APPLICATIONS OF KRAMERS-KRONIG TRANSFORMS IN THE ANALYSIS OF ELECTROCHEMICAL IMPEDANCE DATA .3. STABILITY AND LINEARITY

The application of the Kramers-Kronig (K-K) transforms in the analysis of electrochemical impedance data is examined with reference to the conditions of stability and linearity. We show that for iron in 1 M H2SO4, with the impedance being measured using a frequency response analyzer, the K-K transforms are insensitive to violation of linearity but they are very sensitive to interfacial instability. Thus, we conclude that if a system is linear, stable, and causal and if the impedance is finite over the frequency domain, the impedance data will transform according to the K-K relationships. However, if experimental impedance data are found to transform the four conditions noted above are not necessarily satisfied, but if the impedance data do not transform, we can stipulate that all four conditions do not hold simultaneously. It can be shown that this is a direct consequence of the complex function (impedance, Z) being analytical and hence obeying Cauchy's integral. However, the converse of Cauchy's theorem is not true; that is, if Z obeys Cauchy's theorem is not necessarily analytical. We also discuss the "tails" and "singularity" problems that arise when numerically evaluating the K-K transforms. If these problems are not properly recognized, they may lead to the erroneous conclusion that the K-K transforms cannot be used to validate impedance data when the imaginary component does not tend to zero as the frequency tends to zero or infinity. © 1990.