Self-assembly of binary space-tessellating compounds.

The self-assembly of polyhedral particles has been a topic of interest in both experimental and simulation studies due to its potential to help engineer novel materials from colloidal nanoparticles. An important extension to the study of single species of polyhedral particles is the case of binary mixtures. Mixtures that tessellate space are particularly interesting because they are expected to form high-pressure ordered structures. Here, we study three such binary tessellating mixtures; namely, cuboctahedra + octahedra (Mixture 1), octahedra + tetrahedra (Mixture 2), and truncated cubes + octahedra (Mixture 3). We use Monte Carlo methods to first determine their phase behavior when driven by hard-core interactions (i.e., entropic self-assembly). We observe that upon gradual compression of the isotropic system, none of the three cases exhibits a spontaneous ordering into the expected tessellated structure: Mixtures 1 and 2 form a glassy disordered state that is shown to be metastable with respect to the tessellated phase via interfacial simulations; Mixture 3 demixes into a disordered phase and an unusual ordered phase where truncated cubes arrange in a cubic lattice while the octahedra remain disordered occupying interstitial pockets. Using polybead models for Mixtures 1 and 2, we show that the large free-energy barrier that precludes the spontaneous nucleation of the tessellating structure from the isotropic state can be overcome by introducing favorable enthalpic interactions. Our results allow identifying some relations between properties of individual species and the phase behavior of their mixtures, providing a first step toward a "chemistry" of polyhedral compounds, while also raising key questions regarding the kinetics of the pseudo "reactions" involved.