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≈ − F Δ Φ yields a linear relationship between ln j 0 and Φ . The linear increase in ln j₀ 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.