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 k(3)/nu(o), where k is the first-order kinetic rate constant and nu o is the fluid velocity in the center of the channel, the reciprocal of the measured current, 1/i = 1/i(k) + beta/i(lim), where i(k) and i(lim) are the kinetic and diffusion limited currents, respectively, and beta = 27/[8 Gamma(2/3)Gamma(1/3)] = 0.93036. This equation bears striking resemblance to that reported by Koutecky and Levich for a rotating disk electrode, except that beta in the latter case is unity. Rather surprisingly, and in agreement with recent findings [Electrochim. Acta, 52, 4124 (2007)], a plot of 1/i vs k/nu(1/3)(o) was found to be close to linear, with a slope reaching values slightly higher than beta as the magnitude of k/nu(1/3)(o) increased. c 2007 The Electrochemical Society.