Phase Field Model of Electrochemical Impedance Spectroscopy

Abstract

A general phase field model of electrochemistry is presented in the context of simulating electrochemical impedance spectroscopy (EIS) experiments. The model tracks species, phase, and charge distribution to study the link between EIS and microstructure. Governing partial differential equations are derived from a simple set of assumptions including ideal bulk solution thermodynamics, a method of interpolating between bulk phases, physical balance laws, and the second law of thermodynamics. A source term in the conservation of mass expression captures the behavior of the chemical reactions through the interface and in the bulk phases. Two embodiments of the model are presented: finite-length diffusion in a generic electrode | mixed conducting electrolyte and semi-infinite diffusion in a system similar to an SOFC cathode. In both cases, an analytic solution was fit to the model calculations using a small number of adjustable parameters.