Maybe you misunderstood the literatures. We could got the ESR, Rct and Warburg resistance from EIS tests, but the specific capacitances are calculated from the GCD or CV curves.

Dear Simeon, the double-layer capacitance of an interface electrode/solution, is generally obtained from high to intermidate frequencies range and from the imaginary component of the impedance measurement.

At low frequency limits you could see or obtain pseudo-capacitance values related to a particular effects in your system. But, for shure this is not the double- layer capacitance value.

Which material are you studying? Is it a solid/liquid interface or solid/solid interface ?

I am studying the impedance characteristics of soil-type microbial fuel cells. I usually obtain Nyquist plots with one or two semi-circles and an inclined line that looks like a Warburg behaviour. But when I look at the Bode plots the phase angles are somewhat small. Between - 3 and -10 degrees. Can I still use a Warburg element in my model or a constant phase element? Please kindly see the attached document

Dear Simeon,

• it is critical to recheck, please, whether the 'small'[1] phase angles (in: impedance spectra-1.jpg) are shown either in degrees, or in radians.

1. Simeon_Quote: '...But when I look at the Bode plots the phase angles are somewhat small. Between - 3 and -10 degrees...'

I totally agree with Erica's comment.

@ Prof. Ioannis . The angles are in degrees. If I cut a piece of an electrode out of my MFC and perform the EIS with a three-electrode system, I get higher angles as shown in the second figure of the attached file. The impedance spectra I originally shared were obtained in a soil MFC with a two-electrode system.

Dear Simeon Meshach Imologie ,

yes[1], it is, nearly, the capacitance of your electrodes' materials.

Since, the phase angles (in degrees) appear, actually, as 'small'[2], then, let me guess, that you might be using a coil form (coil_phase>0[3]) as your metal-substrate for your material(s). In this (hypothetical) case the cell's ('small') phase angles, at high frequencies (>100Hz), result as an actual difference:

coil_phase + (- electrode_material_phase).

1. Simeon_Question: 'What capacitance value is usually calculated from the low frequency region of a Nyquist plot-is it the capacitance of the electrode material?...'

2. Simeon_Quote: '...But when I look at the Bode plots the phase angles are somewhat small. Between - 3 and -10 degrees...'

3. See my older (some days, ago, September 30) reply, about 'how to measure the coil's impedance spectra'.

"Dear Wang Jingyan,

a) I could explain more/better if you could send, please, a draft photo showing the 4-electrodes' contacts on your coil.

b) Also, show, please, some Bode plot(s) spectra[1] for the wire (0.6mm) of your actual coil either empty and/or with core.

1. Wide (maximum, possible) frequency regime (spectra).", in: https://www.researchgate.net/post/EIS_Nyquist_plot_didnt_show_semicircle_why

4. Try to measure the (plain) distinct coil's impedance spectra, without mat. loading, as proposed, above, in ref[3].

Dear prof. Ioannis Samaras

Thank you very much for your answer.

I have used the same materials in a three electrode system and obtained phase angles between 40 and 70 degrees. I thought that the small phase angles were due to the effect of the two-electrode system in a semi-solid electrolyte. However, I have also found that the phase angles are much larger (up to 70 degrees) when using carbon felt electrodes. My electrodes (both anode and cathode) are made of stainless steel mesh coated with carbon black (Vulka-72), using a polymer adhesive as a binder. Prof., how do I determine the phase angle of the coil or material to be able to use the formula: coil_phase + (- electrode_material_phase)? Could you please suggest publications that could help me with this?

Dear Simeon Meshach Imologie ,

I will say more under the case/condition that you could update and resend your (enriched) graphs ('Doc1.jpeg') including, now, data from the higher freq. band (105 Hz, 106 Hz).

OK Prof @Ioannis Samaras, I can send the file to you through email if you don't mind

Check https://www.sciencedirect.com/topics/engineering/nyquist-plot

Also check https://pubs.acs.org/doi/10.1021/acs.jpcc.7b10582

Check on this paper.

https://library.oapen.org/bitstream/handle/20.500.12657/25190/1004900.pdf?sequence=1&isAllowed=y