Effective medium approximation for the dielectric environment of coated gold nanorods

Abstract

Coated gold nanorods (GNRs) are attractive as chemical sensors because their plasmon resonance energy is strongly dependent on the value of the dielectric constant in the local environment. For thin coatings (<≈20 nm), the plasmon resonance is sensitive to both the coating and the surrounding medium, while for thicker coatings the plasmons are effectively screened from their surroundings. We use finite element modeling to develop a semi-empirical effective medium approximation for the dielectric constant surrounding GNRs 30-50 nm in length with coating thicknesses of 0.5-200 nm. We demonstrate that this approximation can be used to correctly interpret shifts in plasmon resonance energy when the dielectric constant of the surroundings changes with temperature. We compare plasmon resonances of gold nanorods embedded in an epoxy matrix when coated with polyethylene glycol or silica of various thicknesses during thermal cycling. The derived expression for the effective medium dielectric of a coated rod will help device engineers optimize the sensitivity and robustness of coated GNR plasmonic sensors.