Interactions between primitive electrical double layers

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Abstract
A free energy density functional theory is applied to predict the electrostatic force between charged surfaces immersed in the restricted primitive electrolyte, in which ions are represented by charged hard spheres and solvent by a uniform dielectric continuum. The particle correlation due to hard‐core exclusions is incorporated in the nonlocal density functional of inhomogeneous hard sphere fluid. The ion–ion electrostatic correlation is treated in the mean spherical approximation. The surface force is found to depend strongly on the electrolyte concentration, surface charge density, and valency of the counterions. Attractive forces are often observed, especially in electrolytes containing divalent counterions. The maximum of the attraction can be an order of magnitude stronger than the van der Waals force evaluated at the same surface separation. The prediction of the classical Poisson–Boltzmann theory that the surface force is always repulsive is qualitatively correct only for monovalent electrolytes at low concentrations and surface charges. The results for an asymmetrical electrolyte resemble those of a symmetrical electrolyte with counterions of the same valency. The theoretical predictions agree well with available computer simulation results.