Comparison of the Rates of Uni- and Bi-Molecular Diffusion Controlled Reactions on Circular, Filled Aggregate and DLA Fractal Aggregate in Two Dimensions

摘要

The effects of irregular, open structures of two dimensional aggregates on the rates of diffusion controlled reactions are examined by computer simulation. The simulation model describes the reaction between two species, A and B, where A is randomly distributed on a two dimensional square lattice and diffuses like a random walker while B forms a fixed aggregate of different shapes and sizes. Both unimolecular (i.e., B is non-destructive but A disappears upon reaction) and bimolecular (i.e., both A and B disappear after the reaction) mechanisms are examined. Different sizes of DLA aggregates are chosen to model the irregular aggregates and to compare the reaction rates with the circular, compact aggregates of different radii. For unimolecular reaction, with the same total mass, the DLA aggregate shows a faster reaction rate than the circular one for its open structure. In the bimolecular mechanism, the sizes (or radii) of the aggregates decrease during reaction processes, and the reaction rate is slower compared to the unimolecular reaction. This shrinkage effect is more distinct for DLA aggregates than the compact aggregates. Keywords: Fractals, Kinetics, Diffusion, Aggregation, Surface diffusion.