Thermodynamic Studies of Molecular Interactions in Aqueous α-Cyclodextrin Solutions:  Application of McMillan−Mayer and Kirkwood−Buff Theories

Osmotic vapor pressure and density measurements were made for aqueous α-cyclodextrin (α-CD) solutions in the temperature range between 293.15 and 313.15 K. The experimental osmotic coefficient data were used to determine the corresponding activity coefficients and the excess Gibbs free energy of solutions. Further, the activity data obtained at different temperatures along with the enthalpies of dissolution (reported in the literature) were processed to obtain the excess enthalpy and excess entropy values for the solution process. The partial molar entropies of water and of α-cyclodextrin were calculated at different temperatures and also at different concentrations of α-CD. Using the partial molar volume data at infinite dilution, the solute−solvent cluster integrals were evaluated which yielded information about solute−solvent interactions. The application of McMillan−Mayer theory of solutions was made to obtain osmotic second and third virial coefficients which were decomposed into attractive and repulsive contributions to solute−solute interactions. The second and third osmotic virial coefficients are positive and show minimum at 303.15 K. The Kirkwood−Buff (KB) integrals G_ij, defined by the equation G_ij = (g_ij − 1)4πr² dr, have been evaluated using the experimental osmotic coefficient (and hence activity coefficient) and partial molar volume data. The limiting values of KB integrals, G_ij⁰ are compared with molecular interaction parameters (solute−solute i.e., osmotic second virial coefficient) obtained using McMillan−Mayer theory of solutions. We found an excellent agreement between the two approaches.