Mathematics behind Protein-Film Voltammetry of a Surface CirrECirr Mechanism Coupled with Irreversible Preceding and Irreversible Follow-up Chemical Reactions under Butler-Volmer Kinetics

This study presents a theoretical treatment of a surface CirrECirr mechanism relevant to protein-film voltammetry. The mechanism involves an irreversible preceding chemical step, A(ads) → Red(ads), a Butler–Volmer-controlled electron-transfer reaction Red(ads) ⇌ Ox(ads), and an irreversible follow-up chemical transformation Ox(ads) + Z(ads) → Y(ads). A system of kinetic differential equations is derived to describe the temporal redistribution of all adsorbed species participating in the overall mechanism. The model explicitly accounts for the competition between electrochemical generation of Ox(ads) and its irreversible chemical consumption, which significantly affects the backward component of the voltammetric response. Analytical and numerical formulations are developed to evaluate the influence of kinetic parameters, transfer coefficients, and experimental time scale on the observed current. The proposed mathematical framework provides a useful tool for investigating surface-confined redox systems coupled with irreversible chemical transformations in protein-film voltammetry.