Theory of Impedance Response of Porous Electrodes: Simplifications, Inhomogeneities, Non-Stationarities and Applications

Electrochemical impedance spectroscopy is a convenient and powerful tool in characterizing porous electrodes in electrochemical systems. The full potential of impedance characterization can only be achieved when a physically meaningful impedance model is used. This study aims to build a theoretically-consistent framework and to develop a series of impedance models for porous electrodes with different properties. The framework starts from a full problem formulated with the concentrated solution theory and then simplifies it to four limiting cases. In-plane, through-plane, multi-dimensional inhomogeneities are considered. In addition, based on the analytical Fourier transform, the impedance response during dynamic process is numerically calculated. The models developed in this study are then applied to three typical cases: blocking electrode, electrode with faradaic reactions, and electrode constituted of particles with insertion reactions, corresponding to their practical counterparts in electrochemical capacitors, polymer electrolyte fuel cells, and lithium-ion batteries, respectively. In each case, the structure, asymptotic behaviors, and characteristic frequencies of and inhomogeneous effects on the impedance spectrum are analyzed. Special attention is paid to the assumptions and applicability of each model. Experimental strategies to justify the use of an electric circuit model are discussed. The use of Warburg impedance to fit the diffusion coefficient in the solid active particles is scrutinized.