Electrochemical impedance spectroscopy beyond linearity and stationarity - a critical review

Electrochemical impedance spectroscopy (EIS) is a widely used experimental technique for characterising materials and electrode reactions by observing their frequency-dependent impedance. Classical EIS measurements require the electrochemical process to behave as a linear time-invariant system. However, electrochemical processes do not naturally satisfy this assumption: the relation between voltage and current is inherently nonlinear and evolves over time. Examples include the corrosion of metal substrates and the cycling of Li-ion batteries. As such, classical EIS only offers models linearised at specific operating points. During the last decade, solutions were developed for estimating nonlinear and time-varying impedances, contributing to more general models. In this paper, we review the concept of impedance beyond linearity and stationarity, and detail different methods to estimate this from measured current and voltage data, with emphasis on frequency domain approaches using multisine excitation. In addition to a mathematical discussion, we measure and provide examples demonstrating impedance estimation for a Li-ion battery, beyond linearity and stationarity, both while resting and while charging

The time-varying effect of thiourea on the copper electroplating process with industrial copper concentrations

Electrorefining is the process of choice to purify several metals, among which is copper. A crucial process parameter in electrorefining, and electroplating in general, is the additive activity. Several additives are introduced to the electrolyte to ensure a morphological smooth copper deposit. Thiourea is a crucial but complex additive used in copper electrorefining, it is known to degenerate and both the reaction product as thiourea itself can complex with the copper ions. Unfortunately, time dependent additive studies and mechanistic knowledge of the effect of aged electrolyte on the cathodic part of the electrorefining process are scarce. In this work, operando Odd Random Phase Electrochemical Impedance Spectroscopy (ORP-EIS) is used to study the electrochemistry of a copper plating system containing industrial copper concentrations. The approach applied enables the investigation of the time-varying effect of additives, in this case thiourea and chlorides, assisting the electroplating of copper

Operando electrochemical impedance spectroscopy and its application to commercial Li-ion batteries

Electrochemical impedance spectroscopy (EIS) is a non-invasive technique for examining kinetics of electrochemical systems. Applied to energy storage devices, the impedance contains information about the state-of-charge and state-of-health of a battery. Classical EIS measurements, as implemented in many cyclers, are restricted by two important assumptions: linearity and stationarity. However, Li-ion batteries are inherently nonlinear, and are nonstationary while under operation. Classical EIS can thus only be performed on batteries in steady-state, and hence, no information about batteries under operation can be extracted. In this article, operando EIS is introduced as a promising tool for measuring time-varying impedance data of Li-ion batteries. The mathematics behind the impedance extraction are detailed, starting from nonstationary and mildly nonlinear current and voltage data. The technique is then applied to reproducible experiments, while charging and discharging commercial Li-ion batteries, using a commercial potentiostat. The operando impedance is shown to be different from the classical impedance, and the nonlinear behaviour of the battery is studied. Applications of operando EIS are discussed, with the focus on the modelling of the operando impedance data through equivalent circuit models, revealing the evolution of the ECM parameters over time

Frequency domain parametric estimation of fractional order impedance models for Li-ion batteries

The impedance of a Li-ion battery contains information about its state of charge (SOC), state of health (SOH) and remaining useful life (RUL). Commonly, electrochemical impedance spectroscopy (EIS) is used as a nonparametric data-driven technique for estimating this impedance from current and voltage measurements. In this article, however, we propose a consistent parametric estimation method based on a fractional order equivalent circuit model (ECM) of the battery impedance. Contrary to the nonparametric impedance estimate, which is only defined at the discrete set of excited frequencies, the parametric estimate can be evaluated in every frequency of the frequency band of interest. Moreover, we are not limited to a single sine or multisine excitation signal. Instead, any persistently exciting signal, like for example a noise excitation signal, will suffice. The parametric estimation method is first validated on simulations and then applied to measurements of commercial Samsung 48X cells. For now, only batteries in rest, i.e. at a constant SOC after relaxation, are considered

Operando odd random phase electrochemical impedance spectroscopy (ORP-EIS) for in-situ monitoring of the Zr-based conversion coating growth in the presence of (in)organic additives

Operando odd random phase electrochemical impedance spectroscopy (ORP-EIS) is introduced as an in-situ monitoring tool to directly monitor the conversion treatment of zinc in a hybrid Zr-based solution containing aminosilane and Cu additives. SEM and EDX are applied to investigate the morphology and elemental composition of the oxide film. Results show that the operando ORP-EIS provides an opportunity to investigate the growth of the conversion layer and its surface homogeneity as well as the charge transfer reaction during conversion. Moreover, the presence of aminosilane in the Zr solution containing Cu improves the morphology and barrier properties of the conversion film