Gradient theory of the electric double layer at hydrocarbon–water interfaces

Abstract

Gradient theory of inhomogeneous fluids is used to model the electric double layer at a hydrocarbon–aqueous electrolyte interface. It is applied to a four-component regular solution (two solvent components and two ionic species) in which the dielectric permittivity is also inhomogeneous. The permittivity is determined by a Clausius–Mossotti constitutive equation based on the local densities of the solvent species. The gradient equations are coupled to Poisson’s equation and are solved using a Galerkin/finite element scheme. The results indicate that in dilute solution, the dependence of the interfacial tension on bulk electrolyte concentration is linear, and the sign and magnitude of the deviation of the tension from the pure solvent value depends strongly on the degree of ion partitioning between the two phases. In more concentrated solutions, the deviation becomes nonlinear and can change sign as the electrolyte concentration is increased.