Theory of nonionic hydrophobic solutes in mixture solvent: Solvent-mediated interaction and solute-induced phase separation.

Abstract

We present a theory of nonionic solutes in a mixture solvent composed of water-like and alcohol-like species. First, we show the relationship among the solvation chemical potential, the partial volumes vi, the Kirkwood-Buff integrals, the second osmotic virial coefficient, and the Gibbs transfer free energy. We examine how the solute density n3 is coupled to the solvent densities n1 and n2 in thermodynamics. In the limit of small compressibility, we show that the space-filling condition ∑i vini = 1 nearly holds for inhomogeneous densities ni, where the concentration fluctuations of the solvent can give rise to a large solute-solute attractive interaction. We also derive a solute spinodal density n3spi for solute-induced instability. Next, we examine gas-liquid and liquid-liquid phase transitions induced by a small amount of a solute using the Mansoori, Carnahan, Starling, and Leland model for hard-sphere mixtures [J. Chem. Phys. 54, 1523-1525 (1971)]. Here, we assume that the solvent is close to its gas-liquid coexistence and the solute interacts repulsively with the water-like species but attractively with the alcohol-like one. We calculate the binodal and spinodal curves in the phase diagrams and examine nucleation for these two phase transitions.