A nonlocal free-energy density-functional approximation for the electrical double layer

Abstract

We construct a free-energy density-functional approximation for the primitive model of the electrical double layer. The hard-sphere term of the free-energy functional is based on a nonlocal generic model functional proposed by Percus. This latter model functional, which is a generalization of the exact solution for the nonuniform hard-rod model, requires as input the free energy of a homogeneous hard-sphere mixture. We choose the extension of the Carnahan–Starling equation of state to mixtures. The electrostatic part of the nonuniform fluid ion–ion correlations present in the interface is approximated by that of a homogeneous bulk electrolyte. Using the mean spherical approximation for a neutral electrolyte, we apply the theory to symmetrical 1:1 and 2:2 salts in the restricted primitive model. We present comparisons of density profiles and diffuse layer potentials with Gouy–Chapman theory and Monte Carlo data. We also compare our results with data from other recent theories of the double layer. For highly charged surfaces, the profiles show the layering of counterions and charge inversion effects, in agreement with Monte Carlo data.