Speed of Sound, Density, and Molecular Modeling Studies on the

Langmuir 1997, 13, 2235-2241

2235

Speed of Sound, Density, and Molecular Modeling Studies on the Inclusion Complex between Sodium Cholate and β-Cyclodextrin Gustavo Gonza´lez-Gaitano,† Aurora Compostizo,‡ Luis Sa´nchez-Martı´n,§ and Gloria Tardajos*,‡ Departamento de Quı´mica-Fı´sica I, Facultad de Ciencias Quı´micas, Universidad Complutense de Madrid, 28040 Madrid, Spain, and Departamento de Quı´mica Orga´ nica, Facultad de Ciencias Quı´micas, Universidad Complutense de Madrid, 28040 Madrid, Spain Received August 13, 1996. In Final Form: January 29, 1997X The system sodium cholate (NaC) + β-cyclodextrin (β-CD) in water has been studied by speed of sound and density measurements to obtain the corresponding apparent and partial molar volumes and adiabatic compressibilities. For pure NaC the values for the micellization volumes and compressibilities have been obtained, as well as the transference properties due to the complexation for the ternary system. When the β-CD is present, a shift in the critical micelle concentration of the surfactant equivalent to the amount of β-CD added is observed, due to the complex formation between solutes that delays the micellization. At infinite dilution, there is a marked change in the compressibility of the surfactant, although it is not appreciable in the volume. A detailed molecular modeling study has been carried out to elucidate, together with 1H NMR data, the microscopic structure of the complex.

Introduction β-Cyclodextrin (β-CD) is a cyclic oligosacharide obtained as the main product from the enzymatic conversion of the starch. It consists of seven R-D-glucopyranose units, linked by glycosidic bonds R-1,4. Due to a lack of free rotation about the glycosidic bonds, β-CD (as the rest of CDs) has a unique spatial configuration, showing a cylindrical or hollow truncated cone shape. The cavity, with 6 Å of width and 7.9 Å of height, has a hydrophobic character, while the rims are hydrophilic: the wider one, with 14 secondary hydroxyl groups, and a narrower one, with the 7 primary OH groups (Figure 1a). These structural features give the CD the property of forming inclusion complexes between molecules that fit into the hydrophobic cavity. There are many studies dealing with inclusion complexes of β-cyclodextrin, either in its natural state or with modified β-CDs, and with a great variety of guest molecules, that find application in different fields.1 Bile salts are natural amphiphiles which are synthesized in the liver. They form small aggregates2 which help to solubilize and disperse dietary lipids. They have a considerable aqueous solubility and also a great capacity to solubilize molecules such as lecithin and cholesterol.3 Bile salts are also commonly used for membrane solubilization and reconstitution, specially the sodium cholate, NaC.4 From the group of biological surfactants constituted by bile acids salts, sodium cholate is one of the most used. It is made up (Figure 1b) of a rigid steroid nucleus, in * To whom correspondence should be addressed: Departamento de Quı´mica-Fı´sica I, Facultad de Ciencias Quı´micas, Universidad Complutense de Madrid, 28040 Madrid, Spain. Fax: 34-1-3944135. E-mail: [email protected]. † Departamento de Quı´mica-Fı´sica I. ‡ Departamento de Quı´mica Orga ´ nica. X Abstract published in Advance ACS Abstracts, March 15, 1997. (1) (a) Szelti, J. Cyclodextrins and Their Inclusion Complexes; Akademiai Kiado: Budapest, Hungary, 1982. (b) Bender, M. L.; Komiyama M. Cyclodextrin Chemistry; Springer-Verlag: Berlin, 1978. (c) Saenger, W. Angew. Chem., Int. Ed. Engl. 1980, 19, 344-362. (d) Song Li; Purdy, W. C. Chem. Rev. 1992, 92, 1457-1470. (2) Mazer, N. A.; Carey, M. C.; Kwasnick, R. F.; Benedek, G. B. Biochemistry 1979, 18 (14), 3064-3075. (3) Carey, M. C.; Small, D. M. J. Clin. Invest. 1978, 61, 998. (4) Tauskela, J. S.; Akler, M.; Thompson, M. Anal. Biochem. 1992, 201, 282-287.

