Theory of electrochemical hydrogen evolution reactions: Part I. The model and fundamental relationships

Abstract

A model of electrochemical hydrogen ion discharge and hydrogen desorption processes (reactions I and II, respectively) is developed which combines the principal features of the Marcus-Levich-Dogonadze theory of electron transfer in a polar medium and the theory of electron transfer into reaction complex applied by Gurney, Butler and Bockris to reaction (I). The present model is based on the following underlying assumptions: (1) reactions (I) and (II) are reactions of electron tunnelling from metal to reaction complex, the tunnelling length exceeding the Helmholtz layer thickness; (2) the final transition state term is, due to instability of the H 3O radical, a decay term and at large H-OH 2 distances becomes a final product term (H ads and H 2 in reactions I and II, respectively), so that an electronic transition involves spontaneous hydrogen atom abstraction from H 3O. It is shown that within this model the effect of solvent reorganization on reaction rate is determined by the final state term slope F, since the vertical transition energy is divided between the reaction coordinate and degrees of freedom of the solvent in the ratio: ζ= F 2 δ 2/2 E p kT ( δ is the initial state zero-point energy; E p is the reorganization energy). Due to the different F in reactions (I) and (II) (20 eV nm −1 and 50 eV nm −1 respectively), the first one is dominated by the solvent reorganization and the second by transition along the reaction coordinate. In the region of normal H 3O + discharge according to reaction (I) transition probability w obeys the Tafel law and, since the transition along the reaction coordinate is considered, the transfer coefficient is constant (0.5±0.05) when w varies within 13–14 orders of magnitude at realistic E p values (1.5 to 2.0 eV) and discharge current values consistent with the experiment. In the same potential range, reaction (II) is activationless, but the exponential dependence of w upon φ is preserved because the barrier height changes with the potential φ. Coefficient b in the Tafel equation is a linear function of temperature, and Conway's treatment of the experimental results has shown it to equal: b= b 1 kT+b 2, with b 2/ b 1 kT=ζ