Acoustic dispersion in silica aerogels observed by brillouin scattering : Evidence for phonon-fracton crossover

Small angle neutron scattering and Brillouin scattering experiments have been performed in porous silica aerogels with densities ranging from 0.1 to 0.4 gcm−3. The results demonstrate the fractal structure of these materials. The fractal dimension is D = 2.40 ± 0.02. The high dispersion observed was interpreted in terms of phonon to fracton crossover. From the scaling exponents, we deduced the spectral dimension d = 1.25 ± 0.12. The numerical value of these exponents raises the interesting question of whichis the proper elasticity theory to be applied to these weakly connected structures.