Does Shape Anisotropy Control the Fractal Dimension in Diffusion-Limited Cluster-Cluster Aggregation?

Motivated by recent experiments of soot formation in premixed flames where a minority population of the stringy aggregates is found to have a fractal dimension as low as 1.2 instead of the classic diffusion-limited cluster-cluster aggregation (DLCA) value of 1.8, we address this same question in our simulation study: is there a distribution of fractal dimensions in a given ensemble of aggregates and does shape anisotropy of clusters control the fractal dimension? Our results, however, clearly show classic DLCA yields aggregates of a broad range of shapes all with D(f) approximate to 1.8 independent of their shape, but with a shape dependent pre-factor k(0), in the relation between radius of gyration R(g), mass N, monomer radius a, and fractal dimension D(f), N = k(0)(Rg/a)(Df). Thus the pre-factor k(0) gains in status as a descriptor of aggregate morphology so that aggregates should be described by the pair of parameters D(f) and k(0), i.e., (D(f), k(0)).