Structure of a three-dimensional nano-powder subjected to repeated fragmentation and sedimentation

Abstract

We revisit the problem of the structure of a nano-powder subjected to repeated fragmentation and sedimentation, and extend the analysis to the more relevant three-dimensional (3D) case. One important question not addressed previously is how the fractal dimension and dust exponent depend on space dimension. We find that the qualitative behavior of the nano-powder in three dimensions is similar to that in two dimensions. But the fractal dimension changes from 1.6 ± 0.1 in two dimensions to 2.1 ± 0.1 in three dimensions. The scaling relation between the fractal dimension and the dust exponent characterizing the fragment size distribution is the same as in two dimensions. The universality of these exponents is addressed by comparing the results with a much simpler lattice model. Although the different settling kinetics of the fragments leads to different anisotropies, the fractal properties are not affected.