How does a reversible electrode respond in a.c. voltammetry? Part 1: An analytic solution for the semiintegral for amplitudes less than 40 mV

• Components of a.c. voltammetric response are derived mathematically.
• Semiintegral expressions are exact, consisting of d.c. and a.c. terms.
• Even harmonics are in-phase, odd harmonics are out-of-phase.

It proves possible to analyze exactly the electrode response in reversible a.c. voltammetry without resorting to simulation. The procedure involves segmenting the timescale and deducing the semiintegral. In this study, the temporal evolution of each harmonic semiintegral components is predicted, as is the aperiodic component, which includes faradaic rectification as well as a Randles–Ševčik term. A.c. and d.c. responses are cleanly separated. As the title states, the analysis is confined to a restricted range of a.c. amplitudes, but there is no restriction on the frequency.