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J. Phys. Chem. B 1998, 102, 480-488

Volumetric Study of Modified β-Cyclodextrin/Hydrocarbon and /Fluorocarbon Surfactant Inclusion Complexes in Aqueous Solutions Lee D. Wilson and Ronald E. Verrall* Department of Chemistry, ThorValdson Building, UniVersity of Saskatchewan, 110 Science Place, Saskatoon, SK, S7N 5C9 Canada ReceiVed: August 1, 1997; In Final Form: October 17, 1997X

The apparent molar volumes (Vφ,S) of homologous series of hydrocarbon (hc) [CxH2x+1CO2Na, x ) 5, 7, 9, 11, 13] and perfluorocarbon (fc) [CxF2x+1CO2Na, x ) 3, 6-9] surfactants (S) have been determined in water and in binary solvent (H2O + modified β-cyclodextrin (R-β-CD)) systems at 25 °C. The apparent molar volumes (Vφ,R-β-CD) of 2,6-di-O-methyl-β-CD (DM-β-CD) and 6-(2-hydroxypropyl)-β-CD (HP-β-CD) in water and in binary (H2O + S) systems containing hc and fc surfactants have also been obtained. The magnitudes of Vφ,S and Vφ,R-β-CD are greater in ternary solutions than in the binary aqueous systems. The apparent molar volumes of the modified cyclodextrins and the surfactants at infinite dilution (V°φ) in ternary solutions are found to depend on the following factors: (i) the magnitude of the binding constant (Ki), (ii) the alkyl chain length of the surfactant, (iii) the mole ratio of the host to guest species, (iv) the nature of the host/guest stoichiometry, and (v) the physicochemical properties of the CD and/or the surfactant. The volumetric properties of the ternary systems have been analyzed in terms of the additive contributions of the complexed and uncomplexed species. R-β-CD/surfactant complexes having 1:1 and 1:1 plus 1:2 stoichiometries were successfully modeled using two-site and three-site equilibrium models, respectively. The binding affinities of hc and fc surfactants with DM-β-CD and HP-β-CD show different behavior.

Introduction Cyclodextrin (CD) compounds have attracted considerable interest because of their ability to form stable inclusion complexes with various inorganic and organic guest molecules in aqueous solution.1,2 The potential utility of alkylated cyclodextrins, R-β-CD, over unmodified CDs in various applications derives from the fact that, while their binding properties may be expected to be similar, the modified CDs are far more soluble in water and organic solvents.3 Previous studies4-10 have examined the relative binding affinities of R-βCD and β-CD with guest species in order to evaluate the effects of alkylation of the host on the magnitude of the binding constants. However, there does not appear to have been any attempt to systematically vary the chemical nature of the guest and host, and consequently, it has been difficult to attribute substituent effects in the alkylated CDs to specific physicochemical factors such as H-bonding, steric effects, hydrophobic effects, increased cavity depth, and increased lipophilicity of the macrocycle. Recently, theoretical studies of computergenerated molecular lipophilicity patterns (MLPs)11,12 have shown that methylation of β-CD increases its relative hydrophobicity. Also, MLPs have been applied to correlate the binding affinity between various host-guest systems with their complementary hydrophobic surface areas. The hydrophobic effect has been implicated as one of the key factors contributing to the rather strong noncovalent interactions between CD and apolar guest molecules.13 Spectral displacement14 and volumetric15 studies of β-CD/surfactant complexes have shown that a good correlation exists between * Author to whom correspondence may be addressed. Telephone: 306966-4669. Fax: 306-966-4730. E-mail: [email protected]. X Abstract published in AdVance ACS Abstracts, December 1, 1997.

the magnitude of the binding constant and the hydrophobicity of the guest molecule. The sensitive dependence of the apparent molar volume properties of the host (β-CD) and guest (sodium salts of hydrocarbon and fluorocarbon carboxylic acids)15 species on their physicochemical characteristics led us to consider a similar study to examine the effect of alkyl substitution of the cyclodextrin host on the binding processes in R-β-CD/S systems. This paper presents the results of an apparent molar volume study of the complexes formed between 2,6-di-O-methyl-β-CD (DM-β-CD) or 6-(2-hydroxypropyl)-β-CD (HP-β-CD) and a homologous series of hydrocarbon (hc) [CxH2x+1CO2Na, x ) 5, 7, 9, 11, 13] and fluorocarbon (fc) [CxF2x+1CO2Na, x ) 3, 6-9] surfactants (S) in the premicellar region, using highprecision density data. The apparent molar volumes (AMVs) of the guest and host species have been determined in both water and in ternary (H2O + R-β-CD + S) aqueous solutions. The merits of systematically studying a homologous series of surfactants of variable alkyl carbon chain length (nx) have been outlined previously.15 The effect of alkyl substituents may be inferred from a comparison of the analysis of the volumetric data for systems of R-β-CD or β-CD with a common surfactant. Finally, the utility of applying model equations, based on Young’s additivity rule,16 to analyze the volumetric behavior of the modified CD/S complexes of different stoichiometries is assessed. Experimental Section Instrumentation. The instrumentation used for density measurements has been described previously.15 Materials. DM-β-CD [lot no. CY-2004.0, relative molar mass (M) ) 1331 g mol-1, degree of substitution (DS) ) 14, purity > 70% as 2,6-DM-β-CD regioisomer] and HP-β-CD [lot

S1089-5647(97)02513-3 CCC: $15.00 © 1998 American Chemical Society Published on Web 01/08/1998

β-Cyclodextrin/Hydrocarbon and /Fluorocarbon Complexes SCHEME 1: 1:1 and 1:2 Binding Equilibria for Various R-β-CD/S Complexes, Where R ) 2,6 Di-O-methyl- (DM) and/or 6-(2-Hydroxypropyl)- (HP), and S ) Hydrocarbon or Perfluorocarbon Sodium Alkyl Carboxylate Salts

no. CY-2005.2, M ) 1384 g mol-1, DS ) 4.6, purity ≈ 95%] were obtained from Cyclolab and used without further purification. The preparation and purification of other materials used in this study were as described previously.15 The AMV property was calculated using the following expression:17

Vφ )

