From static micrographs to particle aggregation dynamics in three dimensions

Studies on colloidal aggregation have brought forth theories on stability of colloidal gels and models for aggregation dynamics. Still, a complete link between developed frameworks and obtained laboratory observations has to be found. In this work, aggregates of silica nanoparticles (20 nm) are studied using diffusion limited cluster aggregation (DLCA) and reaction limited cluster aggregation (RLCA) models. These processes are driven by the probability of particles to aggregate upon collision. This probability of aggregation is one in the DLCA and close to zero in the RLCA process. We show how to study the probability of aggregation from static micrographs on the example of a silica nanoparticle gel at 9 wt%. The analysis includes common summary functions from spatial statistics, namely the empty space function and Ripley's K-function, as well as two newly developed summary functions for cluster analysis based on graph theory. One of the new cluster analysis functions is related to the clustering coefficient in communication networks and the other to the size of a cluster. All four topological summary statistics are used to quantitatively compare in plots and in a least-square approach experimental data to cluster aggregation simulations with decreasing probabilities of aggregation. We study scanning transmission electron micrographs and utilize the intensity-mass thickness relation present in such images to create comparable micrographs from three-dimensional simulations. Finally, a characterization of colloidal silica aggregates and simulated structures is obtained, which allows for an evaluation of the cluster aggregation process for different aggregation scenarios. As a result, we find that the RLCA process fits the experimental data better than the DLCA process.