2258
Langmuir 1993,9, 2258-2263
Articles A Surface Tension Method for Determining Binding Constants for Cyclodextrin Inclusion Complexes of Ionic Surfactants Udeni R. Dharmawardana,? Sherril D. Christian,**tEdwin E. Tucker,t Richard W. Taylor> and John F. Scamehord Institute for Applied Surfactant Research, The University of Oklahoma, Norman, Oklahoma 73019 Received May 25,1993 A new method has been developed for determining binding constants of complexesof cyclodextrinswith surface-activecompounds, including water-soluble ionic surfactante. The technique requires measuring the change in surfacetension causedby addition of a cyclodextrin (CD)to aqueoussolutions of the surfactant; the experimental results lead directly to inferred values of the thermodynamic activity of the surfactant. Surface tension results are reported for three different surfactante (sodium dodecyl sulfate (SDS), cetylpyridinium chloride (CPC), and cetyltrimethylammoniumbromide (CTAB))in the presence and in the absence of added 8-CD. Data for CPC have been obtained at surfactant concentrations below and above the critical micelle concentration. Correlations between surface tension and surfactant activity are expressed by the Szyszkowskiequation, which subsumes the Langmuir adsorption model and the Gibbe equation. It is observed that the surface tension increases monotonically as 8-cyclodextrin is added to ionic surfactant solutions. At concentrations of CD well in excess of the surfactant concentration, the surface tension approaches that of pure water, indicating that neither the surfactant-CD complexes nor CD itself are surface active. Binding constants are inferred from a model that incorporates the parameters of the Szyszkowskiequation and mass action constants relating to the formation of micelles from monomers of the surfactant and the counterion. Evidence is given that two molecules of CD can complex the (2-16 hydrocarbon chain of the cetyl surfactants.
Introduction Cyclodextrins (CD's) are known to form inclusion complexes with a wide variety of molecular species.13 Association constants for such adducts have been determined by using a number of physical methods, including UV and visible spectroscopy,4calorimetry,6 conductivity,6 NMR,7*8and other method^.^ A precise vapor pressure method has been used to determine the binding constants of benzene with a-,@-, and T-CD.~ Previous work has demonstrated that a- and 8-cyclodextrins interact strongly with long chain aliphatic carboxylic aciddo and their salts, with alcohols,4 and with fluorinated analogs of these compounds.8 The strength
* To whom correspondence may be addressed. t Department of Chemistry and Biochemistry, the University of Oklahoma, Norman, OK 73019. t School of Chemical Engineering and Materials Science, The University of Oklahoma, Norman, OK 73019. (1) Saenger, W. Inclusion Compounds; Atwood, J. L., Davis, J. E. D., MacNicol, D. D., E&.; Academic Press: London, 1984; Vol. 2, p 234. (2) Thoma, J. A.; Steward, L. Starch Chemistry and Technology; Whistler, R. L., Paschall, E. F.,Eds.;Academic Press: New York, 1965; VOl. 1, p 209. (3) Szejtli, J. Cyclodertrin Technology;Kluwer Academic Publishers: Hingham, MA, 1988. (4) Sasaki, K. J.; Chriitian,S.D.;Tucker,E. E.Fluid PhaseEquilibria, 1989, 49, 281. (5) (a) Cromwell, W. C.; BystrGm, K.; Eftink, M. R. J.Phys. Chem. Perkin 1985,89, 326. (b) Cooper, A.; MacNicol, D. D., J. Chem. SOC., Perkin Tram. 2 1978,760. (c) Lewis, E. A.; Hansen, L. D. J. Chem. SOC., Tram. 2 1973, 2081. (6) Okubo, T.; Kitano, H.; Ise, N. J. Phys. Chem. 1976,80, 2661. (7) Wishnia, A.; Lappi, S. J. J. Mol. Biol. 1974, 82, 77. (8) Fung, B. M.; Guo,W.; Christian, S. D. Langmuir 1992,8, 446. (9) Tucker, E. E.; Christian, S. D. J. Am. Chem. SOC. 1984,106,1942. (IO) Schlenk, H.; Sand, D. M. J. Am. Chem. SOC. 1961,83, 2312.
