Mathematical Modeling of Surface-Confined EC′E Mechanism in Protein-Film Voltammetry-Electrode Reaction Scheme of two-step Consecutive Redox Mechanism featuring Intermediate Regenerative Step, with all Redox Forms Present in Adsorbed State

A mathematical framework for the analysis of a surface-confined EC′E mechanism is presented, describing a two-step consecutive redox process involving an intermediate regenerative chemical step, where all participating redox forms are immobilized on the electrode surface. The model is developed under conditions of complete surface confinement, neglecting mass transport effects, and is based on a system of coupled differential equations formulated within the Butler–Volmer kinetic formalism. The regenerative chemical reaction, treated under pseudo-first-order conditions, introduces catalytic feedback that significantly alters the dynamic distribution of surface species and the resulting electrochemical response. Numerical simulations are performed for various kinetic regimes of the electron-transfer steps and the chemical regeneration, available in the free MATHCAD File deposited in Repository of the Goce Delcev University in Stip in 2026. The model demonstrates that the relative rates of the two electron-transfer steps and the regenerative reaction govern the shape, position, and magnitude of the voltammetric peaks, enabling mechanistic discrimination and kinetic parameter evaluation. Under limiting conditions, the proposed framework converges to simpler surface-confined mechanisms, including EE, EC′E, E, and single-step EC′ systems, highlighting its versatility as a unified modeling platform. The presented theoretical approach is particularly relevant for interpreting voltammetric responses of surface-immobilized redox systems, such as protein-film electrochemistry and catalytic interfaces, where intermediate species undergo rapid regenerative transformations. This work provides entire mathematical approach and differential equations needed to describe the considered mechanisms in order to develop a robust basis for mechanistic analysis and quantitative evaluation of complex surface-confined electrochemical systems.