SCATTERING STRUCTURE FACTOR FROM FAT FRACTALS

Recent results have revealed that "concave" small-angle scattering (SAS) data, (i.e. a succession of power-law decays with decreasing values of the scattering exponents), can be successfully modeled in the framework of fat fractals. In this paper, the SAS structure factor for deterministic fat fractals is studied in momentum space. We show that fat fractals are exact self-similar in the range of iterations having the same values of the scaling factor, and therefore in each of these ranges all the properties of regular fractals can be inferred to fat fractals. In order to illustrate the above findings we introduce deterministic "fattened" versions of two well-known 3D structural models: Cantor and Vicsek regular deterministic fractals. We calculate the mono- and polydisperse structure factor and study its scattering properties.