Hierarchical self-assembly of hard cube derivatives

Hierarchical, self-assembled structures are ordered on multiple scales, and formed by objects comprised of even smaller elements. Such structures are widely reported for nanoparticles, macromolecules, and peptides, and even in entropy-driven hard particle assembly hierarchical colloidal crystals have been reported. Here we consider the hierarchical self-assembly of a cubic colloidal crystal from congruent hard cube derivatives, and investigate how various ways of slicing and dicing a cube can affect the ability of the pieces to entropically re-assemble the initial colloidal crystal formed from perfect cubes. We present design rules that support heuristics reported for different systems, and present evidence for a previously unreported cubatic phase from 2 : 1 rectangular prisms.