0743-7463/93/2409-2258$04.oo/o
of CD-hydrocarbon chain interactions increases for the common water-soluble ionic surfactants as the length of alkyl chains increase^;^ conductometric, UV-visible epectral methods, and NMFt have all been used to infer binding The binding constants for sodium dodecyl sulfate (SDS)with 8-CD reported by Okubo et al.S and by Satake et al. (1985),11and by Satake et al. (1986),12using the conductometric method, are 356,1120, and 3630 M-l, respectively at 25 "C.A more recent study of eurfactantcyclodextrin interactions by conductometric measuremental3 shows that the binding constant of 8-CD with SDS appears to depend on the total SDS concentration. For example, values of binding constants reported by them at SDS concentrations of 1.00, 2.00, 3.00, and 5.00 mM were 7230,4690,3340, and 1380 M-l, respectively. However, problems inherent in the conductometric method may limit its utility in determining binding constants for CD-surfactant complexes. Direct UV or visible absorbance methods can only be used with compounds having suitable chromophoric groups. However, a convenient indirect method involves determination of the displacement of dyes that form CD complexes by observing the variation in spectral absorbance; phenolphthalein4 or methyl orange3has been used as the indicator in obtaining values of the association constants of CD with molecules lacking a chromophore. A disadvantage of the spectral displacement method using phenolphthalein is that very often it requires the addition (11) Satake, I.; Ikenoue, T.;Takeshita, T.; Hayakawa, K.; Maeda, T. Bull. Chem. SOC. Jpn. 1985,58, 2746. (12) Satake, I.; Yoshida, S.; Hayakawa, K.; Maeda, T.; Kusumoto, Y. Bull. Chem. SOC. Jpn. 1986,59, 3991. (13) Palepu, R.; Reinsborough, V. C. Can. J. Chem. 1988,66,325.
0 1993 American Chemical Society
Binding Constants of Complexes of Cyclodextrim
of a pH buffer and a significant added electrolyte concentration. Unfortunately, the indicator method cannot be used with ionic solutes containing the pyridinium ring (for example alkylpyridinium surfactants) because of the instability of the pyridinium group at pH = 10.5, the optimum pH for the method. In the present report, we describe a new method based on the use of surface tension measurements to infer changes in the thermodynamic activity of solutes such as the ionic surfactants, and thereby to obtain association constants of CD with these surface-active compounds. Although the effect of CD on the surface tension of surfactants has been reported previ~usly,'~J~ we are not aware of any attempts to use accurate measurement of this effect to determine CD binding constants of surfactants. Detailed modeling of surface tension data leads to the determination of both the parameters which pertain to the formation of micellesand their counterion binding and of the association constants for 1:l and higher order CD-surfactant complexes. Correlation of surfactant activities with surface tension values in the CDhrfactant solutions are made by using the Szyszkowski equation.l6J7 A somewhat similar analysis has been used previously by Lucassen-Reynders18 to relate surface tension to surfactant concentration and properties. The method described here can also be extended to investigate the binding of CD to any other solution component that is not surface active. This is done by including competitive binding equilibria for the surfactant and the second solute in the model, and using variation in surface tension as a measure of the change in activity of the surfactant.
Experimental Section Surface tension measurementswere made usingthe SensaDyne 6000 bubble pressure surface tensiometer, modified to permit variation of bubble times from about 1 s to as long as 25 s. About 30-50 measurements were made for a particular solution (using a bubble time of about 8-15 s) and the standard deviation of surface tension from the mean value was found to be less than h0.2 mN m-l. All surface tension measurements were made at 25 OC. The surfactants used in this study were sodium dodecyl sulfate (SDS) of 99% purity, obtained from Fisher Scientific Co., cetylpyridiniumchloride (CPC) of purity greater than 98%, obtained from Hexcel Specialty Chemicals, and cetyltrimethylammonium bromide (CTAB) of purity 98% obtained from Aldrich Co. SDS was recrystallized from 95% ethanol before use. CPC and CTAB did not show a minimum in the surface tension versus log concentration plot. The 8-CD was obtained from Aldrich and used as received. Surface tension versus concentration measurements were made for SDS, CPC, and CTAB in the absence of CD. Results were also obtained for solutions containing 2.00 mM CD and varying surfactant concentrations. Additional data were obtained for SDS at fixed surfactant concentration (5.08 mM) and variable CD concentration.
