Electrochemical impedance spectroscopy (EIS) has been broadly used to characterize and quantify kinetic parameters in electrochemical systems, thanks to the possibility to observe and uncouple with a single experiment the electrochemical phenomena occurring in a broad range of time constants, from a few μs up to hours. However, EIS is strongly limited by the necessity to have a time invariant system, i.e. a system which stationary behaviour is stable in time. When this condition is missing, the interpretation of the spectra can be misleading. In order to overcome this limitation, in 1977 Bond et al. have introduced the measurement of dynamic impedance spectra (DEIS) based on multi-sine perturbation signals and short time windowed Fourier transform [1]. Recently, using the concept of quadrature filter and inverse Fourier transform, we have developed the dynamic multi-frequency analysis (DMFA) as a method for extracting high quality dynamic impedance spectra from an electrochemical system with high temporal accuracy in a broad range of frequencies [2, 3]. Despite these progresses, the concept of dynamic impedance remains obscure due to the empirical and heuristic description of DEIS given in previous works. Starting from the physical definition of impedance in non-linear systems, its relationship to the Volterra kernel will be given and it will be shown how to accurately measure and model it. Fitting routines and minimization objective functions for the qualitative and quantitative analysis of the large amount of acquired data will be proposed and discussed. Finally, as example, the results of DEIS acquired through DMFA on a Pt microelectrode during hydrogen evolution in acidic environments will be shown. In particular, the effect of HClO4 concentration (from 2 mM up to 50 mM) on the kinetic parameters will be discussed..
[1] A.M. Bond, R.J. Schwall, D.E. Smith, J. Electroanal. Chem. 85 (1977) 231–247.
[2] A. Battistel, G. Du and F. La Mantia, Electroanal. 28 (2016) 2346-2353.
[3] D. Koster, G. Du, A. Battistel and F. La Mantia, Electrochim. Acta 246 (2017) 553-563.