Alternating Current Voltammetry: Predicting and Visualizing Harmonics

Alternating current voltammetry (ACV) is gaining popularity for its ability to improve the yield of electrochemical syntheses, and for its ability to improve the sensitivity of electroanalytical measurements. Chief among the analytical advantages of ACV is its ability to generate an alternating current at integer multiples (harmonics) of the applied frequency, effectively gathering several datasets at once. However, interpretation of ACV data is hindered by the lack of a unified theory to predict higher harmonics for arbitrary reaction schemes, and by the experimental artefacts of uncompensated cell resistance and background current. The present paper outlines a method for predicting an arbitrary number of harmonics for systems with up to two charge transfer events and any number of coupled first-order chemical reactions, accounting also for cell resistance and background current described by a constant phase element. Results for an ``ideal" experiment (no cell resistance and no background current) are presented up to the third harmonic for schemes with first-order reactions, and up to the first harmonic for schemes with second-order reactions. After these ``ideal" cases, the effects of cell resistance and background current are explored. In general, irreversible charge transfer causes smaller phase angles, and coupled chemical reactions cause the aspect ratios of complex-plane ACV plots to become more circular. Uncompensated cell resistance can also lower the phase angle, imitating the effects of slow charge transfer or fast chemical reactions. At high frequencies, a combination of cell resistance and capacitance can cause the error in the potential to be so great that the current magnitude actually decreases with the onset of charge transfer. An ability to interpret the electrochemical fingerprints of each system in ACV experiments, as a function of the underlying physical parameters, can aid in the design of electrochemical devices that rely on the controlled utilization of electrochemical reactivity.