STRUCTURE AND CHARACTERISTIC LENGTH SCALES IN CLUSTER-CLUSTER AGGREGATION SIMULATION

The structure of a system of aggregating particles is studied by simul ation, in both two and three dimensions, using the on-lattice diffusio n-limited cluster aggregation model. We calculate static structure fac tors S(Q) and pair distribution functions for the aggregating system a s a whole. The peak in the scattering function, reported for many expe rimental aggregating colloidal systems and observed in the simulated s tructures, is shown to correspond to the characteristic outer radius o f a 'depletion zone' around clusters. The time-scaling properties of S (Q) are examined. A scaling of the structure factor analogous to the c ase of spinodal decomposition has been observed in experiments; we fin d reasonable structure factor scaling at intermediate densities and in termediate times but, due to the relatively small systems studied here , we must be cautious in either confirming or denying the presence of similar structure factor scaling for the simulation model throughout t he aggregation, especially at early time and at high density. We exami ne various 'characteristic' length scales in the model system, such as the average radius of gyration of clusters, the radius of the largest cluster, the length scale equivalent to the position of the structure factor peak, and so on, in a more general attempt to determine whethe r the system can be characterised by a single important length scale. From this there is reasonable indication that approximate scaling is d emonstrated over a limited region of time. This is consistent with res ults from light-scattering experiments. Lastly, an examination of the total perimeter length of the ensemble of clusters in the simulation i ndicates that we may divide the aggregation into three distinct time r egimes, corresponding to a pre-aggregation, a pre-fractal, and a fract al regime.