RESUMEN
Monte Carlo simulations are employed to determine the differential capacitance of an electric double layer formed by small size-symmetric anions and cations in the vicinity of weakly to moderately charged macroions. The influence of interfacial curvature is deduced by investigating spherical macroions, ranging from flat to moderately curved. We also calculate the differential capacitance using a previously developed mean-field model where, in addition to electrostatic interactions, the excluded volumes of the ions are taken into account using either the lattice-gas or the Carnahan-Starling equation of state. For both equations of state, we compare the mean-field model for arbitrary curvature with a recently developed second-order curvature expansion. Our Monte Carlo simulations predict an increase in the differential capacitance with growing macroion curvature if the surface charge density is small, whereas for moderately charged macroions the differential capacitance passes through a local minimum. Both mean-field models tend to somewhat overestimate the differential capacitance as compared with Monte Carlo simulations. At the same time, they do reproduce the curvature dependence of the differential capacitance, especially for small surface charge density. Our study suggests that the quality of mean-field modeling does not worsen when weakly or moderately charged macroions exhibit spherical curvature.
RESUMEN
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.