Theory of Electrochemistry for Nanometer-Sized Disk Electrodes

It has been shown previously that conventional voltammetric theories may become inapplicable at electrodes of nanometer scale due to enhanced effects of the diffuse double layer on the interfacial charge transport and transfer processes (Anal. Chem. 1993, 65, 3343; J. Phys. Chem. B 2006, 110, 3262). As well as the diffuse double layer effects, we show in present study that the voltammetric responses of nanometer-sized electrodes would differ from the macroscopic electrodes due to significant edge effects of dielectric screening and electron tunneling if the electrode has planar geometries. These nanoedge effects arise because of the comparable size of the electrode with the dipole molecules and the effective electron tunneling distance. Models for these nanoedge effects are developed and combined with Poisson-Nernst-Planck theory and Marcus electron-transfer theory to describe the voltammetric characteristics of nanometer-sized disk electrodes. Marcus theory instead of Butler-Volmer theory is used to describe the electrochemical electron transfer kinetics because the greatly increased mass transport rates at the nanoscale electrochemical interface would render most of the electron transfer reaction to become largely irreversible so that the kinetics-controlled voltammetric behavior would extend to very large overpotentials at which the Marcus inversion of the electron transfer rate may occur. The theoretical calculations based on present models show the pronounced radial heterogeneities of interfacial potential, concentrations, and rate constant of charge transfer at the electrochemical interface of nanodisk electrodes, which in turn can significantly alter the voltammetric responses of these electrodes. It is indicated that the radial extension of electron transfer at the nanodisk electrode overwhelmingly determines the limiting currents on the voltammetric responses of the nanodisk electrode, while the electrical double layer effects can severely impact the kinetic characteristics of voltammetric responses (e.g., half-wave potential).