S0743-7463(96)00803-7 CCC: $14.00

a

b

Figure 1. (a) β-Cyclodextrin structure (β-CD). (b) Cholate ion structure.

which the cyclohexanes A and B are in the cis position; there are three hydroxyl groups inserted at positions 3, 7, and 12. Position 17 is occupied with a short aliphatic tail, with a carboxylate group at the end. Thus, the molecule presents a hydrophobic face (with three methyl groups, C18, C19, and C21), an aliphatic chain finished in a carboxylate anion, and a hydrophilic face. There are several reports on inclusion complexes between NaC and CDs studied by liquid chromatography,5 fluorescence,6 microcalorimetry,7 or NMR.8 The aim of this work was to study not only the complex structure but mainly the role that β-CD plays in the micellization behavior of the NaC. The study has been performed through two partial and apparent molar properties, namely, molar adiabatic compressibility and molar vol(5) Shimada, K.; Oe, T.; Hirose, Y, Komine, Y. J. Cromatogr. 1989, 478, 339. (6) Miyahima, K.; Yokoi, M.; Komatsu, H.; Nakagaki, M. Chem. Pharm. Bull. 1986, 34, 1395. (7) Tan, X.; Lindembaum, S. Int. J. Pharm. 1991, 74, 127. (8) Tan, Z. J.; Zhu, X. X.; Brown, G. R. Langmuir 1994, 10, 1034.

© 1997 American Chemical Society

2236 Langmuir, Vol. 13, No. 8, 1997

Figure 2. Experimental setup.

ume, obtained by very precise measurements of density and speed of sound. Given the short range of concentrations available and the small changes in these properties, it has been necessary to make use of a high-precision technique, designed by us, to obtain simultaneously both sound velocity and density. Molecular modeling techniques and 1H NMR spectroscopy have been employed as well to elucidate the microscopic structure of the complexes and to estimate the energies involved in the inclusion process. Experimental Section Materials. β-CD was obtained from Aldrich and NaC from Sigma. The purity of the β-CD was 99.5% and that for NaC is better than 98%. The water content of the cyclodextrin was determined by thermogravimetric analysis and was found to be 13.5%. All the products were used as received, without further purification. For the NMR measurements deuterium oxide was employed as solvent, from Merck, with a deuteration degree not less than 99.95%. The water of the β-CD was taken into account in the concentration of the solutions, which were prepared by weight. Apparent Molar Properties. Measurements of the speed of sound and density were performed simultaneously with a technique designed in this laboratory (Figure 2). The measurement of both properties was carried out in a continuous way, as described below, thus permitting higher precision in the partial molar properties. The part of the technique related to the speed of sound is described extensively in a previous report.9 It consists of measuring the time that it takes a wave-packet of defined ultrasonic frequency to travel the distance between a piezoelectric transducer and a reflector. A digitizing oscilloscope of high sampling rate (20 MS s-1) counts the time between two consecutive reflections and the speed of sound is obtained directly from the travel time of the wave-packet and the known distance transducer-reflector, which is calibrated in each experiment with a reference liquid (pure water). The ultrasonic cell is immersed in a thermostat, controlled by a TRONAC PTC41 and a cryostat. The stability in the temperature is better than 1 mK (all the experiments were carried at 298.15 K). The densities were measured with a vibrating tube densimeter Anton Paar DMA 601 HT, calibrated with water and air in each set of measurements, and thermostated by recirculation of the water of the thermostat (there is no temperature difference between the solution in the densimeter and in the cell). A peristaltic pump suctions liquid to the densimeter from the ultrasonic cell, where a magnetic stirrer produces, together with the recirculation, the adequate homogenization of the medium. When the recirculation is judged to be completed, the pump is turned off, and the vibration period of the densimeter and the time of flight of the wave-packet (9) Gonza´lez-Gaitano, G.; Tardajos, G.; Montero de Espinosa, F. Rev. Sci. Instrum. 1994, 65, 2933.

