Scaling description of the structure factor of fractal soot composites

This paper studies the static structure factor of a system of fractal aggregates at various degrees of densification. The system we use for this study is carbonaceous soot, which is composed of diffusion limited cluster aggregates with a fractal dimension of 1.8. The range of density is great, from the aerosol to a system of lightly touching clusters and then to ground and compressed samples. The data involve a combination of light scattering and small-angle x-ray scattering over a q range of $3\times {10}^{-3}<~q<~6{\mathrm{nm}}^{\mathrm{-}1}.$ We are able to explain all the features of the data with scaling arguments based on comparisons of the scattering length scale $q^{-1},$ where q is the magnitude of the scattering wave vector, and the various length scales of the system that are density dependent.