Modeling the Effect of Ligands on Growth and Assembly of Nanocrystals

Ligands play a central role for the energetics and kinetics of plasmonic nanocrystals. During nanocrystal synthesis, ligands bind to the surface of a growing seed. Growth can result in shapes distinct from equilibrium Wulff polyhedra if ligands are designed with specificity for crystallographic facets. Ligands are also important during nanocrystal assembly. They act as spacers and provide functionality by controlling nanoparticle interactions. Finally, a surplus of ligand molecules in solution can result in depletion effects. Here, we present advances in the computational modeling of ligand effects on both nanocrystal growth and nanocrystal assembly. We model nanocrystal growth via a grand-canonical kinetic Monte Carlo simulation where ligand covering is described by kinetic factors. We observe a roughening transition at high temperature and search for optimal conditions for desired nanocrystal shapes. For understanding the effects of ligands on assembly, we utilize coarse-grained simulations of nanoprisms with directional, facet-specific interactions. For this purpose, we develop a generalizable two-step simulation methodology that, in a first step, generates a table for the interaction of two ligand-covered nanocrystals and, in a second step, utilizes this table in molecular dynamics. We apply our simulations to a number of self-assembly experiments of anisotropic nanocrystals with polymer ligands. Our macromolecular ligand-engineering strategies control, characterize, and model four molecular parameters of grafted polymer chains: chain length, chain dispersity, grafting density, and chain distribution. This work is a step towards theoretical models for particle brush materials and paves the way for the precision synthesis of nanocrystal hybrid materials.