Application of the Kramers–Kronig Relations to Multi-Sine Electrochemical Impedance Measurements

Abstract

Impedance spectra obtained by fast Fourier transformation of the response to a multi-sine potential perturbation are shown to be consistent with the Kramers–Kronig relations, even for systems that are nonlinear and nonstationary. These results, observed for measurements on a Li/SOCl2 battery, were confirmed by numerical simulations. Consistency with the Kramers–Kronig relations was confirmed by use of the measurement model developed by Agrawal et al. and by a linear measurement model approach developed by Boukamp and implemented by Gamry. The present work demonstrates that application of the Kramers–Kronig relations to the results of multi-sine measurements cannot be used to determine whether the experimental system satisfies the conditions of linearity, causality and stability.

Methods for the Determination of Valid Impedance Spectra in Non‐stationary Electrochemical Systems: Concepts and Techniques of Practical Importance

“…On the other hand, in a recent work it has been demonstrated that application of the Kramers‐Kronig relations to the results of multi‐sine measurements cannot be used to determine whether the experimental system satisfies the conditions of linearity, causality and stability [62] …”

“…[61] On the other hand, in a recent work it has been demonstrated that application of the Kramers-Kronig relations to the results of multi-sine measurements cannot be used to determine whether the experimental system satisfies the conditions of linearity, causality and stability. [62] Nevertheless, correct Hilbert (or K-K) transformation of the data is a necessary but not sufficient condition to ensure that the system has satisfied the above mentioned four criteria and does not guarantee the validity of the data, but it can increase our confidence in their correctness.…”

Investigation of supercapacitor cyclic degradation through impedance spectroscopy and Randles circuit model

“…The deviation between KKT and experimental data suggests non‐linearity, instability, or influence of unknown variables to the sample 21,22 …”

Electrochemical impedance spectroscopy

“…125 The nonlinear Voigt measurement model approach described here has greater sensitivity to inconsistency with the Kramers-Kronig relations, making it easier to identify frequencies for which a given data set does not satisfy the Kramers-Kronig relations. 126…”

“…The multi-sine method has been proposed to alleviate the problem by reducing the measurement time, 166 but the result represents an averaged behaviour that is always consistent with the Kramers-Kronig relations. 126 Thus, the Kramers-Kronig relations cannot be used to detect the influence of nonstationary behaviour on multi-sine measurements.…”