  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.
