Scaling phonon-fracton dispersion laws in fractal aerogels

Abstract The fractal character of silica aerogels has been undoubtedly established by small-angle neutron scattering experiments (SANS). These materials are particularly well suited to the study of the vibrational dynamics of fractal media. Brillouin scattering spectra have given strong evidence for a cross-over from long-wavelength phonons to ‘fractons’ in the gigahertz range. The main quantities deduced from these experimental results, namely the non-dispersed velocity of sound and the phonon-fracton cross-over frequency, are found to scale with the density of the materials. From the scaling exponents, values of the fractal and spectral dimensions are derived. The fractal dimension is very close to that deduced from SANS data. The results of a preliminary study of vibrational modes in the terahertz range by Raman scattering are also presented and briefly discussed.