Disentangling optical effects in 3D spiral-like, chiral plasmonic assemblies templated by a dark conglomerate liquid crystal

Chiral thin films showing electronic and plasmonic circular dichroism (CD) are intensively explored for optoelectronic applications. The most studied chiral organic films are the composites exhibiting a helical geometry, which often causes entanglement of circular optical properties with unwanted linear optical effects (linearly polarized absorption or refraction). This entanglement limits tunability and often translates to a complex optical response. This paper describes chiral films based on dark conglomerate, sponge-like, liquid crystal films, which go beyond the usual helical type geometry, waiving the problem of linear contributions to chiroptical electronic and plasmonic properties. First, we show that purely organic films exhibit high electronic CD and circular birefringence, as studied in detail using Mueller matrix polarimetry. Analogous linear properties are two orders of magnitude lower, highlighting the benefits of using the bi-isotropic dark conglomerate liquid crystal for chiroptical purposes. Next, we show that the liquid crystal can act as a template to guide the assembly of chemically compatible gold nanoparticles into 3D spiral-like assemblies. The Mueller matrix polarimetry measurements confirm that these composites exhibit both electronic and plasmonic circular dichroisms, while nanoparticle presence is not compromising the beneficial optical properties of the matrix.

Glassy relaxation in a de Vries smectic liquid crystal consisting of bent-core molecules

We report experimental investigations of a liquid crystal comprising thiophene-based achiral bent-core banana shaped molecules. The compound exhibits the following phase sequence on cooling: Isotropic (517.4 K), N (514.9 K), de Vries SmA (402 K), SmC. Practically no layer contraction was observed across the SmA to SmC transition, confirming the "de Vries" nature of the SmA phase. Interestingly, the crystallization does not occur on cooling the sample, unlike most other liquid crystals. Instead, the SmC phase undergoes a glass transition at 271 K even at a slow cooling rate. The dielectric spectroscopy studies carried out on the sample reveal the presence of a dielectric mode whose relaxation process is of the Cole-Cole type. The relaxation frequency of the mode was found to drop rapidly with decreasing temperature, confirming the glassy behavior. The variation of relaxation frequency with temperature follows the Vogel-Fulcher-Tammann equation, indicating the fragile glassy nature of the sample. This report identifies a bent-core liquid crystal exhibiting a "de Vries" SmA phase and glassy behavior at lower temperatures.

Organic chiral nano- and microfilaments: types, formation, and template applications

Organic chiral nanofilaments are part of an important class of nanoscale chiral materials that has recently been receiving significant attention largely due to their potential use in applications such as optics, photonics, metameterials, and potentially a range of medical as well as sensing applications. This review will focus on key examples of the formation of such nano- and micro-filaments based on carbon nanofibers, polymers, synthetic oligo- and polypeptides, self-assembled organic molecules, and one prominent class of liquid crystals. The most critical aspects discussed here are the underlying driving forces for chiral filament formation, potentially answering why specific sizes and shapes are formed, what molecular design strategies are working equally well or rather differently among these materials classes, and what uses and applications are driving research in this fascinating field of materials science.

Gonçalves DP, Zhu C, Tilki T, Prévôt ME, Hegmann T. Controlling the Structure and Morphology of Organic Nanofilaments Using External Stimuli

In our continuing pursuit to generate, understand, and control the morphology of organic nanofilaments formed by molecules with a bent molecular shape, we here report on two bent-core molecules specifically designed to permit a phase or morphology change upon exposure to an applied electric field or irradiation with UV light. To trigger a response to an applied electric field, conformationally rigid chiral (S,S)-2,3-difluorooctyloxy side chains were introduced, and to cause a response to UV light, an azobenzene core was incorporated into one of the arms of the rigid bent core. The phase behavior as well as structure and morphology of the formed phases and nanofilaments were analyzed using differential scanning calorimetry, cross-polarized optical microscopy, circular dichroism spectropolarimetry, scanning and transmission electron microscopy, UV-vis spectrophotometry, as well as X-ray diffraction experiments. Both bent-core molecules were characterized by the coexistence of two nanoscale morphologies, specifically helical nanofilaments (HNFs) and layered nanocylinders, prior to exposure to an external stimulus and independent of the cooling rate from the isotropic liquid. The application of an electric field triggers the disappearance of crystalline nanofilaments and instead leads to the formation of a tilted smectic liquid crystal phase for the material featuring chiral difluorinated side chains, whereas irradiation with UV light results in the disappearance of the nanocylinders and the sole formation of HNFs for the azobenzene-containing material. Combined results of this experimental study reveal that in addition to controlling the rate of cooling, applied electric fields and UV irradiation can be used to expand the toolkit for structural and morphological control of suitably designed bent-core molecule-based structures at the nanoscale.