3 M 10 (d - do) d mddo

(1)

where d and do are the densities of the solution and solvent, respectively, M is the relative molar mass of solute, and m is the concentration in molal units. The solvent in binary solutions is water (W), whereas in ternary solutions it is either (W + S) or (W + R-β-CD). For the determination of Vφ,S in ternary systems, the binary solvent concentration was held constant between 0.004 and 0.005 m R-β-CD and the concentration of surfactant, CS, was varied but always kept below the critical micelle concentration (cmc). The conditions used for the determination of Vφ,R-β-CD in ternary systems are analogous to those described previously for the case of Vφ,β-CD.15 The volumetric behavior of R-β-CD/S complexes having different stoichiometries, shown in Scheme 1, was analyzed using equations based on Young’s additivity rule:16

Vφ ) XdVφ,d + X1:1Vφ,1:1

(2)

Vφ ) XdVφ,d + X1:1Vφ,1:1 + X1:2Vφ,1:2

(3)

where Xd, X1:1, and X1:2 are the mole fractions of the dispersed component (surfactant or R-β-CD), 1:1 complex, and 1:2 complex, respectively, and Vφ,d, Vφ,1:1, and Vφ,1:2 are the AMVs of the dispersed species, 1:1 complex, and 1:2 complex, respectively. The methodology used in the determination of the equilibrium binding constants (Ki) from the host or guest volumetric data is similar to that described in a previous study.15 Results and Discussion Surfactant Volumes: VO,S. Values of the apparent molar volumes at infinite dilution (V°φ,S) for the hc and fc surfactants

J. Phys. Chem. B, Vol. 102, No. 2, 1998 481 in water and aqueous R-β-CD solutions and abbreviations used for the surfactants in this paper are shown in Tables 1 and 2, respectively. From the values of V°φ,S in Tables 1 and 2 for hc and fc surfactants in water, an average volume change of 15.7 ( 0.11 and 23.9 ( 0.16 cm3 mol-1 was obtained per CH2 and CF2 group, respectively. These values are in good agreement with previous results.15 The AMVs of the hc surfactants in aqueous binary solutions of the R-β-CDs increase as nx increases, but the rate of increase diminishes for the longer carbon chain surfactants. It decreases from 20.5 to 17.3 and from 21.6 to 17.3 cm3 mol-1 per CH2 between the shortest and longest hc surfactant homologs studied in DM-β-CD/S and HP-β-CD/S systems, respectively. This is in contrast to the large increase in the AMV observed for the longer chain hc surfactant homologues in aqueous β-CD, which has been shown to be due to the onset of 2:1 complexation. The absence of 2:1 complexes in the R-β-CD systems is consistent with the increased length of the macrocycle arising from alkylation of β-CD. As a consequence, an additional macrocycle is not required to include the longer hydrocarbon chain surfactants in these hosts.3 In Table 2, the magnitude of the AMV per CF2 group of the fc surfactants in DM-β-CD/S and HP-β-CD/S systems also decreases, from 27.0 to 23.7 and from 26.8 to 24.2 cm3 mol-1, respectively. However, these changes occur between nx ) 3 and 6, with virtually no decrease occurring thereafter. By contrast, the incremental change in V°φ,S per CF2 group in aqueous β-CD15 is 28.4 ( 0.51 cm3 mol-1 for the longer carbon chain homologues. The smaller change in volume above nx ) 6 for the R-β-CD/S complexes indicates that no additional CF2 groups are included in the host cavity beyond this alkyl chain length and that 1:1 stoichiometry predominates, at least for the fc chain lengths examined in this work. It appears that, while β-CD can form 2:1 complexes with longer fc chain lengths, R-β-CDs do not for the reasons discussed above in the case of the hc surfactants. The transfer volume at infinite dilution, ∆V°S, of a surfactant from water to a binary aqueous R-β-CD solution is defined as follows:

∆V°S(WfW+R-β-CD) ) V°φ,S(R-β-CD)aq - V°φ,S(H2O) (4) An analogous relation can be defined for the transfer volume of R-β-CD, ∆V°R-β-CD(WfW+S). Also, transfer volumes at finite concentrations (∆VS and ∆VR-β-CD) are defined, as in eq 4. Transfer properties can be interpreted in terms of the relative change in solvation that occurs upon complex formation. Positive values of ∆V°S (Tables 1 and 2) are consistent with the fact that inclusion complexes are formed since the process

TABLE 1: Apparent Molar Volume Data of Sodium Alkyl Carboxylate Salts in Water and Aqueous DM-β-CD and HP-β-CD Solutions at pH 10.5 and 298 K surfactant C6H11O2Na SHex C8H16O2Na SO C10H19O2Na SDec C12H23O2Na SDodec C14H27O2Na ST a

V°φ,S (cm3 mol-1) water

V°φ,S (cm3 mol-1) aqueous DM-β-CDa

∆V°S (cm3 mol-1)b aqueous DM-β-CD

V°φ,S (cm3 mol-1) aqueous HP-β-CDc

∆V°S (cm3 mol-1)b aqueous HP-βCD

100.9

104.0

3.1

102.1

1.2

133.0

145.0

12.0

145.2

12.2

165.1

184.5

19.4

182.6

17.5

196.9

221.3

24.4

219.4

22.5

226.7

255.9

29.2

254.0

27.3

CDM-β-CD ≈ 4.0 × 10-3 m in all cases. b ∆V°S ) V°φ,S(R-β-CD(aq)) - V°φ,S(water). c CHP-β-CD ≈ 5.0 × 10-3 m in all cases.

482 J. Phys. Chem. B, Vol. 102, No. 2, 1998

Wilson and Verrall

TABLE 2: Apparent Molar Volume Data of Perfluorinated Sodium Alkyl Carboxylate Salts in Water and Aqueous DM-β-CD and HP-β-CD Solutions at pH 10.5 and 298 K surfactant C4F7O2Na SPFB C7F13O2Na SPFH C8F15O2Na SPFO C9F17O2Na SPFN C10F19O2Na SPFD

