ECE versus DISP electrochemical competition

The ECE (Electrochemical, Chemical, Electrochemical) and DISP (DISProportionation) mechanisms describe electrochemical reactions between four species in a diffusive solution. The general set of reactions which encompass both mechanisms is modelled by: \[ A + {e^ - } \to B\] (at the electrode) (i) \[ B \rightleftharpoons C\] (throughout the solution) (ii) \[ C + {e^ - } \to D\] (at the electrode) (iii) \[ B + C \rightleftharpoons A + D\] (throughout the solution) (iv) in the case when the applied overpotential is large enough that only the forward steps in (i) and (iii) are present. The ECE mechanism follows the pathway (i), (ii), (iii). The DISP mechanism follows the pathway (i), (ii), (iv). These electrochemical mechanisms play an important role in many organic reactions such as cleavage processes and in inorganic reactions such as the production of forms of technicium used as a radiopharmaceutical. It is important to understand these mechanisms in order to better predict product synthesis and performance. This paper uses asymptotic expansion and perturbation techniques to provide rigorous, relatively simple analytic/numerical solutions for the (linear) ECE mechanism, the (weakly nonlinear) DISP mechanism and a (weakly nonlinear) “competition” mechanism involving all four pathway steps. It is shown that for large dimensionless time, the ECE mechanism evolves to a state with only two species present in order one quantities. Yet, the DISP mechanism retains all four species in order one amounts when step (iv) is reversible. The competition mechanism behaves like the ECE mechanism for small time yet evolves for large time to a form more similar to the DISP mechanism showing that nonlinear effects eventually dominate the mechanistic behavior.