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In the automotive industry, ageing mechanisms and diagnosis of Li-ion batteries depending on charge rate are of tremendous importance. With this in mind, we have investigated the lifetime degradation of lithium-ion battery cells at three distinct charging rates using Electrochemical Impedance Spectroscopy (EIS). Impedance spectra of high-energy Panasonic NCR18650B batteries have been analysed in light of two distinct approaches, namely the time-dependent evaluation of the Constant Phase Element (CPE), and the single parameter investigation of resonance frequency of the circuit. SOH percentages were used to validate our approach. By monitoring the CPE-Q parameter at different charge rates of 0.5 C, 1 C, and 1.5 C, respectively, we applied a degradation speed analysis, allowing us to predict a quantitative value of the LIBs. The results are in complete agreement with the resonance frequency single parameter analysis, in which quite a similar trend was obtained after the spline fitting. [ABSTRACT FROM AUTHOR]

As electrochemical research undergoes rapid technological progression, the acquisition of substantial amounts of electrochemical impedance spectra (EIS) becomes increasingly feasible. Yet, this advancement introduces intricate challenges in data processing, automation, and interpretation. This paper delves into the sufficiency of unsupervised machine learning (ML) and in particular dimensionality reduction methods in decoding EIS complexities, examining its strengths, limitations, and potential pathways for optimization. As we navigated the intricacies of non‐linear dimensionality reduction, spotlighting t‐distributed stochastic neighbor embedding (t‐SNE) and uniform manifold approximation and projection (UMAP) algorithms, a pattern emerged: these techniques excel at categorizing divergent impedance spectra but show limitations when faced with analogous circuit configurations, especially those substituting a capacitor with a constant phase element. This observation not only underscores a limitation but also accentuates that unsupervised ML approaches, alone, may not fully unravel the nuances of EIS spectra. In the concluding section of our manuscript, we discuss the implications of this finding from a practical standpoint, particularly for electrochemists seeking to apply these methods in their work. [ABSTRACT FROM AUTHOR]

Ageing of rechargeable batteries is routinely characterized in the frequency domain by electrochemical impedance spectroscopy, but the technique requires laboratory measurements to be made on a time scale of days. However, the normal cycling of a battery as it is used in situ provides equivalent information in the time domain, though extracting robust frequency information from a time series is challenging. In this work, we explore, in the time domain, the relationship between instantaneous voltage-current phase difference and cycle efficiency. Moreover, we demonstrate that phase measures can be used to identify battery ageing. We have cycled a 250 mA h Nickel-Cobalt cell several hundred times and used Hilbert Transforms to identify phase difference between voltage and current. This phase difference becomes closer to zero as the battery ages, commensurate with a drop in energy cycle efficiency. In another experiment, we applied a synthetic current profile mimicking behaviour of an electric car cell, to a 3.2 A h LiNiMnCoO2 cell, for ~100 days. For this more complicated profile with a wide range of frequency content, we used wavelet analysis to identify changes in phase difference and impedance as the battery aged. For this cell, drop in cycle efficiency was associated with a rise in internal resistance. The results imply that time-series analysis of in situ measurements of voltage and current, when applied with equivalent circuit models and underlying theory, can identify markers of battery ageing.

Abstract As electrochemical research undergoes rapid technological progression, the acquisition of substantial amounts of electrochemical impedance spectra (EIS) becomes increasingly feasible. Yet, this advancement introduces intricate challenges in data processing, automation, and interpretation. This paper delves into the sufficiency of unsupervised machine learning (ML) and in particular dimensionality reduction methods in decoding EIS complexities, examining its strengths, limitations, and potential pathways for optimization. As we navigated the intricacies of non‐linear dimensionality reduction, spotlighting t‐distributed stochastic neighbor embedding (t‐SNE) and uniform manifold approximation and projection (UMAP) algorithms, a pattern emerged: these techniques excel at categorizing divergent impedance spectra but show limitations when faced with analogous circuit configurations, especially those substituting a capacitor with a constant phase element. This observation not only underscores a limitation but also accentuates that unsupervised ML approaches, alone, may not fully unravel the nuances of EIS spectra. In the concluding section of our manuscript, we discuss the implications of this finding from a practical standpoint, particularly for electrochemists seeking to apply these methods in their work.

