise were placed in the permeate compartment to minimize the osmotic pressure-induced flow through the membrane. The presence of the piece of glass in the permeate compartment mechanically opposes the transfer of water owing to the osmotic pressure difference between the two solutions. Analytical concentrationsof the organic (0)and surfactant (CPC) are determinedby UV ~ p e c t r o s c o p y ; ~the ~ . experimental ~~-~~ results comprise collections of [Olper, [CPCJper, [Olret, and [CPCIret, corresponding to the stated equilibration times. The symbol [ ] denotes the total or analytical concentration of organic or surfactant, and the subscripts per and ret indicate permeate and retentate compartments. ReSultS
Table I includes results of a series of experiments performed at the indicated initial concentrations of surfactant in both compartments and the concentration of organic in the retentate. Values of [Olper, [CPCIper, [Olret, and [CPC],,t at 24,48, and 72 h are also tabulated. In every case, there is a significant initial decrease in the concentration of surfactant in the retentatecaused by an influx of water into the retentate, owing to the difference in osmotic pressure between the two compartments. But the salient feature of the results is that, after an initial equilibration period of 1 day, there is very little additional change in the surfactant or organic solute concentrationsin either Compartment. Values of the solubilization constant, K = X/cor,(where X is the
0 A 0
0
0.1
0.2
0.3
24hrs 48hra 7th Klrom Re119
0.4
0.5
Mole fraction of phenol in micelle (XOrg) Figure 1. Dependence of solubilization equilibrium constantsfor phenol in hexadecylpyridinium chloride (CPC) micelles on intramicellar mole fraction of phenol.
TABLE II: Thermodynamic Activities and Species Concentrations for Hexadecylpyridinium Chloride (CPC) in Aqueous Solution at 25 'C [CPCI (MI 106as(M2) CCP (M) CCI- (M) C+ (MI 0.01 0.02 0.03 0.05 0.07 0.10
1.19 1.43 1.61 1.86 2.05 2.27
0.00041 0.000 27 0.000 21 0.000 15 0.000 12 0.000 10
0.0032 0.0060 0.0088 0.0146 0.0204 0.0291
0.001 14 0.001 27 0.001 36 0.001 49 0.001 59 0.001 70
mole fraction oforganic solutein the micelleand corgisthemolarity of monomeric or free organic solute in the bulk aqueous phase), can be calculated using mathematical methods introduced in a previous report.27 The derived Kvalues are plotted against mole fraction of the organic in the micelle in Figure 1 and compared with the Kvalues obtained previously using the conventional SED method.I9 Except at Xvalues KO.1, for which small errors in the chemical analysis can greatly affect the derived K values, there is excellent agreement between results obtained with the original and the modified SED techniques. Discussion It is interesting to consider the thermodynamics of transfer of the surfactant from the retentate to the permeate during the equilibration period. Table I1 provides data indicating the dependence of solution properties of CPC on total CPC molarity at 25.0 OC; included are values of the activity of CPC on the unit molarity, ideal dilute solution standard state basis (as), the molarities of the free surfactant cation and the free chloride anion (CCP+ and CCI-), and the mean ionic molarity (c*). These results have been estimated from correlations of reported vapor pressure osmometry and surface tension data,28using a mass action model developed previously to calculate ion activities and species concentration^.^^^^^ Figure 2 includes plots of mean ionic molarity (c~),the molarity of the cetylpyridinium cation (ccP+),and the surfactant activity (a, = ra2ccp+cc1-)for total CPC concentrations in the range 0.01-0.10 M. The derived quantities shown in Table I1 and Figure 2 are useful in determining the driving force responsible for transport of the surfactant across the dialysis membrane in SED experiments. If, for example, a 0.10 M CPC solution is placed in the retentatecompartmentand0.020M CPCisplacedin thepermeate compartment, values of the mean ionic molarity in the two compartments (c*) are approximately 1.7 X l W and 1.3 X 10-3 M, respectively, and the corresponding activity values (a,) are about 2.3 X and 1.4 X 1od MZ.Thus, the driving force for transfer of CPC is quite small compared to that obtained in ordinary SED experiments, where initially a surfactant solution
10870 The Journal of Physical Chemistry, Vol. 97, NO. 41, 1993 0.0020 ’
.-.
