Revisiting electrocatalytic oxygen evolution reaction microkinetics from a mathematical viewpoint

Oxygen evolution reaction (OER) is attractive for various sustainable energy storage and conversion devices, and microkinetic analysis is critical to gain vital reaction details for clarifying the underlying reaction mechanisms. Although many microkinetic studies have been conducted for OER and remarkable achievements have been obtained in both theory and experiment in the recent decades, several "clouds" still need to be swept: (1) the implicit and complex rate expression for kinetic current by conventional equation sets; (2) the empirical exponential relationship between the rate constant and the applied potential; (3) the inconsistently used overpotentials for microkinetic analysis. In this article, we clarify the above points by introducing the graph theory for chemical kinetics to straightforwardly obtain the steady-state expression of OER kinetic current. Taylor's theorem and transition state theory are further applied to rationally determine the relationship among rate constant, free energy of activation, and applied potential. Through this, the Butler-Volmer equation is deduced from the 1st-order Taylor polynomial, and analogous Marcus equation is accessible by the 2nd-order Taylor polynomial. Based on the above mathematical framework, we finally clarify two overpotentials (nominal and elementary overpotentials) commonly used in microkinetic OER and prove that they are equally reliable for steady-state rate analysis by a combination of theory and experiment. The above mathematics-based discussion may be conducive to understanding fundamental electrode processes to inspire the design of highly efficient electrochemical devices in the future.