Abstract
Quasicrystalline ordering was first observed in synthetic multi-component metallic alloys. These solid state materials exhibit quasicrystalline atomic ordering at nanometer length scales. Softmatter systems are another class of versatile materials that can exhibit quasicrystalline ordering across supra-nanometer (>10 nm) to supra-micrometer (>10 μm) length scales as recently observed in materials like-supramolecular dendritic molecules, ABC star polymers, binary nanoparticle systems and block co-polymers in condensed matter systems. The underlying mechanism in most of these soft quasicrystals seems to be the presence of two or more length scales in the system. Another class of development in self-assembled quasicrystals in softmatter is being observed in low molecular weight chiral and achiral nematic liquid crystals. Liquid crystal forms an efficient matrix for self- and directed-assemblies of colloidal structures where surface and geometry-tuning the particles in nematic liquid crystals gives rise to complex inter-particle interactions while the long-range order results in self-assembled structures of higher order rotational symmetries. Furthermore, there has also been attempts to generate colloidal quasicrystalline defect structures by directing the assemblies using multiple and single beam lasing techniques. In the present article, we will review self- and assisted-assembly of quasicrystalline structures in nematic liquid crystals (both chiral and achiral) and discuss the underlying mechanisms.
Highlights
Quasicrystalline ordering has been first observed in synthetic multicomponent metal alloys governed by an irrational ratio of two or more atomic length scales [1,2]
We start our report with a brief listing of high molecular weight soft matter systems where quasicrystalline structures are produced by chemical synthesis in supra-molecular dendritic molecules, star terpolymers and block co-polymers
A low molecular nematic liquid crystal is found to form an efficient matrix for the self-organized quasicrystals as colloidal interactions can be tailored either by geometrical manipulation or by changing the surface anchoring
Summary
Quasicrystalline ordering has been first observed in synthetic multicomponent metal alloys governed by an irrational ratio of two or more atomic length scales [1,2]. Micron scale quasicrystalline patterns are induced by complex optical fields by trapping of colloidal particles [28], patterned photopolymerization of monomers dispersed in liquid crystals [29], and chiral nematics by creating an array of defects [30]. Perspectives of optical applications stimulated advances in this field, including formation of materials with large near-complete photonic bandgaps [31] and miniature lasers [29] In this short review, we focus on liquid crystal-based quasicrystalline structures where anisotropic media enable specific colloidal and defect interactions. We will present and discuss the quasicrystalline structures predicted [26] and experimentally realized [27,32] in thin layers of achiral and chiral nematic liquid crystals by self-organization of faceted colloidal particles or by inducing array of defects with complex optical fields. We briefly discuss the role of symmetry of the colloidal particles in nematic liquid crystal to form quasicrystalline tilings in 2D
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