Twisted and frustrated states of matter

Abstract

The World, and much of Nature that we see within it, experiences an environment of reduced symmetries. For example, living organisms are dependent on asymmetric or dissymmetric structures for their life processes. In the solid state, a large number of space groups are chiral. Conversely, in liquids, the effects of reduced symmetries are smeared out owing to the dynamical fluctuations of the constituent molecules, atoms or ions. Thus, on progressing from the strongly ordered solid to the amorphous liquid state, the effects of reduced symmetries weaken as the molecular or atomic correlations and penetration lengths fall. Between these two states of matter, the fourth state of organized fluids can be markedly affected by chirality, and over substantial length scales, owing to both the fluidity and partial ordering of the molecules. In effect, complex fluids can amplify the effects of chirality at the molecular level. Broken symmetries in selforganizing systems can lead to the formation of novel phases of matter and to the creation of structured liquids, and to the generation of nonlinear properties such as heli-, ferro-, ferri-and antiferro-electricity, and electroclinism, which can be harnessed in a wide range of applications including thermal sensors, imaging devices and information displays, to name but a few.

Nature‐Inspired Emerging Chiral Liquid Crystal Nanostructures: From Molecular Self‐Assembly to DNA Mesophase and Nanocolloids

“…[67] Chiral thermotropic LCs include diverse mesophases such as the cholesteric with helicoidal organization, blue phases with cubic nanostructures, chiral smectic with spontaneous polarization, and twist grain boundary (TGB) phase with frustrated helical superstructures. [28,31,32] In the following, the recent advances in the development of chiral thermotropic LCs and their emerging applications are discussed.…”

“…The introduction of molecular chirality, i.e., the breaking of mirror symmetry, into LCs has resulted in multitudinous chiral liquid crystalline phases such as the cholesteric, chiral smectic, twist grain boundary, and cubic blue phases each with unprecedented and unique properties. [28][29][30][31][32][33] Among chiral LCs, the phase with helicoidal organization, i.e., cholesteric superstructure, is omnipresent in many living systems, including some plant tissues, the cuticles of beetles, crabs, arthropods, and others. [34][35][36][37][38][39][40][41][42] The cuticle of beetles consists of natural biocomposites with well-organized chitin nanofibrils embedded in aqueous matrix of lipids, proteins, and polyphenols.…”

Colloquium: Geometry and optimal packing of twisted columns and filaments

“…Inter-molecular forces between chiral molecules favor textures with non-trivial, and twisted, gradients in orientation [17,18], the simplest example of which being cholesteric order. Crucially, the patterns of orientation driven by chirality are not always compatible with other types ordering of the given system, as in chiral smectics [19][20][21], or even with the geometrical constraints of space itself [22] as occurs for the double-twist textures of the liquid crystal blue phases [23,24]. [9]; C, twisted collagen fibrils derived from tendon (diameter ∼ 100 nm) [10]; D, twisted fibers of chiral organogel assemblies (diameter ∼ 100 nm) [11]; and E, mesoporous silica templated by twisted columnar assemblies of worm-like surfactant micelles, with schematic in the inset (diameter ∼ 100 nm) [12].…”

Chiral Bent‐Shaped Molecules Exhibiting Unusually Wide Range of Blue Liquid‐Crystalline Phases and Multistimuli‐Responsive Behavior

“…[3][4][5] Compared with chiral liquids, LC materials, due to their ordered nature, along with liquidity,c an amplify the molecular chirality by manyfold. [6,7] BP is af rustrated phase, consisting of doubletwist cylinders, that occurs just belowt he isotropic liquid over an arrow temperaturer ange. [8][9][10] BPs are extremelyi mportant for the development of next-generation optoelectronicd evices that do not requirea lignment layers( i.e.,p olyimide coating), which simplifies the LC display manufacturing process.…”

“…On one side of the core, there is ac holesterol moiety attached through an ester linkage, whereas, on the other side, there is a4 -n-alkoxy-2-hydroxybenzaldehyde moiety attached through an imine linkage.The homologous series with even chains, from n = 4t o 18, was synthesized. An increase in the alkyl chain length leads to the thermodynamic stabilization of the liquid-crystallinem aterial enantiotropically,a st he series makes at ransition from nonliquid crystalline (1-4, 1-6) to monotropic LC (1-8, 1-10, 1-12, and 1-14) and enantiotropic LC (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18). Compound 1-10 exhibited as table BP over aw ide range of 16.4 8C.…”