Formation dynamics of branching structure in the slippery DLCA model.

We numerically investigated the aggregation dynamics and resulting network structures of colloidal gels using the slippery diffusion-limited cluster aggregation (DLCA) model. In this model, bonds are irreversibly formed upon the particle contacts, but the angles among them are not fixed, unlike the conventional DLCA. This allows clusters to be deformed in the process of aggregation. By characterizing the aggregation dynamics and using a reduced network scheme, our simulation revealed two distinct branching structure formation routes depending on the particle volume fraction ϕ. In lower volume fraction systems (ϕ ≤ 8%), the deformations of small-size clusters proceed prior to the percolation. When the Maxwell criterion is satisfied and the clusters become mechanically stable, the formation of the branching structure is nearly completed. After forming the branching structures, they aggregate and form a larger percolating network. Then, the aggregation proceeds through the elongation and straightening of the chain parts of the network. In higher volume fraction systems (ϕ > 8%), on the other hand, the clusters percolate, and a fine and homogeneous branching structure is formed at the early stage of the aggregation. In the aging stage, it collapses into a denser and more heterogeneous structure and becomes more stable. Our quantitative analyses of the branching structure will shed light on a new strategy for describing the network formation and elasticity of colloidal gels.