Data Analysis According to the Gibbs equation,lgthe variation of the surface tension (y) of a binary liquid solution caused by variation in the thermodynamic activity of a solute (in sufficiently dilute solution) can be expressed by ~~
(14) Kralova, K.;Mitterhauazerova,L.,First International Symposium on Cyclodeztrim; Budapest, Hungary, 1981, p 217. (15) Cserhati, T.;Szejtli, J. Carbohydr. Res. 1992, 224, 165. (16) Szyszkowaki,B. Von 2.Phys. Chem. 1908,64, 385. (17) Tipton, R. J. M.S. Thesis, University of Oklahoma, Norman, Oklahoma, 1989. (18) Lumen-Reynders, E.H.J. Phys. Chem. 1966, 70, 1777. (19) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed. John Wiley: New York, 1990; Chapter 111.
Langmuir, Vol. 9, No. 9, 1993 2259
-dy = r2R T d In a2 (1) where the surface excessquantity (r2)denotes the number of moles of the solute adsorbed per unit area at the liquidvapor interface and 0 2 is the thermodynamic activity of the solute. In the case of aqueous surfactant solutions, it has been long been recognized that the surface excess of the solute is also a function of 0 2 , and therefore knowledge of I'2 as a function of a2 at constant temperature makes it possible to infer changes in y for the aqueous solutions by integration of the Gibbs Even in the presence of added electrolyte, the dependence of I'2 on the surfactant activity (a21 appears to be practically the same as in the binary surfactant s o l ~ t i o n , ' ~although J~ some correction may be required to account for the surface excess concentrations of ions contributed by the added electrolyte.17JS21S3 Given the close relationship between surface tension and solute activity, it seems reasonable to suggest that determinations of the variation in the surface tension of surfactant solutions, caused by the addition of a second solute, could be used as a sensitive method for inferring values of formation constants for complexes formed between the surfactant and the added solute. For this method to have validity, it would be necessary that both the second solute and the complex be non-surface active, so that the same relationship between I'2 and a2 would obtain in the presence as in the absence of that component. Preliminary measurements provided an indication that ternary aqueous solutions containinga cationicsurfactant and varying amounts of 8-cyclodextrin do meet this criterion. O-CD is not itself surface active and solutions of cationic surfactants containing large excesses of &CD are observed to have a surface tension virtually equal to that of pure water. Therefore, measurement of surface tension alone should suffice to determine the change in a2 caused by addition of the cyclodextrin. Surface tension data for surfactant solutions in the absence of cyclodextrin were fitted with a nonlinear leastsquares method, using the Szyszkowski equation, which combines the Langmuir model for surface adsorption and the Gibbs equation. Some correlations were also made with the Frumkin surface adsorption model. In analysis of the data for solutionscontaining both CD and surfactant, equilibrium constants were introduced as independent parameters to account for the stepwise binding of CD to the alkyl moieties of surfactants. In the case of surfactant solutions at concentrationsgreater than the criticalmicelle concentration (cmc), parameters were also included to represent micelle formation by a mass action model (micelle formation constant, counterion binding fraction, and micelle aggregation number). By analyzing all of the surface tension vs concentration data, for systems below and above the cmc, and for solutions with and without added CD, it was possible to infer best values of the CD/ surfactant association constants as well as some of the parameters in the mass action model for micelle formation.20-22The theoretical model formulated for the premicellar region can be extended to apply to solutions containing CD, surfactant, and an additional organic solute which is not surface active but which binds to CD. (1) Model Equations for the Premicellar Region of Surfactant Solutionsin the Absence of CD. Modeling (20) Elworthy, P.H.;Mysele, K. J. J. Colloid Interface Sci. 1966,21, 331. (21) Tucker, E.E.;Christian, S. D. J. Colloid Interface Sci. 1986,104, 562. (22) Christian, S. D.;Tucker, E. E.; Lane, E. H. J . Colloid Interface Sei. 1981,84,423. (23) Okuda, H.;Ozeki, S.; Ikeda, S. Bull. Chem. SOC.Jpn. 198457, 1321.
Dharmawardanu et al.
