Theoretical derivation of partition coefficient from solubility parameters

Using the free energy expansion series of Scatchard and Prentiss, we have derived an expression for the partition coefficient in terms of solubility parameters of solute and solvents, their molar volumes, and the partial molal volumes of the solute in these solvents. This treatment assumes: (1) total separation of phases; (2) absence of complexes; (3) no contribution from three-center interaction; (4) low concentration of solute; and (5) geometric mean assumption for unlike interactions.