Application of Danckwerts' expression to first-order EC′reactions. Transient currents at inlaid and recessed microdisc electrodes
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A general relationship, arising from Danckwerts' expression (P.V. Danckwerts, Trans. Faraday Soc. 47 (1951) 1014), allows the computation of the transient limiting current in a system with a homogeneous first-order reaction regenerating the electroactive species (an EC′ mechanism), with diffusion and convection, from the limiting currents at the same electrode when there is no homogeneous reaction. For the method to apply the boundary conditions and hydrodynamic regime must be time independent. A simple procedure (which could serve as an alternative to convolution or semi-integral methods) to determine the kinetic parameter from limiting currents obtained in an electrode of arbitrary geometry and size is suggested. An estimation of the time needed to approach steady-state is provided. Diffusion-limited transient currents at the inlaid and recessed microdisc electrode with first-order homogeneous kinetics are studied in detail, checking approximate analytical expressions and simulation data arising from the Finite Element Method. If diffusion is the only transport phenomenon, all currents tend to the planar (cottrellian) behaviour when t tends to 0, regardless of the kinetic constant or the shape of the electrode.