Knowing that each hump (peak) in phase angle Bode plot can qualitatively indicate a time constant, is there another mathematics approach to investigate that, for example, imagine a case that you have two time constant with similar Tau (RC), then you can see only one peak in Bode plot.
I have synthesize TiO2 directly on Ti substrate by Plasma Electrolytic Oxidation. The obtained film is normally and inherently should be consisted of two layers namely porous and compact. I always have two time constants in my Bode plot which arguably confirmed the aforementioned morphological properties as was in agreement also with cross section SEM.
Now I have modified my films with adding some Ni content to dope the TiO2 film. The sample without Ni still shows two time constants while adding very low amount of Ni i.e 0.2mM, 0.4mM and 0.6mM changes the number of time constants to one. This is far from expectation that such low concentration of of Ni change the two layers morphology to one layer morphology (either compact or porous).
Considering that, I wonder to know how can I be sure if I have only one time constant and not two overlap ones?
Dear Hamed Arab ,
another (common, mathematical) very useful approach is to investigate an impedance (Z-)fitting[1,2] with respect of an Equivalent[3,4] Circuit Model (artless, simple, EC-Model : R1C1, in series with, R2C2, or other, similar, wise models[4,5]).
1. https://www.researchgate.net/post/How_can_I_find_equivalent_circuit_model_component_values_that_fit_an_EIS_data_of_an_electrode-electrolyte_interface_using_a_software
2. https://www.researchgate.net/post/How_to_fit_EIS_data_using_zview_software
3. https://www.researchgate.net/post/The_accuracy_of_the_suggested_parameters_of_impedance_by_the_softwares_zview_zsimp
4. https://www.researchgate.net/post/How_to_evaluate_the_valid_limit_of_CPE_in_dielectric_layer
5. see Fig10.d, in: Mesoporous TiO2 and Co-doped TiO2 Nanotubes/Reduced Graphene Oxide Composites as Electrodes for Supercapacitors https://www.sciencedirect.com/science/article/pii/S0013468616300408
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