Hydrogen Evolution Reaction: Log j0 Versus Work Function Φ As Viewed from Transition State Theory As an Eyring Plot

Abstract

In 1972, Trasatti correlated the log of the exchange current density (j0) for the hydrogen evolution reaction (HER) with the work functions of 31 metal electrodes to yield two parallel regression lines. [1] The lines are separated by Δ log j0 = 3. Thermodynamically, work function 𝚽 is the energy to remove an electron from a metal to infinity. Perhaps counterintuitively, platinum group metals (PGMs) with the highest 𝚽 sustain the highest j0 values.The elementary, interfacial electron transfer occurs between the electrode and adsorbed hydrogen cation and adsorbed hydrogen atom.H+ ads + e ⇌ H● ads A materials dependent rate expression is developed as follows. [2]The properties of the metal are introduced explicitly into reaction mechanism, characterized by M(e) and M(0), the metal electrode with and without the electron.M(e) + H+ ads ⇄ M(0) + H● ads Classical transition state theory (TST) characterizes the free energy of activation ΔG‡ as the energy difference between the transition state (TS) and the minimum energy of the reactants. The TS forms at equilibrium, where adsorbed hydrogen and metal electrode share the electron.M(e) + H+ ads ⇌ [M ●●● e ●●● Hads]‡ ⇌ M(0) + H● ads Electrochemical potentials set the energy difference in the products and reactant, which sets ΔG‡. Chemical potential (𝞵) difference for the metal without and with the electron define 𝚽. F𝚽 = 𝞵M(0) - 𝞵M(e) F𝚽 is further defined as a chemical free energy that that lowers ΔG‡. F𝚽 is a material specific property that is atypically specified in the rate equation. Because log j0 ∝ - ΔG‡, and chemical free energy F𝚽 lowers ΔG‡, log j0 ∝ F𝚽. Thus, j0 increases exponentially with F𝚽, so PGMs with highest 𝚽 sustain highest j0. Further, the rate expression embeds material specific property 𝚽.The classical Eyring perspective for generic rate constant k’ is k’ = A’ exp[-ΔG‡/RT]. Rate constant is typically determined by varying temperature in a plot of ln k’ versus T-1, where ln k’ = ln A’ - ΔG‡/RT. For isothermal measurements, log j0 is linear with 𝚽 because F𝚽 is a term ΔG‡ chem that is a component in the total ΔG‡. For metals, where 𝚽 > 0, F𝚽 always lowers ΔG‡ for HER; the total activation energy is lowered in proportion to F𝚽. The slopes of log j0 versus 𝚽 is proportional to 𝝰𝚽F𝚽/2.303, where partition coefficient 𝝰𝚽 characterizes ∂ΔG‡/∂𝚽. For the parallel lines in Trasatti’s plot, 𝝰𝚽 = 0.38. The intercepts are independent of 𝚽.The material specific rate expressions derived from classical TST and electrochemical potentials may provide guidance on design of electrocatalysts and provide a path to integration of classical and contemporary modeling of important reaction processes such as HER.