Differential capacitance of an electric double layer with asymmetric solvent-mediated interactions: mean-field theory and Monte Carlo simulations

Abstract

The differential capacitance of an electrical double layer is directly affected by properties of the electrolyte solution such as temperature, salt concentration, ionic size, and solvent structure. In the present work, we employ a mean-field approach and Monte Carlo simulations to investigate how the inclusion of asymmetric solvent-mediated ion–ion and ion–surface interactions affects the differential capacitance. We focus on a charged flat electrode immersed in an electrolyte solution of monovalent ions at physiological concentration in a uniform dielectric background. Solvent-mediated anion–anion, anion–cation and cation–cation interactions are modeled on the basis of Yukawa potentials with three independent strengths that add to Coulomb and excluded volume pair-potentials, the latter accounted for through a lattice gas approach. We use the three interaction strengths to produce and analyze asymmetric profiles of the differential capacitance as function of the electrode's surface charge density. While solvent-mediated anion–anion and cation–cation interactions mainly affect the behavior at medium charge densities of the electrode, anion–cation repulsion increases the differential capacitance of a weakly charged electrode. We present a simple phenomenological model to rationalize this finding. Most importantly, because the added solvent-mediated interaction potential is comparatively soft, our mean-field model is able to qualitatively – and in some cases quantitatively – reproduce all Monte Carlo simulation results, even at high surface charge densities of the electrode.