2260 Langmuir, Vol. 9, No. 9, 1993 in the premicellar region is simple and straightforward; the acronym CPC (or CP+ for the surfactant cation) denotes the surfactant in all of the equations, and the counterion is assumed to be C1-. (Extension of the model equations to other Surfactants, including anionics, is straightforward). Denoting the mean ionic activity coefficient of the solution by y+,the following equations can be written using the Debye-Hiickel equation"*u to relate the activity of the surfactant to the ionic strength (I) QCPC
= YtCck, YICCP,
I = [CPCI,,
(2)
(3)
log(y,) = -0.5091'/2/(1 + 1.3111/2)+ 0.0491
(4)
where cclh and ccp, are molar concentrations of the free chloride and CP+ ions, respectively. It should be noted that formation of the complex in the premicellar region does not affect the ionic strength. When the Langmuir model for surface adsorption is combined with the Gibbs equation, the surface tension can be expressed in terms of the thermodynamic activity of the surfactant by the Szyszkowski equationl&ls (5) Y = yo- tD M I + Bacpc) where tD = P R T , r" is the value of surface excess of the surfactant when a complete monolayer is present, and B is related to the equilibrium constant in the Langmuir equation for adsorption of the surfactant at the liquid/ vapor interface. In applying the Frumkin the following two equations are substituted for the preceding equation
+
= Yo tD[in(i- 8)
+ ae2~
8/(1- 8) = Bacpc exp(2a8)
(6)
(7)
where a is a parameter accounting for interactions between adsorbed molecules and 8 is the fraction of the surface covered by a monolayer of the surfactant. When a = 0 the Frumkin model reduces to the Langmuir model. (2) Model Equations for the Premicellar Region in the Presence of CD. The previous equations can be augmented by including binding constants for 1:l and 1:2 complexes of the surfactant with CD. In this case, K1 represents the binding constant for the 1:l complex and K2 is the equilibrium constant for binding an additional CD molecule with the 1:l complex. The equations included in the model to account for the 1:l and 1:2 complexes were, therefore CDw, = CCD + KlCc~Ccp+ m$2Cc$Ccp (9) where ccp and CCD are the concentrations of CP+and CD, respectively. (3) ModelfortheMicellarRegionoftheSurfactant in the Presence of CD. By use of the mass action model, the equilibrium constant for forming ionic micelles from monomers of the surfactant and the counterion CM be written (K,,J'+q = [CPl,ceuJ(a"cp aqcl) (10) where n is the number of surfactant monomers and q is (24) Robinson, R. A.; Stokes, R. H., Electrolyte Solutions, 2nd ed.; Butterworthe: London, 1959; Chaptera 8 and 9. (25) (a) Frumkin, A. Z . Phys. Chem. 1929,103,55. (b) Adamson, A. W . Physical Chemistry of Surfaces,5th ed.; John Wiley: New York, 1990; p 236.
0
0.002 0.004 0.006 0.008
Molarity of SDS
Figure 1. Surface tension resulta for sodium dodecyl sulfate (SDS)in the presence and in the absence of B-cyclodextrin. Symbols represent experimental data and the dashed l i e s conform to the model (see text). the number of counterions in the micelle and where acp and ac1 are the individual ion activities of the surfactant cation and the counterion. The formation constant for the micelle is expressed as (KdJn+q,rather than K d o ,for convenience in the computer analysis of data. The ionic strength of the solution is expressed as
I = (cCl + ccP + KICCDCCP + K1K,CC$CCp)/2
(11) In calculation of the ionic strength, the contributions of the free counterions and the free and complexed surfactant are included, but the charged micelles are assumed not to contribute to I. (A discussion of the justification for omitting the effect of the micellar ion on ionic strength is given later). The mass balance equations for the surfactant and CD are
[ c p l b d = CCp + [cpldmUw + K1cCDccp + K1K2CC$CCP (12)
A similar equation is written to relate the total concentration of the counterion (e.g. chloride) to the concentration of free chloride and the concentration of surfactant in micelles: [Cll,, = ccl + [CPl,wUwq/n (14) In fitting data to this model, an iterative procedure is required within the least-squares program to infer the concentrations of individual species (free and bound counterions, CP monomer, CD monomer, and CP in micelles), the ionic strength, and the activity coefficients of the free CP ion and the counterion, for chosen values of the fitting parameters in the model.
