Integral equation-based simulation of transient experiments for an EC₂ mechanism: Beyond the steady state simplification

Transient electrochemical experiments are usually described theoretically by systems of reaction–diffusion partial differential equations. Converting them to integral equations is a classical and valuable modelling approach. Unfortunately, if any reaction–diffusion equation contains nonlinear reaction rate terms, up to now such a conversion has only been possible by assuming a steady state for the equation. Consequently, only sufficiently fast homogeneous reactions could be handled. In this work a novel integral equation-based modelling approach is described. The steady state assumption is replaced by a two-term singular perturbation expansion of the concentration–flux relationship, recently published by the authors. The expansion is valid for homogeneous reactions of (integer) order m≥1, occurring at planar electrodes. An example simulation of cyclic voltammetry for an EC₂ reaction mechanism involving a second order dimerization reaction is performed. It is found that in this way the voltammograms can be satisfactorily simulated for homogeneous reaction rate constants smaller by about one order of magnitude than was previously possible.