EIS versus CV for adsorbed systems with CPE and kinetic distributions: physicochemical consequences

• Complex capacitance is useful for adsorbed systems with fast electron transfers • CPE behaviour suggests frequency dispersion of surface concentrations • Gaussian distance distribution from the electrode causes log-normal rate distribution • Both CPE and rate distributions are evidenced in a giant electroactive rotaxane • Fast CV and EIS are very complementary techniques to assess these distributions Electrochemical analysis of adsorbed systems integrating redox centres in their structure often show deviations from ideal behaviours, revealing thermodynamic or kinetic distributions. In this work, we revisit theoretically the influence of the constant phase element (CPE), often introduced to fit data obtained by electrochemical impedance spectroscopy (EIS), together with distributions of the electron transfer rate constants between the electrode and electroactive entities. If such approaches have already been developed in EIS, we extend it in this study to ultrafast CV measurements, and further explore their physicochemical consequences. We thus propose on the one hand an interpretation of the CPE in terms of frequency dispersion of the charge transferred to the electrode, referred here as a “pseudo-Nernstian” model in EIS, and for which a mathematical derivation is suggested. It results in the variation of the apparent surface concentration with the time scale of the technique, probed in CV by the non-linear dependency of the voltammetric peak area with the scan rate. On the other hand, since the distance distributions of redox entities with the electrode lead to log-normal distributions of rate constants, the apparent rate deduced from the measurement may be biased, possibly explaining some discrepancies in the literature. Finally, we apply our model to reinterpret CV and EIS results obtained for giant rotaxanes bearing ten ferrocene centres adsorbed onto gold electrodes, demonstrating a good agreement between the techniques, and the potential for accessing complex mechanisms by time-resolved electrochemical measurements.