Theoretical background for the behavior of molecules containing multiple interacting or noninteracting redox centers in any multipotential step technique and cyclic voltammetry

In this paper, we obtain the simple explicit analytical expressions which demonstrate that for any voltammetric technique (of single pulse, multipulse or potential sweep, like cyclic voltammetry) the I/E response corresponding to molecules containing any number of identical noninteracting electroactive centers, has the same shape and characteristics as that obtained with molecules containing only one center. This was predicted 26 years ago by Flanagan et al. [J. Am. Chem. Soc. 100 (1978) 4248] for a planar diffusion field or stationary conditions, but until now, in multipotential step or potential sweep techniques, it has been possible to prove only by using numerical and experimental methods. The equations deduced here are valid for any molecules whose electroactive centers are interacting or not, both in spherical and planar diffusion. These equations point out that the excellent predictions of the above mentioned reference of Flanagan et al. corresponding to the particular case of noninteracting centers, are a logical consequence of the fact deduced in this paper that for any potential pulse sequence, the surface concentrations of reactants and products are independent of time and are dependent only on the potential of the pulse which is being applied at each moment.