Short- and long-range topological correlations in two-dimensional aggregation of dense colloidal suspensions

We have studied the average properties and the topological correlations of computer-simulated two-dimensional (2D) aggregating systems at different initial surface packing fractions. For this purpose, the centers of mass of the growing clusters have been used to build the Voronoi diagram, where each cell represents a single cluster. The number of sides (n) and the area (A) of the cells are related to the size of the clusters and the number of nearest neighbors, respectively. We have focused our paper in the study of the topological quantities derived from number of sides, n , and we leave for a future work the study of the dependence of these magnitudes on the area of the cells, A . In this work, we go beyond the adjacent cluster correlations and explore the organization of the whole system of clusters by dividing the space in concentric layers around each cluster: the shell structure. This method allows us to analyze the time behavior of the long-range intercluster correlations induced by the aggregation process. We observed that kinetic and topological properties are intimately connected. Particularly, we found a continuous ordering of the shell structure from the earlier stages of the aggregation process, where clusters positions approach a hexagonal distribution in the plane. For long aggregation times, when the dynamic scaling regime is achieved, the short- and long-range topological properties reached a final stationary state. This ordering is stronger for high particle densities. Comparison between simulation and theoretical data points out the fact that 2D colloidal aggregation in the absence of interactions (diffusion-limited cluster aggregation regimen) is only able to produce short-range cluster-cluster correlations. Moreover, we showed that the correlation between adjacent clusters verifies the Aboav-Weaire law, while all the topological properties for nonadjacent clusters are mainly determined by only two parameters: the second central moment of number-of-sides distribution mu(2) = sumP (n) (n-6)(2) and the screening factor a (defined through the Aboav-Weaire equation). We also found that the values of mu(2) and a calculated for two-dimensional aggregating system are related through a single universal common form a proportional to mu2(-0.89), which is independent of the particle concentration.