Distribution of Relaxation Time (DRT) Method

Distribution of Relaxation time (DRT) analysis for impedance data provides unique perspective than standard EIS analysis based on equivalent circuit modeling.

When fitting a given EIS data with equivalent circuit, a priori knowledge of electrochemical processes inside an electrochemical system is required to choose proper circuit and find optimal fitting parameters.

While equivalent circuit model fitting gives you a predetermined finite number of parameters, DRT analysis outputs a continuous response function g(τ).  In nature g(τ) is similar to the resistive part of RC circuits appearing in equivalent circuit model, but it is different in that g(τ) provides the electrochemical system’s resistive property at all timescales of interest in functional form.  Roughly, it can be said that DRT method uses equivalent circuit with infinite number of infinitesimal RC circuits.

Attached video is an illustrative demo for your reference, showing an example of cycle-dependent evolution of EIS spectra (measured at the end of CCCV charging and followed resting for each cycle) and their corresponding DRT analysis results.  DRT analysis was done with open-sourced software of pyDRTtools¹, and I could find some public cycle retention and EIS data to conduct this analysis from Y Zhang, Q Tang et. al. (2020)², where the authors publicized their data in public repository. The paper is not about DRT but shows great approach of using EIS for ML-powered battery degradation prediction so give it a look if you are interested - It is open access!

1. ciuccislab/pyDRTtools: An intuitive python GUI to compute the DRT ↩

2. Y Zhang, Q Tang et. al., Nat. Commun. (2020); 10.1038/s41467-020-15235-7 ↩