From Single to Double Catalysis: Diffusional EC′EC″ Framework in Cyclic Voltammetry-MATHCAD Simulation Platform

Multistep redox transformations in solution frequently proceed through sequential electron-transfer events coupled to regenerative chemical reactions, yielding stable intermediates that can re-enter catalytic cycles. Such behavior is characteristic of numerous molecular systems, including organic mediators, quinone/hydroquinone couples, and cofactor-driven processes (e.g., flavins and NAD(P)H analogues), where all redox forms may participate in feedback loops that shape the observed electrochemical response. Here we present, for the first time, a comprehensive theoretical treatment of a two-step double catalytic EC′EC″ mechanism under conditions of mass transfer occurring exclusively via diffusion in cyclic voltammetry. The model describes a sequence of two electron transfers separated by consecutive regenerative chemical steps, with both catalytic loops explicitly incorporated into the mass-transport–kinetic framework. Numerical solutions of the governing equations reveal distinct voltammetric signatures arising from the interplay between diffusion, electron-transfer kinetics, and the rates of the two catalytic steps. Systematic variation of the kinetic parameters for each regenerative pathway demonstrates how peak currents, peak separations, and waveform distortions encode the relative contributions of the two catalytic cycles, enabling their discrimination and quantification.
Importantly, under well-defined limiting conditions, the general EC′EC″ scheme can converge to several classical mechanisms, including EE, EC′E, EEC′, EC′, and simple E mechanism. This convergence establishes the present formulation as a unified theoretical platform for interpreting a wide range of electrochemical behaviors within a single framework. The results provide new mechanistic insight into complex catalytic redox systems and offer practical guidance for extracting kinetic information from cyclic voltammetric data in systems exhibiting tandem catalytic processes. Original MATHCAD platform is available for free on the Repository of Goce Delcev University, Stip.