Topological structure prediction in binary nanoparticle superlattices

Systems of spherical nanoparticles with capping ligands have been shown to self-assemble into beautiful superlattices of fascinating structure and complexity. In this paper, I show that the spherical geometry of the nanoparticle imposes constraints on the nature of the topological defects associated with the capping ligand and that such topological defects control the structure and stability of the superlattices that can be assembled. All these considerations form the basis for the orbifold topological model (OTM) described in this paper. The model quantitatively predicts the structure of super-lattices where capping ligands are hydrocarbon chains in excellent agreement with experimental results, explains the appearance of low packing fraction lattices as equilibrium, why certain similar structures are more stable (bccAB₆vs. CaB₆, AuCu vs. CsCl, etc.) and many other experimental observations.