Thermodynamics of ternary electrolytes: Enhanced adsorption of macroions as minority component to liquid interfaces

We study the equilibrium thermodynamics between two ternary ionic systems in immiscible solvents characterized by different dielectric constants. We consider system geometries wherein the two phases of immiscible solvents occupy, respectively, semi-infinite regions of space separated by neutral and charged planar interfaces. Specifically we analyze the case where the ternary system is composed of a pair of symmetric ions plus a minority charged component of high valence. We describe the system by means of a nonlinear mean-field theory. We first obtain exact analytical solutions for the electrostatic potentials, as well as density profiles for a symmetric binary system, and then extend these results to the ternary case using the perturbation theory. We show that the corresponding adsorption and depletion of multivalent macroions at the interface are highly enhanced when compared with the monovalent case.