Dependence of the distribution constant in liquid-liquid partition equilibria on the van der Waals molecular surface area

Abstract

The direct calculation of free energy of interactions between a solute j and two immiscible liquids shows a linear dependence between the (logarithm of) the distribution constant in liquid-liquid partition equilibrium log K(j) and the van der Waals surface area of the solute. The study provides a thermodynamic proof for the formula log K(BA,j) = c1 log K(BC,j) + c2 that describes the linear dependence between (the logarithm of) the distribution constant for a solute j in a solvent system (B/A) and (the logarithm of) the distribution constant for the same solute in a different solvent system (B/C). This relation has been well proven by various experimental studies and it is frequently used in liquid chromatographic separations as well as in liquid-liquid extractions, but was not explained previously based on thermodynamic results. The theory was verified using the prediction of octanol/water distribution constants log K(ow) for a wide range of molecules, including hydrocarbons and compounds with a variety of functional groups. The results have also been verified for the distribution constants in other solvent systems. The expression for the distribution constant obtained in this study also gives a theoretical base for the additive fragment methodology used for the prediction of log K(ow).