Gonza´ lez-Gaitano et al. are registered. The complete process of stirring and stabilization of the measurements use to take about 15 min. After the measurement, an automatic buret, Metrohm 665, changes the concentration in the cell by adding volumes of a more concentrated solution, and the process of recirculation is repeated. A PC controls both the oscilloscope and the buret and it is programmed to follow the evolution of the wave-packets with the concentration. It calculates the volumes to be added, to keep constant the increments of concentration, and takes the measurements of added volume, time, and period. Measured data are stored on the hard disk and sent to the printer. The densimeter, the peristaltic pump, and the buret are contained in a polymethacrylate box at 25 ( 0.05 °C, to avoid temperature gradients. In these conditions, precision in speed of sound and density are 2 × 10-3 m s-1 and 1 × 10-6 g cm-3, respectively. In all the experiments a stock solution was prepared by weighing an amount of β-CD in water. Part of this solution was introduced into the measuring cell, and with the rest another was prepared with the desired molality of NaC. The latter is filling the buret and it is added to the ultrasonic cell. This permits variation of the surfactant molality keeping constant the molality of β-CD. Molecular Modeling. The calculations were done with the Insight II program,10 implemented in an IRIS 4D/310VGX workstation of Silicon Graphics. The molecular structure of the β-CD has been generated by linking of seven units of R-Dglucopyranose, and that of the cholate ion by means of the Sketch utility from the main module Builder. Energy minimizations of the isolated host and guest molecules were performed with the Discover program, employing the CVFF forcefield,11 and with several algorithms (at first a steepest descents algorithm, finishing with a modified Newton-Raphson to refine the structures), until the root mean squares of the derivatives were less than 0.0001 kcal Å-1. Afterward, molecular dynamic calculations of the system at 298 K were performed, and the process of minimization was repeated, to find the absolute minimum of energy. The structure of the CD thus obtained is highly regular (the O4 atoms are almost coplanar), more than the crystalline structure that is obtained from X-ray and neutron diffraction data available at the Cambridge Structural Data Base.12 We have chosen this highly symmetric structure rather than the crystalline one, which is slightly distorted because of the hydration water that is inside and outside the cavity. To fit the cholate anion into the cavity, rigid docking experiments were carried out with the refined structures. The cholate was approximated by the steroid nucleus and by the aliphatic tail, and directed toward the two rims of the CD, until the position that gives a minimum interaction energy was found. This position was taken as the starting point to minimize the complex. The algorithm employed in the minimization of these complexes was a conjugate gradients, until the root mean squares were less than 0.001 kcal Å-1. The cut-off distances for the Coulomb and van der Waals energies were of 100 Å, to include all the possible interactions. The association energies were obtained by subtracting the complex energy from that of the CD and the cholate ion. Cross-terms and harmonic potentials for bonding energies were included in the force field. To account for solvent effects, a relative dielectric constant of 80 dependent on inverse of the distance was introduced into the Coulombic term of the force field. A common strategy usually followed when modeling these CD complexes is to assume that the molecules are in a vacuum. However, it is known that for these complexes solvent plays a decisive part, so going without it could be a rather drastic approximation when energies are estimated or geometries are predicted. NMR Measurements. The samples for NMR were prepared in D2O as solvent, at several molar ratios NaC:β-CD, and keeping fixed the β-CD concentration at 0.015 M. The NMR spectra were recorded in a Varian VXR 300S, at 300 MHz, fitted with a thermostating unit. All the records were carried out at 20 ( 0.4 °C. The chemical shifts are relative to the HDO signal, at 4.63 ppm. (10) Insight II version 2.1.0. San Diego: Biosym Technologies, 1992. (11) Dauber-Osguthorpe, P.; Roberts, V. A.; Osguthorpe, D. J.; Wolff, J. Proteins: Struct., Funct., Genet. 1988, 4 (1), 31-47. (12) CSD, Cambridge Crystallographic Data Centre, Cambridge, U.K.

