Mathematical Model beyond a Surface EEC’ Mechanism under Butler-Volmer Kinetics in Protein-Film Voltammetry

This work presents a theoretical model for a surface-confined EEC′ mechanism under conditions of protein-film voltammetry. The mechanism consists of two consecutive one-electron transfer reactions, Red(ads)⇌Int(ads) ⇌ Ox(ads), followed by a regenerative catalytic step in which Ox(ads) reacts with a co-reactant Y(ads) to regenerate the intermediate state Int(ads). The model is formulated within the Butler–Volmer kinetic framework, allowing simultaneous treatment of heterogeneous electron-transfer kinetics and catalytic regeneration. Differential equations describing the temporal evolution of the surface concentrations of all electroactive species are derived together with the corresponding current expressions. The theoretical formalism provides a quantitative basis for analyzing the influence of electron-transfer rates, catalytic turnover, transfer coefficients, and experimental time scale on the voltammetric response. The developed algorithm can be directly implemented for numerical simulations of square-wave and cyclic voltammetric experiments involving adsorbed redox proteins and catalytic surface-confined systems.