Aggregates, DLCA

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... 

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 ... 

The results of off-lattice diffusion limited cluster-cluster aggregation (DLCA) simulations in two dimensions are presented in Fig. 9.26. Simulations are limited to two dimensions because it enables one to use large unit cells with many particles. Brownian trajectories are followed. Larger aggregates are generated as a result of bond formation between overlapping aggregates. One finds crossover from fractal to Euclidean behavior when a particular monomer concentration is exceeded. 

The concept of diffusion-limited cluster-cluster aggregation (DLCA) is very useful and applied in many simulations. In this type of simulation process, particles are placed in a box and subjected to Browni m (random walk) movements. Aggregation (clustering) may occur when two or more particles/clusters come within the vicinity of each other and the combined cluster continues the random walk. The simulation is stopped at the gelation point (percolating system) or when all particles are combined in one final aggregate. The fractal dimension of the DLCA aggregates is approximately 1.8. 

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],... 

---