Diffusion-limited aggregation computer simulation

The basic theoretical approach for the analysis of diffusion controlled reactions is due to Smoluchowski [9] who developed it for the analysis of diffusion limited aggregation of colloidal particles. We discuss the generalization of this approach to the case of rodlike molecules here. The computational method best suited for the simulation of the polymerization of rodlike molecules is Brownian dynamics. We discuss in this review both multiparticle Brownian dynamics and pairwise Brownian dynamics the latter is a hybrid method combining Smoluchowski s [9] theory and Brownian... 

The patterns produced by the diffusion-limited aggregation (DLA) processes are characterized by the open random and tree-type structures and can be well described as fractals. Computer simulations of fractal growth have been shown to produce structures... 

Figure la. Fractal aggregate, constructed by computer simulated diffusion limited aggregation. Fractal dimension D = 1.44... 

Self-similar behavior has also been observed in computer simulation of aggregation processes. Thus aggregates of colloidal particles in diffusion-limited aggregation processes have been found to display self-similar behavior (Meakin, 1983). 

Fig. 6. Domain shape obtained by computer simulation with the diffusion limited aggregation model (a), in comparison with experimental observation following a pressure jump (b).

Transport control of flocculation is realized in an especially direct way in the process known as diffusion-limited cluster-cluster aggregation5 (aggregation as used in this term means flocculation in the present chapter). In this process, which is straightforward to simulate and visualize on a computer, particles undergo Brownian motion (i.e., diffusion) until they come together in close proximity, after which they coalesce instantaneously and irreversibly to form floccules (or clusters ). The clusters then diffuse until they contact one another and combine to form larger clusters, and so on, until gravitational... 

Figure 8. Transmission electron micrographs of typical clusters of gold, silica, and polystyrene colloids, prepared by both diffusion-limited and reaction-limited cluster aggregation and by computer simulation. There is a striking similarity in the structure of the clusters of different colloids in each regime.

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. 

Pierce F, Sorensen CM, Chakrabarti A (2006) Computer simulation of diffusion-limited cluster-cluster aggregation with an epstein drag force. Phys Rev E 74 021411. 

These procedures not only indicate the kinetics of aggregation, but also allow study of the size distribution and the fractal geometry of the clusters. Typical results for the fractal dimension of clusters grown in computer simulations are summarized in Table 5. Note that the monomer-cluster aggregation models produce dense nonfractal clusters, except for the diffusion-limited case, whereas cluster-cluster models yield fractal dimensions in good agreement with experiments on real colloids. 

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