Cluster-cluster aggregation

Photo

The clusters shown in the figure are the result of a diffusion and aggregation process on a square lattice. In the beginning one has a random distribution of individual particles at a given density that perform a Brownian motion. When two particles touch they aggregate irreversibly. The such formed clusters continue diffusing and aggregating. This model is called cluster-cluster aggregation at finite density and describes for instance the formation of soot or of colloidal suspensions.

With Max Kolb we found that using the model of cluster-cluster aggregation one obtains a type of sol-gel transition with a critical behaviour different from the usual percolation as shown in the paper published in J.Phys.A, Vol.18, L435-L441 (1985). In a further paper published in J.Phys.A, Vol.19, L1027-L1031 (1986) we were able to present the scaling relations pertaining to the different regimes defined by different initial densities. Finally in the paper published in Physical Review Letters, Vol. 59, p.454-457 (1987) we showed that only at low densities the clusters are volume fractals while at higher densities one obtains clusters that are compact but have a fractal surface with a new dimension.

A short review about the scaling laws and relations to mean-field can be found in the proceedings of the Cargese School "On Growth and Forms" (Martinus Nijhoff Publishers, Dordrecht, 1986), pp. 222-226.