surface plasmon resonance in small gold nanoparticles: introducing a size-dependent plasma frequency for nanoparticles in quantum regime

Study of surface plasmon resonance for small nanoparticles (r < 10 nm) has many theoretical complexities due to lack of a simple quantitative model for describing plasmonics in such quantum regime. here, a modification of the drude model has been proposed to account for quantum constrains of small nanoparticles. this modification leads to introducing a size-dependent plasma frequency with the functionality of 1/r added to the standard local dielectric function. the modified dielectric model has been used to calculate the plasmonic spectrums of gold nanoparticles in a wide range of sizes from 3.6 to 48.3 nm. by comparing the calculated results with various experimental data, the modified dielectric function in comparison with other models can better describe the plasmonic peak of gold nanoparticles especially for the sizes smaller than 10.0 nm.