Circularly Polarized Laser Emission from Homochiral Superstructures based on Achiral Molecules with Conformal Flexibility

Without external chiral intervention, it is a challenge to form homochirality from achiral molecules with conformational flexibility. We here report on a rational strategy that uses multivalent noncovalent interactions to clamp the molecular conformations of achiral D-A molecules. These interactions overcome the otherwise dominant dipole-dipole interactions and thus disfavor their symmetric antiparallel stacking. It in turn facilitates parallel packing, leading to spontaneous symmetry breaking during crystallization and thus the formation of homochiral conglomerates. When this emergent homochirality is coupled with optical gain characteristics of the molecules, the homochiral crystals are explored as excellent circularly polarized micro-lasers with low lasing threshold (16.4 μJ cm^-2 ) and high dissymmetry factor g_lum (0.9). This study therefore provides a facile design strategy for supramolecular chiral materials and active laser ones without the necessity of intrinsic chiral element.

Effect of Nematogen Doping in Bent-Core Molecular Systems with a Helical Nanofilament and Dark Conglomerate

Two types of binary mixtures were prepared. One consisted of a calamitic nematogen and bent-core molecule with a helical nanofilament, whereas the other contained a calamitic nematogen and bent-core molecule with a dark conglomerate. The chiroptical features of these two mixtures were investigated using polarized optical microscopy and circular dichroism. In addition, X-ray diffraction analysis was performed on the two binary mixtures. The chiroptical features of the two mixtures were remarkably different. One mixture showed enhanced chiroptical features, whereas the other did not show chiroptical features. This method may help in distinguishing between helical nanofilaments and dark conglomerates which originate from bent-core molecular systems.

Switching Chirophilic Self-assembly: From meso-structures to Conglomerates in Liquid and Liquid Crystalline Network Phases of Achiral Polycatenar Compounds

Spontaneous generation of chirality from achiral molecules is a contemporary research topic with numerous implications for technological applications and for the understanding of the development of homogeneous chirality in biosystems. Herein, a series of azobenzene based rod-like molecules with an 3,4,5-trialkylated end and a single n-alkyl chain involving 5 to 20 aliphatic carbons at the opposite end is reported. Depending on the chain length and temperature these achiral molecules self-assemble into a series of liquid and liquid crystalline (LC) helical network phases. A chiral isotropic liquid (Iso1 [ *] ) and a cubic triple network phase with chiral I23 lattice were found for the short chain compounds, whereas non-cubic and achiral cubic phases dominate for the long chain compounds. Among them a mesoscale conglomerate with I23 lattice, a tetragonal phase (Tetbi ) containing one chirality synchronized and one non-synchronized achiral network, an achiral double network meso-structure with Ia3 ‾ $\bar 3$ d space group and an achiral percolated isotropic liquid mesophase (Iso1 ) were found. This sequence is attributed to an increasing strength of chirality synchronization between the networks, combined with a change of the preferred mode of chirophilic self-assembly between the networks, switching from enantiophilic to enantiophobic with decreasing chain length and lowering temperature. These nanostructured and mirror symmetry broken LC phases exist over wide temperature ranges which is of interest for potential applications in chiral and photosensitive functional materials derived from achiral compounds.

Chiroptical Performances in Self-Assembled Hierarchical Nanosegregated Chiral Intermediate Phases Composed of Two Different Achiral Bent-Core Molecules

In this paper, chiral intermediate phases composed of two achiral molecules are fabricated by utilizing nanophase separation and molecular hierarchical self-organization. An achiral bent-core guest molecule, exhibiting a calamitic nematic and a dark conglomerate phase according to the temperature, is mixed with another achiral bent-core host molecule possessing a helical nanofilament to separate the phases between them. Two nanosegregated phases are identified, and considerable chiroptical changes, such as circular dichroism and circularly polarized luminescence, are detected at the transition temperatures between the different nanophase-separated states. The nanosegregated chiral phase-wherein the helical nanofilament and dark conglomerate phases are phase-separated-exhibits the highest chiroptical intensities. The luminescence dissymmetry factor, |g_lum|, in this phase is amplified by an order of magnitude compared with that of another nanosegregated phase, wherein the helical nanofilament and nematic phases are phase-separated.

