Detailed theoretical treatment of homogeneous chemical reactions coupled to interfacial charge transfers

The mathematical modelling of heterogeneous charge transfer processes complicated by the reactivity of the redox species in solution is revisited, elaborating on powerful and accurate theoretical approaches and simplifications that can facilitate and speed up the mathematical resolution, the solution implementation, the design of experiments and the calculation and analysis of the electrochemical response. The physicochemical fundamentals and mathematical implications behind such approaches will be discussed for frequent and paradigmatic reaction mechanisms involving homogeneous chemical equilibria and (pseudo)first-order and second-order chemical kinetics. The cases considered will point out how the suitable preliminary examination of the boundary value problem offers profound insights into the electrochemical system that can assist the design of theoretical and experimental studies. This provides criteria for the assessment of complex simulations (for example, by comparison with exact analytical solutions for particular cases) and it can alert about meaningless results derived from blind use of approximations and/or 'brute force' approaches.