Liquid Quasicrystals

Following the discovery of quasicrystals by Shechtman and Cahn in 1984$^{\mathrm{1}}$, for the following 20 years the new field of QCs was confined to metal alloys and atomic-scale structures. Then, with the discovery of a liquid crystal phase possessing dodecagonal QC symmetry$^{\mathrm{2}}$], research interest has extended from metal alloys to those where the motifs were no longer single atoms but assemblies of many molecules. In dendron-based liquid quasicrystals (LQC) between 10-50 molecules form a supramolecular sphere with 10$^{\mathrm{3}}$ -- 10$^{\mathrm{4}}$ atoms. In 2007 a 2-d quasiperiodic phase was found in three-arm star ABC polymers$^{\mathrm{3}}$. In 2012 the first linear diblock copolymer was reported to form a sphere-based bulk QC phase, similar to that in dendrimer LQC but on a still larger scale$^{\mathrm{4}}$. In the same year bulk QC domains were reported in ``hard'' nanoporous silica, produced however, again from a ``soft'' lyotropic template$^{\mathrm{5}}$. The symmetry of all confirmed soft QCs so far is 12-fold. Another important development in soft QCs is the observation of complex QC approximants in a number of side-branched polyphilic LC honeycombs, described by multicolour tilings$^{\mathrm{6,7}}$. In fact, recently we found a genuine dodecagonal QC in such systems, the first example of a 2D LQC. Furthermore, we succeeded in direct AFM imaging of the \textit{xy} plane of a dendrimer LQC. The images confirm the ``half-step'' inflation rule, proposed earlier$^{\mathrm{7}}$ but not confirmed until now. (1) D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn, \textit{PRL} 1984, \textbf{53}, 1951. (2) X.B. Zeng et al, \textit{Nature} 2004, \textbf{428}, 157. (3) K. Hayashida, et al. \textit{PRL }2007, \textbf{98}, 195502. (4) J. Zhang, F. Bates, \textit{J. Am. Chem. Soc.} 2012, \textbf{134}, 7636. (5) C. Xiao et al \textit{Nature} 2012, \textbf{487}, 349. (6) B. Chen et al \textit{Science} 2005, \textbf{307}, 96. (7) X.B. Zeng et al \textit{Science} 2011, \textbf{331}, 1302. X.B. Zeng and G. Ungar, \textit{Phil. Mag. }2006 \underline {86} 1093.