In the automotive industry, ageing mechanisms and diagnosis of Li-ion batteries depending on charge rate are of tremendous importance. With this in mind, we have investigated the lifetime degradation of lithium-ion battery cells at three distinct charging rates using Electrochemical Impedance Spectroscopy (EIS). Impedance spectra of high-energy Panasonic NCR18650B batteries have been analysed in light of two distinct approaches, namely the time-dependent evaluation of the Constant Phase Element (CPE), and the single parameter investigation of resonance frequency of the circuit. SOH percentages were used to validate our approach. By monitoring the CPE-Q parameter at different charge rates of 0.5 C, 1 C, and 1.5 C, respectively, we applied a degradation speed analysis, allowing us to predict a quantitative value of the LIBs. The results are in complete agreement with the resonance frequency single parameter analysis, in which quite a similar trend was obtained after the spline fitting.

Electrical energy storage devices exhibit dispersive properties that control their charge and discharge processes. To get a deeper understanding of these anomalous phenomena, it is essential to go beyond static viewpoints of circuit theory in order to accurately characterize the complex interplay of internal mechanisms. Specifically, the (dis)charging time of resistive-capacitive networks is commonly estimated as four times the product of the Thévenin resistance and the capacitance itself by assuming ideal exponential relaxations in spite of the intrinsic fractional dynamics of the real energy storage materials, leading to inaccurate and erroneous characterization protocols. The purpose of this work is to provide recommended practices to find the steady-state operation of such type of devices from time-domain data with a decelerated behavior of the Mittag-Leffler function at long time scales, introducing the concept of "incremental capacitance" in the transition from ideal to fractional-order capacitor and thus, an estimation of the charge/discharge time delay. Our theoretical analysis is validated by providing a representative example of experimental application, based on an electrochemical power source, such as supercapacitors under switching-type operation. We hope to bring such study to the attention of multidisciplinary readers, both from academia and industry, focused on energy storage device research. • Steady-state analysis of the fractional-order capacitor. • Concept of "incremental capacitance" in the transition from C to CPE. • Charge/discharge time depends strongly on the dispersive exponent. • Experimental study of supercapacitors using the theory proposed. [ABSTRACT FROM AUTHOR]

A resistance R s in series with a constant phase element (CPE) of frequency-dependent impedance given by the power law function Z c (s) = 1 / (C α s α) is commonly used for the analysis of steady-state frequency response data exhibiting non-purely capacitive behavior. This is the case in most (bio)(electro)chemical systems including dielectrics, batteries, supercapacitors, capacitive deionization units, biological tissues and bioelectrodes. Passing to the time domain, the current, voltage and charge of the system are governed by differential equations with non-integer, fractional-order operators. The purpose of this study is to provide the exact analytical expressions for the electrical response of an R s -CPE model under linear sweep voltammetry with the use of the Laplace transform method. The electrical variables are expressed in terms of special functions regularly encountered with fractional calculus such as the Fox's H -function and the Mittag-Leffler function, and can be used for modeling non-ideal devices as well as extracting their characteristic parameters. • Exact expressions for the electrical response of non-ideal capacitors to linear voltage excitation. • Charge-voltage relationship is nonlinear in non-ideal capacitors. • Capacitance is non-constant, and follows a power law of time. [ABSTRACT FROM AUTHOR]

Objective. Producing realistic numerical models of neurostimulation electrodes in contact with the electrolyte and tissue, for use in time-domain finite element method simulations while maintaining a reasonable computational burden remains a challenge. We aim to provide a straightforward experimental-theoretical hybrid approach for common electrode materials (Ti, TiN, ITO, Au, Pt, IrOx) that are relevant to the research field of bioelectronics, along with all the information necessary to replicate our approach in arbitrary geometry for real-life experimental applications. Approach. We used electrochemical impedance spectroscopy (EIS) to extract the electrode parameters in the AC regime under different DC biases. The pulsed electrode response was obtained by fast amperometry (FA) to optimize and verify the previously obtained electrode parameters in a COMSOL Multiphysics model. For optimization of the electrode parameters a constant phase element (CPE) needed to be implemented in time-domain. Main results. We find that the parameters obtained by EIS can be used to accurately simulate pulsed response only close to the electrode open circuit potential, while at other potentials we give corrections to the obtained parameters, based on FA measurements. We also find that for many electrodes (Au, TiN, Pt, and IrOx), it is important to implement a distributed CPE rather than an ideal capacitor for estimating the electrode double-layer capacitance. We outline and provide examples for the novel time-domain implementation of the CPE for finite element method simulations in COMSOL Multiphysics. Significance. An overview of electrode parameters for some common electrode materials can be a valuable and useful tool in numerical bioelectronics models. A provided FEM implementation model can be readily adapted to arbitrary electrode geometries and used for various applications. Finally, the presented methodology for parametrization of electrode materials can be used for any materials of interest which were not covered by this work., (Creative Commons Attribution license.)