Detection of nonlinearities in electrochemical impedance spectra by Kramers–Kronig Transforms

Nonlinear electrochemical impedance spectra (EIS) of electrochemical reactions with adsorbed intermediates were generated by numerical simulations and the conditions under which direct integration of Kramers–Kronig Transforms (KKT) flag the violations of linearity criterion were investigated. In addition, the spectra were validated using measurement model analysis and linear KKT method. A reaction with an adsorbed intermediate species, an electrochemical–chemical reaction with two adsorbed intermediate species and a third reaction with two adsorbed intermediate species and exhibiting negative resistance were chosen as candidate mechanisms. Large amplitude perturbations were used and the governing equations were solved without linearization. The results show that when the relationship between the logarithm of the faradaic current and dc potential is nonlinear, all the three methods are sensitive and successfully flag the nonlinear effect in the spectra. On the other hand, if the logarithm of the faradaic current is linearly related to the dc potential, the nonlinear effects are not identified by the direct integration of KKT. However, even in these cases, measurement model analysis and linear KKT validation method are sensitive to the violation of linearity criterion.