Statistical thermodynamics of regular solutions and solubility parameters

Solubility parameters, developed originally for regular solutions, have been applied to solutions beyond the presumed weak non-ideality, implying that the true foundation of the solubility parameters may be more general than the regular solution theory. To assess the root of regularity on rigorous statistical thermodynamics, here we re-examine the classical iodine dissolution experiments by Shinoda and Hildebrand, who concluded that the entropy of mixing is ideal regardless of solute-solvent size ratio.We show that iodine solubility is concerned with the limit of infinite dilution,while the regular solution theory is a scheme to describe the dependence on the solute concentration. This means that the solubility of iodine cannot be a foundation of the regular solution; it is further shown that the differences in the solvation free energy among organic solvents are dominated by enthalpy with negligible role of the entropic component. In addition, the validity of the regular solution concept, i.e., the enthalpic nature of the solution non-ideality, can now be examined quantitatively by expressing the Margules model in terms of the Kirkwood-Buff integrals, which incorporate the excluded volume effects and the potential of mean force nature of interactions that were beyond the reach of the classical thermodynamic models. Such insights into the physical basis of solubility parameters may be useful for improving solubility prediction.