Numerical Algorithm to Solve the Poisson-Boltzmann Equation in Rectangular Coordinates for High Surface Potentials

Abstract

The Poisson-Boltzmann equation is set for multiple general electrolytes in rectangular coordinates, and a numerical method is developed to solve it for a wide range of constant surface potentials. An expression to calculate the free energy of repulsion for mixtures of symmetrical and asymmetrical electrolytes is then derived following the method of Bell and Peterson (1972). The electric double-layer potential distribution calculated with the numerical method compares very accurately to approximations from the literature. Unlike most of the approximate solutions and methods proposed previously, the numerical solution developed in this work can handle many types of symmetrical and asymmetrical electrolytes as well as mixtures of them. The results presented explore some features of the behavior of constant potential plates immersed in mixtures of electrolytes in solution.