Evaluation of the fractal properties of cluster-cluster aggregates

While the fractal dimension of cluster-cluster aggregates, D-f, appears to be a well-established property, the Fractal prefactor, k(g) (also known as structural coefficient), continues to exhibit a large range of possible values, In the present paper, an attempt is made to clarify this issue which leads to conclusive results concerning the value to adopt for the fractal prefactor of simulated aggregates. Starting from a large population of "free" numerically simulated aggregates (i.e., where no restrictions to aggregate formation were imposed) the fractal properties obtained were estimated both using morphological concepts as well as light scattering theories, Furthermore, studies for aggregates having predefined morphological k(g) values (namely, k(g) >2 and ca. 1) were also performed in order to check the viability of these values. The results obtained for the three different populations of aggregates considered were used to infer, through a best-fit analysis, the fractal properties. Our best estimates are k(g) approximate to 1.27 and D-f approximate to 1.82, which are approximately independent of aggregate size and composition. These results are in very good agreement with numerical predictions reported by previous authors. However, experimental results systematically indicate k(g) > 2 This motivated the present authors to identify possible reasons for these large discrepancies. Present calculations indicate that partial sintering in conjunction with the polydispersity of aggregates (resulting in a cut-off function coefficient, k(p), > 1) contributes to a systematic increase in k(g), possibly justifying the differences between numerical and experimental results.