How does the Butler-Volmer equation describe electrode reactions?

The Butler-Volmer equation is a fundamental relationship in electrochemistry that describes how the rate of an electrochemical reaction—expressed as electric current density—depends on the electrode potential.12

Specifically, the equation relates the net current density to the overpotential ($\eta$), defined as the difference between the actual electrode potential ($E$) and the reversible potential ($E_{rev}$), where the rates of oxidation and reduction are equal. The equation incorporates the exchange current density ($i_0$), which represents the magnitude of the partial current densities at the reversible potential.12

The Butler-Volmer equation demonstrates that the reaction rate is exponentially dependent on the electrode potential. As overpotentials increase, the equation simplifies; when the overpotential is sufficiently large, one of the exponential terms becomes negligible, leading to a logarithmic dependence of overpotential on current density. This theoretical result aligns with experimental observations known as Tafel lines, where the slope of the plot provides the transfer coefficient ($\alpha$) for the reaction.12