Evaluation of electrochemical impedance spectra by the distribution of relaxation times

Abstract

Electrochemical impedance spectroscopy is a well suited method for studying the properties of electrochemical systems. In recent decades electrochemical systems were investigated at different scales, from small model electrodes to high power devices, such as fuel cells and batteries. In the latter case, the measurement of reliable spectra and their evaluation is challenging because (i) the impedance is usually very low (1 ³), (ii) there is more than one rate limiting, electrochemical process per electrode, (iii) their charge transfer and transport processes are coupled and (iv) cathodic and anodic contributions overlap in the frequency domain. The Distribution of Relaxation Times (DRT) is supportive when deconvoluting complex impedance spectra, and has therefore gained increased attention. In this paper we introduce selected results of advanced impedance analysis. We discuss the impact of impedance data quality, statistically distributed noise and single errors in the spectra. Furthermore, the applicability of DRT for establishing adequate equivalent circuit models for ceramic electrochemical devices, such as batteries and fuel cells will be discussed.

A model-based approach for current voltage analyses to quantify degradation and fuel distribution in solid oxide fuel cell stacks

“…This indicates that the ASR RU does not vary (e. g. as a model assumption) as a function of the available fuel amount and gas concentration, respectively. In principle, ASR RU varies with temperature since it depends on electrode polarization resistance, electrolyte and oxide scales conductivities, which have a temperature dependency themselves [20,21,30,31]. However, for the Hexis stack design including metallic interconnects with high thermal conductivities in the range of 24e94 W m À1 K À1 [32,33] the heat transfer between the stack and the post combustion zones [12] is very efficient.…”

“…Furthermore, the overall temperature level and the temperature distribution over the stack both can vary and therefore cause additional scatter in observed stack performances. This is because temperature influences the cell potential, but also ohmic and polarization losses [20,21]. Note however that recent advances in the thermal management of SOFC stacks led to well controllable and rather homogeneous stack temperatures [16,22].…”

A Comparative Study on the Influence of DC/DC-Converter Induced High Frequency Current Ripple on Lithium-Ion Batteries

“…As mentioned in [34], this task requires the calculation of an ill posed problem because the improper 'Fredholm integral' in Equation 3or the corresponding sum in Equation 4has to be calculated. According to [31,32,34] a promising approach is the 'Tikhonov-regularisation' that converts Equation 3to the optimisation problem…”

“…It consists of the matrix A ∈ R m×n , representing the unweighted RC-elements with the arbitrarily chosen time constants τ k , whose quantity and bandwidth should surpass those of the angular frequencies ω i of the measurement [32], the vector b ∈ R m , representing the measured impedance Z(ω i ) and the optimisation factor λ that has to be chosen carefully, [31,34]. The distribution function g(τ) is stored in x after a successful numerical optimisation with a feasible solving method such as the non-negative least squares (NNLS) algorithm [31].…”

Impedance Spectroscopic Investigation of the Impact of Erroneous Cell Assembly on the Aging of Lithium‐Ion Batteries

“…A substantial advantage of EIS in lithium‐ion battery studies is its ability to differentiate the different loss processes that contribute to the overall cell kinetics . An ideal tool for the qualitative interpretation of impedance spectra of complex electrochemical systems—as lithium‐ion batteries—is the distribution of relaxation times (DRT) method . It enables a well‐founded determination of the number of time constants and thus of the number of loss processes from the spectrum .…”