Determination of plasma frequency, damping constant, and size distribution from the complex dielectric function of noble metal nanoparticles

Abstract

This paper develops a novel method for simultaneously determining the plasma frequency ωP and the damping constant γfree in the bulk damped oscillator Drude model, based on experimentally measured real and imaginary parts of the metal refractive index in the IR wavelength range, lifting the usual approximation that restricts frequency values to the UV-deep UV region. Our method was applied to gold, silver, and copper, improving the relative uncertainties in the final values for ωp (0.5%–1.6%) and for γfree (3%–8%), which are smaller than those reported in the literature. These small uncertainties in ωp and γfree determination yield a much better fit of the experimental complex dielectric function. For the case of nanoparticles (Nps), a series expansion of the Drude expression (which includes ωp and γfree determined using our method) enables size-dependent dielectric function to be written as the sum of three terms: the experimental bulk dielectric function plus two size corrective terms, one for free electron, and the other for bound-electron contributions. Finally, size distribution of nanometric and subnanometric gold Nps in colloidal suspension was determined through fitting its experimental optical extinction spectrum using Mie theory based on the previously determined dielectric function. Results are compared with size histogram obtained from Transmission Electron Microscopy (TEM).