Electron self-exchange between Au140+/0 nanoparticles is faster than that between Au38+/0 in solid-state, mixed-valent films

The well-defined one-electron steps in the voltammetry of solutions of the nanoparticles Au-38(SC2Ph)(24) and Au-140(SC6)(53) (SC2Ph = phenylethanethiolate; SC6 = hexanethiolate) enable preparation of solutions containing, for example, Au-38(SC2Ph)(24) and Au-38(SC2Ph)(24)(+)(ClO4)(-) nanoparticles in known relative proportions. From these solutions can be cast dry, mixed-valent films demonstrably containing the same proportions. Electronic conduction in such mixed-valent films is shown to occur by a bimolecular electron self-exchange reaction at a rate proportional to the concentration product, [Au-38][Au-38(+)]. The observed Au-38(+/0) rate constant, similar to 2 x 106 M-1 s(-1), is much smaller than that previously observed for Au-140(+/0) films (ca. 4 x 10(9) M-1 s(-1); Wuelfing, W. P.; et al. J. Am. Chem. Soc. 2000, 122, 11465). To our knowledge, this is the first example of a significant size effect in metal nanoparticle electron-transfer dynamics. Thermal activation parameters for the electron-hopping conductivities of the two nanoparticles reveal that the rate difference is mainly caused by energy barriers (E-A) for Au-38(+/0) electron transfers that are larger by similar to 3-fold than those for Au-140(+/0) electron transfers (ca. 20 vs 7 kJ/mol). Differences in pre-exponential terms in the activation equations for the two nanoparticles are a smaller contributor to the rate constant difference and can be partly ascribed to differences in tunneling distances.