Nernst is a subset of butler-volmer, when kinetic rate constant approachs to infinity.

Dear Wang Shuo. thank you for your reply. I understand your point, but I have seen many models in the field of microbial electrochemistry that use Nernst equation or the butler Volmer equation or a combination of both equations for different processes (i.e. Nernst for substrate conversion into electrons and Butler-Volmer for the surface electron transfer) and in the particular example of the cyclic simulation, I also have seen the use of both equations in the literature and the ability of many models to simulate reduction-oxidation processes in a cyclic voltammogram. So, that's why I am still asking this question.

Dear sir, fundamental equation nernest allows to calculate effects directly interms of reactant and product pressures for substrate conversion into electrons. Nernest equation does not fully account for how the reversible voltage varies with temperature, but still u can use it for both temperature and pressure changes. Nernest equation describes the relationship between the voltage and the concentration of species in a given electrochemical reaction at equilibrium. The Butler-Volmer equation does not the same under non equilibrium conditions. Nernest equation is a special form of butler - volmer equation when the current density is zero or when the reaction is at equilibrium

Dear Nelaturi, thank you very much for your comments regarding my question. Very helpful comments regarding the reversibility of the Butler-Volmer equation and its role with equilibrium reactions. Are you familiar with the Nernst-Monod equation or the Butler-Volmer equations and their role in modeling electroactive bacteria? Thank you.

Not much. I am interested in the field of DMFC mechanical engineering areas. During the academics, I came across these above fundamentals.