Understanding the Role of Trapezoids in Honeycomb Self-Assembly-Pathways between a Columnar Liquid Quasicrystal and its Liquid-Crystalline Approximants.

Quasiperiodic patterns and crystals-having long range order without translational symmetry-have fascinated researchers since their discovery. In this study, we report on new p-terphenyl-based T-shaped facial polyphiles with two alkyl end chains and a glycerol-based hydrogen-bonded side group that self-assemble into an aperiodic columnar liquid quasicrystal with 12-fold symmetry and its periodic liquid-crystalline approximants with complex superstructures. All represent honeycombs formed by the self-assembly of the p-terphenyls, dividing space into prismatic cells with polygonal cross-sections. In the perspective of tiling patterns, the presence of unique trapezoidal tiles, consisting of three rigid sides formed by the p-terphenyls and one shorter, incommensurate, and adjustable side by the alkyl end chains, plays a crucial role for these phases. A delicate temperature-dependent balance between conformational, entropic and space-filling effects determines the role of the alkyl chains, either as network nodes or trapezoid walls, thus resulting in the order-disorder transitions associated with emergence of quasiperiodicity. In-depth analysis suggests a change from a quasiperiodic tiling involving trapezoids to a modified one with a contribution of trapezoid pair fusion. This work paves the way for understanding quasiperiodicity emergence and develops fundamental concepts for its generation by chemical design of non-spherical molecules, aggregates, and frameworks based on dynamic reticular chemistry.

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.

Chirality Induction through Nano-Phase Separation: Alternating Network Gyroid Phase by Thermotropic Self-Assembly of X-Shaped Bolapolyphiles.

The single gyroid phase as well as the alternating double network gyroid, composed of two alternating single gyroid networks, hold a significant place in ordered nanoscale morphologies for their potential applications as photonic crystals, metamaterials and templates for porous ceramics and metals. Here, we report the first alternating network cubic liquid crystals. They form through self-assembly of X-shaped polyphiles, where glycerol-capped terphenyl rods lie on the gyroid surface while semiperfluorinated and aliphatic side-chains fill their respective separate channel networks. This new self-assembly mode can be considered as a two-color symmetry-broken double gyroid morphology, providing a tailored way to fabricate novel chiral structures with sub-10 nm periodicities using achiral compounds.

Polar Order, Mirror Symmetry Breaking, and Photoswitching of Chirality and Polarity in Functional Bent-Core Mesogens.

In recent years, liquid crystals (LCs) responding to light or electrical fields have gained significant importance as multifunctional materials. Herein, two new series of photoswitchable bent-core liquid crystals (BCLCs) derived from 4-cyanoresorcinol as the central core connected to an azobenzene based wing and a phenyl benzoate wing are reported. The self-assembly of these molecules was characterized by differential scanning calorimetry (DSC), polarizing light microscopy (POM), electro-optical, dielectric, second harmonic generation (SHG) studies, and XRD. Depending on the direction of the COO group in the phenyl benzoate wing, core-fluorination, temperature, and the terminal alkyl chain length, cybotactic nematic and lamellar (smectic) LC phases were observed. The coherence length of the ferroelectric fluctuations increases continuously with decreasing temperature and adopts antipolar correlation upon the condensation into superparaelectric states of the paraelectric smectic phases. Finally, long-range polar order develops at distinct phase transitions; first leading to polarization modulated and then to nonmodulated antiferroelectric smectic phases. Conglomerates of chiral domains were observed in the high permittivity ranges of the synclinic tilted paraelectric smectic phases of these achiral molecules, indicating mirror symmetry breaking. Fine-tuning of the molecular structure leads to photoresponsive bent-core (BC)LCs exhibiting a fast and reversible photoinduced change of the mode of the switching between ferroelectric- and antiferroelectric-like as well as a light-induced switching between an achiral and a spontaneous mirror-symmetry-broken LC phase.

A Self-Assembled Bicontinuous Cubic Phase with a Single-Diamond Network.

The first single-diamond cubic phase in a liquid crystal is reported. This skeletal structure with the F d 3 ‾ m space group is formed by self-assembly of bolaamphiphiles with swallow-tailed lateral chains. It consists of bundles of π-conjugated p-terphenyl rods fused into an infinite network by hydrogen-bonded spheres at tetrahedral four-way junctions. We also present a quantitative model relating molecular architecture to the space-filling requirements of six possible bicontinuous cubic phases, that is, the single- and double-network versions of gyroid, diamond, and "plumber's nightmare".

