Shape-controlled crystallisation pathways in dense fluids of ccp-forming hard polyhedra

Emergent directional entropic forces that favour facet-to-facet alignment of neighbouring colloidal particles – arising from multi-body interactions upon crowding – should cause the process by which colloidal crystals form from fluids of hard polyhedra to be different than that from fluids of hard spheres. We compute nucleation-free energy barriers for a family of shapes that all self-assemble the same cubic close-packed (ccp) crystal structure formed by hard spheres and find that changing rhombicuboctahedra into rhombic dodecahedra by successively removing facets that compete with the ccp structure cause a systematic decrease in barrier heights. We show that this decrease arises from the increased prominence of facets aligned with neighbouring shapes in the target crystal, which produce local environments in the fluid that facilitate crystallisation.