Packings of Soft Spheres Self-assembled from Block Copolymers

Block copolymers, obtained when two or more chemically distinct sub-chains or blocks are covalently linked together, tend to organize into assemblies of different shapes (spheres, cylinders, and lamellae) due to the competition between block–block repulsion and chain connectivity. The packing of these malleable assemblies leads to the formation of various ordered phases. For the case of spherical assemblies resembling soft spheres, their packing leads to, besides the commonly observed simple body-centred-cubic phase, the emergence of several complex spherical packing phases, i.e. the Frank–Kasper phases. Several mechanisms, including conformational asymmetry, copolymer architecture, and blending of different polymeric species, have been identified to stabilize the complex spherical packing phases. These developments shed light on our understanding of the packing of soft spheres self-assembled from soft matter.