Mean-Field Approximation to the Hydrophobic Hydration in the Liquid-Vapor Interface of Water

A mean-field approximation to the solvation of nonpolar solutes in the liquid-vapor interface of aqueous solutions is proposed. It is first remarked with a numerical illustration that the solvation of a methane-like solute in bulk liquid water is accurately described by the mean-field theory of liquids, the main idea of which is that the probability (Pcav) of finding a cavity in the solvent that can accommodate the solute molecule and the attractive interaction energy (uatt) that the solute would feel if it is inserted in such a cavity are both functions of the solvent density alone. It is then assumed that the basic idea is still valid in the liquid-vapor interface, but Pcav and uatt are separately functions of different coarse-grained local densities, not functions of a common local density. Validity of the assumptions is confirmed for the solvation of the methane-like particle in the interface of model water at temperatures between 253 and 613 K. With the mean-field approximation extended to the inhomogeneous system the local solubility profiles across the interface at various temperatures are calculated from Pcav and uatt obtained at a single temperature. The predicted profiles are in excellent agreement with those obtained by the direct calculation of the excess chemical potential over an interfacial region where the solvent local density varies most rapidly.