Time-Dependent Diffusion−Migration at Cylindrical and Spherical Microelectrodes: Steady- and Quasi-Steady-State Analytical Solution Can Be Used under Transient Conditions

Abstract

Mass transport at cylindrical and spherical microelectrodes involving diffusion and migration is analyzed by means of numerical simulation under transient conditions. The origin of the intrinsic difficulties encountered during the numerical solution of the diffusion-migration equations using implicit finite differences are outlined, especially for the particular case when the number of electrons transferred equals the charge number of the electroactive species. The numerical results for transient conditions have been compared to the general analytical solutions for the current enhancement or diminishment due to migration under steady- and quasi-steady-state conditions at 1D geometry microelectrodes (Amatore, C.; Fosset, B.; Bartelt, J.; Deakin, M. R.; Wightman, R. M. J. Electroanal. Chem. 1988, 256, 255-268). This yields that the analytical limiting currents are applicable, within experimental error, to the analysis of transient diffusion-migration current responses at microelectrodes of cylindrical and spherical geometries except extremely short times after the application of the potential step, i.e., when current measurements are anyway already corrupted by ohmic drop when the supporting electrolyte concentration is low. Also, this confirms that the current enhancements or diminishments due to migration are identical for both electrode geometries when steady- or quasi-steady states are approached and do not drastically differ even under transient regimes.