2.5 x 10‘
Meu ionic molvily molvilv
0-0 MOlulIy of CP‘
t t Swfsount uctivity
P
. I
0.0015
.e 10‘ 3
E
m er m
lr
c,
1 0.0010
c)
0
-
0.0005
0 ’ 0
1 . 5 10‘ ~
I
a . /
0.02
0.04
0.06
0.08
a
m
1.0 x 10‘ 0.1
[CPCI(M) Figure 2. Mean ionic molarity, molarity of CP+, and surfactant activity as a function of CPC concentration.
a t a concentration well above the cmc is placed in the retentate compartment and pure water is placed in the permeate. In such experiments, the relative change in surfactant concentration in the permeate compartment is necessarily quite large during the first few hours, and even after the cmc is reached (at approximately 8 or 10h), an additional 3040% change in the CPC concentration may beexpected tooccur during thesubsequent 12h. Incontrast, the conditions maintained in the experiments performed here (with concentrations of surfactant greatly exceeding the cmc in both compartments) should ensure that the relative change in the total surfactant concentration (except for the osmotic effect) will be at most a few percent for an equilibration period of approximately 24 h. Therefore, the organic solute (which may be expected to have a half-life for transfer from the retentate to the permeateofonly 1 or 2 h9) should have little difficulty “keeping up” with the changes in surfactant concentration occurring concurrently in either compartment. The results in Table I are consistent with the conclusions drawn here, in that they indicate that there is little variation in the organic or surfactant concentration in either compartment of the dialysis cell for equilibration times of at least 20 h. In fact, the major reason for change in surfactant concentration during the first few hours is the osmotic pressure, which forces a significant volume of water through the membrane between the permeate and retentate compartments. An advantage of the modified SED procedure introduced here is that the concentration of monomeric surfactant (cc~+)is quite small compared with the micellar concentration in both compartments. Thus, in the example given in the preceding paragraph, the concentration of free surfactant cations is about 0.1% [CPC] in the retentateandless than 1.5% [CPC] in thepermeate. Adding an organic solute will ordinarily further reduce these percentages, so to a very good approximation, the presence of free surfactant can be ignored in inferring the extent of solubilization in micelles. This greatly simplifies the analysis of SED data to obtain solubilization equilibrium constants, because the mass balance relations for the organic solute are quite simple:
Making the usual assumption that values of X and cor, (the concentration of unbound organic solute) are the same in both compartment^,^-'^ one can compute both cor, and X from these relations, knowing the analytical concentrations of the organic and the surfactant in both compartments; therefore, the solubilization constant, K = X/corg,is readily calculated. Using the assumption that all of the surfactant is in micellar form leads to K values differing by no more than 3% from the values plotted in Figure 1.
Uchiyama et al. If it is necessary to account for the (small) concentration of surfactant existing in monomeric form in the permeate, such corrections can readily be made using the estimated value of K inferred by the procedure just described. It may also be mentioned that adding the same concentration of an electrolyte to both sides of the dialysis cell would further suppress the ionization of an ionic surfactant, making eqs 1 and 2 even better approximations than in the absence of added electrolyte. One problem inherent in the SED method-the difficulty in determining the extent of solubilization in micelles when K is greater than 1000 M-I-can be understood in relation to the concepts discussed here. Thus, if an SED experiment is to be performed with a given solute having a large affinity for the surfactant micelles, and a correspondingly small value of the unbound (monomer) concentration, the percentage of organic that is bound to micelles will be nearly unity in both compartments. In this case, the ratios [O]pr/[CPC]p and [O]ret/[CPC]ret will be practically equal, so that exceptionally good analytical