Computational self-assembly of colloidal crystals from Platonic polyhedral sphere clusters†
We explore a rich phase space of crystals self-assembled from colloidal “polyhedral sphere clusters (PSCs),” each of which consists of equal-sized “halo” spheres placed at the vertices of a polyhedron such that they just touch along each edge. Such clusters, created experimentally by fusing spheres, can facilitate assembly of useful colloidal crystal symmetries not attainable by unclustered spheres. While not crucial for their self-assembly, the center of the PSC can contain a “core” particle that can be used as a scaffold to build the PSC. Using Brownian dynamics simulations, we show the self-assembly of eight distinct crystalline phases from PSCs that correspond to the five Platonic polyhedra, and that are made of spheres with purely repulsive interactions. Strong crystalline order is seen in the centers of mass of the PSCs, or equivalently the core particles. The halo particles also may organize into crystal structures, usually with weaker crystalline order than the core particles. Notably, however, in crystals assembled from the octahedral and icosahedral PSCs, the halo particles are also well ordered, nesting within the crystals formed by the cores. Interestingly, despite the rounded nature of the PSCs, in some cases we obtain structures similar to those of the corresponding faceted polyhedra interacting only via excluded volume. Only the tetrahedral PSCs fail to self-assemble into a crystal, but we demonstrate that a pre-assembled crystal – whose halo particles sit on a close-packed face-centered cubic lattice, and whose core particles form a diamond structure – is stable at high density and melts into a hexagonal phase at lower density.