The generalized van der Waals theory applied to the electrical double layer

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Abstract
The generalized van der Waals theory expression for ion density distribution is used with Poisson’s equation to solve the electrical double-layer problem for 1:1, 2:1, and 2:2 restricted primitive model electrolytes in contact with a diffusively charged, hard, planar surface. Electrical potential and ion density profiles are compared to Monte Carlo results and are shown to be more accurate at lower electrolyte concentration and surface charge density than at higher. In addition, values for the diffuse layer potential drop are shown to be less exact than those predicted by the hypernetted chain equation, modified Gouy–Chapman theory and modified Poisson–Boltzmann equation, but could be brought closer to Monte Carlo results by an appropriate choice of excluded volume parameter. Surface tension, ion adsorption, and differential capacitance are also reported.