Structure and cohesion of weakly agglomerated fractal systems

We investigated the cohesion of agglomerates formed by sticking together two fractal clusters with the assumption that this parameter can be measured by the number of connections that were established on sticking. In a first step, clusters of selected mass were generated by numerical simulation of the aggregation process on a cubic lattice using the usual algorithm of the diffusion- or reaction-limited aggregation process. Then, agglomerates of various configurations were formed by assembling two by two clusters of even or uneven masses. For each system, the average connection frequency and the total number of configurations were determined. This investigation provided agglomerate characteristics that were determined to be independent of the agglomerate mass (in the domain of large agglomerates) and only dependent of the conditions of the cluster formation. In a second step, aggregates were formed in experiments carried out under conditions of diffusion- or reaction-limited aggregation (as fixed by the electrolyte concentration) as well as under orthokinetic and perikinetic aggregation conditions for aggregates formed in the presence of a small amount of polyvinylpyridine. The fragmentation of all these aggregates was promoted by immersing aggregate samples in polyvinylpyridine solutions of high concentration. Whereas the rate of decrease of the average masses of the aggregates was found to depend on the aggregate mass or the characteristics of the fragmenting medium, the rate of fragmentation a(n) for aggregates of mass n might be expressed by the scaling law a(n)∝nλ. The exponent λ was found to only depend of the experimental conditions of the aggregate formation. The comparison between results of the numerical and experimental investigations seems to indicate that the number of intra-agglomerate connections effectively control the rate of fragmentation and thus the aggregate cohesion.