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

We construct a free energy density functional approximation for the primitive model of the electrical double layer. The hard shape 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 non-uniform 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 of mixtures. The electrostatic part of the non-uniform fluid ion-ion correlations present in the interface, is approximated by that of an 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. When available, 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.