STRUCTURE AND ARRANGEMENT OF CLUSTERS IN CLUSTER AGGREGATION

We study cluster structure and the arrangement of clusters in the diff usion-limited cluster-cluster aggregation (DLCA) simulation model of c olloidal aggregation analyzing our data using techniques that allow di rect comparison with scattering experiments. As is well known, individ ual 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 DL CA clusters, In two-dimensional (2D) simulations the DLCA average form factor deviates from the Fisher-Burford form, though power-law fits t o the data do give fractal dimensions: in agreement nt with the ''acce pted'' fractal dimension of 2D DLCA clusters previously obtained from the fractal mass-radius relation, The average form factor in 3D simula tions agrees better with the Fisher-Burford form though there remain i ndications of some deviation. Near gelation, the average form factor a t long length scales begins to decrease, corresponding to the interpen etration 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'' interactio n between the clusters. As the aggregation proceeds, while larger clus ters are distributed more or less evenly. there is a marked inhomogene ity in the distribution of the smallest clusters. especially pronounce d at high particle concentration, The polydispersity of the clusters t hus 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 i n part to the size-position correlation thus induced by the cluster po lydispersity. We also examine the ''mass-weighted'' cluster structure factor as considered previously by other authors [F, Sciortino, A, Bel loni, and P. Tartaglia, Phys, Rev, E 52, 4068 (1995)].