colloids order into cubic-close packings?

The hard sphere system has been utilized as a model system to understand the mechanism of self-assembly. Advances in synthesis techniques and the drive towards materials discovery has led to research on polyhedral shapes that are easily synthesized in the lab, and how their self-assembly compares to that of spheres. Hard spheres assemble into the face-centered cubic (FCC) lattice type, with cubic-close packing (CCP) structure at packing fractions of 0.5–0.7. Here we ask: which polyhedral shapes will likewise assemble CCP? Literature has offered some guidelines to the assembly of plastic crystals with CCP structure from symmetric polyhedral particles [1], but a general understanding is lacking. We examine one parameter that influences the assembly structure, the sphericity of a particle shape, and the role it plays in the likelihood of assembling CCP from polyhedral particles of various shapes and vertex numbers.

[1] P. Damasceno, M. Engel, and S.C. Glotzer, Science 337 (2012).