The R(CT) or charge transfer resistance is related to the polarisability of your electrode, which in turn strongly affects the structure of your electrical double layer at the electrode/eclectrolyte interface. As such, the capacity and, more importantly, the reactance of your electrical double layer "capacitor" will be affected if the R(CT) changes.

You may be interested in the following:

https://www.gamry.com/application-notes/EIS/basics-of-electrochemical-impedance-spectroscopy/

Thanks Tomasz

Am I right if I say" decrease in Rp(Rct) increases the capacitance of the double layer?

You're welcome.

When communicating with someone who knows the details of your system or as a summary, there should be no problem. Otherwise, I would advise against it, as this is not a direct dependence. Since, due to the adsorption/chemisorption of your proteins on Au, the equivalent circuit will be slightly different than that of an Au electrode in PBS, it would be better to talk about C(dl) increasing due to a polarisability change in the electrode/electrolyte interface.

Thanks Tomasz...Can you also please explain the slightly different equivalent circuit for the proteins attached gold...I use the Randles circuit (CPE instead of Cdl) for all of my cases and it fits the best???

Thanks

For the pure Au WE in the PBS solution, the Randles circuit should be a perfect fit (as it is designed to model just such a situation).

Since even covalently bound proteins (assuming that this is how they are attached to the WE) can undergo adsorption and "cover" the WE, affecting how charge passes through the system. Experimentally, you should still be able to model it with the Randles circuit (since the adsorbed 'protein layer' will most likely just add another capacitor), but, depending on the mechanism of adsorption, there may be some deviations from the model (particularly if you are using proteins, which have thiol groups).

While I would expect those deviations to be very minor, you may wish to account for them anyway. As such, I would recommend the following paper, providing some insight on specific vs non-specific adsorption on a crystal face:

https://www.bioee.ee.columbia.edu/courses/upload/Bibliography/jovic1_electroan_chem.pdf

You are probably well-aware of this report, but I will also recommend one more relevant to your application:

Article Method for equivalent circuit determination for electrochemi...

Going back to the philosophy of accounting for such adsorption - while the model that fits best is the model you should be using, if it is to be theoretically sound (and not just empirically), it should account for any phenomena taking place in your system. Ideally, it would be good to prove that the effect of adsorption is negligible (if it is), allowing you to simplify the more complex theoretical equivalent circuit down to the Randles circuit.

Thanks Tomasz...appreciated for your help

Dear Roshan

Aiming to bring a complement for other's responses, yes, both Rct (charge transfer resistance) and Cdl (double layer capacitance) are correlated. Although impedance spectroscopy uses equivalent circuits for modeling the interface electrode/solution for fitting the experimental spectrum, the electrochemical cell can be modeled as a Randles circuit for chronoamperometry explanation of faradaic current (see Chapter 1 in Bard's electrochemical book).

If you use a Randles circuit, you can correlate the maximum frequency by phase angle Bode plot using this equation:

wmax = (Rct Cdl)-1

So the maximum frequency is influenced by both charge transfer and double layer capacitance.

Of course, the real working electrode isn't smooth, so CPE (constant phase element) should be used and the correlation between charge transfer and "capacitance" brought by CPE differs.

Thanks Othon for your comments and suggestions

Cheers