Critical review on dynamic electrochemical impedance spectroscopy

Dynamic electrochemical impedance spectroscopy extends classical impedance to time-varying electrochemical systems, enabling kinetic characterization during operation. This critical review examines the three primary experimental approaches to dynamic impedance: the short-time Fourier transform, dynamic multi-frequency analysis, and best linear time-varying approximation. We present their assumptions, practical implementations, and theoretical justification. A key limitation, common to all the methods, is the requirement that the system changes slowly and remains almost constant on the time scales probed by the impedance measurement: this limitation leads to a minimum frequency threshold. We show that, in most of experimental works, the impedance is analyzed for frequencies well above this minimum frequency threshold. We discuss a mathematical definition of ideal impedance in terms of dynamic system theory, independent of the minimum frequency threshold, which is implicitly assumed in literature to represent the target of experimental impedance measurement. Two challenges for the progress of the field are identified: (i) developing a standardized validation protocol for non-stationary spectra and checking the relevance of the test based on Kramers-Kronig relations, and (ii) evaluating the ability of experimental measurements to approximate the ideal impedance when the minimum frequency threshold is approached.