V°φ,S (cm3 mol-1) in H2O

V°φ,S (cm3 mol-1) aqueous DM-β-CDa

∆V°S (cm3 mol-1)b aqueous DM-β-CD

V°φ,S (cm3 mol-1) aqueous HP-β-CDc

∆V°S (cm3 mol-1)b aqueous HP-β-CD

104.7

110.2

5.5

109.5

4.8

175.9

191.2

15.3

189.8

13.9

200.6

216.3

15.7

214.7

14.1

225.1

240.8

15.7

238.8

13.7

249.0d

264.5

15.5

263.0

14.0

CDM-β-CD ≈ 4.0 × 10-3 m in all cases. b ∆V°S ) V°φ,S(R-β-CD(aq)) - V°φ,S(water). c CHP-β-CD ≈ 5.0 × 10-3 m in all cases. d Extrapolated from volume data in the concentration range (0.5-2.0) × 10-3 m. a

involves the transfer of hc or fc segments from an aqueous to an apolar environment.18 In Table 1, ∆V°S for the hc surfactants in DM-β-CD and HPβ-CD solutions exhibit a monotonic increase as nx increases, a result similar to that observed for the β-CD/S systems.15 However the magnitude of ∆V°S is slightly smaller in R-β-CDs, and it does not increase sharply for longer chain length hc surfactants, as seen in the case of β-CD. These results are consistent with the formation of 1:1 R-β-CD/S complexes, whereas both 1:1 and 2:1 complexes are formed in β-CD/S systems. In Table 2, ∆V°S for the fc surfactants in DM-β-CD and HPβ-CD solutions increases up to nx ) 6 and changes little thereafter. However, the magnitude of ∆V°S is greater for these same fc homologues in β-CD, supporting the argument that they tend to form 2:1 β-CD/S complexes. The plateau for ∆V°S beyond nx ) 6 affirms the absence of 2:1 binding and indicates that the R-β-CD compounds can include approximately 6 CF2 groups when they form 1:1 complexes, provided that the carboxylate group is not included. In contrast, β-CD can include approximately 4 CF2 groups.15 On the basis of a greater number of CH2 than CF2 groups being included in the macrocycle cavity, it would appear that the hc chain may exist in a gauche conformation and coil within the host cavity, whereas the larger fc chain is unable to do so. Semiquantitative estimates of the transfer volume, ∆V°S(WfW+R-β-CD) can be obtained using eq 5:15

∆V°S(WfW+ R-β-CD) ) [yVW(CH2) + VW(CH3) + z(18.0)] - [yV°φ(CH2) + V°φ(CH3)] (5) The method uses the volume contributions of appropriate groups in fc and hc surfactants based on their van der Waals volume (VW) and their AMV at infinite dilution (V°φ) in water, with the following assumptions: y methylene groups and one methyl group of the surfactant can be included within, and z water molecules can be expelled from, the CD cavity during the inclusion process; the alkyl chain within the cavity is unsolvated; and neither the COO- group nor the Na+ ion is included within the CD cavity. For example, ∆V°SO(WfW+R-β-CD) ) [5(10.2) +13.7 + 3(18.0)] - [5(15.7) + 27.1] ) 13.1 cm3 mol-1 compared to an experimental value of 12.0 cm3 mol-1 (Table 1). The estimated values for other systems are as follows: ∆V°SDodec ) 21.6 cm3 mol-1 for y ) 10 and z ) 5; ∆V°SPFB ) 3.4 cm3 mol-1 for y ) 2 and z ) 2.5; ∆V°SPFH ) 13.6 cm3 mol-1 for y ) 5 and z ) 4.5; and ∆V°SPFN ) 14.0 cm3 mol-1 for y ) 6 and z ) 5. In each case, good agreement between the calculated and experimental values (cf. with Tables 1 and 2) of ∆V°S is obtained. The estimated numbers of water

TABLE 3: Binding Constants (Ki) for DM-β-CD/Surfactant HP-β-CD/Surfactant Complexes Obtained from the Simulationa,b of Host and Guest Apparent Molar Volume Data in Ternary Aqueous Solutionsc at 298 K surfactant system C6H11O2Na C8H15O2Na C10H19O2Na C12H23O2Na C14H27O2Na C4F7O2Na C7F13O2Na C8F15O2Na C9F17O2Na C10F19O2Na

C6H11O2Na C8H15O2Na C10H19O2Na C12H23O2Na C14H27O2Na C4F7O2Na C7F13O2Na C8F15O2Na C9F17O2Na C10F19O2Na

Ki obtained from Vφ,S dataa,b

Ki obtained from Vφ,R-β-CD dataa,b

(a) DM-β-CD/Surfactant 2.09 × 102(8.12 × 101)d 1.00 × 102(5.02 × 101)d 2.99 × 102(3.46 × 101)d 3.15 × 102(6.37 × 101)d 3.53 × 103(9.73 × 102)d 2.42 × 103(3.50 × 102)d 1.68 × 104(4.42 × 103)d 1.00 × 104(2.92 × 103)d 8.00 × 104(4.00 × 104)d 3.56 × 104(1.28 × 104)d 3.00 × 103(1.50 × 103)e 1.30 × 102(5.59 × 101)d 4.28 × 101(3.91 × 100)d 4.00 × 104(1.55 × 104)d 3.00 × 104(1.19 × 104)d 6.01 × 104(2.65 × 104)d 4.00 × 104(1.87 × 104)d 7.00 × 104(3.50 × 104)d 6.00 × 104(3.00 × 104)d 5.00 × 102(2.50 × 102)e 3.00 × 103(1.50 × 103)e 1.00 × 105(5.00 × 104)d 1.00 × 105(5.00 × 104)d 6.00 × 103(2.50 × 103)e 5.00 × 103(2.50 × 103)e (b) HP-β-CD/Surfactant 1.00 × 102(6.32 × 101)d 1.21 × 102(4.08 × 101)d 3.26 × 102(3.28 × 101)d 1.72 × 102(2.08 × 101)d 5.50 × 103(1.21 × 103)d 1.00 × 103(5.63 × 102)d 4.48 × 104(1.40 × 103)d 2.72 × 103(1.22 × 103)d 8.00 × 103(2.55 × 103)d 1.00 × 104(4.14 × 103)d 1.30 × 102(5.59 × 101)d 1.76 × 102(3.45 × 101)d 1.70 × 104(7.89 × 103)d 1.67 × 104(7.68 × 103)d 3.14 × 104(2.10 × 104)d 2.61 × 104(1.05 × 104)d 4.00 × 104(2.91 × 104)d 3.33 × 104(1.01 × 104)d 5.00 × 104(2.02 × 104)d 4.10 × 104(3.02 × 104)d

a Two-site model: Vφ ) XdVφ,d + X1:1Vφ,1:1, for both complexes. Three-site model: Vφ ) XdVφ,d + X1:1Vφ,1:1 + X1:2Vφ,1:2, for DM-βCD/surfactant complexes only. c CDM-β-CD ) 4 × 10-3 m. CHP-β-CD ) 5 × 10-3 m unless otherwise noted. d K1:1(kg mol-1) with standard error in parentheses. e K1:2(kg2 mol-2) with standard error in parentheses. b

molecules expelled from the R-β-CD cavities are similar to that calculated for β-CD.15 This suggests that alkylation of the annular hydroxyl groups does not significantly alter the nature of the water in the CD cavity. Table 3a,b lists the values of Ki for DM-β-CD/S and HP-βCD/S complexes, respectively, obtained from the analysis of AMV data in ternary aqueous solutions. Values of Ki have been derived from the AMV data of the host and guest since Vφ,S and Vφ, R-β-CD were obtained over a suitable concentration range. In previous work,15 the binding constants from the AMV data of the guest were not investigated due to the limited solubility of β-CD in water. The magnitude of Ki increases monotonically as nx increases for both hc and fc surfactants in R-β-CD/S complexes. Generally, DM-β-CD and HP-β-CD display similar binding affinities with hc surfactants of a given alkyl chain length, whereas different binding affinities are found

