"Voigt Circuit" which is a series combination of Voigt elements (i.e. parallel RC's), is commonly used for Kramers-Kronig relations checking; and as I imagine it is generally believed to be able to be fitted to various electrochemical impedance spectra?
Is this belief true or not?
And if the answer is "Yes", is there any theoretical basis for that or it is only a practical sense (I mean that it is approved according to fitting results of experimental data to Voigt circuit)?
Yes (true) and yes (theoretical basis). That said, it doesn't have much value for most researchers beyond a quick check to verify the data is linear, stable and causal. It doesn't even guarantee that the data is valid EIS data, since common artifacts produce linear, stable and causal results (e.g. cable capacitance).
Dear Dr.Ketter
Thanks for your attention. You are true. In fact, I mean "mathematical proof" by use of expression "theoretical basis". If there is any, would you please guide me to some references in this field?
There are some strong differences of opinion on Kramers Kronig. I'll just give the one name I know who has (had) done research involving K-K: Digby MacDonald. I'm probably short changing someone (most likely several someones) but I remember a conversation with a grad student from his lab (years ago) who was doing theoretical work involving K-K transform (simulation maybe?).
I was heard about him before, and probably have studied some articles from him. Maybe need to study them again, and hope to find anything useful.
By the way, may I ask what do you mean by "There are some strong differences of opinion on Kramers Kronig" ?
I think that if you are thinking in the sense of having an EIS spectra and you want to know whether there is a "unique" Voigt circuit fitting it, then I guess this is not true. I think this is because you have a finite number of measurements which define your spectra, so the "function" you are fitting is not well defined in a mathematical sense.
But, from a conceptual point of view, if you think you measured "infinite" points in your EIS measurement, then there is a unique solution for the Voigt circuit. This is because in the end of the day you are solving a differential equation, and the unicity theorem (https://en.wikipedia.org/wiki/Picard%E2%80%93Lindel%C3%B6f_theorem) says there is one and only one solution to the problem (if the).
Nevertheless, I remember the Macdonald book (DOI:10.1002/0471716243) says there is more than one solution, but I think this is because the finite-amount-of-points nature of any experiment.
Check out this article from Schönleber et al. (2015): Approximability of impedance spectra by RC elements and implications for impedance analysis - ScienceDirect
Hopefully this addresses your question as to the theoretical validity of a serial-connected RC ECM?
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