Expanding quasiperiodicity in soft matter

Significance As the formation of quasicrystalline ordering in both metal alloys and soft matters reinforces the scale-invariance principle, however, it remains unknown that why metallic quasicrystals prefer decagonal quasicrystalline (DQC, 10-fold) ordering, and the condensed soft maters only exhibit dodecagonal quasicrystalline (DDQC, 12-fold) ordering. By tuning the self-sorting ability in a pair of giant molecules, the well-mixed binary blends generate a metastable DQC phase and corresponding unprecedent phase sequence (DQC → DDQC → Frank–Kasper σ) during thermal annealing. These peculiar assembling behaviors result from interplays of submesoatomic and mesoatomic packings. Reducing the self-sorting strength has induced an extra complexity in the sub-mesoatomic packings of giant molecules, which further influences the clustering on the mesoatomic level.
The quasiperiodic structures in metal alloys have been known to depend on the existence of icosahedral order in the melt. Among different phases observed in intermetallics, decagonal quasicrystal (DQC) structures have been identified in many glass-forming alloys yet remain inaccessible in bulk-state condensed soft matters. Via annealing the mixture of two giant molecules, the binary system assemblies into an axial DQC superlattice, which is identified comprehensively with meso-atomic accuracy. Analysis indicates that the DQC superlattice is composed of mesoatoms with an unusually broad volume distribution. The interplays of submesoatomic (molecular) and mesoatomic (supramolecular) local packings are found to play a crucial role in not only the formation of the metastable DQC superlattice but also its transition to dodecagonal quasicrystal and Frank–Kasper σ superlattices.