Combined deterministic-stochastic framework for modeling the agglomeration of colloidal particles

We present a multiscale model, based on molecular dynamics (MD) and kinetic Monte Carlo (kMC), to study the aggregation driven growth of colloidal particles. Coarse-grained molecular dynamics (CGMD) simulations are employed to detect key agglomeration events and calculate the corresponding rate constants. The kMC simulations employ these rate constants in a stochastic framework to track the growth of the agglomerates over longer time scales and length scales. One of the hallmarks of the model is a unique methodology to detect and characterize agglomeration events. The model accounts for individual cluster-scale effects such as change in size due to aggregation as well as local molecular-scale effects such as changes in the number of neighbors of each molecule in a colloidal cluster. Such definition of agglomeration events allows us to grow the cluster to sizes that are inaccessible to molecular simulations as well as track the shape of the growing cluster. A well-studied system, comprising fullerenes in NaCl electrolyte solution, was simulated to validate the model. Under the simulated conditions, the agglomeration process evolves from a diffusion limited cluster aggregation (DLCA) regime to percolating cluster in transition and finally to a gelation regime. Overall the data from the multiscale numerical model shows good agreement with existing theory of colloidal particle growth. Although in the present study we validated our model by specifically simulating fullerene agglomeration in electrolyte solution, the model is versatile and can be applied to a wide range of colloidal systems.