Analytical solution for the triple-pulse problem in pulse techniques: zeroth-order solution and higher-order corrections

A rigorous solution for the triple-pulse problem for a slow charge transfer reaction is presented. The treatment is based on the methodology developed previously to derive the general solution for the double pulse-problem for an irreversible electrode reaction (J. Galvez, M.L. Alcaraz, Electrochim. Acta 39 (1994) 2143). The solution obtained for the triple-pulse problem can be applied without restrictions for any pulse height and duration and is therefore general for all modes of triple-pulse voltammetry. For computational purposes, the equation derived involves a main contribution, the zeroth-order solution, and higher-order corrections so that we can compute the response to any degree of accuracy by adding to the zeroth-order solution as many of these corrections as necessary. Finally, the procedure that illustrates how this methodology can be extended to solve the boundary value problem for a larger number of potential steps is discussed.