Inter-cluster scaling in two-dimensional colloidal aggregation

Cluster-cluster aggregation has been studied experimentally in two-dimensional colloidal systems of moderately high area fraction. In the diffusion limited regime the system spontaneously exhibits ordering beyond the scale of the fractal aggregates, which persists into the gelled state. This ordering arises from an effective inter-cluster repulsion due to the mutually exclusive depletion zones surrounding each cluster. Various metrical and topological properties of the system indicate that this long-range order is stationary, apart from the inherent change of scale as the clusters grow. Topological correlations show that the inter-cluster self-organization is compatible with maximum entropy: the non-equilibrium system behaves as if it were in statistical equilibrium, and no physical forces are involved in the long-range order. For the reaction-limited case no such inter-cluster ordering is evident at any stage, the system is nonstationary, and the aggregation is governed by specific physical forces.