Understanding interactions between capped nanocrystals: three-body and chain packing effects.

Self-assembly of capped nanocrystals (NC) attracted a lot of attention over the past decade. Despite progress in manufacturing of NC superstructures, the current understanding of their mechanical and thermodynamic stability is still limited. For further applications, it is crucial to find the origin and the magnitude of the interactions that keep self-assembled NCs together, and it is desirable to find a way to rationally manipulate these interactions. We report on molecular simulations of interacting gold NCs protected by capping molecules. We computed the potential of mean force for pairs and triplets of NCs of different size (1.8-3.7 nm) with varying ligand length (ethanethiol-dodecanethiol) in vacuum. Pair interactions are strongly attractive due to attractive van der Waals interactions between ligand molecules. Three-body interaction results in an energy penalty when the capping layers overlap pairwise. This effect contributes up to 20% to the total energy for short ligands. For longer ligands, the three-body effects are so large that formation of NC chains becomes energetically more favorable than close packing of capped NCs at low concentrations, in line with experimental observations. To explain the equilibrium distance for two or more NCs, the overlap cone model is introduced. This model is based on relatively simple ligand packing arguments. In particular, it can correctly explain why the equilibrium distance for a pair of capped NCs is always approximately 1.25 times the core diameter independently on the ligand length, as found in our previous work [Schapotschnikow, R. Pool, and T. J. H. Vlugt, Nano Lett. 8, 2930 (2008)]. We make predictions for which ligands capped NCs self-assemble into highly stable three-dimensional structures, and for which they form high-quality monolayers.