pH Dependence of the Electron-Transfer Coefficient: Comparing a Model to Experiment for Hydrogen Evolution Reaction

The empirical electron-transfer coefficient a is a valuable electrochemical observable that bridges the thermodynamics and kinetics of redox reactions. For reactions that involve protons, the value of a is expected to be pH dependent. However, even for the simplest redox processes, the nature of this dependency remains unclear. Toward clarifying this problem, we follow two goals. First, we calculate the electron-transfer coefficient a and its pH-dependence based on a model 2D potential energy surface that has been investigated by Koper and Schmickler for proton reduction. According to the model, a is pH-independent for high-pH values and pH-dependent for low-pH values, with a increasing as the pH is lowered. Second, we report our experimentally measured a for hydrogen evolution on several electrode materials over a wide pH range. We observe that several features of the data show similarities to the predictions of the model. The data. show different behavior in two distinct pH regions. In the acidic region, a linearly increasing a with decreasing pH and in the basic side a pH-independent a are observed for several electrodes. However, certain predictions of the model, in particular the transition pH between the two regions, do not seem consistent with the data, which we propose likely arises due to mass-transfer limitations of the rate. We hope that this work will help better understand the pH dependence of interfacial electron-proton transfer reactions. and, in particular, inspire further work to isolate mass-transfer limitations from interfacial chemistry effects in measuring and interpreting the electron-transfer coefficient.