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.

Network Phases with Multiple-Junction Geometries at the Gyroid-Diamond Transition.

A novel phase sequence for the transition from the double diamond to the double gyroid cubic phases via two non-cubic intermediate phases, an orthorhombic Fmmm (O69) phase and a hexagonal P63/m (H176) phase, is reported for specifically designed bolapolyphiles composed of a linear rod-like bistolane core with sticky glycerol ends and two branched central and two linear peripheral side chains. These liquid crystalline (LC) phases represent members of a new class of unicontinuous network phases, formed by longitudinal rod bundles with polar spheres acting as junctions and the alkyl chains forming the continuum around them. In contrast to previously known bicontinuous cubic networks, they combine different junctions with different angles in a common structure, and one of them even represents a triple network instead of the usually found double networks. This provides new perspectives for the design of soft network phases with enhanced structural complexity, inspiring the search for new supramolecular networks, nano-particle arrays, and photonic band-gap materials.

Supramolecular meso-Trick: Ambidextrous Mirror Symmetry Breaking in a Liquid Crystalline Network with Tetragonal Symmetry.

Bicontinuous and multicontinuous network phases are among nature's most complex structures in soft matter systems. Here, a chiral bicontinuous tetragonal phase is reported as a new stable liquid crystalline intermediate phase at the transition between two cubic phases, the achiral double gyroid and the chiral triple network cubic phase with an I23 space group, both formed by dynamic networks of helices. The mirror symmetry of the double gyroid, representing a meso-structure of two enantiomorphic networks, is broken at the transition to this tetragonal phase by retaining uniform helicity only along one network while losing it along the other one. This leads to a conglomerate of enantiomorphic tetragonal space groups, P41212 and P43212. Phase structures and chirality were analyzed by small-angle X-ray scattering (SAXS), grazing-incidence small-angle X-ray scattering (GISAXS), resonant soft X-ray scattering (RSoXS) at the carbon K-edge, and model-dependent SAXS/RSoXS simulation. Our findings not only lead to a new bicontinuous network-type three-dimensional mesophase but also reveal a mechanism of mirror symmetry breaking in soft matter by partial meso-structure racemization at the transition from enantiophilic to enantiophobic interhelical self-assembly.

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 Ia 3 ‾ $\bar 3$ 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.

Tetrahedral Liquid-Crystalline Networks: An A15-Like Frank-Kasper Phase Based on Rod-Packing.

The Pm 3 ‾ n cubic and other low-symmetry Frank-Kasper phases are known to be formed by soft spheres, ranging from metals to block copolymer micelles and colloidal nanoparticles. Here, we report a series of X-shaped polyphiles composed of sticky rods and two non-symmetric branched side-chains, which self-assemble into the first example of a cubic liquid-crystalline phase representing a tetrahedral network of rods with a Pm 3 ‾ n lattice. It is the topological dual to the Weaire-Phelan foam, being the Voronoi tessellation of the A15 sphere packing, from which this network is obtained by Delaunay triangulation.

Mirror Symmetry Breaking and Network Formation in Achiral Polycatenars with Thioether Tail.

Mirror symmetry breaking in systems composed of achiral molecules is of importance for the design of functional materials for technological applications as well as for the understanding of the mechanisms of spontaneous emergence of chirality. Herein, we report the design and molecular self-assembly of two series of rod-like achiral polycatenar molecules derived from a π-conjugated 5,5'-diphenyl-2,2'-bithiophene core with a fork-like triple alkoxylated end and a variable single alkylthio chain at the other end. In both series of liquid crystalline materials, differing in the chain length at the trialkoxylated end, helical self-assembly of the π-conjugated rods in networks occurs, leading to wide temperature ranges (>200 K) of bicontinuous cubic network phases, in some cases being stable even around ambient temperatures. The achiral bicontinuous cubic Ia 3 ‾ d phase (gyroid) is replaced upon alkylthio chain elongation by a spontaneous mirror symmetry broken bicontinuous cubic phase (I23) and a chiral isotropic liquid phase (Iso1 [ *] ). Further chain elongation results in removing the I23 phase and the re-appearance of the Ia 3 ‾ d phase with different pitch lengths. In the second series an additional tetragonal phase separates the two cubic phase types.

Liquid Organic Frameworks: The Single-Network "Plumber's Nightmare" Bicontinuous Cubic Liquid Crystal.

Novel bolapolyphiles, built of a p-terphenyl or bistolane core with polar glycerol end-groups and two laterally attached n-alkyl or semiperfluoroalkyl chains, form the first "single plumber's nightmare network", the simplest soft-matter cubic phase (Pm3̅m). Its cage-like grid comprises bundles of aromatic rods lying along the cubic unit cell edges, connected by six-way hydrogen-bonded junctions. Side-chains fill the remaining volume of this unique noninterpenetrating liquid-crystalline organic framework.

Molecular Packing in Double Gyroid Cubic Phases Revealed via Resonant Soft X-Ray Scattering.

