Aerogels fractal range

Natural fractals such as clouds, polymers, aerogels, porous media, dendrites, colloidal aggregates, cracks, fractured surfaces of solids, etc., possess only statistical self-similarity, which, furthermore, takes place only in a restricted range of sizes in space [1,4,16]. It has heen shown experimentally for solid polymers [22] that this range is from several angstroms to several tens of angstroms. 

Figure 7.14. The small-angle diffraction pattern of a silica aerogel (left) that consists of clusters of size R built up of dense smooth particles of size r. Within a size range bounded by r and R the clusters are fractal. At right the scattering pattern of Vycor glass is shown. From D. W. Schaefer, A. J. Hurd, and A. M. Glines. In Random Fluctuations and Pattern Growth Experiments and Models p. 62. With kind permission from Kluwer Academic Publishers.

Hasmy A, Foret M, Pelous J, JuUien R (1993) SmaU-angle neutron-scattering investigation of short-range correlations in fractal aerogels - simulations and experiments. Phys Rev B 48 9345-9353. 

Inelastic light scattering has been also extensively used to study the vibrational properties of fractal systems silica aerogels, with their porosity extending on a wide range of sizes, are very nice examples of fractal systems. The peculiar vibrational dynamics of these systems, with spatially localized vibrational modes, is at the origin of the exttemely low measured thermal conductivity. 

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