β-Cyclodextrin/Hydrocarbon and /Fluorocarbon Complexes

Figure 1. Vφ,S vs CS1/2 for sodium octanoate (SO) in water and aqueous DM-β-CD and HP-β-CD, respectively, at pH 10.5 and T ) 298 K.

for the fc surfactants. The latter is attributed to steric effects that occur when alkyl substituents impede the relatively strong interactions between the CD hydroxyl groups and the carboxylate head group of the fc surfactant. This accounts for the variation in the binding affinities of a given fc surfactant with different modified CDs. However, in the case of the hc surfactants these specific interactions are not as strong and steric effects have a less pronounced effect on the binding affinities. Nevertheless, R-β-CDs exhibit slightly greater binding affinity than β-CD with hc surfactants, which can be attributed to increased hc-hc van der Waals interactions. For hc surfactants, the binding affinities of the host systems follow the order DMβ-CD ≈ HP-β-CD > β-CD, whereas for the fc surfactants the relative order is β-CD > DM-β-CD > HP-β-CD. Figure 1 is a typical plot of Vφ,S vs CS1/2 for a short chain hc surfactant, SO, in water and in aqueous DM-β-CD and HP-βCD solutions. The data in the ternary solutions are offset from one another for purposes of clarity. In water, SO displays a positive linear dependence of Vφ,S vs CS1/2 in agreement with that predicted by the Debye-Hu¨ckel limiting law for a 1:1 electrolyte. In ternary (W + R-β-CD + S) solutions, a negative linear dependence for the AMV is observed. The dashed lines through the ternary solution data represent the “best fit” according to the two-site model described by eq 2, which assumes that the total AMV is comprised of volumetric contributions from complexed, 1:1, and uncomplexed surfactant species. The magnitude of Vφ,1:1 is greater than Vφ,d, since inclusion complex formation involves the transfer of S from water to a more apolar environment, and this process is associated with a positive transfer volume.18 In previous work, it was shown that the magnitude of X1:1 decreases as CS1/2 increases.15 Thus, the total AMV decreases as CS1/2 increases because of an increasing fraction of unbound surfactant (Xd) and the lower magnitude of Vφ,d relative to Vφ,1:1. Figure 2 illustrates a typical plot of Vφ,S vs CS1/2 for a longer chain hc surfactant, SDodec, in water and aqueous solutions of DM-β-CD and HP-β-CD. Again, the ternary solution data are offset for purposes of clarity. In water, SDodec displays a linear dependence vs CS1/2; however, the AMV data in the ternary solutions are qualitatively different from those shown in Figure 1. The magnitude of the AMV up to a R-β-CD/S mole ratio of 1:1 is relatively constant but displays a sharp, nonlinear decrease thereafter due to the contribution of unbound surfactant species. In ternary solutions, the magnitude of ∆V°S for SDodec is greater, and the AMV behavior is more sigmoidal than that of SO. The magnitude and concentration dependence of the AMV in these ternary solutions are representative of strongly bound

J. Phys. Chem. B, Vol. 102, No. 2, 1998 483

Figure 2. Vφ,S vs CS1/2 for sodium dodecanoate (SDodec) in water and aqueous DM-β-CD and HP-β-CD, respectively, at pH 10.5 and T ) 298 K.

Figure 3. Vφ,S vs CS1/2 for sodium perfluorooctanoate (SPFO) in water and aqueous DM-β-CD and HP-β-CD, respectively, at pH 10.5 and T ) 298 K.

1:1 complexes, and the dashed lines through the experimental data represent the “best fit” according to eq 2. DM-β-CD and HP-β-CD display similar behavior with hc surfactants despite the different chemical nature of the alkyl substituents on each host. These results suggest that the interactions between the surfactant alkyl chain and the CD interior may play a more important role in determining the binding affinity between host and guest. Figure 3 illustrates a typical plot of Vφ,S vs CS1/2 for a medium chain length fc surfactant, SPFO, in water and in aqueous DMβ-CD and HP-β-CD solutions. The features of the AMV data for SPFO in water and in ternary solutions are similar to those for SDodec shown in Figure 2. The dashed lines through the ternary solution data represent the “best fit” according to eq 2. Apparent molar volume data for SPFO in 0.004 and 0.013 m DM-β-CD show that the magnitudes of V°φ,S are similar and that Vφ,S remains constant up to a R-β-CD/S mole ratio slightly below 1:1. Thereafter, a large decrease in the AMV is observed with increasing surfactant concentration. The AMV data for SPFO in aqueous solutions of DM-β-CD indicate the formation of strongly bound (cf. Table 3) complexes since estimates of X1:1 do not show a marked dependence on the concentration of the binary solvent system below the 1:1 DM-β-CD/S mole ratio. In 0.005 m aqueous HP-β-CD, the magnitude of the AMV of SPFO is smaller and the decrease in AMV at the 1:1 HP-βCD/S mole ratio is less sharply defined than in 0.004 m DMβ-CD, consistent with a reduced binding affinity for the HPβ-CD/S complex. The different binding affinities shown by

484 J. Phys. Chem. B, Vol. 102, No. 2, 1998

Figure 4. Vφ,S vs CS1/2 for sodium perfluorononanoate (SPFN) in water and binary aqueous solutions of DM-β-CD, HP-β-CD, and β-CD, respectively, at pH 10.5 and T ) 298 K.

