Editors’ Choice—The Butler-Volmer Equation Revisited: Effect of Metal Work Function on Electron Transfer Kinetics

We revisit the classical derivation of the Butler-Volmer equation to include the effect of the electrode metal. If the metal is replaced by one with a different work function, keeping other conditions in the electrode constant, the chemical potential of electrons {μ}_e and the Galvani potential φ change in a complementary manner. Changes in {μ}_e and φ each impact the free energies of activation of the forward and backward electron transfer reactions, so we modify the classical expressions which relate them to applied voltage E by including also the effect of {μ}_e. Inserting these expressions in an Eyring-Polyani or Arrhenius type equation in the traditional way, we obtain a modified Butler-Volmer equation which expresses current density as a function of both E and Δ{μ}_e. The exchange current density {j}₀ appears as an exponential function of Δ{μ}_e. For the work function Φ of the metal, the approximation Δ{μ}_e≈−FΔΦ yields a linear relationship between ln{j}₀ and Φ. The linear increase in ln{j}₀ with Φ has long been reported. We show two experimental examples: the aqueous Fe²⁺/Fe³⁺ couple with positive slope and the hydrogen evolution reaction (HER) with parallel lines for the d and sp metals, both with positive slopes.