Is it an acceptable method to use a bounded Warburg element to fit EI spectra associated with metal corrosion and O2 diffusion across a porous layer? I suppose that Orazem & Tribollet have proposed more elaborated and correct solutions to this case. Anyway, can the Warburg element be used as an approximation independent of more exact solutions? Under which considerations?
Dear Luis
You can use Warburg element as an approximation to fit the second semi circle and its extention in Nyquist plot by determining the average and the standard of deviation of a set of at least two EIS tests. This way you would know how far your approximation from the exact solution.
Dear Dr. Luis Frederico P. Dick ,
I suggest you to have a look at the following, interesting documents:
- How to Model Warburg Impedance in Circuit Simulators by Cadence PCB Solutions
Available at: https://resources.pcb.cadence.com/blog/2020-how-to-model-warburg-impedance-in-circuit-simulators
and
- Diffusion impedance of electroactive materials, electrolytic solutions and porous electrodes: Warburg impedance and beyond
Jun Huang
Electrochimica Acta, Vol. 281,, Pages 170-188 (2018)
Available as abstract at: https://www.sciencedirect.com/science/article/abs/pii/S0013468618311824?via%3Dihub
and on Rg (Reaquested possibility) at: https://www.researchgate.net/publication/325351710_Diffusion_impedance_of_electroactive_materials_electrolytic_solutions_and_porous_electrodes_Warburg_impedance_and_beyond
My best regards, Pierluigi Traverso.
My assumption was already confirmed. Warburg does not consider migration.
Dear Luis,
Basically this is a constant phase element used in diffusion impedance. This comprises diffusion length, diffusion coefficient and diffusion constant time. This can be understood in term of EIS , the lower frequency limit (ref. bode plot can be moved down to 1 mHz(constant is always good) to better illustrate the differences in the slope of the magnitude and in the phase between the capacitor and the Warburg impedance. In this regard, multiple two equivalent circuit with two time constant models can good fit to data.
Ashish
Dear Luis Frederico P. Dick
I would like to contribute by the following explanations:
The intact and high integrity conductive or non-conductive coating layer (highly protective barrier) will result in hiding the contribution of this layer to the impedance and can slow down the under coats substrate corrosion process so that the bulk diffusion contributions are not detectable at the common measuring frequencies even after a very long immersion time.
In case of the coating is porous layer, non conductive and permeable for the corrosive electrolyte through the inter-connected porosity, the substrate corrosion reactions are going on at the bottom of the percolating pores and so the equivalent electrical circuit proposes the introduction of different time constants. One of these is correlated to oxygen diffusion process which is the rate determining step in corrosion progress for oxygen reduction cathodic reaction and so diffusion contributions are detectable at the common measuring frequencies ( Warburg elements assumptions is acceptable).
Now, if the coating is porous layer, conductive and permeable for the corrosive solution through the inter-connected porosity, the impedance at the pore walls/ electrolyte interface, taken here as a simple charge transfer resistance and double layer capacitance and the impedance at the bottom of the percolating pores, taken also as a parallel charge transfer resistance and double layer capacitance. This means that the cathodic reaction area is higher than of the anodic reaction and so the oxygen diffusion process and rate of oxygen reduction cathodic reaction is not the rate determining step in corrosion progress and their contributions are not detectable at the common measuring frequencies time.
Best regards
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