Lamellar Liquid Crystals of In-Plane Lying Rod-Like Mesogens with Designer Side-Chains: The Case of Sliding versus Locked Layers.

The dimensionality of self-assembled nanostructures plays an essential role for their properties and applications. Herein, an understanding of the transition from weakly to strongly coupled layers in soft matter systems is provided involving in-plane organized π-conjugated rods. For this purpose, bolaamphiphilic triblock molecules consisting of a rigid biphenyl core, polar glycerol groups at the ends, and a branched (swallow-tail) or linear alkyl or semiperfluoroalkyl chain in lateral position have been synthesized and investigated. Besides weakly coupled lamellar isotropic (LamIso ), lamellar nematic (LamN ) and sliding lamellar smectic phases (LamSm ), a sequence of three distinct types of strongly coupled (correlated) lamellar smectic phases with either centered (c2mm) or non-centered rectangular (p2mm) lattice and an intermediate oblique lattices (p2) were observed depending on chain length, chain branching and degree of chain fluorination. This new sequence is explained by the strengthening of the layer coupling and the competition between energetic packing constraints and the entropic contribution of either longitudinal or tangential fluctuations. This example of directed side chain engineering of small generic model compounds provides general clues for morphological design of two-dimensional and three-dimensionally coupled lamellar systems involving larger π-conjugated molecular rods and molecular or supramolecular polymers, being of actual interest in organic electronics and nanotechnology.

Hydrogen-bonded mesomorphic complexes combining hydrophilic and fluorophilic molecular segments.

A 2,4-diamino-6-phenyl-1,3,5-triazine carrying a single oligo(ethylene oxide) (EO) chain has been investigated in binary mixtures with two-chain and three-chain semiperfluorinated benzoic acids. Mixtures of the triazine with three equivalents of the complementary acids exhibit a hexagonal columnar (Colh) mesophase. Docking of three acid molecules to the diaminotriazine nucleus leads to the formation of disc-like aggregates with a central hydrogen-bonded polar core surrounded by the peripheral fluoroalkyl chains, which self-assemble in columns arranged on a hexagonal lattice. The polar EO chains at the triazine cores do not segregate into a distinct sub-space but are included into the polar cores, providing increased flexibility of the cores with respect to conformations and available hydrogen bonding sites. In equimolar (1 : 1) triazine/benzoic acid mixtures macroscopic phase separation of excess triazine from the columnar LC phases occurs. These Colh phases are formed by [1 : 3] or [2 : 4] complexes, depending on the number of fluorinated chains. However, some of the excess triazine component is accommodated within the polar column cores, contributing to space filling and providing additional hydrogen bonding along the columns. Thus the EO chain, despite of being fixed at the periphery, assemble in the core region of the aggregates, this is distinct from the self-assembly of related alkyl or semiperfluoroalkyl substituted diaminotriazines with fluorinated benzoic acids, forming discrete disc-like [1 : 3] or rod-like [1 : 1] complexes. Obviously, the flexible EO chains decrease the effect of the aggregate shape on self-assembly and lead to an increased contribution of general amphiphilicity to self-assembly.

Development of Polar Order by Liquid-Crystal Self-Assembly of Weakly Bent Molecules.

Organic ferroelectrics are of growing importance for multifunctional materials. Here we provide an understanding of the distinct stages of the development of sterically induced polar order in liquid-crystalline (LC) soft matter. Three series of weakly bent molecules derived from 4-cyanoresorcinol as the bent core unit with laterally fluorinated azobenzene wings have been synthesized, and the effects of the position of fluorine substitution, alkyl-chain length, and temperature on the LC self-assembly and polar order were studied. In the LC phases a paraelectric-ferroelectric transition took place as the size of the polar domains gradually increased, thereby crossing a permittivity maximum, similar to inorganic solid-state ferroelectrics. An increase in polar coherence length simultaneously led to a transition from synpolar to antipolar domain correlation in the high-permittivity paraelectric range. Associated with the emergence of polar order was the development of a tilted organization of the molecules and a growing coherence of tilt. This led to a transition from non-tilted via tilt-randomized uniaxial to long-range-tilted biaxial smectic phases, and to surface-stabilized symmetry breaking with the formation of chiral conglomerates and field-induced tilt. Moreover, there is a remarkably strong effect of the position of fluorination; polar order is favored by peripheral core substitution and is suppressed by inside-directed fluorination.

