Non-local free-energy density-functional theory applied to the electrical double layer

Abstract

A theoretical study of the restricted primitive model of the electrical double layer using a free-energy density-functional theory is presented. The ion-ion hard-core repulsive contribution to the free energy is incorporated through a non-local excess hard-sphere free-energy density functional. The electrostatic part of the ion-ion direct correlation function of the inhomogeneous electrolyte in the interfacial region is approximated by that of the homogeneous bulk electrolyte. The generalized van der Waals model and the Tarazona model are used to construct the respective excess hard-sphere free-energy density functionals and compared with each other. Each model requires as input a hard-sphere equation of state. The Carnahan-Starling equation of state is chosen. The theory correctly predicts the layering effect of the counterions and the charge-inversion phenomenon. The results for 1:1 and 2:2 electrolytes agree well with Monte Carlo simulations. The Tarazona model gives results in closer agreement with Monte Carlo data than does the generalized van der Waals model. The diffuse-layer potentials predicted by the Tarazona model are not as accurate as those predicted by the generalized hard-rod model, which has been applied to the same problem in a previous study.