Structure Factors for Fractal Aggregates Built Off-Lattice with Tunable Fractal Dimension

Abstract
Structure factors for fractal aggregates with a range of fractal dimensions have been studied. To this end, a hierarchical computer algorithm is presented which is able to build, in the three-dimensional space, disordered off-lattice fractal aggregates made of identical tangent spheres, whose fractal dimension can be varied from 1 up to an upper limit of about 2.55. The correlation functions and their Fourier transforms S(q) (structure factors) are calculated for various fractal dimensions. It is shown that the S(q) curve exhibits a characteristic sigmoidal shape for D>2 and that it is necessary to include a cluster size power-law polydispersity to recover a power-law behavior of S(q) in a large range of q values, as observed in experiments.