Solving the EC′E Diffusional Mechanism –Mathematical Model

The EC′E mechanism, involving two consecutive electron-transfer steps coupled with a homogeneous catalytic regeneration of the intermediate, represents a fundamental yet complex class of electrochemical reactions frequently encountered in redox-active systems. In this work, a comprehensive mathematical model of the fully diffusional EC′E mechanism is developed under conditions of semi-infinite planar diffusion. The mathematical model (explained step-by-step) is based on coupled reaction–diffusion equations incorporating Butler–Volmer kinetics for both electrode processes and second-order chemical kinetics for the catalytic step. Numerical solutions presented in MATHCAD reveal the interplay between electron-transfer rates and catalytic regeneration, highlighting their combined influence on voltammetric response. The simulation analysis demonstrates how variations in kinetic parameters govern the transition between limiting mechanistic regimes and identifies characteristic features in the current–potential profiles that can be used for mechanistic discrimination. Under specific conditions, the model converges to simpler mechanisms, including E, EC′, and EE systems, providing a unified theoretical framework for their interpretation. This study offers a robust platform for understanding complex catalytic electrochemical processes and supports the quantitative analysis of EC′E-type systems in modern voltammetry.