Results and Discussion Figures 1-5 show results of nonlinear least-squares fitting of data obtained for the three surfactants, in the presence and in the absenceof added CD, using the modela described above. Table I summarizesvalues of the fitting parameters that were inferred for each system. The derived parameter values were obtained by a global search method, in which they are allowed to vary in an unrestricted way so as to attain an absolute minimum in the sum of squares of deviations between the observed surface tensions and values predicted by the model. In the case of the CTAB and SDS systems, the experimental measurements were limited to regions in which micelles do not
Langmuir, Vol. 9, No. 9, 1993 2261
Binding Constunts of Complexes of Cyclodextrins
2
E
v
'4
40'
0
'
'
'
'
"
'
'
"
"
0.001
5*10°4
'
" '
'
'
0.0015
Molarity of CTAB Figure 2. Surfacetension resulta for cetyltrimethylammonium bromide (CTAB)in the presence and in the absence of &cyclodextrin. Symbolsrepresent experimentaldata and the dashed lines conform to the model (see text).
0
W1m20Qrr3VlCD
0
0.002
0.001 0.002 0.003 0.004 0.005
Molarity of CD Figure 6. Surface tension resulta for cetylpyridiniumchloride (CPC)solutionscontaining2.00 mM CPC and variable amounte of added 8-cyclodextrin. Symbols represent experimental data and the dashed lines conform to the model (see text).
Table I. Table of Best Fit Parameter Values Obtained by Least-Sauares Data Analysis.
K2-265X102
SDS
CPC
CTAB
(4.18f 0.43) x 1P 9.58 i 0.39 (8.36 1.2) x 103 0
(4.19 i 0.25) x 101 7.24 & 0.140 (4.88 f 0.18)
(3.27 i 0.09) x 107 9.69 i 0.110 (6.55 i 0.03) x 104 398 i 71
7
B (M-2) tn (mN m-1) I
I
Ki (M-9 K2
(M-')
Q &C
RMSD(mN m-l)
0.77
x 104
265 i 95 64 f 29 974 i 87 0.47
0.27
B and t~ are values of parameters in the Szyszkowski equation as defined in eq 6. K1 is the association constant for formation of the 1:l complex between &cyclodextrin and surfactant. K2 is the equilibrium constant for binding a second &cyclodextrin to the 1:l complex. q and K,,,jc represent the number of bound counterions and the micellization constant (we eq 10 in model 3). SDS, CPC, and CTAB denote sodium dodecyl sulfate,cetylpyridiniumchloride. and cetyltrimethylammoniumbromide, respectively. a
40'. , " 0 5*10°4 0.001 0.0015 Molarity of CPC "
'
"
"
'
" '
'
'
,
'
0.002
Figure 3. Surface tension results for cetylpyridiniumchloride (CPC)in the presence and in the absence of 8-cyclodextrin.
Symbols represent experimental data and the solid dashed conform to the model (see text). ; 70 E Z
-E C al
t,g
6o
40
1 0
,
0.002
0.004 0.006 0.008 Molarity of CD Figure 4. Surfacetenaionresultsof sodium dodecylsulfate (SDS) when 8-cyclodextrin (CD)is graduallyadded to a 5.08 mM SDS solution. Symbolsrepresent experimental data and the dashed lines conform to the model (see text).
exist, so it was not possible to infer parameters characteristic of micelle formation. The data for CPC were fitted using a value of n (the micelle aggregation number) equal to 100, as estimated from vapor pressure osmometry measurements26and other information about the aggre(26)Buahong, D. S. Ph.D. Dwrtntion University of Oklahoma,
Norman,OK, 1985.
gation numbers of similar surfactants. However, the micelle formation constant and number of counterions per micelle ( 9 ) could both be inferred by the nonlinear least-squares analysis. The least-squares analysis of data for all three surfactants,in the absence of &CD, indicated that a reasonably good correlation can be obtained by using the Szyszkowski equation (asshown in Figures 1to 3). In the case of analysis of the present results for CPC as well as data reported previ~usly,'~ a reduction in the sum of squares of deviations is attained by employing the more-complicated Frumkin However, the goodness of fit obtained for CPC using the Szyszkowski equation is also quite satisfactory, provided the data are restricted to solutions having values of surface tension less than about 70 mN m-l. In fitting the surface tension data for solutions containing added CD (in the premicellar region) the inclusion of 1:2 complexes in the model (in addition to the 1:l complex) significantly improved the goodness of fit for the CPC and CTAB systems. Quite good agreement between the data and model resulta was obtained, as is indicated by the very small root mean square deviation (RMSD) values and small standard deviations in parameter values (see Table I and Figures 2 and 3). However, in the case of the SDS results, inclusion of the 1:2 complex did not significantly improve the agreement between the model and the observed surface tension results (seeFigure 1). This suggests that the contribution of the 1:2 complex is less important with SDS because the C12 hydrocarbon chain is too short to accommodate two CD molecules.