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Results and Discussion Apparent and Partial Molar Properties. The apparent molar volume and apparent molar adiabatic compressibility of a solute i in a mixture where the molality of the other components is kept constant can be calculated using the usual definitions:

vφ,i ) (V - V0)/mi

{( ) ( ) }

1 ∂V mi ∂P

κS,φ,i ) -

∂V0 ∂P

-

S

)

S

(1)

1 (β V - βS,0V0) (2) mi S

where βS ) (Fu2)-1 is the adiabatic compressibility, and the zero subindex stands for the initial state when the molality mi is zero. In this paper the molality is defined as moles of solute per kilogram of solvent according to the IUPAC, where the solvent, w, is pure water. According to the above definition of molality the resulting expressions for the apparent molar properties are

vφ,j ) Mi/F - (1 + mjMj)(F - F0)/miFF0

(3)

κS,φ,i ) βSvφ,i + (1 + mjMj)(βS - βS,0)/miF0

(4)

F is the density of the solution, F0 the density when mi ) 0, Mi and Mj are the molar mass of solutes i and j, and mi and mj the molalities. The partial molar properties can be obtained from the apparent ones by using

( ) ( ( ))

vi ) κS,i ) -

∂V ∂ni

)

nw,nj

∂ ∂V ∂ni ∂P

d (v m ) dmi φ,i i )

S nw,nj

(5)

d (κ m ) dmi S,φ,i i

(6)

It is possible to define another molality scale, where the molality of i would be moles of i per kilogram of mixed solvent w + j, although in this case, in which i and j are solid solutes it is more appropriate to use the IUPAC definition of molality. Anyway the conversion between both scales is straightforward and, for dilute systems, differences are minimal. The difference between eqs 3 and 4 and those usually found in the literature is that mj (the molality of the third component) does not appear in the above expressions. β-Cyclodextrin. The density and ultrasonic velocity for β-CD solutions in water as a function of the molality are plotted in Figure 3. The apparent molar volumes and compressibilities were calculated according to eqs 3 and 4, and they are represented in Figure 4 together with values from the literature.13-15 The experimental points were fitted to the following equations:

vφ,CD ) v0CD + BvmCD ) 704.04 + 17mCD (cm3 mol-1) 0

κS,φ,CD ) κ

+ Bκ,SmCD ) -2.59 × 10

-15

S,CD

0.145 × 10

-12

+

mCD (Pa

-1

m3 mol-1)

where the superindex zero stands for the corresponding (13) Paduano, L.; Sartorio, R.; Vitagliano, V.; Constantino, L. J. Solution Chem. 1990, 19, 31. (14) Milioto, S.; Bakshi, M. S.; Crisantino, R.; De Lisi, R. J. Solution Chem. 1995, 24, 103. (15) Nomura, H.; Koda, S.; Matsumoto, K.; Miyahara, Y. Studies in Physical and Theoretical Chemistry; Elsevier Science Publishers: Amsterdam, 1982; Vol. 27, p 151.

Figure 3. (a) Density measurements and (b) speed of sound versus molality for pure substances and β-CD + NaC mixtures (fixed concentrations of β-CD 0.008 44 m and 0.012 14 m).

properties at infinite dilution (standard state) and the B coefficients account for the solute-solute interactions. Our results for the volumes are in good agreement with the literature data, especially with those of Milioto et al.,14 although they obtained a slightly higher value at infinite dilution (706.5 cm3 mol-1) and a negative Bv coefficient (-95 cm3 mol-2 kg). A negative value is indicative of an hydrophobic interaction, something which lacks consistency with the 21 hydroxyl groups of the β-CD. With

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Gonza´ lez-Gaitano et al.

Figure 5. Apparent and partial molar volumes for pure NaC.

Figure 4. Apparent molar volumes and compressibilities for β-CD.