Shear-induced birefringence in an optically isotropic cubic liquid crystalline phase

We report an unusually strong flow-induced birefringence in an optically isotropic cubic phase occurring below the isotropic chiral conglomerate phase formed by a low-molecular-weight polycatenar mesogen. The transition into the birefringent state occurs thresholdless and the induced birefringence is comparable with that observed in polymeric systems. We suggest that the flow-induced deformation of the cubic structure is responsible for the strong rheo-optical response.

Liquid crystal-templated chiral nanomaterials: from chiral plasmonics to circularly polarized luminescence

Chiral nanomaterials with intrinsic chirality or spatial asymmetry at the nanoscale are currently in the limelight of both fundamental research and diverse important technological applications due to their unprecedented physicochemical characteristics such as intense light-matter interactions, enhanced circular dichroism, and strong circularly polarized luminescence. Herein, we provide a comprehensive overview of the state-of-the-art advances in liquid crystal-templated chiral nanomaterials. The chiroptical properties of chiral nanomaterials are touched, and their fundamental design principles and bottom-up synthesis strategies are discussed. Different chiral functional nanomaterials based on liquid-crystalline soft templates, including chiral plasmonic nanomaterials and chiral luminescent nanomaterials, are systematically introduced, and their underlying mechanisms, properties, and potential applications are emphasized. This review concludes with a perspective on the emerging applications, challenges, and future opportunities of such fascinating chiral nanomaterials. This review can not only deepen our understanding of the fundamentals of soft-matter chirality, but also shine light on the development of advanced chiral functional nanomaterials toward their versatile applications in optics, biology, catalysis, electronics, and beyond.

Chiroptical Characteristics of Nanosegregated Phases in Binary Mixture Consisting of Achiral Bent-Core Molecule and Bent-Core Base Main-Chain Polymer

In this paper, a binary mixture system consisting of an achiral bent-core molecule and a bent-core base main-chain polymer is described. The mixture exhibits an intriguing nanosegregated phase generated by the phase separation of the helical nanofilament B4 phase (originating from the bent-core molecule) and the dark conglomerate phase (originating from the bent-core base main-chain polymer). This nanosegregated phase was identified using polarized optical microscopy, differential scanning calorimetry, and X-ray diffraction analysis. In this nanosegregated phase, the enantiomeric domains grew to a few millimeters and a giant circular dichroism was observed. The structural chirality of the helical nanofilament B4 phase affected the conformation of the bent-core base main-chain polymer embedded within the helical nanofilament networks of bent-core molecules.

Cumulative geometric frustration and superextensive energy scaling in a nonlinear classical XY-spin model

Geometric frustration results from a discrepancy between the locally favored arrangement of the constituents of a system and the geometry of the embedding space. Geometric frustration can be either noncumulative, which implies an extensive energy growth, or cumulative, which implies superextensive energy scaling and highly cooperative ground-state configurations which may depend on the dimensions of the system. Cumulative geometric frustration was identified in a variety of continuous systems including liquid crystals, filament bundles, and molecular crystals. However, a spin-lattice model which clearly demonstrates cumulative geometric frustration was lacking. In this paper we describe a nonlinear variation of the XY-spin model on a triangular lattice that displays cumulative geometric frustration. The model is studied numerically and analyzed in three distinct parameter regimes, which are associated with different energy minimizing configurations. We show that, despite the difference in the ground-state structure in the different regimes, in all cases the superextensive power-law growth of the frustration energy for small domains grows with the same universal exponent that is predicted from the structure of the underlying compatibility condition.

Hierarchical self-assembly into chiral nanostructures

One basic principle regulating self-assembly is associated with the asymmetry of constituent building blocks or packing models. Using asymmetry to manipulate molecular-level devices and hierarchical functional materials is a promising topic in materials sciences and supramolecular chemistry. Here, exemplified by recent major achievements in chiral hierarchical self-assembly, we show how chirality may be utilized in the design, construction and evolution of highly ordered and complex chiral nanostructures. We focus on how unique functions can be developed by the exploitation of chiral nanostructures instead of single basic units. Our perspective on the future prospects of chiral nanostructures via the hierarchical self-assembly strategy is also discussed.