Polyphilic hydrogen bonded block molecules involving semiperfluorinated and silylated molecular fragments.

2,4-Diamino-6-phenyl-1,3,5-triazines grafted with one or two semiperfluorinated chains at the phenyl substituent have been investigated in binary mixtures with one-chain and two-chain oligo(dimethylsiloxy) terminated 4-alkoxy- and 3,4-dialkoxybenzoic acids. Equimolar mixtures of the triazines with the complementary acids form discrete double hydrogen-bonded heterodimers with an elongated central core. Mesomorphic properties are observed only if at least two terminal fluoroalkyl chains are attached to the triazine entity. Three to four heterodimers generate aggregates with preferably parallel adjusted rod-like H-bonded cores. The space requirement of the segregated peripheral fluoroalkyl and oligosiloxane segments considerably exceeds that of the central core region, leading to an overall circular geometry of the associates which organize in columnar LC phases. The chains initiate a local segregation which is however not long range and retains a time and space averaged two-dimensional hexagonal lattice.

Emergence of tilt in square honeycomb liquid crystals.

First liquid crystalline phases with tilted organization of rod-like aromatics in a square honeycomb structure were discovered. The developing tilt is temperature, chain length and chain volume dependent, and has a dramatic effect on the optical properties, occasionally leading to an inversion of birefringence. The observed effects of chain branching on tilt contributes to a general understanding of lateral chain engineering in tailoring the self-assembly of π-conjugated molecular rods.

Transition from nematic to gyroid-type cubic soft self-assembly by side-chain engineering of π-conjugated sticky rods.

A sequence of liquid crystalline phases, involving cybotactic nematics, a lamellar phase, bicontinuous cubics and triangular honeycombs, was observed for oligo(phenylene ethynylene) based X-shaped bolapolyphiles with two long lateral alkyl chains and sticky ends provided by glycerol groups. In the cubic phase with Ia3[combining macron]d lattice - which is tailored by alkyl chain engineering - the aromatic cores are organized on the gyroid minimal surface in 3D curved layers of almost parallel aligned π-conjugated rods. It is shown that this type of cubic phase is a general mode of soft self-assembly of X-shaped bolapolyphiles at the cross-over from the (long or short range) lamellar to the triangular honeycomb-like organization. Cubic phase formation is found only in a narrow range with respect to temperature and chain-length for the non-fluorinated compounds and in much wider ranges for related core-fluorinated molecules.

Emergence of polar order and tilt in terephthalate based bent-core liquid crystals.

A new bent-core liquid crystalline material consisting of a 4-cyanoresorcinol unit with two terephthalate based rod-like wings and terminated by two short alkyl chains was synthesized. Its liquid crystalline (LC) self-assembly and the development of polar order in the LC phases were investigated. The polar order is characterised using second harmonic generation and dielectric spectroscopy techniques in addition to XRD and DSC characterisations of the mesophase structure and investigation of freely suspended films. We demonstrate the growth of ferroelectric domains in the paraelectric SmA phase (SmAPR), which adopt antipolar correlations (SmAPAR) and eventually condense into a weakly tilted antiferroelectric smectic phase (SmCaPA).

Chirality Synchronization of Hydrogen-Bonded Complexes of Achiral N-Heterocycles.

2,4-Diamino-6-phenyl-1,3,5-triazines carrying a single oligo(ethylene oxide) (EO) chain form an optically isotropic mesophase composed of a conglomerate of macroscopic chiral domains with opposite sense of chirality even though the constituent molecules are achiral. This mesophase was proposed to result from the helical packing of hydrogen-bonded triazine aggregates, providing long-range chirality synchronization. The results provide first evidence for macroscopic achiral symmetry breaking upon conglomerate formation in an amorphous isotropic phase formed by hydrogen-bonded associates of simple N-heterocycles that are related to prebiotic molecules.

Helical Nano-crystallite (HNC) Phases: Chirality Synchronization of Achiral Bent-Core Mesogens in a New Type of Dark Conglomerates.

