Advanced dielectric continuum model of preferential solvation

Abstract

A continuum model for solvation effects in binary solvent mixtures is formulated in terms of the density functional theory. The presence of two variables, namely, the dimensionless solvent composition y and the dimensionless total solvent density z, is an essential feature of binary systems. Their coupling, hidden in the structure of the local dielectric permittivity function, is postulated at the phenomenological level. Local equilibrium conditions are derived by a variation in the free energy functional expressed in terms of the composition and density variables. They appear as a pair of coupled equations defining y and z as spatial distributions. We consider the simplest spherically symmetric case of the Born-type ion immersed in the benzene/dimethylsulfoxide (DMSO) solvent mixture. The profiles of y(R) and z(R) along the radius R, which measures the distance from the ion center, are found in molecular dynamics (MD) simulations. It is shown that for a given solute ion z(R) does not depend significantly on the composition variable y. A simplified solution is then obtained by inserting z(R), found in the MD simulation for the pure DMSO, in the single equation which defines y(R). In this way composition dependences of the main solvation effects are investigated. The local density augmentation appears as a peak of z(R) at the ion boundary. It is responsible for the fine solvation effects missing when the ordinary solvation theories, in which z=1, are applied. These phenomena, studied for negative ions, reproduce consistently the simulation results. For positive ions the simulation shows that z>>1 (z=5-6 at the maximum of the z peak), which means that an extremely dense solvation shell is formed. In such a situation the continuum description fails to be valid within a consistent parametrization.