Structure and characteristic length scales in cluster—cluster aggregation simulation

The structure of a system of aggregating particle is studied by simulation, in both two and three dimensions, using the on-lattice diffusion-limited cluster aggregation model. We calculate static structure factors S(Q) and pair distribution functions for the aggregating system as a whole. The peak in the scattering function, reported for many experimental aggregating colloidal systems and observed in the simulated structures, is shown to correspond to the characteristic outer radius of a ‘depletion zone’ around clusters. The time-scaling properties of S(Q) are examined. A scaling of the structure factor analogous to the case of spinodal decomposition has been observed in experiments; we find reasonable structure factor scaling at intermediate densities and intermediate 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 the aggregation, especially at early time and at high density. We examine 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 whether the system can be characterised by a single important length scale. From this there is reasonable indication that approximate scaling is demonstrated over a limited region of time. This is consistent with results from light-scattering experiments. Lastly, an examination of the total perimeter length of the ensemble of clusters in the simulation indicates that we may divide the aggregation into three distinct time regimes, corresponding to a pre-aggregation, a pre-fractal, and a fractal regime.