the R-β-CDs may be due to steric effects arising from the alkyl groups on the host. In a previous study, the binding affinity of β-CD/fc surfactant complexes was attributed, in part, to substantial surfactant head group/CD hydroxyl group interactions (cf. Scheme 2, ref 14). Thus, the presence of alkyl groups in the R-β-CDs may result in a lower binding affinity relative to β-CD for reasons given above. Figure 4 illustrates a plot of Vφ,S vs CS1/2 for SPFN in water and aqueous solutions of β-CD, DM-β-CD, and HP-β-CD. In water, SPFN exhibits a slight negative linear dependence, and this is attributed to its relatively hydrophobic character, though it is a 1:1 electrolyte. In 0.005 m HP-β-CD, SPFN shows behavior comparable to SPFO (Figure 3); however, a larger value of ∆V°S and a more sharply defined transition at the 1:1 R-β-CD/S mole ratio is observed. The latter is consistent with an increase in binding affinity, and the dashed line through the ternary solution data represents the “best fit” according to eq 2. The AMV of SPFN in several binary solutions of differing DM-β-CD concentration is also shown in the graph. In 0.015 m DM-β-CD, the AMV exhibits a negative quasi-linear dependence and a small slope because X1:1 is relatively large over the entire concentration range. In 0.003 and 0.004 m DMβ-CD, the AMV of SPFN exhibits a more complex nonlinear dependence. It shows a gradual decrease at the 1:1 DM-β-CD/S mole ratio, a minimum near the 1:2 mole ratio, and an increase beyond the 1:2 mole ratio. The absence of a decrease beyond the 1:2 DM-β-CD/S ratio indicates that there is no apparent contribution from unbound SPFN, since Vφ,d < Vφ,i. Independent 19F NMR and conductivity studies have provided additional support for the existence of 1:2 DM-β-CD/SPFN complexes.19 The formation of such complexes appears to be a general phenomenon and is observed for more hydrophobic surfactants such as SPFN and ST. Also, a correlation with the degree of methylation of the CD is apparent since both TM-β-CD and DM-β-CD form 1:2 CD/S complexes. A 1:2 inclusion complex provides a favorable means of minimizing the polar/apolar interactions and optimizing the apolar/apolar interactions, particularly, when [S]total . [CD]total. In contrast to SPFO, the magnitude of V°φ,S for SPFN in aqueous DM-β-CD depends on the binary solvent concentration despite the large magnitude of K1:1. The increase of V°φ,S as the concentration of modified CD increases in the binary solvent suggests that there may be additional equilibria besides 1:1 complex formation. In 0.003 and 0.004 m DM-β-CD, eq 3 provides a reasonable fit of the experimental data up to a concentration equivalent to a 1:2 DM-β-CD/S mole ratio. However, a poorer fit was obtained at higher host/guest mole

Wilson and Verrall ratios. In 0.015 m DM-β-CD, a poor fit was obtained using eq 3, possibly due to nonideal effects. Thus, as the concentration of DM-β-CD increases, deviations between the experimental and simulated AMV data become more pronounced. To illustrate that other possible stoichiometries, such as 2:1 complexes, are not the cause of this unusual behavior, the ternary solution data for the β-CD/SPFN system is shown for comparison. The latter displays markedly different behavior from the DM-β-CD/SPFN systems, as shown by the greater magnitude of V°φ,S and the sigmoidal-shaped curve. The positive increase in the AMV of SPFN beyond the 1:2 DM-β-CD/S mole ratio in 0.003 and 0.004 m DM-β-CD may be due to an aggregation process, since there is minimal contribution to the volume from unbound surfactant, and the effect is more pronounced as CR-β-CD or CS increases. Also, this phenomenon is only observed for the more hydrophobic guests and lipophilic hosts, such as DM-β-CD. Aggregation processes such as micelle formation are accompanied by positive volume changes.18,20 The increase in AMV beyond the 1:2 CD/S mole ratio may be due to extracavity association between the 1:1 and 1:2 complexes with the dispersed SPFN. It does not appear to occur in the case of β-CD or HP-β-CD, possibly due to the more dipolar character of these cyclodextrins. The greater lipophilicity of methylated CDs is evident from their surface activity and tendency to form mixed monolayers.21,22 Further studies are in progress to determine whether such aggregrates are formed under these conditions. The volumetric data presented above for hc and fc surfactants in ternary aqueous solutions containing R-β-CD/S complexes indicate that the AMV is dependent on several factors: (i) the magnitude of Ki, (ii) the mole ratio of the host and guest, (iii) the nature of the host/guest stoichiometry, (iv) the alkyl chain length of the surfactant, and (v) the physicochemical properties of the R-β-CD and the surfactant. The arguments presented above can also be applied to rationalize the volumetric behavior of the host molecule in ternary aqueous solutions, and this will now be discussed. R-β-CD Volumes: VO,R-β-CD. Tables 4 and 5 list the values of V°φ,R-β-CD and ∆V°R-β-CD for the modified cyclodextrins in aqueous solutions of hc and fc surfactants, respectively. The magnitudes of ∆V°R-β-CD in water are lower than in ternary solutions, and this is consistent with the formation of R-β-CD/S complexes, vide infra. In aqueous hc surfactant solutions, DMβ-CD and HP-β-CD exhibit an increase in V°φ,R-β-CD of ca. 4.3-4.5 cm3 mol-1 per CH2 in the surfactant hydrocarbon chain up to chain length nx ) 9, and then a smaller increase of ca. 1.9-1.7 cm3 mol-1 per CH2 occurs for the longer carbon chain members of the series. This result suggests that the R-β-CDs can include a hc alkyl chain of approximately 10 CH2 groups, whereas β-CD can include only 8 CH2 groups. Aside from small differences, the volumetric behavior of the modified CDhydrocarbon guest complexes (Table 4) is somewhat similar, and this is consistent with their similar binding affinities. In aqueous fc surfactant solutions, V°φ,R-β-CD of DM-β-CD and HP-β-CD show some general features similar to those exhibited in aqueous hc surfactants solutions, but there are differences between the host species when the guest species have longer fluorocarbon chains. An increase in V°φ,R-β-CD occurs for both modified CDs up to nx ) 6. Then the values remain approximately constant when an additional CF2 group is added to the surfactant. For nx g 8, differences in V°φ,R-β-CD between DM-β-CD and HP-β-CD arise when the surfactant alkyl chain is lengthened by another CF2 group. In the case of the former there is a large increment of ca. 9 cm3

β-Cyclodextrin/Hydrocarbon and /Fluorocarbon Complexes

J. Phys. Chem. B, Vol. 102, No. 2, 1998 485

TABLE 4: Apparent Molar Volumes of DM-β-CD and HP-β-CD in Aqueous Solutions of Sodium Alkyl Carboxylate Salts at pH 10.5 and 298 K surfactant

