Volume fraction dependence and reorganization in cluster–cluster aggregation processes

Off-lattice diffusion limited cluster aggregation simulations in two dimensions have been performed in a wide volume fraction range between 0.001 and 0.60. Starting from a system of 10 000 monomers with radius 0.5, that follow Brownian trajectories, larger aggregates are generated by bond formation between overlapping aggregates. No rings are present in the nonaged structures. The influence of the initial monomer volume fraction on the fractal properties of the gels is studied and interpreted by calculation of small angle scattering structure factor patterns to find the fractal dimension. It is found that an increase of the volume fraction leads to the development of two distinct fractal regions. The fractal dimension at short length scale shows the diffusion limited cluster aggregation value of 1.45 up to the correlation length, while the long range fractal dimension gradually increases from 1.45 to 2.00, the Euclidean dimension of the simulation space. It is shown that high volume fractions lead to changes in the local morphology of the monomers as a function of the volume fraction with corresponding changes in the high-q region of the structure factor pattern. A new method to simulate aging of aggregates at modest (low pH and temperature) reaction conditions by an off-lattice nonbreaking reorganization process, called shaking, is presented. The shaking process induces small changes in the local mass distribution, causing ring formation, but does not affect the radius of gyration of the aggregates. It is found that shaking leads to the formation of a polydisperse collection of new primary scatterers with a volume fraction dependent radius between 6 and 8 initial monomer radii. For low volume fractions the fractal dimension decreases approximately by 0.2, due to the formation of the new primary scatterers. The shaking process induces changes in the fractal properties at length scales up to ∼40. A simple theory that relates the volume fraction with the correlation length and describes the influence of aging on fractal properties such as monomer radius, fractal dimension, and correlation length is developed. The diffusion limited cluster aggregation simulation results of nonaged and aged gels are compared with this theory. Satisfactory quantitative agreement between simulated and theoretical results is found.