Raman and Brillouin scattering of spherical nanoparticles and their clusters

Abstract

The inelastic light scattering of the acoustic vibration of spherical nanoparticles is reviewed. For particles much smaller than the wavelength of the exciting light (λ), with a diameter (d) smaller than about 20 nm, the dominant physical mechanism, called Raman, is the polarizability fluctuation due to dipole dipole or bond polarizability induced effects. Only spheroidal modes with l = 0 and l = 2 are Raman active. For particles of size comparable with λ (d larger than about 100 nm) a different physical mechanism is dominant, the mass displacement and relative polarization associated with the vibration, as for the usual Brillouin scattering of liquid and solids. As the size increases, higher and higher l modes with higher and higher n, the index that labels the radial wavevector, become important and many dozen of peaks appear for d > 500 nm. A simple model allows to reproduce the main features of the observed spectra. A more precise agreement is obtained by a refinement that considers the interaction among the particles in a phononic crystals. The interaction produces broadening and shift of the lines and accounts for the presence of a very low frequency broad band, attributed to the density of states of the modes of the sound propagation in the crystal. The analysis of the spectra allows to obtain information on the dynamics of the single free sphere and on the strength of the interaction. By measuring the temperature-dependence of the Brillouin spectra in clusters of polystyrene nanoparticles during the sintering process, it is possible to identify the glass- transition temperature and calculate the elastic modulus of individual nanoparticles as a function of particle size and chemistry. Surface mobility is evidenced by a size dependence of the interaction among the particles and of the glass transition temperature.