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.

The dielectric continuum solvent model adapted for treating preferential solvation effects

“…The second term DG rest includes different non-electrostatic interactions, the interference electrostatic/ non-electrostatic effects and the mixing entropic contribution. The last two effects were shown to be negligibly small, and, altogether, it is a reasonable approximation to assume that DG rest = DG rest (n), neglecting the dependence of this term on n 2 [13]. The equilibrium conditions are extracted by the variation of Eq.…”

“…To be definite, we consider the sample mixture of benzene and dimethylsulfoxide (DMSO) as non-polar and polar solvent ingredients, respectively [9,13]. Notations c 1 , c 2 , c are used, respectively, for local concentrations of benzene, DMSO and the total (c = c 1 + c 2 ) concentrations.…”

“…Such a strategy is controversial and hardly adequate as applied to the systems under consideration. A more consistent approach [9,13] takes into account explicitly that the solvent composition is essentially non-uniform and is therefore based on the concept of the variable permittivity e(r), where r is a space point. This idea, supplemented by the specially formulated local equilibrium condition, provides the equation required to establish the variable values of space-dependent permittivity and concentrations of solvent ingredients.…”

“…This idea, supplemented by the specially formulated local equilibrium condition, provides the equation required to establish the variable values of space-dependent permittivity and concentrations of solvent ingredients. Such an approach was implemented for the simplest solute case of a Born-like spherical ion [13]. Thereby, the space variable point r reduced to a scalar variable R, measuring the radial distance from the ion centre.…”

“…Firstly, the basic idea of the local equilibrium in a non-uniform solution system, with variable solvent composition and variable dielectric function e(R) [9,13], is formulated and illustrated using spherical ionic solutes as the elementary example (Sections 2 and 3). We describe next the advanced continuum-level algorithm for solving the electrostatic problem in non-uniform dielectric media, which is addressed for treating solutes of arbitrary shape with non-spherical charge distributions (Sections 4 and 5).…”