Surface geometric irregularity of particulate materials: The fractal approach

Surface geometric irregularities of a wide variety of particulate materials are determined by applying the fractal theory of surface science (P. Pfeifer and D. Avnir, J. Chem. Phys. 79, 3558 1983). Reanalysis and reinterpretation of previously published experimental data, revealed the following surface-fractal dimensions, all falling in the expected range 2.0 to 3.0, for the following materials: periclase-1.95; a number of quartzes-2.02 to 2.21; iron oxide-2.59; porous silica gel-3.0; coal dusts-2.33 and 2.53; six carbonate rocks-2.16 to 2.97; seven types of soils-2.19 to 2.99; a number of crushed rocks from nuclear test site-2.7 to 3.0. We describe in detail the method by which these fractal dimensions were determined, i.e., studying the dependence of monolayer values (n) on particle radii (R): n ∝ R^D-3. Interestingly, several authors had presented their experimental results as log n vs log R, yet no explanation was offered to the straight lines obtained; the notion of self-similarity (fractal surfaces) fits nicely in all these studies. The various features of our approach are described in connection with the analyzed examples, e.g., we exemplify estimation of particle diameters by this approach. Attention is given to the question of range of self-similarity. It is suggested that materials with fractal surfaces were formed in general by an iterative mechanism. Based on the massive list of fractal surfaces found (D. Avnir, D. Farin, and P. Pfeifer, Nature (London) 308, 261, 1984), this is probably the operative mechanism for the majority of natural and synthetic materials.