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

TL;DR

This paper develops a theoretical framework for understanding how nonionic hydrophobic solutes interact within a mixture solvent, revealing how solute density couples with solvent composition and induces phase separation.

Contribution

It introduces a comprehensive theory linking solvation properties, thermodynamic coupling, and phase behavior of nonionic solutes in mixed solvents, including phase transition predictions.

Findings

Large solute-solute attraction due to solvent fluctuations.

Derived solute spinodal density for instability.

Predicted phase diagrams for 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 relationship among the solvation chemical potential, the partial volumes $v_i$, the Kirkwood-Buff integrals, the second osmotic virial coefficient, and the Gibbs transfer free energy. We examine how the solute density $n_3$ is coupled to the solvent densities $n_1$ and $n_2$ in thermodynamics. In the limit of small compressibility, we show that the space-filling condition $\sum_i v_i n_i=1$ 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 $n_3^{\rm spi}$ 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.} {\bf 54}, 1523 (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.