reference to the adiabatic compressibility, the low extrapolated value (only slightly negative, -2.59 × 10-15 Pa-1m3 mol-1) agrees well with Nomura et al. data,15 showing, as in the volume, a positive slope. The small value of the standard compressibility suggests a strong reorganization of the hydration water of the β-CD. Sodium Cholate. The results of density and ultrasonic velocity for NaC are shown in Figure 3. Although deviations of the density from a single straight line are negligible, on the u graph it is possible to plot two lines with different slopes that intercept at 0.015 m that corresponds to the critical micelle concentration (cmc).16 With this technique it has been possible to make enough measurements below the cmc and to obtain the partial molar volumes and compressibilities of NaC at infinite dilution. The scattering in the plots of partial molar properties is in part a consequence of the direct derivative over the experimental values, without any previous fitting. The calculated volumes obtained according to eqs 3 and 5 are plotted in Figure 5. At infinite dilution vNaC is 322.7 cm3 mol-1. The micellization volume, defined as the difference of the molar partial volume of the surfactant in micellized form (plateau region) and in monomeric form, is ∆vM ) 6.4 cm3 mol-1. This value is similar to that obtained for ionic surfactants with a long alkyl chain (e.g., 7 cm3 mol-1 for dodecyltrimethylammonium bromide17) but the shape of the curve is different: the range of concentration needed to reach a stationary value after the beginning of the aggregation is larger for the NaC. Such a broad micellar region indicates a multistep aggregation process in which species of different aggregation number are involved, as reported by Djavanbakht et al., based on measurements using ultrasonic absorption.18 (16) O’Connor, C. J.; Wallace, R. G. Adv. Colloid Interface Sci. 1985, 22, 1-111. (17) Gu¨velli, D. E.; Kayes, J. B.; Davies, S. S. J. Colloid Interface Sci. 1981, 82, 307.

In Figure 6 are plotted the apparent and partial molar compressibilities. These data are less noisy than the volumes, because the relative changes in the speed of sound are larger than those of the density. The above comments related to the nature of the aggregation process are more noticeable in this property. Although observing this figure we can appreciate that κS does not reach an absolutely constant value, which would be a clear indication that the aggregation continues well above the initial aggregation point, we can give an estimated value of the micellization compressibility, ∆κSM, of 7.2 × 10-14 Pa-1 m3mol (obtained in the same way as ∆vM), a value that falls within the same order of many surfactants in water.19,20 The adiabatic molar compressibility of the surfactant in its micellized form increases along a broad region from a low negative value to another close to zero. The low value of the compressibility of the NaC in the micelles is indicative of a persistence of the interaction via hydroxyl groups with the solvent and/or between the cholate ions in the aggregates, in keeping with Small’s model for the aggregation of bile salts.21 Despite the low cmc concentrations it is possible to obtain with accuracy the compressibility of the monomer at infinite dilution, resulting in -8.1 × 10-14 Pa-1 m3 mol-1 (see Figure 6). Ternary System. In parts a and b of Figure 3 the results of density and velocity are shown respectively for two different β-CD molalities (0.00844 m and 0.01214 m). Given the straight line appearance of both plots, we have obtained the derivative of the speed of sound data with respect to the molality of NaC to detect changes in the slope. Such values are shown in Figure 7, and given that the derivatives are obtained at moles of water and β-CD constant, they just represent the change in u per mole of NaC added. The use of derivatives in the speed of sound to detect structural changes as a function of the temperature has been used by Glatter,22 but to our knowledge there are no studies on the derivative with the concentration. Regarding the pure cholate in the monomeric form, we can observe an initial linear zone that extrapolates at a value of 290 m s-1 mol-1kg, and with a negative slope that should be a consequence of all the interactions. As this is a differential property, it is easier to see the (18) Djavanbakht, A.; Kale, M.; Zana, R. J. Colloid. Inerface Sci. 1977, 59, 139. (19) De Lisi, R.; Ostiguy, C.; Perron, G.; Desnoyers, J. E. J. Colloid Interface Sci. 1979, 71 (1), 147. (20) Vikingstad, E.; Skauge, A.; Høiland, H. J. Colloid Interface Sci. 1978, 66 (2), 240. (21) Small, D. M. In The bile acids; Nair, P. P., Kritchevsky, D., Eds.; Plenum Press: New York, 1971; Vol 1, Chapter 8. (22) Glatter, O. J. Phys. IV 1995, 3, 27.

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Langmuir, Vol. 13, No. 8, 1997 2239

Figure 6. Apparent and partial molar compressibilities for pure NaC.