Symmetry breaking-induced double-strand helices in H-bonded coassembly

Double-strand helical structures are important in information storage of biomacromolecules, while the artificial synthesis depends on chirality transfer from the molecular to supramolecular scale, and the synthesis through symmetry breaking has yet been accomplished. In this work, we present the multiple-constituent coassembly of a melamine derivative and an N-terminal aromatic amino acid into double helical nanoarchitectures via symmetry breaking. Multiple intramolecular H-bond formation between constituents played key roles in directing the formation of helical structures. Intertwining of single helices with identical helical parameters afforded double helical structures, benefiting from the uniformity and monodispersity of nanoarchitectures. With introduction of coded chiral amino acid derivatives as chiral sources, the handedness could be readily manipulated with exclusive correlation to the absolute chirality of amino acids. Molecular flexibility of the melamine derivative facilitates the propeller-shaped complex formation to afford helical columnar coassemblies and double helical structures. This work presents a rational control over the emergence and properties of double helical structures in multiple-constituent coassemblies through symmetry breaking, which provides an alternative method towards the synthesis of topological chiral composites and chiroptical materials.

Single-Handed Double Helix and Spiral Platelet Formed by Racemate of Dissymmetric Cages

Spontaneous deracemization has been used to separate homochiral domains from the racemic system. However, homochirality can only be referred to when the scales of these domains and systems are specified. To clarify this, we report self-assembly of racemates of dissymmetric cages DC-1 with a cone-shape propeller geometry, forming a centrosymmetric columnar crystalline phase (racemic at crystallographic level). Owing to their anisotropic geometry, the two enantiomers are packed in a frustrated fashion in this crystalline phase; single-handed double helices are observed (single-handedness at supramolecular level). The frustrated packing (layer continuity break-up) in turn facilitates screw dislocation during the crystal growth, forming left- or right-handed spiral platelets (symmetry-breaking at morphological level), although each platelet is composed of DC-1 racemates. The symmetry correlation between DC-1 molecules, the crystalline phase and spiral platelets, all exhibit C₃ symmetry.

Molecular Conformation of Bent-Core Molecules Affected by Chiral Side Chains Dictates Polymorphism and Chirality in Organic Nano- and Microfilaments

The coupling between molecular conformation and chirality is a cornerstone in the construction of supramolecular helical structures of small molecules across various length scales. Inspired by biological systems, conformational preselection and control in artificial helical molecules, polymers, and aggregates has guided various applications in optics, photonics, and chiral sorting among others, which are frequently based on an inherent chirality amplification through processes such as templating and self-assembly. The so-called B4 nano- or microfilament phase formed by some bent-shaped molecules is an exemplary case for such chirality amplification across length scales, best illustrated by the formation of distinct nano- or microscopic chiral morphologies controlled by molecular conformation. Introduction of one or more chiral centers in the aliphatic side chains led to the discovery of homochiral helical nanofilament, helical microfilament, and heliconical-layered nanocylinder morphologies. Herein, we demonstrate how a priori calculations of the molecular conformation affected by chiral side chains are used to design bent-shaped molecules that self-assemble into chiral nano- and microfilament as well as nanocylinder conglomerates despite the homochiral nature of the molecules. Furthermore, relocation of the chiral center leads to formation of helical as well as flat nanoribbons. Self-consistent data sets from polarized optical as well as scanning and transmission electron microscopy, thin-film and solution circular dichroism spectropolarimetry, and synchrotron-based X-ray diffraction experiments support the progressive and predictable change in morphology controlled by structural changes in the chiral side chains. The formation of these morphologies is discussed in light of the diminishing effects of molecular chirality as the chain length increases or as the chiral center is moved away from the core-chain juncture. The type of phase (B1-columnar or B4) and morphology of the nano- or microfilaments generated can further be controlled by sample treatment conditions such as by the cooling rate from the isotropic melt or by the presence of an organic solvent in the ensuing colloidal dispersions. We show that these nanoscale morphologies can then organize into a wealth of two- and three-dimensional shapes and structures ranging from flower blossoms to fiber mats formed by intersecting flat nanoribbons.

