Voltammetric lability of metal complexes at spherical micorelectrodes with various radii

The size of a microelectrode can have a dramatic impact on the relative importance of the diffusional and kinetic contributions to the voltammetric current of an electroactive metal ion in a complexing medium. Decreasing the radius enhances the diffusional contribution and, as a consequence, the complex system tends to move away from labile behaviour (where an equilibrium relationship holds). Therefore, sufficiently small microelectrodes (either or not combined with short measuring times) should be able to sense free metal concentrations directly for not too fast association/dissociation kinetics. The particular case of steady-state spherical (or hemispherical) diffusion under ligand excess (pseudo-first-order kinetics) is solved analytically. The ensuing lability criterion is shown to be in accordance with a geometrical derivation based on an analysis of the random walk of the free metal ions produced by the dissociation of the complex. It is shown that, for a generated metal ion, the probability of reaching the microelectrode surface can be quite different from the planar case. Alternatively, the classical reaction layer concept can be used in the derivation of the lability criterion for spherical geometry as is shown in this work. All treatments show quantitatively how the lability of metal complexes is reduced with decreasing dimension of microelectrode