Monte Carlo simulation of diffusion controlled colloid growth rates in two and three dimensions

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Abstract
The kinetics of diffusion limited aggregation have been explored in two and three dimensions using Monte Carlo simulations. If the initial particle concentration is very low, our model is equivalent to the Witten–Sander model of diffusion limited aggregation, and the resulting cluster has a Hausdorff dimensionality (D) substantially lower than the ordinary Euclidean dimensionality (d) (D≂5d/6). Under these conditions, the radius of gyration (R g ) of the clusters grows according to the rate law R g (t)∼t [1/(2+D−d)] obtained previously. If the initial particle concentration is large, the radius of gyration increases linearly with time, and the clusters are uniform (D=d) on all but very short length scales. In general, the clusters grow like Witten–Sander clusters during the early stages of growth. As the clusters grow larger and larger, they become less and less dense until their density approaches that of the surrounding medium. At this stage of growth, there is a crossover from a growth exponent of 1/(2+D−d) for R g to linear growth, and the dependence of the radius of gyration on cluster size crosses over from R g ∼N β (β≂6/5d) to R g ∼N β′ (β′=1/d). The structure of the cluster is Witten–Sander‐like on short length scales but uniform on long length scales. At no stage does the cluster growth follow the classical t 1 / 2 behavior. In two dimensional space, the rate of increase of m a s s is given by N(t)∼t for diffusion limited aggregation in the early stages of growth.