Dharmawardarua et al.
2262 Langmuir, Vol. 9, No. 9, 1993 Moreover, the value of the parameter K (the 1:l binding constant) obtained for SDS has a much larger standard error than K for the other surfactants, perhaps reflecting the difficulty of obtaining accurate values of surface tension for this compound because of the presence of surface active impurities not readily removed by recrystalli~ation.~' The reported binding constant for SDS (8.36 X lo3 M-l) was obtained by fitting the combined data, which include results for a fixed SDS concentration and variable CD concentrations and vice versa. The derived K value from this analysis is considerably lower than that inferred by the visible spectral displacement method using phenolphthalein4 (K1 = 18500 M-l), possibly because of the presence of the buffer and added electrolytes in the displacement studies. With CPC and CTAB the first binding constant is much larger than that for SDS (Table I). The large increase in binding reflects the increase in the hydrophobic alkyl chain length from Clz to C16; a similar effect was reported previously for the aliphatic alcohols and several ~urfactants.~ Figure 4 shows the dependence of the surface tension of SDS solutions (at fixed SDS concentration) on the concentration of added CD. A satisfactory fit of the data is obtained, althoughthe goodness of fit is somewhat poorer than for the other surfactants. The likelihood of having a significant amount of the 1:2 surfactant-CD complex may be considered in relation to estimates of the geometry of the CD cavity and the length of the alkyl chain of the surfactant. The height of the torus of the 8-CD molecule3 is 7.8 (fO.l) A, whereas the approximate extended chain lengths of dodecyl and cetyl groups are approximately 15 and 20 A, respectively, calculated based on the C-C chain with tetrahedral angle of 109O and the van der Waals' radius of the terminal methyl group (-2.0 Ahz8 Thus, although the C-16 group is long enough to accommodate two CD molecules, steric factors and other entropic effects may be expected to reduce the stability constant for the addition of the second CD by as much as 2 orders of magnitude. The 1:lcomplex would have a protruding alkyl chain no longer than approximately half of the C-16 chain of the uncomplexed CTAB or CPC molecule and, barring cooperactivity, the stepwise 1:2 binding constant might be comparableto that of an aliphatic alcohol having approximatelyeight carbons. Previously, the 1:l formation constant for octanol$-CD was reported3 to be 1600 M-4 The stepwise equilibrium constant for the association reaction CD + CPC*CD= CPC*(CD)z
(15)
is equal to 398 M-' for CTAB and 265 M-l for CPC (see Table I), less than one-third the value of the association constant for the CD-octanol complex. For SDS, the protruding alkyl chain in the 1:l complex should be no longer than the C-4 or C-5 chain, so that the expected stepwiseequilibrium constant should be no grater than K for the 1:l complexes of butanol or pentanol with CD (19 and 62 M-l, respectively% Therefore, it would be difficult to obtain an accurate KZusing the SDS surface tension data. The binding constant of CTAB is somewhatlarger than that of CPC, although the two surfactants have the same alkyl chain length. Through complexation of the surfactant alkyl groups within the CD cavity, a large part of the hydrophobicsurface of the surfactant molecule is removed from contact with water. The exterior of the CD cavity (27) Tanford, C. J. Phys. Chem. 1972, 76, 3020. (28) Hill,R. M. Ph.D. Dissertation,University of Oklahoma, Norman, OK,1982.
