Hi Farhad,

You kind of answered your question yourself. Surface area is typically measured on a macroscopic scale because it is easy. Electrochemical reaction are however proportional to the microscopic surface area. So we can write:

Measured Activity = Specific Activity * Geometric surface area * microscopic roughness

A single crystal have a roughness of 1. Anything else have a higher value.

So you see, making the electrode porous would increase the microscopic roughness a lot and the measured activity would go up. But if you would actually measure the total microscopic area and normalize your activity to it, you will see that the porosity did not change specific activity.

Cheers

Gustav

Article Investigation of the Oxygen Reduction Activity on Silver – A...

Article The effect of particle proximity on the oxygen reduction rat...

Gustav makes an accurate point, that per geometric area, you'll see an increase in current, but per microscopic area, you should get the same current density.

A key feature here, though, is mass transfer, and that will determine much of your system behavior. So, if for example, you have a porous  electrode with 10x the geometric area, you'll get 10x the current at t=0 (assuming potentiostatic conditions). However, after that, the current will drop rapidly, and at some point it will approach the current of a planar electrode. In other words, reactants in your pores will deplete, and eventually most of your  reaction will occur at the surface and/or in pore openings, leaving only a fraction of your initial microscopic area engaged in electrochemistry. This can lead to some interesting effect, such as CV peaks closer together than the 58 mV that would indicates a fully reversible reaction (an impossible result with planar electrodes). This is because the Randles-Sevcik equaiton used for characterization of CV is designed for planar electrodes, and doesn't account for porosity.

I hope this helps.

Thanks Pavel and Gustav, very good points. I'm doing numerical modeling, in my equations I calculate current density which I think is not supposed to be affected by surface area. But as Pavel mentioned we might have situations (t>0) that current of a porous electrode approaches to that of a planar one. This will change current density (porous electrode would eventually have lower current density). How can this effect be implemented in Butler-Volmer or Faraday's law?

You must apply the Koutecky-Levich relation. Note to use the correct area for mass transport (geometric area) and the kinetic current (ECSA).

https://en.wikipedia.org/wiki/Kouteck%C3%BD-Levich_equation