Quantized Capacitance Charging of Monolayer-Protected Au Clusters

A theoretical model based on electrostatic interactions is developed to account for the formal potentials of current peaks observed in differential pulse voltammetry of solutions of 10 different nanometer-sized alkylthiolate and arylthiolate monolayer-protected gold clusters. The current peaks arise from successive, quantized (single-electron) capacitative charging of ensembles of individual cluster cores (i.e., electrochemical ensemble Coulomb staircase charging). Experimental peak potentials for a given cluster change roughly linearly with changes in its core charge state, as predicted by the theory, and the sub-attofarad capacitances (CCLU) of individual clusters obtained from the slopes of such plots agree with those estimated from a simple concentric sphere capacitor model. The charging of clusters with very small cores becomes redox moleculelike, indicating as reported recently, the emergence of HOMO-LUMO energy gaps. Because the quantized charging currents of the clusters are diffusion controlled, their voltammetric behavior can be readily simulated, but requires attention to dispersities in CCLU that occur in experimental samples of these materials. Simulations of microelectrode voltammetry incorporating Gaussian dispersions in cluster properties display features similar to those observed experimentally. The simulations show that quantized charging features are more difficult to detect when the nanoparticles are not monodisperse, but can be seen in polydisperse samples when the cores are small (small CCLU) and not highly charged.