is quite hydrophilic and therefore the complexed molecule as a whole should become much less surface active; in fact
the surface tension data for CD solutions without surfactant and for solutions containing a large mole ratio of CD to surfactant indicate no surface activity whatever for either CD or the CD-surfactant complex(es). The variation in surface tension caused by adding CD to micellar solutions of CPC is of particular interest. Before obtaining the data shown in Figure 5, we had predicted that the surface tension would decrease on addition of CD, primarily owing to the release of free counterions, which could be expected to increase the activity of the surfactant. However, it is impressive that the analytical procedure derived for fitting all the data (a combination of models 2 and 3 above) provides a near-quantitative prediction of the entire surface tension vs concentration curve. The prediction of an initial decrease in the surface tension as CD is added to micellar CPC reflects two factors: (1) the release of counterions as surfactant monomers are removed from the micelles and (2) the concomitantincrease in ionic strength, both of which affect the activity of the surfactant, but in opposite directions. The model also predicts accurately the concentration of CD at which all of the micelles are "used up" through removal of CP+ ions from micelles to form the complex, and at which point the surface tension curve exhibits an apparent discontinuity in slope. We believe that the success of the model in fitting surface tension data for CPC in the micellar region, both in the presence and in the absence of added CD, provides some support for the assumption (vide supra) that the charged micelles do not contribute to the ionic strength. Previous investigator^^^^^^ have argued that the effect of ionic micelles (with their bound counterions) on ionic strength is considerably less than would be predicted by using the conventional '/2cizi2 term that is included for solutions containing smaller ions.17~20~24 The so-calledpseudophase equilibrium model for surfactant solutions treats the "micellar phase" and the "bulk aqueous solution" as separate regions possessing their own local thermodynamic proper tie^;^^ thus the assumption that the charged micelle can be ignored in ionic strength calculations is in agreement with the pseudophase model. A recent study of the effect of CY- and 8-CD's on the surface tension of poly(oxyethy1ene) (POE) nonionic surfactants15provides information that is quite different from that obtained here for the ionic surfactants. In a series of studies of aqueous solutions of nonylphenyl and tributylphenyl POE surfactants, it was found that adding CD increases the surface tension of the more hydrophobic surfactants and decreases the surface tension of the more hydrophilic surfactants. However, in the case of nonmicellar solutions of the ionic surfactants,the surface tension is increased in every case, and the highly hydrophobic C-12 and (2-16 alkyl groups are clearly prevented from being surface active by encapsulation in the 8-CD cavity. Conclusions The present report describes a novel method for determining binding constants of cyclodextrins with surface-active solutes. Numerical methods are described for fitting surface tension vs concentration data with reasonable models for surface activity, complex formation, and micelle formation. Possible additional applications (29) Burchfield, T. E.; Woolley, E. M.J . Phys. Chem. 1984,88,2149. (30) Shinoda,K. In Colloid Surfactants; Shinoda,K., Tamamuhi,T., Nakagawa, T., Isemure, T., Eds.;Academic Press: New York, 1963; Chapter 1.
Binding Conetants of Complexes of Cyclodextrins of the technique may include the analytical determination of surfactant concentrationsand investigationsof micellar association and counterion binding. The formation of surfactantlcyclodextrin complexes, in the presence of added electrolytesand at varying pH, could also be studied without significantly increasing the complexity of the mathematical model. Measurement of the dependence of surface tension on surfactant concentration within the micellar region might also prove to be a valuable tool for investigating the thermodynamicsof solubilizationof nonsurface-active solutes. The ability of CD to screen hydrophobic moieties of surfactant molecules from contact with the surrounding aqueous medium is an interesting feature that may be useful in elucidating the solution behavior of surfactants and their properties in adsorbed layers at liquid-vapor and liquid-liquid interfaces. The fact that nonionic (POE) surfactants do not behave in the same way as the ionic
Langmuir, Vol. 9, No. 9,1993 2263 eurfactant16 may provide a key to interpreting characteristic structural effects occurring at interfaces or within micelles for these two different classes of surface-active compounds. Acknowledgment. The authors appreciate the financial support of the Office of Basic Energy Sciences, Department of Energy, Contract DE-FG05-87ER13678, National Science Foundation Grant CBT 8814147, EPA Grant R-817450-01-0, Bureau of Mines Contract 90-09, and an Applied Research Grant from the Oklahoma Centers for the Advancement of Science and Technology. In addition, they gratefully acknowledge the assistance of industrial sponsors of the Institute for Applied Surfactant Research, including Aqualon Company, Kerr-McGee Corporation, Sandoz Chemicals Corp., E. I. du Pont de Nemours & Co., Union Carbide Corporation, Unilever, Inc., IC1 Corp., and Shell Development Company.
