Analysis of the DRT as Evaluation Tool for EIS Data Analysis
Authors: Nohl Markus , Raut Gaurav , Wolf Stephanie Elisabeth , Duyster Tobias , Dittrich Lucy , Vinke I. C. , Eichel Rüdiger-A. , De Haart L. G. J. 
Published: July 2021

The Distribution of Relaxation Times (DRT) is an important analysis tool that is capable of giving initial information from Electrochemical Impedance Spectra (EIS) with respect to the number of relaxation processes occurring in the system and their corresponding relaxation frequencies. From this the possible number of circuit elements for the equivalent circuit model in the nonlinear least square fit of the data can be selected. There are several techniques and possibilities to perform the transformation [1–3], nevertheless every possibility has its limitation and/or will remain an ill-posed problem [4]. For our EIS data, the DRT transformation with the Tikhonov regularization is used for further analysis. Hence, we want to understand and more precisely describe the effects of this transformation together with occurring pitfalls on the most commonly implemented circuit elements used to describe EIS data for characterizing Solid Oxide Fuel or Electrolysis Cells (SOFC/SOEC) operating at high temperatures. Therefore, a database with the future possibility of pattern recognition is created for DRT transformations on selected circuit elements like a resistor in series with a finite length diffusion or Warburg-short element (R-Ws) or a resistor in parallel with a constant phase element (RQ). A parameter interval is selected for each occurring element. The origin for these data comes from a series of experiments where quite well fitting Equivalent Circuit Models (ECM) were analyzed with respect to their minimum and maximum values per element. Depending on the coverage of the interval, useful intermediate numbers are selected in order to perform parameter sweeps for every possible combination together with a downstream DRT transformation step. We obtain the behavior of the DRT transformation as a function of the individual circuit element parameters and can evaluate which occurring peaks belong to a circuit element and which ones are artefacts or numerical issues in the transformation. Additionally, the regularization parameter (λ) is taken as a sweep parameter as well to see its influence on the transformation. From both perspectives, we can state a range of optimal numbers of recorded data points per decade of frequency for experiments. We also can give a direction for selecting λ depending on what exactly is to be evaluated with the respective DRT transformation. Additionally, we are able to categorize peak-forming behavior of the transformation since the selected ECMs are known and so, in theory, its transformation result. Knowledge for the DRT behavior is also useful for modeling the electrolysis process where theoretical characteristics (i-V, EIS data) are calculated in order to validate and evaluate the model.

Figure caption: Figure 1: The DRT transformation of the model RQ-RQ is converted into the frequency domain with a variation of αP1 from 0.5 to 1.0. The fixed parameters are q1 = 10-1 S, r1 = 0.303 Ω, q2 = 10-2 S, r2 = 0.303 Ω, αP2 = 0.8, λ = 10-7.

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Figure 1