Mathematical Algorithm of Protein-Film Voltammetry of a Surface CirrECrev Mechanism Coupled with an Irreversible Preceding Chemical Step and a Homogeneous Reversible Follow-up Chemical Reaction

A comprehensive mathematical model is proposed for a surface CirrECrev mechanism under conditions of protein-film voltammetry. The reaction sequence consists of an irreversible preceding chemical step, A(ads) → Red(ads), followed by a reversible electron-transfer process Red(ads) ⇌ Ox(ads) and a reversible chemical reaction Ox(ads) ⇌ Y(ads), characterized by forward and backward rate constants and an equilibrium constant, Keq. The model is formulated using Butler–Volmer kinetics and incorporates both kinetic and equilibrium descriptions of the coupled chemical transformation. Differential equations governing the evolution of surface concentrations are derived together with analytical relationships linking the equilibrium constant to the distribution of adsorbed species. The developed formalism enables systematic evaluation of the effects of electron-transfer kinetics, chemical equilibrium, and precursor conversion on voltammetric behavior. The algorithm is particularly suitable for simulating square-wave and cyclic voltammetric responses of adsorbed proteins and other surface-confined redox systems coupled with reversible chemical reactions.