V°φ,DM-β-CD (cm3 mol-1)a

∆V°DM-β-CD (cm3 mol-1)b

V°φ,HP-β-CD (cm3 mol-1)c

∆V°HP-β-CD (cm3 mol-1)b

C6H11O2Na C8H15O2Na C10H19O2Na C12H23O2Na C14H27O2Na

986.7 995.3 1004.0 1007.3 1011.9

2.2 10.8 19.5 22.8 27.4

961.3 970.0 979.0 986.0 985.7

3.1 11.8 20.8 27.8 27.5

a C ≈ 4.0 × 10-3 m in all cases. V° 3 -1 b c s φ,DM-β-CD ) 984.5 cm mol . ∆V° R-β-CD ) V° φ,R-β-CD(surfactant(aq)) - V° φ,R-β-CD(water). Cs ≈ 5.0 × 10-3 m in all cases. V°φ,HP-β-CD ) 958.2 cm3 mol-1.

TABLE 5: Apparent Molar Volumes of DM-β-CD and HP-β-CD in Aqueous Solutions of Perfluorinated Sodium Alkyl Carboxylate Salts at pH 10.5 and 298 K surfactant

V°φ,DM-β-CD (cm3 mol-1)a

∆V°DM-β-CD (cm3 mol-1)b

V°φ,HP-β-CD (cm3 mol-1)c

∆V°HP-β-CD (cm3 mol-1)b

C4F7O2Na C7F13O2Na C8F15O2Na C9F17O2Na C10F19O2Nad

991.3 1000.4 1000.3 1009.0 1010.8

6.8 15.9 15.8 24.5 26.3

964.9 972.6 973.4 975.3 975.6

6.7 14.4 15.2 17.1 17.4

a C ≈ 4.0 × 10-3 m in all cases. V° 3 -1 b c s φ,DM-β-CD ) 984.5 cm mol . ∆V° R-β-CD ) V° φ,R-β-CD(surfactant(aq)) - V° φ,R-β-CD(water). Cs ≈ 5.0 × 10-3 m in all cases. V°φ,HP-β-CD ) 958.2 cm3 mol-1. d Cs ) 1 × 10-3 m.

mol-1, whereas for the latter there is an increment of ca. 2 cm3 mol-1. Then V°φ,R-β-CD remains virtually constant for HP-βCD and increases by ca. 2 cm3 mol-1 for DM-β-CD when nx is increased to 9. These results are consistent with the formation of 1:1 R-β-CD/S complexes and the ability of these hosts to include ca. 6 or 7 CF2 groups of a fc chain, as compared to only 4 CF2 groups being included in the case of β-CD. DMβ-CD exhibits a slightly greater increase in V°φ,R-β-CD than HP-β-CD for fc surfactants with nx > 7 due to its tendency to form 1:2 complexes and, possibly, aggregates of complexes and dispersed surfactant, as discussed above. The increment in V°φ,CD of β-CD per CF2 group of the inclusate is greater than that observed for V°φ,R-β-CD of the R-β-CDs and is attributed to the nature of the stoichiometry and the differences in binding affinity of the host systems. In aqueous hc surfactants, the magnitude of ∆V°R-β-CD increases uniformly up to nx ) 13 and 11 for DM-β-CD and HP-β-CD (Table 4), respectively, whereas the magnitude of ∆V°CD for β-CD levels off at nx g 11, due to the formation of 2:1 complexes in the latter system. The increase in the magnitude of ∆V°R-β-CD is due to greater inclusion of the S alkyl chain and the expulsion of more hydrate water from the CD interior. When the value of ∆V°R-β-CD becomes constant, this indicates that the guest has fully occupied the host cavity and no additional water molecules can be expelled from the CD cavity as nx of the guest increases. These results provide further support that the number of hc alkyl groups included in the modified CDs exceeds that found in the case of β-CD and corroborates conclusions drawn from the Vφ,S data presented above. This increase is consistent with the extended hydrophobic cavity that is created by appending alkyl substituents to β-CD. The changes in transfer volume for β-CD in aqueous fc surfactants parallel changes in V°φ,R-β-CD (Table 5) for DM-βCD and HP-β-CD. The data indicate that ca. 7 and 8 fluorocarbon groups can be included in DM-β-CD and HP-βCD, respectively, compared to 4 in the case of β-CD. The tendency of fc chains to adopt an all-trans conformation results in fewer fc alkyl groups being included in the cavity of the host as compared with hc surfactants. The latter may undergo chain coiling through the formation of gauche kinks, as discussed above, and this increases the number of alkyl groups

Figure 5. ∆VR-β-CD vs CR-β-CD for DM-β-CD and HP-β-CD in aqueous sodium dodecanoate (SDodec) at pH 10.5 and T ) 298 K.

that can be included in the host. Also, the increased length of the macrocycle cavity in the modified cyclodextrins, compared to β-CD, enables the inclusion of a longer alkyl moiety. The different number of hc and fc alkyl groups included in a given host can account for some of the differences that are observed between the transfer volumes, ∆V°R-β-CD, for the modified CDs in the presence of fc and hc surfactants. Figure 5 is a typical plot of ∆VR-β-CD vs CR-β-CD for DMβ-CD and HP-β-CD in an aqueous solution of a long chain hydrocarbon surfactant, SDodec. The data are plotted as ∆VR-β-CD (cf. eq 4) since each modified CD has a different AMV in water. The use of the transfer volume provides a method of circumventing this problem. The qualitative features of ∆VDM-β-CD in 0.004 m SDodec resemble the data for the complementary Vφ,S data shown in Figure 2. In 0.004 m SDodec, ∆VDM-β-CD decreases rapidly beyond the 1:1 mole ratio. However, no such decrease is observed in 0.020 m SDodec since the concentration of DM-β-CD lies below the 1:1 R-β-CD/S mole ratio and the host is mainly in the bound state over this concentration range. HP-β-CD displays similar behavior compared to DM-β-CD in 0.004 m SDodec; however, a greater transfer volume is observed for the former due to its more extended cavity depth and/or the prominence of 1:1 complexes. The dashed lines through the ternary solution data represent the “best fit” according to eq 2. In 0.020 m SDodec,

486 J. Phys. Chem. B, Vol. 102, No. 2, 1998

Figure 6. ∆VR-β-CD vs CR-β-CD for DM-β-CD and HP-β-CD in aqueous sodium perfluoroheptanoate (SPFH) at pH 10.5 and T ) 298 K.