Chirality of Liquid Crystals Formed from Achiral Molecules Revealed by Resonant X-Ray Scattering

Intensive research on chiral liquid crystals (LCs) has been fueled by their actively tunable physicochemical properties and structural complexity, comparable to those of sophisticated natural materials. Herein, recent progress in the discovery of new classes of chiral LCs, enabled by a combination of nano- and macroscale investigations is reviewed. First, an overview is provided of liquid crystalline phases, made of chiral and achiral low-weight molecules, that exhibit chiral structure and/or chiral morphology. Then, recent progress in the discovery of new classes of chiral LCs, particularly enabled by the application of resonant X-ray scattering is described. It is shown that the method is sensitive to modulations of molecular orientation and therefore provides information hardly accessible by means of other techniques, such as the sense of helical structures or chirality transfer across length scales. Finally, a perspective is presented on the future scope, opportunities, and challenges in the field of chiral LCs, in particular related to nanocomposites.

The formation of a chiral supramolecular structure acting as a template for chirality transfer

Spontaneous mirror symmetry breaking in self-assembled achiral trimers under a nonequilibrium state induces supramolecular chirality, which is stabilized by a polymer network to produce a homochiral material. Chirality is transferred to the polymer film in the course of polymerization of achiral reactive monomers on the surface.

Spontaneous mirror symmetry breaking in benzil-based soft crystalline, cubic liquid crystalline and isotropic liquid phases

Benzil (diphenylethane-1,2-dione), which is a long known example for an achiral molecule crystallizing in a chiral space group, can also show mirror symmetry breaking in the fluid state if it is suitably functionalized. For some of the new benzil derivatives even three different subsequent mirror symmetry broken soft matter states with a chiral conglomerate structure can be observed. One is an isotropic liquid, the second one a cubic liquid crystal with a complex network structure and the third is a soft crystalline solid. Chirality develops by helical self-assembly combined with dynamic network formation, thus allowing macroscopic chirality synchronization. These achiral molecules, combining a transiently chiral bent core with multiple alkyl chains, provide a unique link between the mirror symmetry breaking phenomena observed for polycatenar and bent-core mesogens. The homogeneously chiral networks are of interest for application as chiral materials, and as templates for chiral recognition, separation and enantioselective catalysis.

Impact of a chiral supramolecular nanostructure on the mechanical and electrical performances of triphenylene-based discotic physical gels

Discotic π-conjugated supramolecular assemblies, especially with chiral supramolecular nanostructures, have been attracting growing research interest due to their significant optoelectronic properties and the possibilities of their applications in the new generation of organic semiconductors. However, the impact of supramolecular chirality on their mechanical and electrical performances remains poorly understood. Herein, a series of optically active supramolecular gels were formed from achiral triphenylene derivatives by introducing limonene as the chiral source. Owing to the well-ordered supramolecular packing, the homochiral supramolecular gels exhibited greater mechanical strength and higher conductivity, compared to heterochiral architectures. The impact of supramolecular packing in homochiral or heterochiral assemblies on their resulting mechanical and electrical performances was investigated in detail, which might be of great fundamental value for the rational design of chiral π-conjugated supramolecular nanostructures for applications in chiral optoelectronics.

Possible Physical Basis of Mirror Symmetry Effect in Racemic Mixtures of Enantiomers: From Wallach’s Rule, Nonlinear Effects, B–Z DNA Transition, and Similar Phenomena to Mirror Symmetry Effects of Chiral Objects

Effects associated with mirror symmetry may be underlying for a number of phenomena in chemistry and physics. Increase in the density and melting point of the 50%L/50%D collection of enantiomers of a different sign (Wallach’s rule) is probably based on a physical effect of the mirror image. The catalytic activity of metal complexes with racemic ligands differs from the corresponding complexes with enantiomers as well (nonlinear effect). A similar difference in the physical properties of enantiomers and racemate underlies L/D inversion points of linear helical macromolecules, helical nanocrystals of magnetite and boron nitride etc., B–Z DNA transition and phenomenon of mirror neurons may have a similar nature. Here we propose an explanation of the Wallach effect along with some similar chemical, physical, and biological phenomena related to mirror image.

