Influence of the local dielectric constant on modeling the optical absorption of silver nanoparticles in silica gels

Silver nanoparticles embedded in silica gels were obtained in sol–gel glasses during heat treatment at 900 °C in air. The corresponding optical absorption was measured and fitted by means of the Gans theory and the model based on the Maxwell–Garnett theory that includes deformation and spatial distribution of particles [M.A. García, J. Llopis, S.E. Paje. Chem. Phys. Lett. 315 (1999) 313]. Assuming two kinds of particles this last theory (model M.A.G) predicted the resonance peak wavelength and the area under the experimental optical absorption very successfully. However, we found contradictions between the M.A.G and Gans theories. The discrepancy arises because the M.A.G model underestimated one resonance mode coming from prolate nanoparticles randomly oriented. However, considering the two modes and two kinds of particles, with high local dielectric constant of the surrounding medium, the Gans and M.A.G theories fitted the optical absorptions very well. The local dielectric constant changes the wavelength maximum compared with that obtained by the dielectric constant from the host matrix. Under these conditions, the theories are compatibles to each other and also with the experimental results. The high values of the dielectric constant are explained due to oxidation process on the surface of the silver nanoparticles. The results are compared and discussed with the coupled core-shell model, too.