Analytical Solution for the Impedance of a Porous Electrode

A macrohomogeneous model is presented for a porous electrode that includes coupled potential and concentration gradients with linear kinetics. The equations are solved to obtain an analytical expression for the impedance of a porous electrode. Complex plane plots are presented that illustrate two well-defined arcs: a kinetic arc and a diffusion arc with their time constants far apart. The effects of parameters such as exchange current density, porosity, diffusion coefficient, thickness, and interfacial area on the impedance spectra are presented. The usefulness of the analytical solution in investigating the effect of solution phase diffusion is also presented.