Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant

Gold nanorods with different aspect ratios are prepared in micelles by the electrochemical method and their absorption spectra are modeled by theory. Experimentally, a linear relationship is found between the absorption maximum of the longitudinal plasmon resonance and the mean aspect ratio as determined from TEM. It is shown here that such a linear dependence is also predicted theoretically. However, calculations also show that the absorption maximum of the longitudinal plasmon resonance depends on the medium dielectric constant in a linear fashion for a fixed aspect ratio. Attempts to fit the calculations to the experimental values indicate that the medium dielectric constant has to vary with the aspect ratio in a nonlinear way. Chemically, this suggests that the structure of the micelle capping the gold nanorods is size dependent. Furthermore, comparison with the results obtained for rods of different aspect ratios made by systematic thermal decomposition of the long rods further suggests that the medium dielectric constant is also temperature dependent. This is attributed to thermal annealing of the structure of the micelles around the nanorods.