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

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 vin_i = 1 nearly holds for inhomogeneous densities n_i, 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.