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

Abstract

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 Δμ_e. The exchange current density j_0 appears as an exponential function of Δμ_e. For the work function Φ of the metal, the approximation Δμ_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.

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Identifiers

DOI

10.1149/1945-7111/ad8f01

Journal

Journal of The Electrochemical Society

Year

2024