Do potential dependent kinetics play a role in photocatalytic rate trends?

Abstract

Recent intriguing studies, focused upon photoanodes, have raised the possibility that higher order reaction rate properties (greater than unity) might be present in photocatalysis under high illumination intensities. Thus far, multi-hole elementary reactions have been primarily suggested to explain high reaction orders with respect to the reacting hole concentration. In this work we employ semiclassical and analytical device modelling to explore the degree to which such trends might partially or wholly emerge from the acceleration of charge transfer by changes in the potential drop across the Helmholtz electrical double layer – commonly referred to as Tafel kinetics. Our analysis demonstrates that, under high illumination intensities, the reactant surface hole concentration in photoanodes can be pushed into the inversion regime such that an abrupt interfacial potential drop forms across the semiconductor–liquid interface giving rise to potential dependent kinetics described by the Tafel equation (more often used to describe electron transfer at metal electrodes). Through a band diagram based analysis, these findings are shown to be independent of the doping density and applied bias in the photocatalytic saturation regime, and further exhibit direct capacitive signatures in line with several experimental reports. Moreover, analytical derivations show that rate behaviour mimicking higher order trends can readily emerge from Tafel contributions to the hole transfer rate constant within photoanodes. However, an examination of temperature dependent trends underscores that more comparison between theory and experiment is needed to fully verify the degree to which Tafel contributions might be present. Within the broader context, these findings show that higher order trends in photocatalysis may have a nuanced origin in which Tafel contributions may play a key role.