Electrical Circuit Modeling Considering a Transient Space Charge for Nonsteady Poisson–Nernst–Planck Equations

Abstract

Transient space charge phenomena at high step voltages are interesting since they play a central role in many exotic nonequilibrium phenomena of ion dynamics in an electrolyte. However, the fundamental equations [i.e., the nonsteady Poisson–Nernst–Planck (PNP) equations] have not been solved analytically at high applied voltages because of their large nonlinearity. In this study, on the basis of the steady PNP solution, we propose an electrical circuit model that considers transient space charge effects and find that the dc and ac responses of the total charge of the electrical double layer are in fairly good agreement with the numerical results even at large applied voltages. Furthermore, on the basis of this model, we find approximate analytical solutions for the nonsteady PNP equations that are in good agreement with the numerical solutions of the concentration, charge density, and potential distribution at high applied voltages at each time in a surface region.