Spontaneous generation of macroscopic homochirality in soft matter systems by self-assembly of exclusively achiral molecules under achiral conditions is a challenging task with relevance for fundamental scientific research and technological applications. Dark conglomerate phases (DC phases), being optically isotropic mesophases composed of conglomerates of macroscopic chiral domains and formed by some non-chiral bent-core mesogens, represent such a case. Here we report two new series of non-symmetric bent-core molecules capable of forming a new type of mirror symmetry broken DC phases. In the synthesized molecules, a bent 4-bromoresorcinol core is connected to a phenyl benzoate wing and an azobenzene wing with or without additional peripheral fluorine substitution. The self-assembly was investigated by DSC, polarizing microscopy, electro-optical studies and XRD. Chiral and apparently achiral DC phases were observed besides distinct types of lamellar liquid crystalline phases with different degree of polar order, allowing the investigation of the transition from smectic to DC phases. This indicates a process in which increased packing density at first gives rise to restricted rotation and thus to growing polar order, which then leads to chirality synchronization, layer frustration and nano-scale crystallization. Topological constraints arising from the twisted packing of helical conformers in lamellar crystals is proposed to lead to amorphous solids composed of helical nano-crystallites with short coherence length (HNC phases). This is considered as a third major type of DC phases, distinct from the previously known liquid crystalline sponge phases and the helical nano-filament phases (HNF phases). Guidelines for the molecular design of new materials capable of self-assembly into these three types of DC phases are proposed.

Polar Order and Symmetry Breaking at the Boundary between Bent-Core and Rodlike Molecular Forms: When 4-Cyanoresorcinol Meets the Carbosilane End Group.

Two isomeric achiral bent-core liquid crystals involving a 4-cyanoresorcinol core and containing a carbosilane unit as nanosegregating segment were synthesized and were shown to form ferroelectric liquid-crystalline phases. Inversion of the direction of one of the COO groups in these molecules leads to a distinct distribution of the electrostatic potential along the surface of the molecule and to a strong change of the molecular dipole moments. Thus, a distinct degree of segregation of the carbosilane units and consequent modification of the phase structure and coherence length of polar order result. For the compound with larger dipole moment (CN1) segregation of the carbosilane units is suppressed, and this compound forms paraelectric SmA and SmC phases; polar order is only achieved after transition to a new LC phase, namely, the ferroelectric leaning phase (SmCLs PS ) with the unique feature that tilt direction and polar direction coincide. The isomeric compound CN2 with a smaller dipole moment forms separate layers of the carbosilane groups and shows a randomized polar SmA phase (SmAPAR ) and ferroelectric polydomain SmCs PS phases with orthogonal combination of tilt and polar direction and much higher polarizations. Thus, surprisingly, the compound with the smaller molecular dipole moment shows increased polar order in the LC phases. Besides ferroelectricity, mirror-symmetry breaking with formation of a conglomerate of macroscopic chiral domains was observed in one of the SmC phases of CN1. These investigations contribute to the general understanding of the development of polar order and chirality in soft matter.

Development of Polar Order in the Liquid Crystal Phases of a 4-Cyanoresorcinol-Based Bent-Core Mesogen with Fluorinated Azobenzene Wings.

A bent-core mesogen consisting of a 4-cyanoresorcinol unit as the central core and laterally fluorinated azobenzene wings forms four different smectic LC phase structures in the sequence SmA-SmCs -SmCs PAR -M, all involving polar SmCs PS domains with growing coherence length of tilt and polar order on decreasing temperature. The SmA phase is a cluster-type de Vries phase with randomized tilt and polar direction; in the paraelectric SmCs phase the tilt becomes uniform, although polar order is still short-range. Increasing polar correlation leads to a new tilted and randomized polar smectic phase with antipolar correlation between the domains (SmCs PAR ) which then transforms into a viscous polar mesophase M. As another interesting feature, spontaneous symmetry breaking by formation of a conglomerate of chiral domains is observed in the non-polar paraelectric SmCs phase.

Effects of molecular chirality on self-assembly and switching in liquid crystals at the cross-over between rod-like and bent shapes.

