The Prefactor of Fractal Aggregates

The prefactor k0 of the fractal aggregate scaling relationship N = k0(Rg/a)Df is determined for both Diffusion Limited and Diffusion Limited Cluster Aggregation processes in spatial dimensions of 2, 3, 4, and 5. For the physically relevant case of DLCA aggregates in three dimensions we find k0 = 1.19 ± 0.1 when Df = 1.82 ± 0.04. Comparison of all aggregation types shows that the prefactor k0 displays uniform trends with the fractal dimension Df. Attempts to explain these trends are made based on either a common small N limit for all clusters or the packing of spheres in space.