Structure of spherical electric double layers: a density functional approach

A density functional theory is presented for the structure of spherical electric double layers within the restricted primitive model, where the macroion is considered as a hard sphere having uniform surface charge density, the small ions as charged hard spheres, and the solvent is taken as a dielectric continuum. The theory is partially perturbative as the hard-sphere contribution to the one-particle correlation function is evaluated using suitably averaged weighted density and the ionic part is obtained through a second-order functional Taylor expansion around the uniform fluid. The theory is in quantitative agreement with Monte Carlo simulation for the density profiles and the zeta potentials over a wide range of macroion sizes and electrolyte concentrations. The theory is able to provide interesting insights about the layering and the charge inversion phenomena occurring at the interface.