Mathematical model based on staircase structure for porous electrode impedance.

Mathematical models for porous electrode impedance have been widely used in energy conversion and storage. They are also utilized for obtaining the physicochemical dynamics, resulting in theoretical understanding and prediction in practical energy devices. The existing mathematical models are limited in their explanations. This limitation can be attributed to the separate consideration of simple (planar electrodes) and complex (porous electrodes) systems and the complexity of parameter distribution with non-uniform processes. Here, to address these limitations, we propose a mathematical model based on a staircase structure that calculates the individual interfacial impedance at each step in the depth direction, which helps not only in describing complex and straightforward systems but also in uniform and non-uniform processes in the form of a simple, seamless general equation. Our study includes mathematical derivations, interpretations of porous electrode impedance, and validation of the experimental data.