Size Dependence of the Surface Plasmon Resonance Damping in Metal Nanospheres

The impact of quantum confinement on the width of the surface plasmon resonance of a metal nanoparticle is theoretically investigated in a model system formed by a silver nanosphere in different environments. Calculations are performed using the time-dependent local density approximation (TDLDA) for nanoparticle diameters up to about 11 nm, permitting precise quantification of the surface plasmon broadening due to size reduction. As expected, this is found to be inversely proportional to the particle diameter, but with an amplitude strongly depending on the environment (increasing by a factor of 4 when changing from vacuum to alumina). This is ascribed to the fact that damping is governed by the electronic surface spill-out (inherent in any quantum model) and thus strongly depends on the surface profile of the confining potential, that is, on the particle surface conditions.