Figure 8. (a) Apparent molar compressibilities and (b) partial molar compressibilities for the NaC + β-CD system. Figure 7. Derivatives with the concentration of NaC for pure NaC and mixtures. Symbols are the same those in Figure 3a.

beginning of the aggregation than with the u plot. Thus, whereas micelles start to form at 0.011 m, the maximum change in the slope of the derivative (second derivative) is around 0.015 m, corresponding to the value obtained at the intercept of two straight lines in u. The values at infinite dilution of (∂u/∂mNaC)w,β-CD are different than those in pure water and, given that the property represents the change in u per mole of added NaC at fixed CD concentration, providing evidence of an interaction between the NaC and the β-CD. These extrapolations are the same (251 m s-1 kg mol-1) with independence of the β-CD concentration. At infinite dilution there is an excess of CD with respect to the NaC, and mNaC/mCD ) 0. Regardless of the value of the equilibrium constant for the complexation, in such conditions all the surfactant will be in complexed form, and the value of the properties at infinite dilution must be independent of the fixed CD concentration. Although the different values of the (∂u/∂mNaC) confirm the interaction between NaC and CD, it is not possible to observe a neat change in the plots corresponding to the 1:1 complex. Nevertheless, it is possible to observe a shift on the cmc of the plots to higher concentrations, in an amount equal to the added β-CD. This confirms the formation of a complex of 1:1 stoichiometry, which is strong enough to modify the micellization equilibrium. Another conclusion that can be drawn from these results is that, provided the values of (∂u/∂mNaC)w,β-CD are the same but shifted to a new molality, m* ) mNaC + mβ-CD, the β-CD is not forming part of the aggregates. In view of the specificity of the

geometric and polarity requirements for the formation of bile salt aggregates,21 it would be difficult for the β-CD to take part in the formation of the micelles. Similar conclusions can be obtained using the more familiar compressibilities. In Figure 8 the apparent and partial molar compressibilities are plotted. The shift in the cmc in the presence of β-CD is, of course, more neat in the molar partial compressibility than in the apparent one. For the pure cholate in water the values at infinite dilution are different from those in the systems with cyclodextrin, yielding the same value with independence of the molality of β-CD. The transfer compressibility, ∆κ0S,comp from the pure water to the complex is 2.25 × 10-14 Pa-1 cm3 mol-1. This positive value can be associated with the water molecules included in the cavity of the β-CD, displaced by the cholate and now forming part of the bulk. Apparent molar volumes, vφ,NaC, have also been calculated. The cholate shows the same volume in the absence or in the presence of cyclodextrin within the experimental uncertainty. The fact that the transfer volume is practically zero proves that the volume occupied by a cholate molecule in water is equivalent to the volume of water displaced from the cavity of the β-CD and now forming part of the bulk water. Molecular Modeling and NMR. Figure 9 shows the structures obtained by molecular modeling according to the methods described in the Experimental Section. The calculated energy values are -37.51 (structure 1) and -37.25 kJ mol-1 (structure 2), practically the same. If the cholate is introduced by the steroid nucleus (see structures 3 and 4), energies are of -32.08 and -33.16 kJ

2240 Langmuir, Vol. 13, No. 8, 1997

Gonza´ lez-Gaitano et al.

a

b

Figure 9. Minimized structures for the complex when (a) the cholate enters by the aliphatic chain and (b) the cholate enters by the steroid nucleus. (Only the protons H3 and H5 of the β-CD and H′3, H′12, H′18, H′19, and H′21 of the cholate are drawn in the structures.)

