Diffusion-limited aggregation in three dimensions: Results from a new cluster-cluster aggregation model

Abstract

Diffusion-limited aggregation has been investigated using three-dimensional lattice models in which both particles and clusters can move and stick together. The final state consists of a single cluster or network of occupied lattice sites with a fractal dimensionality of about 1.75. Two versions of the model have been investigated. In Model 1, the cluster diffusion coefficient is independent of cluster size, and in Model 2, only the smallest clusters are allowed to “diffuse.” Both models give final states which are identical within the accuracy of the simulations. However, the cluster size dispersion at intermediate stages is distinctly different for Model 1 and Model 2. The results taken together with more extensive simulations in two dimensions indicate that a fractal dimensionality of ≈ 1.75 will be obtained for all versions of the model in which the diffusion coefficient of small clusters is equal to or greater than the diffusion coefficient for larger clusters. A number of the geometric properties which characterize final state and intermediate clusters are analyzed. Some of these properties should be amenable to measurement in real systems. The results of the simulations are in good agreement with measurements of the fractal dimensionality of metal particle aggregates.