Butler-Volmer equation

 An equation for the rate of an electro­chemical reaction; it describes the current density at an electrode in terms of the overpotential. The But­ler-Volmer equation is given by:

j = j_a – j_c = j_e[exp(1 – a)Fη/RT- exp(- aF/RT)]

where j_a and j_c are the individual cathode and anode currents espect­tively, and j_e is the equilibrium cur­rent, called the exchange current density. By definition

j_e = j_ce = j_ae

where j_ce is the equilibrium cathode current and j_ae, is the equilibrium anode current. F is the Faraday con­stant, η is the overpotential, R is the gas constant, T is the thermodynamic temperature, and a is a quantity called the transfer coefficient.