Viscoelastic properties of a thioether-based heliconical twist-bend nematogen

The twist-bend nematic (N_TB) phase is one of the new types of nematics found recently, which possesses local nematic order with a heliconical orientational modulation at the nanoscale. Herein, we quantitatively determined, for the first time, the temperature-dependent elastic and viscosity properties in both the nematic (N) and N_TB phases using a thioether-linked cyanobiphenyl dimer CBS7SCB exhibiting a broad temperature range of the N_TB phase which is stable down to room temperature. In the N phase, the fundamental elastic moduli: splay and bend elastic moduli (K₁₁ and K₃₃, respectively) are found to be in the order of 10^-12 N, and the effective rotational viscosity (γ₁) is determined to be in the range of 5-200 mPa s. Meanwhile, the N_TB phase is found to exhibit a compressive elastic modulus B in the order of several tens of kilopascals, the effective K₁₁ in the order of 10^-10-10^-8 N, and a considerably large γ₁ value of ∼68.7 Pa s right below the N-N_TB phase transition. The present study provides insights into the comprehensive viscoelastic properties based on comparison of the obtained experimental data with not only the existing theoretical prediction but also the preceding experimental works.

Stereochemical Rules Govern the Soft Self-Assembly of Achiral Compounds: Understanding the Heliconical Liquid-Crystalline Phases of Bent-Core Mesogens

A series of bent-shaped 4-cyanoresorcinol bisterephthalates is reported. Some of these achiral compounds spontaneously form a short-pitch heliconical lamellar liquid-crystalline phase with incommensurate 3-layer pitch and the helix axis parallel to the layer normal. It is observed at the paraelectric-(anti)ferroelectric transition, if it coincides with the transition from random to uniform tilt and with the transition from anticlinic to synclinic tilt correlation of the molecules in the layers of the developing tilted smectic phase. For compounds with long chains the heliconical phase is only field-induced, but once formed it is stable in a distinct temperature range, even after switching off the field. The presence of the helix changes the phase properties and the switching mechanism from the naturally preferred rotation around the molecular long axis, which reverses the chirality, to a precession on a cone, which retains the chirality. These observations are explained by diastereomeric relations between two coexisting modes of superstructural chirality. One is the layer chirality, resulting from the combination of tilt and polar order, and the other one is the helical twist evolving between the layers. At lower temperature the helical structure is replaced by a non-tilted and ferreoelectric switching lamellar phase, providing an alternative non-chiral way for the transition from anticlinic to synclinic tilt.

Shaping Liquid Crystals with Gold Nanoparticles: Helical Assemblies with Tunable and Hierarchical Structures Via Thin-Film Cooperative Interactions

The availability of helical assemblies of plasmonic nanoparticles with precisely controlled and tunable structures can play a key role in the future development of chiral plasmonics and metamaterials. Here, a strategy to efficiently yield helical structures based on the cooperative interactions of liquid crystals and gold nanoparticles in thin films is developed. These nanocomposites exhibit exceptional long-range hierarchical order across length scales, which results from the growth mechanism of nanoparticle-coated twisted nanoribbons and their ability to form organized bundles. The helical assembly formation is governed by the presence of rationally functionalized nanoparticles. Importantly, the thickness of the achieved nanocomposites can be reversibly reconfigured owing to the polymorphic nature of the liquid crystal. The versatility of the proposed approach is demonstrated by preparing helices assembled from nanoparticles of different geometries and dimensions (spherical and rod-like). The described strategy may become an enabling technology for structuring nanoparticle assemblies with high precision and fabricating optically active materials.

Symmetry Breaking in Self-Assembled Nanoassemblies

The origin of biological homochirality, e.g., life selects the L-amino acids and D-sugar as molecular component, still remains a big mystery. It is suggested that mirror symmetry breaking plays an important role. Recent researches show that symmetry breaking can also occur at a supramolecular level, where the non-covalent bond was crucial. In these systems, equal or unequal amount of the enantiomeric nanoassemblies could be formed from achiral molecules. In this paper, we presented a brief overview regarding the symmetry breaking from dispersed system to gels, solids, and at interfaces. Then we discuss the rational manipulation of supramolecular chirality on how to induce and control the homochirality in the self-assembly system. Those physical control methods, such as Viedma ripening, hydrodynamic macro- and micro-vortex, superchiral light, and the combination of these technologies, are specifically discussed. It is hoped that the symmetry breaking at a supramolecular level could provide useful insights into the understanding of natural homochirality and further designing as well as controlling of functional chiral materials.

