Extensions of the Koutecky-Levich equation to channel electrodes

An analytical solution is herein presented for the current at a channel-type electrode associated with a simple first-order (in the reactant) heterogeneous electron transfer process involving a solution phase species. Assuming a fixed cell geometry, electrolyte composition, and temperature, a series expansion of this solution revealed that in the limit of small values of k3 o, where k is the first-order kinetic rate constant and o is the fluid velocity in the center of the channel, the reciprocal of the measured current, 1i=1 ik +Β ilim, where ik and ilim are the kinetic and diffusion limited currents, respectively, and Β=27[8(23)(13)]=0.93036. This equation bears striking resemblance to that reported by Koutecky and Levich for a rotating disk electrode, except that Β in the latter case is unity. Rather surprisingly, and in agreement with recent findings [Electrochim. Acta, 52, 4124 (2007)], a plot of 1i vs k o 13 was found to be close to linear, with a slope reaching values slightly higher than Β as the magnitude of k o 13 increased.