Two parallel diffusion paths model for interpretation of PITT and EIS responses from non-uniform intercalation electrodes

Two alternative models, including (i) a serial combination of finite-space Warburg (FSW) and finite-length Warburg (FLW) elements, and (ii) two parallel FSW elements with different diffusion time constants, were proposed to describe the most important specific features of potentiostatic intermittent titration (PITT) and electrochemical impedance spectroscopy (EIS) responses of practical intercalation anodes and cathodes. Based on the physical reliability of the fitting parameters, the parallel diffusion path model was seen to describe adequately the EIS and PITT responses obtained from thin, non-uniform composite electrodes (graphite is considered as an example). Some important issues related to impedance modeling (exemplified by comparison of the properties of serial and parallel combinations of distributed diffusion elements) are discussed. We show that dlog|I_d(t)|/dlog t vs. t/τ_d plots are very useful for diagnosing the type of non-uniformity (particle size distribution, PSD) of intercalation electrodes.