Evaluating Analytical Expressions for Scanning Electrochemical Cell Microscopy (SECCM).

Scanning electrochemical cell microscopy (SECCM) maps the electrochemical activity of a surface with nanoscale resolution using an electrolyte-filled nanopipette. The meniscus at the end of the pipet is sequentially placed at an array of locations across the surface, forming a series of nanometric electrochemical cells where the current-voltage response is measured. Quantitative interpretation of these responses typically employs numerical modeling to solve the coupled equations of transport and electron transfer, which require costly software or self-written code. Expertise and time are required to build and solve numerical models, which must be rerun for each new experiment. In contrast, algebraic expressions directly relate the current response to physical parameters. They are simpler to use, faster to calculate, and can provide greater insight but frequently require simplifying assumptions. In this work, we provide algebraic expressions for current and concentration distributions in SECCM experiments, which are formulated by approximating the pipet and meniscus using 1-D spherical coordinates. Expressions for the current and concentration distributions as a function of experimental parameters and in various conditions (steady state and time dependent, diffusion limited, and including migration) all show excellent agreement with numerical simulations employing a full geometry. Uses of the analytical expressions include determination of expected currents in experiments and quantifying electron-transfer rate constants in SECCM experiments.