A compact analytical formalism for current transients in electrochemical systems

Micro and nanostructured electrodes form an integral part of a wide variety of electrochemical systems for biomolecule detection, batteries, solar cells, scanning electrochemical microscopy, etc. Given the complexity of the electrode structures, the Butler-Volmer formalism of redox reactions, and the diffusion transport of redox species, it is hardly surprising that only a few problems are amenable to closed form, compact analytical solutions. While numerical solutions are widely used, it is often difficult to integrate the insights gained to the design and optimization of electrochemical systems. In this article, we develop a comprehensive analytical formalism for current transients that not only anticipate the response of complex electrode structures to complicated voltammetry measurements, but also intuitively interpret diverse experiments such as redox detection of molecules at nanogap electrodes, scanning electrochemical microscopy, etc. The results from the analytical model, well supported through detailed numerical simulations and experimental data from literature, have broad implications for the design and optimization of nanostructured electrodes for healthcare and energy storage applications.