Analysis and spline approximation of surface charge and potential at planar electrochemical interfaces

Abstract

In this paper, we consider the Poisson-Boltzmann theory to model the electrostatic potential of a bulk electrolyte containing a single planar charged surface.In the case of a constant surface charge density, we address the problem as a ODE system by using the stability theory for autonomous dynamical systems. By stating that the surface charge density and the surface potential are non-linearly related through the Grahame equation, we give a description of the stable manifold of the system. To solve the Grahame equation and obtain an approximation for the stable manifold, we propose a smoothing collocation method based on cubic splines, including implementation details and numerical results.