Theoretical and Experimental Study of the Distribution of Capacitive Times

The distribution of relaxation times (DRT) method is a non-parametric approach for analyzing electrochemical impedance spectroscopy (EIS) data. However, we must be careful when using the DRT method on electrochemical systems with blocking electrodes, such as those encountered in batteries and supercapacitors. This is because at low frequencies the asymptotic behavior of the DRT model cannot capture unbounded impedances. To address this issue, we explore the distribution of capacitive times (DCT), a method that, despite being developed decades ago, is still not widely used. In this work, we detail the theoretical underpinnings of the DCT, deriving DCT-specific analytical formulae based on several standard impedance models. We also draw parallels between DCT and DRT and show how these two methods differ in capturing timescales and peaks, elucidating the scenarios where DCT can serve as a viable alternative should the DRT not be applicable. This article seeks to expand the scope of nonparametric approaches for EIS data analysis, particularly to systems characterized by blocking electrodes.