Structure and arrangement of clusters in cluster aggregation

We study cluster structure and the arrangement of clusters in the diffusion-limited cluster-cluster aggregation (DLCA) simulation model of colloidal aggregation analyzing our data using techniques that allow direct comparison with scattering experiments. As is well known, individual clusters in DLCA have a fractal structure, we compare DLCA results with colloidal aggregation experiments by fitting: the Fisher-Burford [Phys. Rev. 156, 583 (1967)] functional form for the scattering by a fractal object to the average scattering function or form factor of DLCA clusters, In two-dimensional (2D) simulations the DLCA average form factor deviates from the Fisher-Burford form, though power-law fits to the data do give fractal dimensions: in agreement nt with the ''accepted'' fractal dimension of 2D DLCA clusters previously obtained from the fractal mass-radius relation, The average form factor in 3D simulations agrees better with the Fisher-Burford form though there remain indications of some deviation. Near gelation, the average form factor at long length scales begins to decrease, corresponding to the interpenetration and assembly of the clusters into the system-spanning gel. We also study the arrangement of clusters or the intercluster structure by; computing the cluster center-of-mass structure factor, The cluster structure factor demonstrates a strong ''excluded-volume'' interaction between the clusters. As the aggregation proceeds, while larger clusters are distributed more or less evenly. there is a marked inhomogeneity in the distribution of the smallest clusters. especially pronounced at high particle concentration, The polydispersity of the clusters thus has important effects on the cluster arrangement. We find that the total scattering function cannot be factorized into the average form factor and the cluster center-of-mass structure factor, due at least in part to the size-position correlation thus induced by the cluster polydispersity. We also examine the ''mass-weighted'' cluster structure factor as considered previously by other authors [F, Sciortino, A, Belloni, and P. Tartaglia, Phys, Rev, E 52, 4068 (1995)].