Quantitative analysis of reversible diffusion-controlled currents of redox soluble species at interdigitated array electrodes under steady-state conditions

Equations for diffusion-controlled currents at interdigitated array electrodes (IDA) were derived analytically for the reversible redox reactions of soluble species under steady-state conditions. The two-dimensional diffusion equation was solved by the Schwarz-Christoffel transformation. Current and concentration distributions were obtained. The total current was expressed by the ratios of the two complete elliptic functions and the geometric widths of the anode, the cathode and the gap. The current at each microband electrode of the IDA depended on the ratios of the three widths rather than the absolute values of the widths. Platinum IDAs were fabricated by photolithography on silicon wafers. The widths of the microband electrodes were 3-10 μm while those of the gap were 2-5 μm. Voltammograms of ferrocene were measured with a dual potentiostat under steady-state conditions. The collection efficiency was ca. 95%. The limiting current agreed with the theoretical prediction.