Study of multistep electrode processes in double potential step techniques at spherical electrodes

Analytical solutions for reversible multistep electrode processes in double potential step techniques at spherical electrodes of any size, including plane electrodes and ultra-microelectrodes, are derived. These solutions are valid when the diffusion coefficients of all species are equal, and they are applicable for any number of the species initially present in the solution, for any values of the formal potentials of the different steps and for any duration of the two potential steps. In differential pulse voltammetry (DPV) and in additive differential pulse voltammetry (ADPV) the effects of the applied potential and of the electrode sphericity on the current are found to be separable and, therefore, the position of the peaks and the cross potentials are not dependent on the size of the electrode. The convenience of using ADPV in determining the formal potentials when some electrochemical steps are not completely separated is shown. It is also demonstrated that the reproportionation/disproportionation homogeneous reactions have no effect either on the surface concentrations nor on the currents in any multipotential step technique under the conditions considered here.