mol-1, depending if it enters by the narrower rim (primary hydroxyl groups) or by the wider rim (secondary hydroxyl groups). From the NMR measurements, in the case of the β-CD one can identify the peaks that correspond to the six types of protons bonded to C.23 When NaC is present, an upfield shift of H5 may be observed, while H3 and H6 shift downfield to a less extent. H1, H2, and H4, that is, the protons located in the outer face of the cavity, are scarcely shifted. These results show that the complexation has taken place. From the plot of ∆δ values against the quotients NaC:β-CD and β-CD:NaC for several R values (Figure 10) a 1:1 complex stoichiometry is evident (∆δ is the chemical shift minus the value in absence of host or guest molecule). For the cholate protons (notation with apostrophes to distinguish from the CD protons), we have chosen the most representative and resolved resonances,24 that is, H′3, H′12, H′18, H′19, and H′21 (doublet). The most affected protons are H′18 and H′21 and, to a less extent, H′12 and H′19. H′3 does not shift within the experimental error. Chemical shifts are produced upfield, in the same direction as H5 of the CD. In general terms, the chemical shifts of the aliphatic chain protons H′18 and H′21 are greater than the rest. This is understandable in light of the cholate structure: these are protons belonging to methyl groups inserted in the hydrophobic side and they will interact much more with the cavity. Methyl protons of the C19 are less affected, meaning that it is undergoing less interaction, although this is a group as bulky as the others. On the other hand, the H′3, located (23) Demarco, P. V.; Thakkar, A. L. Chem. Commun. 1970, 2. (24) Campredon, M.; Quiroa, V.; Thevand, A.; Allouche, A.; Pouzard, G. Magn. Reson. Chem. 1986, 24, 624-629.

Figure 10. (a) Chemical shifts of the β-CD protons versus the molar ratio R and (b) for several protons of the NaC.

at the extremity of the steroid nucleus, do not undergo changes. Accordingly, we may say that the cholate is going to enter into the cavity by the aliphatic chain, that is, by the carboxylate group. These results are the same that those obtained by Tan et al.,7 except in the sense in which H3 protons are shifted (these authors obtain a higher shift and in the opposite sense). Nevertheless, this fact does not change the conclusions. According to the theoretical calculations, any of the first two structures would be possible, since they are almost equal energetically. The fact that H5 of the CD is the proton that suffers a greatest downfield shift suggests a stronger interaction with the cholate (possibly van der Waals shifting or steric perturbation) that should have a corresponding shift in the same direction (if this were the nature of the interaction) in some cholate proton. The greatest displacements are H′18 and H′21. This, in view of the two structures, would be more compatible with structure 2, in which H5 protons are closer to the hydrogens of C21 and C18, since this is the narrow part of the cavity (cholate is bogged down, like a funnel). H3 shifts less indicating a minor contact (wider side) fact that is more reasonable if the cholate enters by the primary hydroxyl border, in light of the minimized structures. Tan8 suggests that the complex forms when the anionic group penetrates the cavity by the secondary rim. Anyway, the carboxylate group is outside the cyclodextrin, as was to be expected (in general, ions have little trend to remain included in the CDs cavity25) and any of these two calculated structures is compatible with the experimental (25) Hersey, A.; Robinson, B. H.; Kelly, H. C. J. Chem. Soc., Faraday Trans. 1 1986, 82, 1271-1287.

Inclusion Complex Studies

results. Regarding structures 3 and 4, besides giving higher energies, they are not consistent with NMR spectra, since the strong chemical shifts of the resonances of H′18 and H′21 should not be observed (because they would be outside the CD) and a change on the chemical shift of H′3 should be expected. The carboxylate group goes through the cavity remaining hydrated, so there is no drawback to the cholate ion to enter by the charged group. ∆δ versus R plots permit us to estimate the binding constant K by application of the Benesi-Hildebrand method, assuming a 1:1 complex. We have obtained an equilibrium constant of K ) 2200 ( 400 M-1 using the H5 proton. For H′18 the calculated value was of 3400 ( 300 M-1. The results are in good agreement with the values of the literature obtained by NMR8 (1500 M-1, only with

Langmuir, Vol. 13, No. 8, 1997 2241

the protons H′18) and microcalorimetry7 (3150 M-1). The value is typical of surfactant guests, and it is high enough to resolve the competitive equilibrium between micellization and complexation in favor of the latter, so a change in the cmc is expected in an amount equal to that of the concentration of CD, as observed in the apparent molar properties, since the complex is 1:1. Acknowledgment. We are grateful to the M.E.C. of Spain for financial support through two DGICYT Grants, PB89-0113 and PB-930448, to the Centro de Espectroscopı´a, and to the Vicerrectorado de Investigacio´ n of the U.C.M. for the postgraduate grant for G.G. LA960803T