Modelling the steady state voltammetry of a single spherical nanoparticle on a surface

The steady-state voltammetry of a one electron reduction, A + e− ⇌ B, is studied numerically for a conductive spherical particle resting on a supporting surface. The process is assumed to occur exclusively on the surface of the sphere and not at all on the support. For electrode kinetics in the fully irreversible limit, we establish a simple relationship between the half-wave potential and the kinetic parameters, α (the transfer coefficient) and k0 (the rate constant of the reaction), the radius of the sphere, and the diffusion coefficient of the species in solution. Further, we develop an expression that completely describes the voltammetric waveform in the same limit. Additionally we describe a simple transformation that maps the irreversible steady-state voltammetry for an isolated spherical electrode, such as may be obtained from any commercially available electrochemical simulation package, onto the voltammetry of a sphere on a surface. The sphere on a supporting plane model has recently been used to explain the current–time behaviour seen for nanoparticle impacted electrode surfaces such that electrode process occur on the sphere surface whilst it is in contact with the plane [J.M. Kahk, N.V. Rees, J. Pillay, R. Tshikhudo, S. Vilakazi, R.G. Compton, Nano Today 7 (2012) 174–179]; accordingly, the theory presented here is of potential significant application in this area.