Extended Hildebrand solubility approach and the log linear solubility equation

The log linear solubility equation, log S = log Sw + sigma f, was studied in relationship to the extended Hildebrand solubility approach. It is shown that the log linear form may be derived beginning with the extended Hildebrand approach. The log linear expression gives a good linear fit for semipolar drugs in a number of water-cosolvent mixtures. It is particularly successful when the solubility parameter, delta 1, of the cosolvent is 3 or more solubility parameter units larger than the solubility parameter, delta 2, of the drug. When the cosolvent tends to solvate the drug strongly, the log linear function may even hold where the solubility parameters of the drug and cosolvent are similar. It appears, however, not to be applicable to nonpolar cosolvent systems. An interfacial model for the solubility of drugs in polar mixed solvents is based on sigma, a parameter that also figures prominently in the log linear solubility equation. When used to describe mixed solvent systems, the interfacial model applies in the region of the solubility profile (solubility versus solvent composition) where the log linear relationships hold. The extended Hildebrand solubility approach is applicable over a wide range of cosolvent composition in mixed systems from nonpolar organic solvents to water.