Use of a distribution function of relaxation times (DFRT) in impedance analysis of SOFC electrodes

Electrochemical Impedance Spectroscopy (EIS) is a frequently used method to characterize electrodes for Solid Oxide Fuel Cells (SOFC) or Electrolyzer Cells (SOEC). The porous microstructures, use of composite structures and sometimes extra functional layers in an electrode, result often in impedance spectra that are difficult to analyze. Transformation of the impedance into a distribution function of relaxation times (DFRT) is about to become a new standard in EIS analysis. This inversion to the tau-domain requires solving a Fredholm integral of the second kind, which is known as an 'ill-posed inverse problem'. Hence the resulting DFRT's should not be trusted directly. In cases were impedance data can be modelled satisfactory with an Equivalent Circuit (EqC), built of known dispersion relations (e.g. (RQ), Gerischer, Finite Length Warburg) an analytic distribution function, G(tau), can be constructed. This can be compared with the inversion results obtained from Fourier Transform (FT), Tikhonov Regularization (TR) and multi-(RQ) CNLS fits (m(RQ)fit), thus allowing evaluation and validation of these methods This is illustrated in this contribution with four examples of SOFC cathodes with quite different properties. The results apply equally well to SOFC anodes (or SOEC cathodes).