We study the assembly of ligated gold nanoparticles by both phenomenological modeling and computer simulations for various ligand chain lengths. First, we develop an effective nanoparticle-nanoparticle pair potential by treating the ligands as flexible polymer chains. Besides van der Waals interactions, we incorporate both the free energy of mixing and elastic contributions from compression of the ligands in our effective pair potentials. The separation of the nanoparticles at the potential minimum compares well with experimental results of gold nanoparticle superlattice constants for various ligand lengths. Next, we use the calculated pair potentials as input to Brownian dynamics simulations for studying the formation of nanoparticle assembly in three dimensions. For dodecanethiol ligated nanoparticles in toluene, our model gives a relatively shallower well depth and the clusters formed after a temperature quench are compact in morphology. Simulation results for the kinetics of cluster growth in this case are compared with phase separations in binary mixtures. For decanethiol ligated nanoparticles, the model well depth is found to be deeper, and simulations show hybrid, fractal-like morphology for the clusters. Cluster morphology in this case shows a compact structure at short length scales and a fractal structure at large length scales. Growth kinetics for this deeper potential depth is compared with the diffusion-limited cluster-cluster aggregation (DLCA) model.

The aggregation of proteins with expanded polyglutamine (polyQ) tracts is directly relevant to the formation of neuronal intranuclear inclusions in Huntington's disease. In vitro studies have uncovered the effects of flanking sequences as modulators of the driving forces and mechanisms of polyQ aggregation in sequence segments associated with HD. Specifically, a seventeen-residue amphipathic stretch (N17) that is directly N-terminal to the polyQ tract in huntingtin decreases the overall solubility, destabilizes nonfibrillar aggregates, and accelerates fibril formation. Published results from atomistic simulations showed that the N17 module reduces the frequency of intermolecular association. Our reanalysis of these simulation results demonstrates that the N17 module also reduces interchain entanglements between polyQ domains. These two effects, which are observed on the smallest lengthscales, are incorporated into phenomenological pair potentials and used in coarse-grained Brownian dynamics simulations to investigate their impact on large-scale aggregation. We analyze the results from Brownian dynamics simulations using the framework of diffusion-limited cluster aggregation. When entanglements prevail, which is true in the absence of N17, small spherical clusters and large linear aggregates form on distinct timescales, in accord with in vitro experiments. Conversely, when entanglements are quenched and a barrier to intermolecular associations is introduced, both of which are attributable to N17, the timescales for forming small species and large linear aggregates become similar. Therefore, the combination of a reduction of interchain entanglements through homopolymeric polyQ and barriers to intermolecular associations appears to be sufficient for providing a minimalist phenomenological rationalization of in vitro observations regarding the effects of N17 on polyQ aggregation.

This paper presents simulation studies of nanoparticle supercluster (NPSC) nucleation from a temperature quenched system. The nanoparticles are represented as 5 nm, spherical gold nanoparticles ligated with alkane thiols. The pair potential accounts for the van der Waals interaction between the metallic cores and ligand-ligand and ligand-solvent interactions. Phenomena well-known for molecular systems are observed including a prenucleation induction period, fluctuating prenucleation clusters that predominately add monomers one at a time, a critical nucleus size, and growth of NPSCs from solution in the presence of an equilibrium supernatant, all consistent with classical nucleation theory. However, only the largest prenucleating clusters are dense, and the cluster size can occasionally range greater than the critical size in the prenucleation regime until a cluster with low enough energy occurs, then nucleation ensues. Late in the nucleation process, the clusters display a crystalline structure that is a random mix of face-centered cubic (fcc) and hexagonal close-packed (hcp) lattices and indistinguishable from a randomized icosahedra structure.

We present results from detailed three-dimensional Brownian dynamics simulations of the self-assembly process in quenched short-range attractive colloids. Clusters obtained in the simulations range from dense faceted crystals to fractal aggregates which show ramified morphology on large length scales but close-packed crystalline morphology on short length scales. For low volume fractions of the colloids, the morphology and crystal structure of a nucleating cluster are studied at various times after the quench. As the volume fraction of the colloids is increased, growth of clusters is controlled by cluster diffusion and cluster-cluster interactions. For shallower quenches and low volume fractions, clusters are compact and the growth-law exponent agrees well with Binder-Stauffer predictions and with recent experimental results. As the volume fraction is increased, clusters do not completely coalesce when they meet each other and the kinetics crosses over to diffusion-limited cluster-cluster aggregation (DLCA) limit. For deeper quenches, clusters are fractals even at low volume fractions and the growth kinetics asymptotically reaches the irreversible DLCA case.

Results from extensive Brownian dynamics simulations are presented for nucleation in a system of colloidal particles interacting via a short-range attractive potential. Our analysis shows that, even though the system is not in equilibrium, structures of small size clusters compare well with the theoretically predicted and experimentally observed ground state structures for short-range colloidal systems. In addition, the distribution of the symmetric structures in nucleation is comparable to the distribution seen in equilibrium. We also investigate how the shape and structure of fluctuating clusters in the prenucleation regime affect the formation of a stable nucleating cluster.