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

01 November 2022, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


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.


Graph theory
Oxygen evolution reaction
Transition state theory
Taylor’s theorem


Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.