The Effect of Overlap between Monomers on the Determination of Fractal Cluster Morphology

Abstract Diffusion limited cluster aggregate (DLCA) morphology is studied as a function of monomeric particle overlap for finite sized clusters. The morphology is parameterized by both the fractal dimension D and the prefactor k 0 . For clusters created on a three-dimensional cubic lattice we find D = 1.80 ± 0.03 and k 0 = 1.30 ± 0.07 when the spherical monomers are in point contact. Both these values increase as overlap increases. Also presented is an analysis of the two-dimensional projection of these clusters in order to facilitate electron micrograph images of real clusters. Quantitative relations between actual three-dimensional cluster parameters such as cluster radius of gyration, fractal dimension and number of monomers per aggregate, and measurable two-dimensional quantities such as longest lengths and projected area are given as a function of monomer overlap. Relationships between lengths can be explained only by use of the proper density correlation function and accounting for cluster anisotropy. Finally, we make an unsuccessful attempt to find the source of recent experimental discrepancies in the prefactor k 0 in terms of a possible unknown degree of overlap.