Many studies on nanocrystal (NC) self-assembly into ordered superlattices have focused mainly on attractive forces between the NCs, whereas the role of organic ligands on anisotropic NCs is only in its infancy. Herein, we report the use of a series of dendrimer ligands to direct the assembly of nanoplates into 2D and 3D geometries. It was found that the dendrimer-nanoplates consistently form a directionally offset architecture in 3D films. We present a theory to predict ligand surface distribution and Monte Carlo simulation results that characterize the ligand shell around the nanoplates. Bulky dendrimer ligands create a nontrivial corona around the plates that changes with ligand architecture. When this organic–inorganic effective shape is used in conjunction with thermodynamic perturbation theory to predict both lattice morphology and equilibrium relative orientations between NCs, a lock-and-key type of mechanism is found for the 3D assembly. We observe excellent agreement between our experimental results and theoretical model for 2D and 3D geometries, including the percent of offset between the layers of NCs. Such level of theoretical understanding and modeling will help guide future design frameworks to achieve targeted assemblies of NCs.

The use of nanocrystal (NC) building blocks to create metamaterials is a powerful approach to access emergent materials. Given the immense library of materials choices, progress in this area for anisotropic NCs is limited by the lack of co-assembly design principles. Here, we use a rational design approach to guide the co-assembly of two such anisotropic systems. We modulate the removal of geometrical incompatibilities between NCs by tuning the ligand shell, taking advantage of the lock-and-key motifs between emergent shapes of the ligand coating to subvert phase separation. Using a combination of theory, simulation, and experiments, we use our strategy to achieve co-assembly of a binary system of cubes and triangular plates and a secondary system involving two two-dimensional (2D) nanoplates. This theory-guided approach to NC assembly has the potential to direct materials choices for targeted binary co-assembly.

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The existence of topological order is frequently associated with strongly coupled quantum matter. Here, we demonstrate the existence of topological phases in classical systems of densely packed, hard, anisotropic polyhedrally shaped colloidal particles. We show that previously reported transitions in dense packings lead to the existence of topologically ordered thermodynamic phases, which we show are stable away from the dense packing limit. Our work expands the library of known topological phases, whose experimental realization could provide new means for constructing plasmonic materials that are robust in the presence of fluctuations.