Ion dynamics near charged electrodes with excluded volume effect

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