Mathematical Algorithm behind Protein-Film Voltammetry of Surface Reaction Coupled with an Irreversible Preceding Chemical Step and an Irreversible Regenerative Catalytic Reaction Considered under Kinetic Conditions

A mathematical model is developed for a surface CirrEC′ mechanism in protein-film voltammetry, consisting of an irreversible preceding chemical reaction, A(ads) → Red(ads), followed by a reversible electron-transfer step Red(ads) ⇌ Ox(ads) and an irreversible regenerative catalytic reaction Ox(ads) + Y(ads) → Red(ads). The model combines Butler–Volmer electron-transfer kinetics with kinetic equations describing the formation and regeneration of electroactive species within the surface-confined film. The resulting differential equations provide a complete description of the evolution of surface concentrations and the corresponding faradaic current. Special attention is given to the interplay between the rate of precursor conversion and catalytic regeneration, both of which strongly influence the shape and magnitude of the voltammetric response. The proposed algorithm enables quantitative simulations of protein-film voltammograms and offers mechanistic insight into catalytic systems exhibiting both chemical activation and regeneration processes at the electrode interface.