From theory to practice: Unlocking the distribution of capacitive times in electrochemical impedance spectroscopy

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. Additionally, we develop a novel method featuring two deep neural networks for DCT deconvolution. We systematically tested this method using a diverse set of synthetic and actual EIS spectra to ensure its efficacy and reliability. Overall, this article seeks to expand the scope of non-parametric approaches for EIS data analysis, particularly to systems characterized by blocking electrodes.