Useful strategy for assuming complex ordered phases possibly formed by ABC-type block copolymers

Largely Asymmetric Binary Mesocrystals beyond Inorganic Crystals Formed in Linear ABC/ABC Blends

“…Although the A-spheres and C-spheres deform from ideal sphere slightly due to the impact of their polyhedral Voronoi cells, their radii are estimated without considering such a tiny deformation. 52 The increase in the asymmetry of CNs is accompanied by an increasing trend for the A-spheres to be arranged into higher-CN lattices. This is why the packing lattice of A-spheres changes from simple cubic of CsCl to The phase transition from C15-A 6 C 34 to BCC-AC 6 along decreasing ϕ 1 is relatively difficult to understand.…”

“…Generally, the CN ratio of the A- and C-spheres in these binary mesocrystals changes from 1:1 to 1:2, 1:3, 6:34, 1:6, 1:8, and 1:10 as γ increases from 1.0 to 2.26, which mainly results from the gradually expanding A-spheres as shown in Figure b. Although the A-spheres and C-spheres deform from ideal sphere slightly due to the impact of their polyhedral Voronoi cells, their radii are estimated without considering such a tiny deformation . The increase in the asymmetry of CNs is accompanied by an increasing trend for the A-spheres to be arranged into higher-CN lattices.…”

“…Another challenging problem to be solved is how to reasonably assume candidate binary spherical phases without resorting to the known prototypes of inorganic crystals. Based on the geometric characteristics and spatial symmetries of ordered phases, recently Dong et al have proposed a useful assumption rule to generate possible candidate phases formed by ABC-type block copolymers . For a binary mesocrystal with large A-spheres and small C-spheres, small C-spheres are preferably positioned at the vertices of the Voronoi cell of the crystal lattice of A-spheres.…”

“…Based on the geometric characteristics and spatial symmetries of ordered phases, recently Dong et al have proposed a useful assumption rule to generate possible candidate phases formed by ABC-type block copolymers. 52 For a binary mesocrystal with large A-spheres and small C-spheres, small C-spheres are preferably positioned at the vertices of the Voronoi cell of the crystal lattice of A-spheres. For the large A-spheres, they tend to be packed into a crystal lattice of high-CN for reducing the deformation caused by the polyhedral shape of the Voronoi cell.…”

Automated Search Strategy for Novel Ordered Structures of Block Copolymers

“…Therefore, the search for novel structures to expand the library of structures is very important for the entire scientific community, not only for the preparation of new materials, but also for mathematical studies . Novel structures can be either mathematically derived or discovered experimentally by preparing new crystallizing or self-assembly systems. − In addition, novel structures can also be inferred from known structures . In any case, the discovery of novel structures is to some extent limited by existing perceptions.…”