Ion dynamics near charged electrodes with excluded volume effect

The goal of this paper is to analyze ion relaxation around a charged electrode taking into account finite ion volume and frequency. Time-dependent and electrostatic equations for ion behaviour near an electrode are developed and include the effects of nonequilibrium and steric hindrance. Time-dependent wave equations for the potentials are developed in the Lorentz gauge. The charge density is expressed as a sum of the quasi-steady state solution plus a nonequilibrium term. For slowly changing potentials the ions are in quasi-equilibrium and we show that in this limit the potential satisfies the sinh-Gordon equation. New solutions to this nonlinear time-dependent equation are developed. In the low voltage limit the equation reduces to the Klein-Gordon equation, time-dependent analog of the Debye-Huckel equation. We also present equations for capacitance and surface charge