title: Finite frequency f-sum rule for assessment of number density of gold nanoparticles (AuNPs) and Kramers-Kronig relation for refractive index of colloidal gold.
abstract: Absorption spectra from colloids containing different concentrations of spherical gold nanoparticles in water were measured with a spectrophotometer. The absorption spectra were used to calculate the number density of nanoparticles (NPs) with the aid of an unconventional finite spectral band f-sum rule applied for gold colloid. Good correlation between the number density of dispersion electrons, obtained from the f-sum rule, and the number density of nanoparticles was found. The effective absolute refractive index of the gold colloid was obtained with the aid of a singly subtractive Kramers-Kronig relation, and in addition the refractive index change due to the nanoparticles was obtained with the aid of a conventional Kramers-Kronig relation. Such optical properties are valuable in studies of light interaction with nanoparticles.
authors: Department of Physics and Mathematics, University of Eastern Finland, Joensuu, Finland. ville.kontturi@uef.fi
authors: Ville
authors: V
authors: Kontturi
authors: Pertti
authors: P
authors: Silfsten
authors: Kai-Erik
authors: KE
authors: Peiponen