Reconstruction of relaxation time distribution from linear electrochemical impedance spectroscopy

Abstract

Linear electrochemical impedance spectroscopy (EIS), and in particular its representation of distribution of relaxation time (DRT), enables the identification of the number of processes and their nature involved in electrochemical cells. With the advantage of high frequency resolution, DRT has recently drawn increasing attention for applications in solid oxide fuel cells (SOFCs). However, the method of DRT reconstruction is not yet presented clearly in terms of what mathematical treatments and theoretical assumptions have been made. Here we present unambiguously a method to reconstruct DRT function of impedance based on Tikhonov regularization. By using the synthetic impedances and analytic DRT functions of RQ element, generalized finite length Warburg element, and Gerischer element with physical quantities representative to those of SOFC processes, we show that the quality of DRT reconstruction is sensitive to the sampling points per decade (ppd) of frequency from the impedance measurement. The robustness of the DRT reconstruction to resist noise imbedded in impedance data and numerical calculations can be accomplished by optimizing the weighting factor λ according to well defined criterion.