Simulations of quantized double layer charging voltammetry of poly-disperse and mono-disperse monolayer-protected clusters

This paper describes simulated differential pulse voltammetry (DPV) of quantized double-layer charging (QDL) in poly-disperse monolayer-protected gold cluster (MPC) solutions. The simulation accounts for the voltage spacing between QDL peaks with a concentric sphere capacitor model, in which core sizes, and the relative proportion of each size, are input using transmission electron microscopy (TEM) data. MPC diffusion coefficients are estimated from hydrodynamic radii, and peaks are broadened to account for DPV pulse height effects. The smallest MPCs are omitted from the simulation because electrochemical HOMO/LUMO gap information is uncertain. The largest ones are shown to produce the underlying DPV current continuum typical of experimental DPV of poly-disperse samples. The simulation produces a fair approximation of the experimental DPV of a poly-disperse MPC sample, and an excellent representation of a relatively mono-disperse sample.