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

Supramolecular crystal phases of self-assembled soft matter share the symmetries of atomic and molecular crystals, but with vastly larger unit cells occupied by huge numbers of flexible molecules. Recent progress in understanding the formation of complex crystals of quasi-spherical soft matter domains derives from a mesoatomic analogy. In this analogy, the ultimate structure is broken down into micelle-like motifs, whose shape, size, and packing dictate thermodynamics. This begs a basic question for complex network phases, such as the double-gyroid: what are the mesoatomic ``building blocks'' of crystals with non-convex, polycontinuous, and inter-catenated domains? Here, the authors propose generic principles for divining the mesoatomic building blocks of network crystals and illustrate these principles for double-networks of diblock copolymers. They also propose and explore a minimal physical model for how mesoatomic shapes and packing can template a rich dynamics for the assembly and link formation of inter-catenating soft matter crystals.