Does Shape Anisotropy Control the Fractal Dimension in Diffusion-Limited Cluster-Cluster Aggregation?

William Heinson (1), Amit Chakrabarti (1), CHRISTOPHER SORENSEN (1)

(1) Kansas State University

     Abstract Number: 414
     Last modified: May 12, 2010

Abstract
In the absence of coalescence, clusters formed by irreversible aggregation are self-similar fractals characterized by a mass fractal dimension, Df. We have performed off-lattice Monte Carlo simulations to investigate how cluster
anisotropy affects fractal dimension. Cluster shape anisotropy was measured using eigenvalues of the inertia tensor similar to a method used earlier by our group (Fry et al., 2004). The fractal dimension was measured using both the ensemble and structure factor methods. Both methods show that even as anisotropy of the clusters increases, fractal dimension remains the same with Df = 1.8 for all shapes. On the other hand, the prefactor k0 of
the fractal scaling relation N = k0(Rg/)$^(Df) shows to be a uniform function of the anisotropy. A general and somewhat surprising conclusion of this work is that shape should not be used as an indicator of fractal dimension. A specific conclusion is that classic DLCA yields aggregates of a broad range of shapes all with Df = 1.8 independent of their shape, but with a shape dependent prefactor k0.

Fry, D., Mohammed, A., Chakrabarti, A. and Sorensen, C.M. (2004). Langmuir, 20, 7871-7879.