Cluster–cluster aggregation with mobile impurities

Abstract

We considered the diffusion-limited cluster–cluster aggregation (DLCA) model in the presence of inert template (mobile impurities) for the simulation of mesoporous materials obtained through sol–gel processes. A computer algorithm based on the off-lattice version of the two-dimensional DLCA model with moving impurities is introduced. If the density of monomers is large enough, a porous matrix results at the end of the aggregation mechanism. Impurities are removed at the final stage of the simulation, assuming that the porous structure is not altered as in some experiments. We are interested in the modification of the resulting porous structure due to the presence of moving inert impurities during aggregation. The resulting porous material consists of a homogeneous structure of interconnected fractal clusters. Such structure is characterized by computing the correlation length and the fractal dimension of these clusters. The numerical analysis of the pore size distribution reveals a strong dependence with the density and sizes of mobile impurities. Compared to the DLCA model, the curve distribution becomes bimodal when impurities are introduced, i.e., it appears a first maximum at small pore sizes (of the order of the monomer dimension), and a second maximum around the impurity size. For large monomer densities the amplitude of the peak around the impurity size becomes larger than the peak of the smallest pore size.