Generalized theory for nanoscale voltammetric measurements of heterogeneous electron-transfer kinetics at macroscopic substrates by scanning electrochemical microscopy.

Here we report on a generalized theory for scanning electrochemical microscopy to enable the voltammetric investigation of a heterogeneous electron-transfer (ET) reaction with arbitrary reversibility and mechanism at the macroscopic substrate. In this theory, we consider comprehensive nanoscale experimental conditions where a tip is positioned at a nanometer distance from a substrate to detect the reactant or product of a substrate reaction at any potential in the feedback or substrate generation/tip collection mode, respectively. Finite element simulation with the Marcus-Hush-Chidsey formalism predicts that a substrate reaction under the nanoscale mass transport conditions can deviate from classical Butler-Volmer behavior to enable the precise determination of the standard ET rate constant and reorganization energy for a redox couple from the resulting tip current-substrate potential voltammogram as obtained at quasi-steady state. Simulated voltammograms are generalized in the form of analytical equations to allow for reliable kinetic analysis without the prior knowledge of the rate law. Our theory also predicts that a limiting tip current can be controlled kinetically to be smaller than the diffusion-limited current when a relatively inert electrode material is investigated under the nanoscale voltammetric conditions.