Compensation effects between the apparent activation energy and pre-exponential factor in simple models of electrocatalytic hydrogen evolution

Abstract

Understanding how activation energies and entropies vary with electrode potential is central to interpreting electrocatalytic kinetics, yet temperature-dependent analyses often yield apparent “compensation effects” whose physical origin remains debated. Here, we model the hydrogen evolution reaction (HER) through both Volmer–Heyrovsky and Volmer–Tafel mechanisms to determine under which conditions compensation effects emerge—even when the entropic contribution to the activation barriers of the individual reaction steps is, by assumption, potential-independent. By simulating steady-state currents across realistic potential and temperature ranges and extracting apparent Arrhenius parameters, we identify two general origins of compensation-like behavior: (i) shifts in the effective rate law arising from changes in coverage or in the rate-determining step, and (ii) the presence of multiple active sites with different equilibrium potentials of reaction steps. Both phenomena generate non-constant Tafel slopes and curvature in Arrhenius plots, producing Constable-plots (log_10⁡〖A_app 〗vs E_app) relations that mimic intrinsic entropy–enthalpy compensation. Our results demonstrate that compensation effects in electrocatalysis can arise purely from kinetic coupling and site heterogeneity rather than from fundamental thermodynamic scaling, underscoring the need for caution when interpreting temperature-dependent kinetic data. We propose that meaningful mechanistic insight requires measurements on well-defined single-crystal electrodes within potential regions where Tafel slopes remain constant.