Periodic and Aperiodic Sphere Packings: A Window into Scale-Invariant Self-Assembly of Amphiphilic Materials

A zoo of low symmetry, tetrahedrally close-packed Frank-Kasper (FK) phases that mimic the structures of metals and their alloys have recently been discovered in amphiphilic materials, such as small-molecule thermotropic and lyotropic liquid crystals (LCs), and high molecular weight block copolymers and giant shape amphiphiles. While the specific chemical interactions directing these assemblies substantially differ, we describe a common framework for understanding the emergence of periodic FK A15 and σ phases and related dodecagonal quasicrystals. This talk will then describe how our discovery that simple additives in lyotropic LCs expands the range of accessible phases translates into blends of particle-forming diblock copolymers with various core-segregating homopolymer additives. These findings furnish enticing opportunities to identify length scale-invariant molecular design principles across amphiphile that classes that could possibly translate to their interfacial activities and applications.