Trade-offs between Translational and Orientational Order in 2D Superlattices of Polygonal Nanocrystals with Differing Edge Count

The goal of this work is to identify factors which modulate structural order in 2D self-assembled superlattices of polygon-shaped colloidal nanocrystals. Using combined experimental and simulation techniques, we quantify order in superlattices of hexagonal prism-shaped CdSe/CdS nanocrystals and cube-shaped CsPbBr₃ nanocrystals. Superlattices derived from cube-shaped nanocrystals display less translational order compared to hexagonal prism-shaped nanocrystals both experimentally and in simulations. This effect can be attributed to geometric considerations inherent to the combined rotational and translational symmetries of different polygonal shapes and their superlattices. Cubes form a simple cubic lattice where nanocrystals can slide without steric overlap, whereas hexagonal prisms interlock, preventing translation. Regarding orientational order, cube assemblies display a narrower orientation distribution. Intuitively, hexagonal prisms are a more "spherical" shape compared to cubes. The results presented here outline a conceptual framework for identifying superlattice structures which favor translationally and orientationally ordered self-assembled superlattices.