Radius dependent shift in surface plasmon frequency in large metallic nanospheres: Theory and experiment

Theoretical description of oscillations of electron liquid in large metallic nanospheres (with radius of few tens of nanometer) is formulated within random-phase-approximation semiclassical scheme in jellium model with retardation included via Lorentz friction. Spectrum of plasmons is determined including both surface and volume type excitations. It is demonstrated that only surface plasmons of dipole type can be excited by homogeneous dynamical electric field. The Lorentz friction due to irradiation of electromagnetic wave by plasmon oscillations is analyzed with respect to the sphere dimension. The resulting shift in resonance frequency turns out to be strongly sensitive to the sphere radius. The form of electromagnetic (e-m) response of the system of metallic nanospheres embedded in the dielectric medium is found. The theoretical predictions are verified by a measurement of extinction of light due to plasmon excitations in nanosphere colloidal water solutions, for Au and Ag metallic components with radius from 10 to 75 nm. Theoretical predictions and experiments clearly agree in the positions of surface plasmon resonances and in an emergence of the first volume plasmon resonance in the e-m response of the system for limiting big nanosphere radii, when dipole approximation is not exact.