Computational Materials Science Center: PUBLICATIONS

On a three-dimensional lattice and at different concentrations we perform extensive numerical simulations of diffusion-limited colloidal aggregation (DLCA). In a previous work, we showed that the fractal dimension d_f of the DLCA aggregates in the flocculation limit presents a square root type of dependence with the initial colloidal concentration. The d_f was obtained from the slope of a standard log-log plot of the number of particles versus size of the formed aggregates. In this work we confirm the concentration dependency using the particle-particle correlation function g(r) and the structure function S(q) of individual aggregates. We demonstrate that the g(r) = A r^{d_f-3} e^{-(r/Rg)^a}, where A, a and R_{g} are parameters characteristic of the aggregates, and a > 1. This stretched exponential law gives an excellent fit to the cutoff of the g(r). The structure function reveals the d_f from the slope of a log-log plot of S(q) vs q for high q values. We also analyze g(r) and S(q), at different times during the reaction, for the whole aggregating system composed of many clusters of different sizes. We observe that the d_f calculated from the g(r) agrees well with that obtained from individual clusters. However, caution should be observed to extract a d_f from the corresponding S(q). Our results indicate that for finite concentrations a d_f systematically larger than the true value is obtained from such analysis.

PACS 64.60.Qb, 02.70.-c, 05.40.+j, 81.10.Dn