Symmetry breaking that symmetry evolves from high to low, is usual in nature, such as energy non-conservation in general relativity, parity non-conservation, phase transition, and chirality. The reversed evolution way, symmetry rising, conforms to the interesting concept of emergence phenomenon in systematics, i.e., a complex system emerges with additional high symmetry that does not belong to any constituent. Up to date, only a few examples of apparent symmetry rising (ASR) in crystallography have been found under the severe processing conditions in the metal or alloy materials, which were endowed with unique properties, such as improved mechanical performance, low thermal conductivity, and striking optical properties. It is still a challenge to fabricate feasible strategies to achieve ASR under mild conditions for better understanding and application of symmetry rising.
The team led by Xinhua Wan and Jie Zhang developed a unique strategy of co-crystallization-driven self-assembly of amphiphilic block copolymers PEO-b-PS, PEO and the inorganic cluster silicotungstic acid (STA) to achieve apparent symmetry rising of nanoparticles under mild conditions. STA/PEO form eutectics in situ in selective solution in the form of intimate ion pairs through electrostatic interaction which induced self-assembly into triangular nanoplates. The triangular nanoplates triply twinned by orthogonal crystals (low symmetry) have an additional triple symmetry (high symmetry) （Fig. 1）. The appropriate crystallization inhibition of short solvophilic PS segments of the block copolymers favors the oriented attachment of homogeneous domains of hybrid nanoribbons, and consequently forms kinetic-controlled triangular nanoplates with twin grain boundaries.
Fig. 1 Schematic representation of co-crystallization-driven self-assembly of STA/PEO/PEO-b-PS and the orientation attachment of the formation mechanism of triangle nanoplates.
The overall SAED exhibits a hexagonal pattern consistent with the triple apparent symmetry of the triangle. Whereas, the local SAED around the edge of the triangle shows an orthogonal pattern with fewer diffraction spot. The overall SAED pattern along the [001] zone can be decomposed into three sets of the local orthogonal patterns connected at 60°, indicating that the triangular nanoplates are pseudo-merohedral twins with twin-lattice quasi-symmetry (Fig. 2). As the orthorhombic cell parameters of triangular nanoplates have a relationship of 
, the lattices after 60° rotation can overlap well with the original one. The sphere-approximate shape and delocalized charges of STA make little difference between STAs of different orientations. The above two factors are beneficial to twinning by pseudo-merohedry.
Fig. 2 Analysis and refinement of crystal structure of triangular nanoplates.
By modulating crystallization inhibition upon varying the volume fractions of PS, the morphology of CCDSA can be tuned into crystalline 1D nanowires, 2D triangular nanoplates, nanoribbons, platelet, and amorphous reversed worm-like micelles (Fig. 3). This work would deepen our fundamental understanding in mechanism of the novel ASR and symmetry evolution in nature.
Fig. 3 Morphological evolution and phase diagram at various volume fractions of PS.
This work has been published as “Apparent symmetry rising induced by crystallization inhibition in ternary co-crystallization-driven self-assembly” in Nat. Commun. Prof. Jie Zhang from Peking University is the corresponding author. Siyu Xie, a Ph.D. student at Peking University is the first author. Prof. Xinhua Wan and Prof. Junliang Sun at Peking University are co-authors. This research was financially supported by the National Natural Science Foundation in China.
The link for the paper: https://www.nature.com/articles/s41467-023-42290-7.
