Distribution of relaxation times in the diffusion response of the blocked-diffusion Warburg impedance with frequency dispersion

The impedance response of the blocked-diffusion Warburg impedance with frequency dispersion (BDWf) is represented in the Nyquist plot by a finite diffusion response at high frequencies, followed by a constant phase element (CPE) response at low frequencies. In this study, a mathematical function to estimate the distribution of relaxation times (DRT) in the diffusion response of the BDWf impedance is derived. The analytical transfer function representing the BDWf impedance, reported in a previous study, is considered for the derivation of the DRT mathematical function. The impedance response of an electrical circuit comprising ZARC elements and the BDWf impedance is fitted to the measured impedance response of a lithium-ion battery. The resulting parameters of the BDWf impedance, estimated from the fitting process, are considered in the DRT function. This study demonstrates that it is possible to simulate the impedance responses of the BDWf impedance and the electrical circuit through DRT functions and the Fredholm integral equation. This study also demonstrates the application of the DRT function of the diffusion response of the BDWf impedance, with parameters estimated from EIS measurements carried out on a solar cell. The new DRT function of the diffusion response of the BDWf impedance could allow the estimation of the distribution of the diffusion processes of charge carriers represented in the low-frequency impedance response of electrochemical systems.