How does your gyroid grow? A mesoatomic perspective on supramolecular, soft matter network crystals

I describe a proposed framework for understanding the structure of supramolecular network crystals formed in soft matter in terms of mesoatomic building blocks, collective groupings of amphiphilic molecules that play a role analogous to atomic or molecular subunits of hard matter crystals. While the concept of mesoatoms is intuitive and widely invoked in crystalline arrangements of spherical or cylindrical (micellelike) domains, analogous notions physically meaningful building blocks of triply periodic network (TPN) crystals, like the double-gyroid or double-diamond structures are obscured by the complex, bicontinuous domain shapes and intercatenated topologies of the double networks. Focusing on the specific example of diblock copolymer melts, I describe generic rules for decomposing TPN crystals into a unique set of mesoatomic building blocks. The combination of simple physical principles for assembly as well as symmetries and topologies of these structures point to mesoatomic elements associated with the nodal connections, leading to mesoatomic volumes that are nonconvex and bound by smoothly curved faces, unlike the more familiar Voronoi polyhedral shapes associated with spherical/cylindrical mesoatoms. I describe the shapes of these mesoatoms, their internal structure, and importantly, their local packing. We further hypothesize that mesoatoms may be kinetically favored intermediate structures whose local shapes and packing template network crystal assembly on long time scales and study a minimal energetic model of mesoatom assembly for three different cubic double-network crystals. Based on these analyses, I discuss several possible elaborations of the mesoatomic description of TPN assemblies, most notably the implications of mesoatomic malleability, a feature that distinguishes soft matter from hard matter crystals.