Extending and Automating Quantitative Microelectrode Voltammetry through an Oblate Spheroidal Coordinate Framework

Voltammetry is a ubiquitous electroanalytical method that can be used to help probe sustainable electrochemical technologies. When conducted with a microelectrode (radius ca. μm), voltammetry enables special interrogation of electrolyte solutions by minimizing distortions and enabling near-steady-state measurements, potentially unlocking in situ or operando analyses. Methodologies aimed to evaluate the behavior of redox-active species often leverage well-established, physically-grounded expressions that can be extended to examine electrolyte solutions under non-ideal conditions (e.g., signal convolution from multiple redox events) by simulating the entire voltammogram. Such models are typically framed in cylindrical coordinates, but leveraging oblate spheroidal coordinates can result in less cumbersome mathematical treatment. Here, we utilize this orthogonal coordinate system to develop and validate frameworks that can be used to derive closed-form steady-state—along with finite difference transient—microelectrode voltammogram models for single and sequential electron transfer mechanisms. We subsequently apply these steady-state models to estimate multiple features from simulated transient voltammograms and from nonaqueous electrolyte solutions containing N-[2-(methoxyethoxy)ethyl]phenothiazine, finding the framework is particularly adept at estimating the degree to which an electrolyte solution is charged (its “state-of-charge”) and remains intact (its “state-of-health”). Finally, we highlight potential extensions of this method towards advancing in situ or operando diagnostic methods.