Nanoconfinement of the Low-Temperature Dark Conglomerate: Structural Control from Focal Conics to Helical Nanofilaments

The helical nanofilament (HNF) and low-temperature dark conglomerate (DC) liquid-crystal (LC) phases of bent-core molecules show the same local layer structure but present different bulk morphologies. The DC phase is characterized by the formation of nanoscale toric focal conics, whereas the HNF phase is constructed of bundles of twisted layers. Although the local layer structure is similar in both phases, materials that form these phases tend to form one morphology in preference to the other. Targeted control of the nanostructures would provide pathways to potential applications and insight into how conditions drive a specific phase formation. Here, W624, a compound known to form the DC phase is confined in nanometer scale channels of porous anodized aluminum oxide (AAO) membranes. Within each nanochannel, the DC phase is suppressed forming the HNF structure instead, indicating the nanoscale spatial limitation can control the phase structure of the DC phase.

Сhiral and Racemic Fields Concept for Understanding of the Homochirality Origin, Asymmetric Catalysis, Chiral Superstructure Formation from Achiral Molecules, and B-Z DNA Conformational Transition

The four most important and well-studied phenomena of mirror symmetry breaking of molecules were analyzed for the first time in terms of available common features and regularities. Mirror symmetry breaking of the primary origin of biological homochirality requires the involvement of an external chiral inductor (environmental chirality). All reviewed mirror symmetry breaking phenomena were considered from that standpoint. A concept of chiral and racemic fields was highly helpful in this analysis. A chiral gravitational field in combination with a static magnetic field (Earth’s environmental conditions) may be regarded as a hypothetical long-term chiral inductor. Experimental evidences suggest a possible effect of the environmental chiral inductor as a chiral trigger on the mirror symmetry breaking effect. Also, this effect explains a conformational transition of the right-handed double DNA helix to the left-handed double DNA helix (B-Z DNA transition) as possible DNA damage.

Indication of a twist-grain-boundary-twist-bend phase of flexible core bent-shape chiral dimers

The effect of the molecular chirality of chiral additives on the nanostructure of the twist-bend nematic (NTB) liquid crystal phase with ambidextrous chirality and nanoscale pitch due to spontaneous symmetry breaking is studied. It is found that the ambidextrous nanoscale pitch of the NTB phase increases by 50% due to 3% chiral additive, and the chiral transfer among the biphenyl groups disappears in the NTB* phase. Most significantly, a twist-grain boundary (TGB) type phase is found at c > 1.5 wt% chiral additive concentrations below the usual N* phase and above the non-CD active NTB* phase. In such a TGB type phase, the adjacent blocks of pseudo-layers of the nanoscale pitch rotate across the grain boundaries.

Linear symmetric liquid crystal trimers exhibiting supramolecular chiral architectures

We prepared a homologous series of achiral liquid crystal trimers (I-n) in which two phenylpyrimidine units and one biphenyl unit were connected via flexible spacers, and investigated the physical properties. All the trimers possessing odd-numbered methylene spacers exhibited soft crystalline chiral conglomerate phases. X-ray diffraction measurements reveal that they have an intercalated layer structure. On the other hand, the trimers possessing even-numbered spacers showed nematic and smectic C phases. We investigated the surface structures of odd-membered trimers in the soft crystalline phases using scanning electron microscopy. Trimers I-3 and I-5 were found to form cylindrical tubes, whereas trimers I-7, I-9 and I-11 toroidal pits. We discuss the formation of diverse supramolecular architectures in terms of the anisotropy of the chirality transfer.

Towards homochiral supramolecular entities from achiral molecules by vortex mixing-accompanied self-assembly

Achieving homochirality is challenging both at the molecular and the supramolecular levels. While the origin of molecular homochirality still remains mysterious, the fabrication of homochiral assemblies from achiral molecules has attracted considerable interest since it provides many clues to understand the origin of molecular chirality. Here, by using a vortex mixing-accompanied self-assembly strategy, we obtained near-unity homochiral entities with controlled handedness from supramolecular gels that consist of exclusively achiral molecules without any chiral additives. The common supramolecular gelation process via heating and cooling of the achiral molecules only resulted in racemic gels. However, if vortex mixing is applied during the self-assembly, near-unity homochiral assemblies with uncontrolled handedness were obtained. Vortex mixing during the nucleation stage was found to be crucial in this case. On the other hand, if a small amount of the above vortex mixing produced assemblies was added as chiral seeds into the racemic gels, the racemic gels turned into near-unity homochiral suspensions with controlled handedness via a ripening process. Our studies provide an intriguing approach for achieving homochiral supramolecular assemblies from achiral molecules.

