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

Abstract

Impedance is a standard and elegant tool in characterizing porous electrodes in electrochemical systems. The full potential of impedance characterization can be achieved only when a physically meaningful impedance model is used. Building a theoretically consistent framework, this study aims to develop a series of impedance models for porous electrodes with different properties. The framework starts with a full problem formulated by the concentrated solution theory and then simplifies it to four limited cases under different assumptions and approximations. In-plane, through-plane, multi-dimensional inhomogeneities are incorporated. In addition, based on the analytical Fourier transform, the impedance response during dynamic processes is numerically calculated. The theory is then applied to three typical cases: blocking, with Faradaic reactions, and with intercalation particles, which find their practical counterparts in electrochemical capacitors, proton exchange membrane fuel cells, and lithium-ion batteries. 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. Figure 1