Effect of Ionic Size on the Structure of Cylindrical Electric Double Layers: A Systematic Study by Monte Carlo Simulations and Density Functional Theory

Abstract

The effect of ionic size on the diffuse layer characteristics of a cylindrical electric double layer is studied using density functional theory and Monte Carlo simulations for the restricted primitive model and solvent primitive model. The double layer is comprised of an infinitely long, rigid, impenetrable charged cylinder also referred to as the polyion, located at the center of a cylindrical cell containing the electrolyte, which is composed of charged hard spheres and the solvent molecules as neutral hard spheres (in the case of the solvent primitive model). The diameters of all the hard spheres are taken to be the same. The theory is based on a partially perturbative scheme, where perturbation is used to approximate the ionic interactions and the hard sphere contribution is treated within the weighted density approach. The Monte Carlo simulations are performed in the canonical ensemble. The zeta potential profiles as a function of the polyion surface charge density are presented for cylindrical double layers at different ionic concentrations, ionic valences, and different hard sphere (ionic and the solvent) diameters of 2, 3, and 4 Å. The theory agrees quite well with the simulation results for a wide range of system parametric conditions and is capable of showing the maximum and minimum in the zeta potential value for systems having divalent counterions. The steric effects due to the presence of solvent molecules play a major role in characterizing the zeta potential and the ionic density profiles. A noticeable change in the concavity of the zeta potential plots with increasing particle size at very low concentrations of monovalent electrolytes is suggestive of the occurrence of infinite differential capacitance for such systems.