Quantized Capacitance Charging of Monolayer-Protected Au Clusters

Abstract

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 (C CLU ) 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 C CLU 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 C CLU ) and not highly charged.

Electrochemical Quantized Capacitance Charging of Surface Ensembles of Gold Nanoparticles

“…The charge state change z ) 0/+1 is, for example, assigned to the first DPV peak that is positive of -0.2V (E PZC ). Such plots have been shown before 8 for DPV results in MPC solutions and are given in Figure 3 for the Figure 2A …”

“…The displacements between the current peaks in positive-and negative-going dc potential scans are thought to be a trivial result of uncompensated solution resistance; averaging of those peak potentials gives a "formal potential" that is characteristic of a certain change in the charge state (z) of the MPC core. The formal potentials for successive quantized double layer capacitance chargings, z/z -1, can be shown 8 to vary with charge state as where E PZC is the MPC potential of zero charge (z ) 0), which is taken to be about -0.2 V versus Ag/AgCl according to the pronounced minima in the DPV traces (Figure 2A,B) and in the C DL results from ac impedance ( Figure 2C,D, see arrows). Double layer capacitance is well known to exhibit a minimum near the potential of zero charge of an electrified interface.…”

Absolute Standard Redox Potential of Monolayer-Protected Gold Nanoclusters

“…This value is significantly larger than that of 3.0 previously used. 8 This value may indicate that electrolyte ions and bulk solvent ( s ) 10 for DCE) can penetrate into the protecting layer to some extent. 19 Considering 53 hexanethiolate ligands on a surface of a 0.8-nm metallic ball, there exist large voids between the ligands especially at the outer boundary of the coating monolayer.…”

“…[3][4][5][6] At ambient temperature, both freely diffusing and electrode-attached MPCs demonstrate the voltammetric responses featuring a series of evenly spaced current peaks. 4,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] This ensemble behavior is equivalent to a series of classical Coulomb staircase charging events or sequential electrochemical redox reactions, which occur as MPCs encompass an intermediate dimension between small molecules and bulk materials. Previously, the sequential electrontransferhasbeenobservedforfullerene(andderivatives) [22][23][24][25][26] and Pt-carbonyl nanoclusters [Pt n (CO) m ], [27][28][29] which led Weaver et al 30 to develop an electrostatic model to relate the electron transfer energetics of molecular capacitances in gas-and solution-phase systems.…”

“…Previously, the sequential electrontransferhasbeenobservedforfullerene(andderivatives) [22][23][24][25][26] and Pt-carbonyl nanoclusters [Pt n (CO) m ], [27][28][29] which led Weaver et al 30 to develop an electrostatic model to relate the electron transfer energetics of molecular capacitances in gas-and solution-phase systems. On the basis of this model, Chen et al 8 ascribed the occurrence of the successive electron transfer for MPCs to the extremely small (sub-attoFarad, aF) molecular capacitances of MPCs associated with a combination of a small metallic core and a dielectric protecting layer. The capacitance of an MPC with a core size smaller than 2 nm is less than 1 attofarad (aF), which is so small that a single electron addition to or removal from its core produces a substantial potential change.…”