Frustrated Assembly of Nanoscale Bipyramids into Uniquely Ordered Superstructures

The self-assembly of anisotropic nanoparticles (NPs) into hierarchical superstructures offers a powerful route for designing advanced functional materials. Particle shape plays a critical role in the result of their assembly, often leading to complex NP superlattices resulting from locally dense particle packing. Right bipyramids (rBPs), with their distinct 110.9° dihedral angles, introduce geometric frustration that prevents conventional crystalline packing. Here, we combine electron microscopy, geometric arguments, and Monte Carlo simulations to investigate the geometrically frustrated assembly of rBPs under drop-casting conditions. We show that rBPs reproducibly self-assemble into energetically favorable, quasi-spherical superstructures composed of 130 rBPs (130-rBP) with hierarchical internal order, formed through a stepwise self-assembly pathway involving intermediates comprising 8 and 35 rBPs. These 130-rBP superstructures serve as fundamental building blocks for larger complex superstructures such as dimers (225 rBPs) and trimers (300 rBPs), in which multiple 130-rBP motifs remain clearly discernible but overlap extensively. Despite their high degree of local order, these assemblies do not form bulk crystals. Monte Carlo simulations of the assembly process predict the observed superstructures, both in the presence and absence of an underlying surface, demonstrating that the assemblies are driven by the unique geometry of the particles rather than the assembly environment. These results reveal a frustrated assembly mechanism in which the particle geometry promotes the formation of highly ordered, albeit noncrystalline, superstructures by inhibiting the unbounded growth of crystalline superlattice structures.