Electrical properties of a charged surface in a general electrolyte solution

Abstract

The electrical properties of a planar charged surface in a general electrolyte solution are examined. Analytical expressions for the electrical potential, surface excess of co-ions, double-layer free energy, and entropy are derived. A perturbation method is proposed for the resolution of the Poisson–Boltzmann equation governing the electrical potential distribution. The analysis extends the classic Gouy–Chapman's result to an arbitrary a:b electrolyte solution. The present approach yields a system of linear ordinary differential equations, which can be solved to an arbitrary order, in principle. The performance of the present perturbation solution is satisfactory for conditions normally encountered in practice. For example, if the second-order solution is adopted, deviations in the electrical potential and thermodynamic properties examined are less than 5%.