Revisiting electrocatalytic oxygen evolution reaction microkinetics from a mathematical viewpoint: implicit rate expression, ambiguous rate constant, and confusing overpotentials

Oxygen evolution reaction (OER) is attractive for many 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, several “clouds” over reaction microkinetics still need to be swept: (1) the implicit and complex rate expression by conventional equation sets; (2) the ambiguous exponential relationship between the rate constant and the applied potential; (3) the inconsistently used overpotentials for the microkinetic analysis. In this article, we clarify the above points by introducing graph theory for chemical kinetics to illustrate the OER microkinetic process, by which we straightforwardly obtain the steady-state expression of OER kinetic current. Taylor’s theorem and transition state theory are further applied to precisely describe the relationship among rate constant, free energy of activation, and applied potential. Through this, the Butler-Volmer equation can be deduced from the 1st-order Taylor polynomial, and analogous Marcus equation is accessible by the 2nd-order Taylor polynomial. Finally, we clarify two overpotentials (nominal and elementary overpotentials) commonly used in microkinetic OER and find that they are equally reliable for steady-state rate analysis. This mathematical discussion will be conducive to understanding fundamental electrochemical processes and designing highly-efficient electrocatalysts.