Problem of Kramers–Kroenig Transformation of EIS Data in Case of Instabilities

Abstract

Electrodes presenting negative resistances or capacitances in their electrical model are often not consistent with Kramers–Kroenig transformations (KKT) due, in most cases, to violation of stability condition. Stability is related to the way of their electrical, either potential or control of the current, and it is determined by the form of the impedance expressed in terms of its zeros and poles. For KKT to be valid, the form of the transformed immittance has to represent stable control. For electrodes stable under potentiostatic and unstable under galvanostatic control, to get satisfying KKT it is adequate to transform data in their admittance representation and not as impedance. For unstable electrodes, to get the transformed spectrum identical as the original one, one may apply the expedient of changing the sign of the part of the electrical model responsible for instability. Two examples presenting problems with KKT compliance are presented here: (i) artificial electric circuit with negative resistance and (ii) the metal/metal ion electrode in the transpassive state. In both cases the expedient of the sign change of the low-frequency segment of the Voigt equivalent circuit was sufficient to reproduce the original electrochemical impedance spectroscopy data after KKT of its otherwise Kramers–Kroenig nontransformable impedance representation.