Stability and Free Energy of Nanocrystal Chains and Superlattices

We discuss the stability and free energy of 1D (chains), 2D (planar superlattices), and 3D (bcc or fcc superlattices) nanocrystals (having hydrocarbons as capping ligands) structures. We start by introducing the method to compute the pressure and free energy. We then analyze the magnitude of many body (or nonadditive) effects, those not described by two body interactions. For 3D superlattices, we examine the relative stability of fcc vs bcc as well as the prevalence of rotator vs crystal phases. We identify a bundling phenomena that occurs during bcc assembly, when next to nearest neighbors begin to make contact. We precisely calculate the density and lattice constant as well as the presence of ligand vortices and find that overall, the simulations fully support the recently introduced Orbifold Topological Model (OTM). By comparing our results with the considerable experimental data available in the literature, we identify a number of subtle effects.