A simple model for evaluating the optical absorption spectrum from small Au-colloids in sol–gel films

A simple model based on the Maxwell–Garnett theory to calculate the effective dielectric function and so predict the optical absorption spectrum for metallic particles embedded into a dielectric matrix is developed. This model includes effects due to particle geometry, for diameters between ∼6 and 50 nm (for gold), and the spatial homogeneity of their distribution. Furthermore, it is shown how the shape of the metallic particles, through a parameter β, may significantly affect the absorption spectrum of the composite. The model is particularly suited to the study of metallic colloids in films or coatings obtained via sol–gel. A good agreement between theory and experiments for the case of gold nanoparticles in coatings of silica and alumina prepared by sol–gel is observed.