Understanding the self-assembly or aggregation mechanism of nanoparticles such as fullerenes and carbon nanotubes, in various solvent media is of importance in myriad applications that use solution processing. For instance, the structure of thin film nanocomposites, used in a range of organic electronic devices such as organic photovoltaic cells, is determined by the size and shape of nanoparticle agglomerates that form during solution processing. To understand the fundamental physics behind agglomeration of nanoparticles, we performed molecular dynamics (MD) simulations of a range of binary systems that comprised fullerene derivatives-solvents and fullerene derivatives-polymer. The simulations provided us fundamental insights that help in selecting favorable solution processing parameters, such as solvents and relative concentration of nanoparticles and polymers. For instance, the results from our simulations illustrated that based on the agglomeration behavior of fullerene derivative [6,6]-phenyl-C61-butyric acid methyl ester (PCBM), indane is a better choice of solvent than toluene for fabricating thin films of OPVs. The study also indicated that 1:1 weight ratio of PCBM and poly (3-hexylthiophene) (P3HT) polymer can attribute to optimal morphology of photoactive layer in OPVs. However, conclusive prediction can only be attained by analyzing systems of length scales relevant to the specific devices, which is not often accessible to MD simulations.
In an effort to bridge this existing gap, we developed a novel multi-scale model, based on molecular dynamics (MD) and kinetic Monte Carlo (kMC), to study the self-assembly driven growth of nanoparticle agglomerates. Coarse-grained molecular dynamics (CGMD) simulations were employed to detect key agglomeration events and calculate the corresponding rate constants. The kMC simulations employ these estimated 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 novel approach 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. We predicted the growth mechanism of fullerene particles by analyzing the size and shape of the growing agglomerates that range in size from 1 nm to 100 nm in electrolyte solutions. 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. The fractal dimension of the aggregates was approximately 1.9, 2.5 and 3.0 for the DLCA, percolating cluster and gelation regime, respectively, which are in good agreement with existing data in the literature. Fullerene agglomeration showed similar trend at varying electrolyte concentrations indicating that the agglomeration mechanism of fullerenes is independent of electrolyte concentrations for high fullerene concentrations (7% mass fraction). Overall the data from the multi-scale numerical model showed 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 where self-assembly of small molecules is of importance.