Scaling of the Structure Factor in Fractal Aggregation of Colloids: Computer Simulations

TL;DR

This study uses extensive simulations to analyze the evolution and scaling behavior of the structure factor in colloid aggregation, revealing differences between diffusion-limited and reaction-limited processes and identifying key exponents and structural features.

Contribution

It provides the first detailed numerical analysis of the structure factor scaling in colloid aggregation, distinguishing between diffusion-limited and reaction-limited cases and identifying associated exponents.

Findings

Scaling of $S(q)$ observed in diffusion-limited aggregation.

Peak in $S(q)$ linked to nearest-neighbor cluster correlations.

Reaction-limited aggregation shows delayed peak development without clear scaling.

Abstract

In the volume fraction range (0.005,0.08), we have obtained the temporal evolution of the structure factor $S(q)$, in extensive numerical simulations of both diffusion-limited and reaction-limited colloid aggregation in three dimensions. We report the observation of scaling of this structure function in the diffusion-limited case, analogous to a spinodal decomposition type of scaling. By comparing $S(q)$ with the pair correlation function between particles, we were able to identify the peak in the structure factor as arising from the correlations between particles belonging to nearest-neighbor clusters. The exponents $a\prime$ and $a\prime \prime$ that relate the position and the height of the maximum in $S(q)$ vs. time, respectively, were also obtained and shown to differ somewhat from the spinodal decomposition exponents. We also found a terminal shape for $S(q)$ that corresponds to a close packing of the clusters after gelation. Moreover, this picture was shown to be valid in a concentration range larger than the one suggested in recent experiments. Although the $S(q)$ for reaction-limited colloid aggregation does not show a pronounced peak for the earlier times, eventually the peak stretches and becomes higher than in the diffusion-limited case. The $S(q)$ curves, however, do not present the scaling shown for diffusion-limited aggregation.