Figure 7. ∆VR-β-CD vs CR-β-CD for DM-β-CD and HP-β-CD in aqueous sodium perfluorooctanoate (SPFO) at pH 10.5 and T ) 298 K.

sensitivity problems arose with the simulation of the ternary solution data using eq 2 because, due to an excess of guest over the concentration range studied, the mole fraction of bound host, X1:1, is large and the change in AMV is small. Also, the approximation that the magnitude of Vφ,d in water is similar to that in concentrated binary solvent breaks down due to nonideal effects.15 Figures 6 and 7 show plots of ∆VR-β-CD vs CR-β-CD for DMβ-CD and HP-β-CD in aqueous SPFH and SPFO solutions, respectively. The magnitude of ∆V°R-β-CD in the dilute binary aqueous surfactant solutions is similar for both modified cyclodextrins, and there is a decrease in ∆VR-β-CD beyond the 1:1 R-β-CD/S mole ratio due to the contribution of the unbound R-β-CD. DM-β-CD exhibits a sharper decrease in the transfer volume relative to HP-β-CD because of the greater binding affinity of DM-β-CD with fc surfactants, as evidenced by a larger magnitude of X1:1 at the 1:1 R-β-CD/S mole ratio. Thereafter, Xd increases and contributes to a lowering of the magnitude of ∆VR-β-CD. As the concentration of the binary solvent (W + S) increases, a large increase in ∆VDM-β-CD is observed at low host concentrations, with the magnitude of ∆V°R-β-CD being considerably greater in 0.025 m SPFO than in 0.025 m SPFH. Also, ∆VDM-β-CD in 0.025 m SPFH shows a linear dependence on the host concentration, whereas in 0.025 m SPFO it is nonlinear. The latter behavior can be attributed to more pronounced interactions between dispersed surfactant and R-β-CD/S complexes as discussed with respect to Figure 4 for the DM-β-CD/SPFN system. A comparison of Figures 6

Wilson and Verrall

Figure 8. ∆VR-β-CD vs CR-β-CD for DM-β-CD and HP-β-CD in aqueous sodium perfluorononanoate (SPFN) at pH 10.5 and T ) 298 K.

and 7 reveals that the magnitude of these interactions appears to increase as the hydrophobicity and the concentration of the surfactant increase. In Figure 6, the dashed line through the ternary solution data in 0.025 SPFH was obtained using eq 2; however, it was found necessary to allow Vφ,d to become an adjustable parameter due to the fact that Vφ,d in water is dissimilar to that in ternary solutions because of nonideal interactions, as mentioned previously. In 0.025 m SPFO, Vφ,d was also treated as an adjustable parameter; however, poor fits were obtained using either eqs 2 or 3. A model accounting for extracavity CD/S interactions seems to be required, but the number of variables that needs to be fit would require more extensive experimental data. Further study of this phenomenon is planned. The dashed lines through the ternary solution data in the more dilute binary (W + S) solvents represent the best fit lines using eq 2. For these conditions, CS is relatively low and it was not necessary to let Vφ,d vary as an adjustable parameter. Consequently, the magnitude of Vφ,d is approximated well by the value for V°φ,CD in water. Figure 8 is a plot of ∆VR-β-CD vs CR-β-CD for DM-β-CD and HP-β-CD in aqueous SPFN. The features of the transfer volume for HP-β-CD are similar to those seen in Figures 6 and 7, except that the magnitude of ∆VHP-β-CD for HP-β-CD is smaller and the inflection at the 1:1 R-β-CD/S mole ratio is more pronounced due to the prominence of 1:1 binding. The dashed line through the ternary solution data for HP-β-CD represents the “best fit” according to eq 2. Three sets of ternary solution data for DM-β-CD are shown for 0.005, 0.007, and 0.009 m SPFN. In each case the magnitude of ∆V°R-β-CD and the nonlinearity of the curves increase near infinite dilution as CS increases. The nonideal behavior of the DM-β-CD in aqueous SPFN parallels that in more concentrated solutions of SPFO and SPFH, respectively. Any aggregation process that occurs between dispersed S and DM-β-CD/S complexes should increase when the alkyl chain length of the surfactant increases. In 0.005 m SPFN, ∆VDM-β-CD was fit using eq 3; however, the goodness of fit is poorer near infinite dilution because of these specific interactions. The absence of extracavity interactions for HP-β-CD may be due to its greater hydrophilic character and steric effects imposed by the hydroxypropyl groups. The formation of 1:2 and extracavity complexes can be rationalized on the basis of the presence of alkyl substituents in the annular hydroxyl region. The alkyl substituents hinder dipolar interactions between the carboxylate head group of the surfactant and the CD hydroxyl groups of the host. HP-β-CD