A bent-core compound derived from a 4-cyanoresorcinol core unit with two terephthalate based rod-like wings and carrying chiral 3,7-dimethyloctyloxy side chains has been synthesized in racemic and enantiomerically pure form and characterized by polarizing microscopy, differential scanning calorimetry, X-ray diffraction and electro-optical investigations to study the influence of molecular chirality on the superstructural chirality and polar order in lamellar liquid crystalline phases. Herein we demonstrate that the coupling of molecular chirality with superstructural layer chirality in SmCsPF domain phases (forming energetically distinct diastereomeric pairs) can fix the tilt direction and thus stabilize synpolar order, leading to bistable ferroelectric switching in the SmC* phases of the (S)-enantiomer, whereas tristable modes determine the switching of the racemate. Moreover, the mechanism of electric field induced molecular reorganization changes from a rotation around the molecular long axis in the racemate to a rotation on the tilt-cone for the (S)-enantiomer. At high temperature the enantiomer behaves like a rod-like molecule with a chirality induced ferroelectric SmC* phase and an electroclinic effect in the SmA'* phase. At reduced temperature sterically induced polarization, due to the bent molecular shape, becomes dominating, leading to much higher polarization values, thus providing access to high polarization ferroelectric materials with weakly bent compounds having only "weakly chiral" stereogenic units. Moreover, the field induced alignment of the SmCsPF(()*()) domains gives rise to a special kind of electroclinic effect appearing even in the absence of molecular chirality. Comparison with related compounds indicates that the strongest effects of chirality appear for weakly bent molecules with a relatively short coherence length of polar order, whereas for smectic phases with long range polar order the effects of the interlayer interfaces can override the chirality effects.

Formation of a Double Diamond Cubic Phase by Thermotropic Liquid Crystalline Self-Assembly of Bundled Bolaamphiphiles.

A quaternary amphiphile with swallow-tail side groups displays a new bicontinuous thermotropic cubic phase with symmetry Pn3‾ m and formed by two interpenetrating networks where cylindrical segments are linked by H bonds at tetrahedral junctions. Each network segment contains two bundles, each containing 12 rod-like mesogens, lying along the segment axis. This assembly leads to the first thermotropic structure of the "double diamond" type. A quantitative geometric model is proposed to explain the occurrence of this rare phase.

Spontaneous Mirror-Symmetry Breaking in Isotropic Liquid Phases of Photoisomerizable Achiral Molecules.

Spontaneous mirror-symmetry breaking is of fundamental importance in science as it contributes to the development of chiral superstructures and new materials and has a major impact on the discussion around the emergence of uniform chirality in biological systems. Herein we report chirality synchronization, leading to spontaneous chiral conglomerate formation in isotropic liquids of achiral and photoisomerizable azobenzene-based rod-like molecules. The position of fluorine substituents at the aromatic core is found to have a significant effect on the stability and the temperature range of these chiral liquids. Moreover, these liquid conglomerates occur in a new phase sequence adjacent to a 3D tetragonal mesophase.

Temperature-dependent in-plane structure formation of an X-shaped bolapolyphile within lipid bilayers.

Polyphilic compound B12 is an X-shaped molecule with a stiff aromatic core, flexible aliphatic side chains, and hydrophilic end groups. Forming a thermotropic triangular honeycomb phase in the bulk between 177 and 182 °C but no lyotropic phases, it is designed to fit into DPPC or DMPC lipid bilayers, in which it phase separates at room temperature, as observed in giant unilamellar vesicles (GUVs) by fluorescence microscopy. TEM investigations of bilayer aggregates support the incorporation of B12 into intact membranes. The temperature-dependent behavior of the mixed samples was followed by differential scanning calorimetry (DSC), FT-IR spectroscopy, fluorescence spectroscopy, and X-ray scattering. DSC results support in-membrane phase separation, where a reduced main transition and new B12-related transitions indicate the incorporation of lipids into the B12-rich phase. The phase separation was confirmed by X-ray scattering, where two different lamellar repeat distances are visible over a wide temperature range. Polarized ATR-FTIR and fluorescence anisotropy experiments support the transmembrane orientation of B12, and FT-IR spectra further prove a stepwise "melting" of the lipid chains. The data suggest that in the B12-rich domains the DPPC chains are still rigid and the B12 molecules interact with each other via π-π interactions. All results obtained at temperatures above 75 °C confirm the formation of a single, homogeneously mixed phase with freely mobile B12 molecules.