Diffusion-limited cluster aggregation

Kolb M. Reversible diffusion-limited cluster aggregation. J Phys A Math Gen 1986 19 L263-L268. 

Figure 3.9 Box-counting analysis of a projection of a computer-generated diffusion-limited cluster aggregate of 10 000 particles with mass fractal dimension of 1.88. The images have box sizes L of (top left to bottom right) 1, 2,4,8,16, 32 and 64 pixels and require 205 245,59519, 17 062, 4895,1436, 462 and 135 squares respectively to cover the image.

Computer simulations have shown that the value of fractal dimension largely depends on whether the aggregation process is controlled by the diffusion rate of the clusters and single particles or by their chemical reactivity at the time of collision, the latter being mainly controlled by the DLVO forces. This observation, in agreement with experimental work on aerosols and colloids, has led to a new classification of aggregation processes the reaction-limited and diffusion-limited cluster aggregation (RLCA and DLCA respectively) processes. 

Diffusion Limited Cluster Aggregation (DLCA) Process whereby clusters of particles undergoing a random walk due to Brownian motion, aggregate together. This theory, proposed by Witten and Sander in 1981... 

DLCA Diffusion-limited cluster aggregation, similar to DLA, but incorporating aggregation... 

The collision kernels Kjj depend on the particle trajectories and the particle interaction. For purely diffusing particles and clusters without any particle interaction (i.e. diffusion-limited cluster aggregation—DLCA), Smoluchowski (1916) derived ... 

Herein, ds is the space dimension, i.e. 2, and df is the fractal dimension (Hausdorff dimension) of the 2D aggregated particle cluster. Typical values for Hausdorff dimensions are e.g. 1.44 for diffusion limited cluster aggregation (DLCA) and 1.55 for reaction limited cluster aggregation (RLCA) [22, 31], Assuming isolated 2D aggregates which were formed by interfacial particle-particle aggregation, an exponent of about —6 is estimated. Close to the two- dimensional sol-gel transition, the system should behave like a percolated network and the corresponding exponent is determined to —9.5 [31],... 

In this section, we will briefly discuss aspherical colloidal particles. Experimental and computational studies of soft materials find significant effects of the particle geometry on the properties of amorphous structures. These include the fractal dimension of colloidal aggregates in diffusion-limited cluster aggregation (Mohraz et al. 2004), percolation threshold of anisometric particles (Garboczi et al. 1995, Yi and Sastry 2004), and maximum packing density of particulate materials (Donev et al. 2004, Mohraz et al. 2004). 

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