Monolayer-protected metallic nanoparticles:: Limitations of the concentric sphere capacitor model

Monolayer-protected clusters (MPC) having metallic core diameters of the order of 1 nm behave as multivalent redox molecules with small capacitances C-MPC approximate to 1 aF. Theoretical estimations of this capacitance are usually based on the concentric sphere capacitor model. We have analyzed critically the predictions of this model over a broad range of experimental parameters: the metallic core radius r(0), the monolayer thickness d, the charge number z of the metallic core, the dielectric constant of the monolayer epsilon(r,m), the base electrolyte concentration c(s), and the dielectric constant of the solvent epsilon(r,s). To this end, we have solved the nonlinear Poisson-Boltzmann equation taking into account ion penetration. It is shown that the concentric sphere capacitance C-0 gives the correct order of magnitude as well as some qualitative features of the total MPC capacitance C-MPC, although significant deviations are obtained for realistic values of the above parameters, especially when ion and solvent penetration are important. The results obtained are compared with recent theoretical and experimental work by Murray et al. (Anal. Chem. 2005, 77, 2662), Girault et al. (J. Phys. Chem. B 2006, 110, 21460), and Quinn et al. (J. Am. Chem. Soc. 2003, 125, 6644) and provide some extensions of these previous studies.