An approximate solution for a pseudocapacitor

Transient analytical solutions are presented for the overpotential and the voltage for a porous electrode that includes both double-layer charging and a faradaic reaction. In addition, a simplified dynamic model is developed for the same process based on a second order, three-parameter polynomial approximate model. The effects of the parameters such as dimensionless exchange current density, conductivity ratio and applied current density on the voltage and overpotential distribution are presented. Also, using the exact transient solution an expression for the dimensionless interfacial current density is derived and the effects of the parameters mentioned above are presented.