determinations of the solute concentrations will be needed to obtain a significant value of K. For example, if K = 2000 M-I, [CPCIpr = 0.010, and [CPCIre, = 0.10, and if [O]r,t/[CPC]ret is 0.100, the ratio [O],,/[CPC],, will be 0.104 (neglecting the contribution of surfactant monomers to the total surfactant concentration in each compartment). In other words, the concentration of free organic molecules is only a small fraction of the total organic concentration, even in the permeate compartment, so that the ratios calculated above differ by only a few percent in the two compartments. Although the original SED method can be used to obtain reasonable values of K in such systems (by using a relatively small concentration of surfactant in the retentate and pure water in the permeate), the corrections applied to account for the formation of micelles in the permeate become critically important, imposing an inherent limit on the accuracy with which K can be calculated. But with the modified procedure it is easy to investigate the effects of analytical errors on derived values of the solubilization equilibrium constant and to determine whether worthwhile results can be obtained with the method. Acknowledgment. The authors appreciate the financial support of the Center for Waste Reduction Technologiesof the American Institute of Chemical Engineers, Agreement No. N12-Nl0. References and Notes (1) Freifelder, D. In Physical Biochemistry-Applications to Biochemistry andMolecularBiologv, 2nded.;W. H . Freeman and Co.: San Francisco, 1982; p 675. (2) Cantor, C. R.; Schimmel, P. R. In Biophysical Chemistry; W. H. Freeman and Co.: San Francisco, 1980; Part 111, pp 1328-1339. (3) Molyneux, P. In Water-SolubleSyntheric Polymers: Properties and Behaoior; CRC Press: Boca Raton, FL, 1984; Vol. 11, pp 101-105. (4) Patel, N. K.; Kostenbauder, H. B. J. Am. Pharm. Assoc., Sci. Ed. 19J8, 47, 289. (5) Kazmi,S. J. A.; Mitchell, A. G . J . Pharm. Pharmacol. 1971,23,482. (6) Mitchell, A. G.; Brown, K. F. J . Pharm. Pharmacol. 1966,18, 115. (7) Patel, N. K.; Foss, N. E. J. Pharm. Sci. 1965,54, 1495. ( 8 ) Patel, N. K.; Foss, N. E. J . Pharm. Sci. 1964, 53, 94. (9) Christian, S. D.; Smith, G . A,; Tucker, E. E.; Scamehorn. J. F. Lungmuir 1985, I , 564. (10) Smith, G . A.; Christian, S. D.; Tucker, E. E.; Scamehorn, J. F. J . Solution Chem. 1986, 15, 519. (11) Higazy, W. S.; Mahmoud, F. Z.; Taha, A. A,; Christian, S.D. J. Solution Chem. 1988, 17, 191. (12) Bhat,S.N.;Smith,G.A.;Tucker,E.E.;Christian,S.D.;Scamehorn, J . F.; Smith, W. Ind. Eng. Chem. Res. 1987, 26, 1217. (13) Smith, G. A.; Christian, S. D.; Tucker, E. E.; Scamehorn, J. F. Lungmuir 1987, 3, 598. (14) Christian, S. D.; Scamehorn, J. F. In Surfactant-Based Separation Processes;Scamehorn, J. F., Harwell, J. H., Eds.; Marcel Dekker: New York, 1989; pp 3-28. (15) Sasaki,K.J.;Burnett,S.L.;Christian,S.D.;Tucker,E.E.;Scamehorn, J. F. Langmuir 1989, 5, 363. (161 Christian, S. D.; Tucker, E. E.; Scamehorn. J. F.; Lee, B. H.; Sasaki, K. J . hngmuir 1989, 5, 876. (17) Mahmoud, F. Z.; Christian, S. D.; Tucker, E. E.; Taha, A. A.; Scamehorn, J. F. J . Phys. Chem. 1989, 93, 5903.
Solubilization in Surfactant Micelles (18) Scamehorn, J. F.; Christian, S.D.; Tucker, E. E.; Tan, B. I. Colloid Sur$ 1990,49. 259. (19) Lee, B.-H.;Christian.S.D.;Tucker,E.E.;Scamehom, J. F.Langmuir I&, 6, 230. (20) Uchiyama, H.; Christian, S.D.; Scamehorn, J. F.; Abe, M.;Ogino, K.Langmuir 1991, 7 , 95. (21) Lee, B.-H.;Christian,S. D.;Tucker, E. E.;Scamehorn, J. F.J. Phys. Chem. 1991, 92, 360. (22) Lec,B.-H.;Christian,S. D.;Tucker,E.E.;Scamehom, J. F.Langmuir 1991, 7, 1332. (23) Lee, B.-H. Ph.D. Dissertation, The University of Oklahoma, 1990.
The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10871 (24) Dunn, R. 0.Ph.D. Dissertation, The University of Oklahoma, 1987. (25) Robert, B. L. Ph.D. Dissertation,The University of Oklahoma, 1993. (26) Osborne-Lee,I. W.;Schechter,R.S.; Wade, W.H.J. CoNoidlnterface Sci. 1983, 94, 179. (27) Christian, S.D.; Tucker, E. E.; Scamehorn, J. F.; Uchiyama, H. In press. (28) Bushong, D. S. Ph.D. Dissertation, The University of Oklahoma, 1985. (29) Dharmawardana, U.; Christian, S.D.; Tucker, E. E.; Taylor, R. W.; Scamehorn, J. F. Langmuir, in press.
