Transient Voltammetry at Electrodes Modified with a Random Array of Spherical Nanoparticles: Theory

The simple one-electron reduction, A + e(-) reversible arrow B, is studied at a random array of spherical nanoparticles attached to a planar electrode. Electron transfer is assumed to occur exclusively on the surface of the nanoparticles; the electrode simply acts as a conductive support. Voltammetry is simulated using the alternating direction implicit (ADI) variant of the finite difference method. The diffusion-controlled chronoamperometric response is studied as a function of nanoparticle surface coverage, and the cyclic voltammetry is studied as a function of electrochemical rate constant, voltage scan rate, and nanoparticle surface coverage. Also considered is the extent to which a random array of spherical nanoparticles can usefully be approximated as an array of discs with an equal surface coverage.