Curved boundaries and chiral instabilities - two sources of twist in homeotropic nematic tori

Many liquid crystalline systems display spontaneous breaking of achiral symmetry, as achiral molecules aggregate into large chiral domains. In confined cylinders with homeotropic boundary conditions, chromonic liquid crystals - which have a twist elastic modulus which is at least an order of magnitude less than their splay and bend counter parts - adopt a twisted escaped radial texture (TER) to minimize their free energy, whilst 5CB - which has all three elastic constants roughly comparable - does not. In a recent series of experiments, we have shown that 5CB confined to tori and bent cylindrical capillaries with homeotropic boundary conditions also adopts a TER structure resulting from the curved nature of the confining boundaries [P. W. Ellis et al., Phys. Rev. Lett., 2018, 247803]. We shall call this microscopic twist, as the twisted director organization not only depends on the confinement geometry but also on the values of elastic moduli. Additionally, we demonstrate theoretically that the curved geometry of the boundary induces a twist in the escaped radial (ER) texture. Moving the escaped core of the structure towards the center of the torus not only lowers the splay and bend energies, but lowers the energetic cost of this distinct source for twist that we shall call geometric twist. As the torus becomes more curved, the ideal location for the escaped core approaches the inner radius of the torus.

Supramolecular polymerization: challenges and advantages of various methods in assessing the aggregation mechanism

Oligothiophenes with branched alkyl end groups show distinct aggregation in organic solvents. The process of supramolecular polymerization is assessed by three different methods (UV-vis absorption and fluorescence emission spectroscopy and dynamic light scattering) to exclude artifacts. An apparent dependence of the degree of aggregation on the concentration of the oligomers is observed. Above the upper limit of concentration (a lower micromolar range for the present class of compounds), experimental data delivered conflicting results and the concentration should not therefore be exceeded. Scanning force microscopy and molecular dynamics simulations confirm the formation of one-dimensional aggregates with presumably helical arrangement of the achiral monomers.

Porous surface of an achiral trimer in the chiral conglomerate phase catalyzes a direct aldol reaction

The honeycomb-like porous surface consisting of linear trimer molecules catalyzes the direct aldol reaction of acetone with benzaldehyde at room temperature to give racemic β-hydroxyketone.

Curvature-Induced Twist in Homeotropic Nematic Tori

We confine a nematic liquid crystal with homeotropic anchoring to stable toroidal droplets and study how geometry affects the equilibrium director configuration. In contrast to the case of cylindrical confinement, we find that the equilibrium state is chiral-a twisted and escaped radial director configuration. Furthermore, we find that the magnitude of the twist distortion increases as the ratio of the ring radius to the tube radius decreases; we confirm this with computer simulations of optically polarized microscopy textures. In addition, numerical calculations also indicate that the local geometry indeed affects the magnitude of the twist distortion. We further confirm this curvature-induced twisting using bent cylindrical capillaries.

Double helical structure of the twist-bend nematic phase investigated by resonant X-ray scattering at the carbon and sulfur K-edges

The mesogenic dimer displaying nematic and NTB phases was investigated by resonant X-ray scattering at both C and S absorption K-edges and supported by single X-ray crystallography. In the crystal resonant studies revealed the forbidden reflection in non-resonant diffraction similar to that found in the NTB phase. The lack of a second harmonic in both C and S resonant X-ray scattering supports the double helical structure of the twist-bend nematic phase.

Geometric frustration and compatibility conditions for two-dimensional director fields

Bent core (or banana shaped) liquid-crystal-forming-molecules locally favor an ordered state of zero splay and constant bend. Such a state, however, cannot be realized in the plane and the resulting liquid-crystalline phase is frustrated and must exhibit some compromise of these two mutually contradicting local intrinsic tendencies. This constitutes one of the most well-studied examples in which the intrinsic geometry of the constituents of a material gives rise to a geometrically frustrated assembly. Such geometric frustration is not only natural and ubiquitous but also leads to a striking variety of morphologies of ground states and exotic response properties. In this work we establish the necessary and sufficient conditions for two scalar functions, s and b to describe the splay and bend of a director field in the plane. We generalize these compatibility conditions for geometries with non-vanishing constant Gaussian curvature, and provide a reconstruction formula for the director field depending only on the splay and bend fields and their derivatives. Finally, we discuss optimal compromises for simple incompatible cases where the locally preferred values of the splay and bend cannot be simultaneously achieved.