β-Cyclodextrin/Hydrocarbon and /Fluorocarbon Complexes tends to form 1:1 complexes; however, a lower binding affinity relative to β-CD is observed and this is attributed to the steric effect of the hydroxypropyl group. Similar steric effects are anticipated for DM-β-CD due to the presence of methyl substituents. In β-CD, dipolar interactions between the surfactant head group and annular CD hydroxyl groups and apolar interactions between the S alkyl chain and CD interior may act in a cooperative fashion, which results in a greater binding affinity.23 Thus, the formation of 1:2 host/guest complexes and extracavity aggregates for the methylated cyclodextrins are consistent with the prominence of apolar-apolar interactions, since S head group/CD hydroxyl group interactions do not play a major role in these host systems. Long chain hc and fc surfactants such as ST, SPFO, and SPFN tend to form 1:2 complexes and extracavity complexes, particularly when [S]total . [CD]total, because of hydrophobic effects. These results are consistent with the large differences in the MLP patterns of DMβ-CD and β-CD.11,12 The presence of methoxy, as opposed to hydroxyl, groups allows for substantially more apolar contacts between a S alkyl chain and the CD annulus. Also, the dipolar character of both annulus regions of β-CD decreases upon alkyl substitution; hence, guests may be included from either end of β-CD. Also, because the modified cyclodextrins are likely to possess greater conformational freedom about their interglycosidic linkages than β-CD, this may result in a better “induced fit” and improved van der Waals contacts between host and guest. The latter provides a suitable explanation for the greater binding affinity of R-β-CD vs β-CD with hc surfactants. The self-consistency between the volumetric data of the host and guest is generally good in terms of the magnitude of the binding constants for a given host/guest complex. However, there are some variances if one compares the magnitudes of ∆V°R-β-CD and ∆V°S for a given host/guest system. The volumetric behavior of the host and guest are affected by the stoichiometry of the complex and the relative changes in hydration of the host and guest. Depending on whether CR-β-CD . CS or CS . CR-β-CD, as is the case of transfer quantities at infinite dilution for the host and guest, a number of possible stoichiometries may predominate. The relative hydration of the guest is more variable than the host because of the ability of the alkyl chain to adopt variable conformations, particularly when its hydrophobic character is large, and there is a need to minimize polar-apolar contacts between the alkyl chain and solvent. Hence, the transfer volume for the host and/or guest are affected by the stoichiometry, conformational motility of the guest, and the relative hydrophobicity of the host and guest as seen in the complexation of hc and fc alkyl surfactants with β-CD and R-β-CD. Conclusion The AMVs, V°φ,S, of a homologous series of hc[CxH2x+1CO2Na, x ) 5, 7, 9, 11, 13] and fc[CxF2x+1CO2Na, x ) 3, 6-9] surfactants were obtained in water and in ternary aqueous solutions of DM-β-CD and HP-β-CD. The complementary AMV data for the modifed cyclodextrins (Vφ,R-β-CD) in water and in binary solutions of hc and fc surfactants were also obtained. In all cases, the magnitude of V°φ,S and V°φ,R-β-CD in ternary solutions was greater than in water. The factors affecting the magnitude of the AMV for the host and guest in ternary (W + S + CD) aqueous solutions include (i) the magnitude of Ki, (ii) the alkyl chain length of the surfactant, (iii) the mole ratio of the host to guest, (iv) the host/ guest stoichiometry, and (v) the physicochemical properties of the cyclodextrin and surfactant.

J. Phys. Chem. B, Vol. 102, No. 2, 1998 487 HP-β-CD forms 1:1 complexes with all hc and fc surfactant systems. DM-β-CD tends to form 1:1 complexes with fc (nx e 6) and hc (nx e 11) surfactants. Longer alkyl chain length hc (nx > 11) and fc (nx g 7) surfactants tend to form both 1:1 and 1:2 complexes with DM-β-CD. The formation of 1:2 complexes and possible evidence of extracavity association were found for DM-β-CD with SPFO, SPFN, and ST, particularly when [S]total . [CD]total. The quality of the fit of two-site or three-site models to the experimental volume data of the various R-β-CD/S systems appears to give a satisfactory picture of the speciation in solution. The binding affinity of fc surfactants to the cyclodextrins follows the order β-CD > DM-β-CD > HP-β-CD, whereas the binding affinity for the hc surfactants follows the order DM-β-CD ≈ HP-β-CD > β-CD. The difference between the relative ordering can be rationalized on the basis of steric effects of the alkyl substituents on fc head group/CD annular hydroxyl group interactions. The use of AMV measurements to study host/guest complexes provides a good method to obtain estimates of binding constants for apolar guest molecules which do not possess a suitable chromophore for study by spectroscopic techniques. Also, it provides good insight into the nature of the interactions and solvation behavior of these host guest systems. The results obtained here for DM-β-CD and HP-β-CD with hc and fc surfactants provide strong support for the prominent role of the hydrophobic effect and the secondary role of surfactant head group/CD annular hydroxyl group interactions in the formation of host/guest complexes. Acknowledgment. Financial assistance provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) is acknowledged. L.D.W. is grateful for the award of a Graduate Teaching Fellowship from the University of Saskatchewan. Supporting Information Available: Tables of concentration, density difference, and apparent molar volume of the surfactants and cyclodextrins examined in this study (12 pages). Ordering information is available on any current masthead page. References and Notes (1) Brewster, M. E.; Loftsson, T. J. Pharm. Sci. 1996, 85, 1017, and references cited therein. (2) Shieh, W. J.; Hedges, A. R. J. Mater. Sci. Pure Appl. Chem. 1996, A33, 673, and references cited therein. (3) Wenz, G. Angew. Chem., Int. Ed. Engl. 1994, 33, 803, and references cited therein. (4) Casu, B.; Reggiani, M. Carbohydr. Res. 1979, 76, 59. (5) Harata, K. J. Inclusion Phenom. Mol. Recognit. Chem. 1992, 13, 77. (6) Lavandier, C. D.; Pelletier, M. P.; Reinsborough, V. C. Aust. J. Chem. 1991, 44, 457. (7) Forgacs, E. J. Inclusion Phenom. Mol. Recognit. Chem. 1994, 18, 229. (8) Kano, K.; Tamiya, Y.; Hashimoto, S. J. Inclusion Phenom. Mol. Recognit. Chem. 1992, 13, 287. (9) Nandi, N.; Bagchi, B. J. Phys. Chem. 1996, 100, 13914. (10) Junquera, E.; Pen˜a, L.; Aicart, E. Langmuir 1995, 11, 4685. (11) Immel, S.; Lichtenthaler, F. W. Starch 1996, 48, 225. (12) Lichtenthaler, F. W.; Immel, S. Starch 1996, 48, 145. (13) Blokzijl, W.; Engberts, J. F. B. N. Angew. Chem., Int. Ed. Engl. 1993, 32, 1545. (14) Wilson, L.D.; Siddall, S. R.; Verrall, R. E. Can. J. Chem. 1997, 75, 927. (15) Wilson, L.D.; Verrall, R. E. J. Phys. Chem. B 1997, 101, 9270. (16) Young, T. F.; Smith, M. B. J. Phys. Chem. 1954, 58, 716. (17) Horne, R. A., Ed. Water and Aqueous Solutions: Structure, Thermodynamics, and Transport Processes; Wiley: New York, 1972; Chapter 13, pp 519.

488 J. Phys. Chem. B, Vol. 102, No. 2, 1998 (18) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed.; Wiley: New York, 1980. (19) Wilson, L.D.; Verrall, R. E. Manuscript in preparation. (20) Milioto, S.; Bakshi, M. S.; Cristantino, R.; Delisi, R. J. Solution Chem. 1995, 24, 103.

Wilson and Verrall (21) Szjeitli, J. In Cyclodextrin Technology; Kluwer Academic Publishers: Dordrecht, 1988, Chapter 1. (22) Klyamkin, A. A.; Topchieva, I. N.; Zubov, V. P. Colloid Polym. Sci. 1995, 273, 520. (23) Connors, K. A. J. Pharm Sci. 1996, 85, 796.