Abstract
The distribution of relaxation times (DRT) analysis offers a model-free approach for a detailed investigation of electrochemical impedance spectra. Typically, the calculation of the distribution function is an ill-posed problem requiring regularization methods which are strongly parameter-dependent. Before statements on measurement data can be made, a process parameter study is crucial for analyzing the impact of the individual parameters on the distribution function. The optimal regularization parameter is determined together with the number of discrete time constants. Furthermore, the regularization term is investigated with respect to its mathematical background. It is revealed that the algorithm and its handling of constraints and the optimization function significantly determine the result of the DRT calculation. With optimized parameters, detailed information on the investigated system can be obtained. As an example of a complex impedance spectrum, a commercial Nickel–Manganese–Cobalt–Oxide (NMC) lithium-ion pouch cell is investigated. The DRT allows the investigation of the SOC dependency of the charge transfer reactions, solid electrolyte interphase (SEI) and the solid state diffusion of both anode and cathode. For the quantification of the single polarization contributions, a peak analysis algorithm based on Gaussian distribution curves is presented and applied.
Highlights
Electrochemical impedance spectroscopy (EIS) is a well-known method applied since the 1970s [1]
If the measured impedance spectrum is not converging towards the real axis at the boundaries of the measured frequency range as demanded by Equations (5) and (6), as is it the case e.g., for diffusion processes at low frequencies, the distribution of relaxation times (DRT) analysis will yield artefacts, i.e., singularities or diverging, steep slopes at the boundaries of the interval of time constants corresponding to the extremes of the measured frequencies
Since real systems will never have a limited bandwidth and a measurement system will never be able to measure an unlimited frequency range, we show in the results that broadening the predefined vector of time constants is beneficial for the analysis of electrochemical systems, especially if polarization processes are not abated at the boundaries of the measured frequencies as it the case for the solid state diffusive behavior of lithium-ion batteries
Summary
Electrochemical impedance spectroscopy (EIS) is a well-known method applied since the 1970s [1]. The study includes the optimization of the regularization parameter, the number of predefined discrete time constants as sampling points of the distribution function and the mathematical formulation of the regularization term It is investigated whether real parts, imaginary parts of the complex impedance or both should be used for the calculation of the DRT. As an instructive example of a complex impedance spectrum comprising inductive, resistive, capacitive and diffusive overlapping polarization contributions of multiple components within an electrochemical system, the algorithm is applied on impedance data from a commercial 3.3 Ah. Nickel–Manganese–Cobalt–Oxide (NMC) lithium-ion pouch cell by Kokam and the results are discussed in detail. The optimization algorithm, the error function, the type of data used, i.e., using real or imaginary parts of the complex impedance, measurement parameters, e.g., current or frequency range, regularization parameter, number of time constants, the pre- and post-processing routine, the minimum and maximum time constants for the DRT
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
