Flory-type approximation for the fractal dimension of cluster-cluster aggregates

We consider the structure and fractal dimension of aggregates formed by cluster-cluster diffusional encounters. Both the fractal dimensions and symmetry properties of these aggregates are found to differ significantly from those found in the case of a single aggregating cluster. We find for the fractal dimension $D\left(d\right)=\frac{d(4d+3)\mathrm{}}{\mathrm{}(9d-2)\mathrm{}}$ for $d<\mathrm{}{d}_c=8\mathrm{}$ and $D\left(d\right)=\frac{d}{2}$ for $d>\mathrm{}{d}_c$.