Controlling the assembly of cuboctahedra

A cuboctahedron has square and triangular facets, and you obtain it by cutting off the corners of a cube. Because it shares the properties of both a cube and an octahedron, it can be made to pack into different structures that are known to form from these two polyhedra. We investigate ways to make a cuboctahedron behave either like a cube, or an octahedron, by adding a second particle species that promotes the cuboctahedra to align with their square facets and behave more like cubes overall.

From our Soft Matter paper with Andrew Karas and Sharon Glotzer:

Depletion interactions arise from entropic forces, and their ability to induce aggregation and even ordering of colloidal particles through self-assembly is well established, especially for spherical colloids. We vary the size and concentration of penetrable hard sphere depletants in a system of cuboctahedra, and we show how depletion changes the preferential facet alignment of the colloids and thereby selects different crystal structures. Moreover, we explain the cuboctahedra phase behavior using perturbative free energy calculations. We find that cuboctahedra can form a stable simple cubic phase, and, remarkably, that the stability of this phase can be rationalized only by considering the effects of both the colloid and depletant entropy. We corroborate our results by analyzing how the depletant concentration and size affect the emergent directional entropic forces and hence the effective particle shape. We propose the use of depletants as a means of easily changing the effective shape of self-assembling anisotropic colloids.