The bicontinuous double gyroid phase is one of the nature's most symmetric and complex structures, the electron density map of which was established long ago. By utilizing small-angle x-ray scattering, resonant soft x-ray scattering at the carbon K edge and model-dependent tensor-based scattering theory, we have not only elucidated morphology but also identified molecular packing in the double gyroid phases formed by molecules with different shapes, i.e., rodlike vs taper shaped, thus validating some of the hypothetical packing models and disproving others. The spatial variation of molecular orientation through the channel junctions in the double gyroid phase can be either continuous in the case of anisotropic channels or discontinuous in the case of isotropic channels depending on the molecular structure and shape.

Controlling Mirror Symmetry Breaking and Network Formation in Liquid Crystalline Cubic, Isotropic Liquid and Crystalline Phases of Benzil-Based Polycatenars.

Spontaneous development of chirality in systems composed of achiral molecules is important for new routes to asymmetric synthesis, chiral superstructures and materials, as well as for the understanding of the mechanisms of emergence of prebiotic chirality. Herein, it is shown that the 4,4'-diphenylbenzil unit is a universal transiently chiral bent building block for the design of multi-chained (polycatenar) rod-like molecules capable of forming a wide variety of helically twisted network structures in the liquid, the liquid crystalline (LC) and the crystalline state. Single polar substituents at the apex of tricatenar molecules support the formation of the achiral (racemic) cubic double network phase with Ia 3 ‾ d symmetry and relatively small twist along the networks. The combination of an alkyl chain with fluorine substitution leads to the homogeneously chiral triple network phase with I23 space group, and in addition, provides a mirror symmetry broken liquid. Replacing F by Cl or Br further increases the twist, leading to a short pitch double gyroid Ia 3 ‾ d phase, which is achiral again. The effects of the structural variations on the network structures, either leading to achiral phases or chiral conglomerates are analyzed.

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.

Frustration between two- and three-dimensional smectic ordering leads to a biaxial nematic phase.

The bola-amphiphilic, T-shaped mesogen CT2 has an aromatic, biphenyl core terminated on both ends by hydrophilic groups and a semi-perfluorinated, aliphatic side chain. Upon cooling from the isotropic phase, the fluorinated tails and the polar, rod-like cores nanophase-segregate to form a fluid lamellar phase. At high temperatures, the biphenyl cores are orientationally disordered in two dimensions (2D) in the lamellar planes but on further cooling the cores order orientationally, giving a biaxial lamellar phase with 2D nematic in-plane ordering. At lower temperature, the aromatic and hydrophilic parts of the cores nanosegregate within the lamellae and 2D smectic correlations of the head groups develop. X-ray diffraction shows that this 2D smectic ordering is incompatible with the initial lamellar structure, with both structures becoming short-ranged, resulting in a 3D biaxial nematic phase with macroscopic orthorhombic symmetry featuring strong smectic correlations in two orthogonal spatial dimensions. Freeze-fracture transmission electron microscopy enables direct visualization of the resulting short-ranged periodic structures.

Liquid Organic Frameworks: A Liquid Crystalline 8-Connected Network with Body-Centered Cubic Symmetry.

Liquid state self-assembly is important for the understanding of the complex structures developed in abiogenesis and biogenesis as well as for numerous potential technological applications. Herein we report the first body-centered cubic liquid crystalline phase with 8-connected network topology and open octahedral network structure. It is formed by dynamic soft self-assembly of X-shaped polyphiles with oligo(para-phenylene-ethynylene) cores. The π-conjugated rods with perfluorinated inner benzene rings form networks conjoined by eight-way junctions, which are formed by nano-segregated spheres involving hydrogen-bonded polar end groups, while the branched aliphatic chains at opposite sides of the cores fill the continuum. This novel cubic phase is based on the I-WP minimal surface separating the frameworks of polyaromatic cores from the most disordered chain segments. It can also be considered as a dense sphere packing. Such liquid organic frameworks, representing hybrids of sphere packings and networks could be of interest for organic photonics and other technologies.

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.

Chiral Incommensurate Helical Phase in a Smectic of Achiral Bent-Core Mesogens.

An achiral, bent-core mesogen forms several tilted smectic liquid crystal phases, including a nonpolar, achiral de Vries smectic A which transitions to a chiral, ferroelectric state in applied electric fields above a threshold. At lower temperature, a chiral, ferrielectric phase with a periodic, supermolecular modulation of the tilt azimuth, indicated by a Bragg peak in carbon-edge resonant soft x-ray scattering, is observed. The absence of a corresponding resonant umklapp peak identifies the superlayer structure as a twist-bend-like helix that is only weakly modulated by the smectic layering.

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.

The Solution of the Puzzle of Smectic-Q: The Phase Structure and the Origin of Spontaneous Chirality.

The so-called smectic-Q (SmQ) liquid crystal phase was discovered in 1983 in rod-like molecules, but its structure remain unclear in spite of numerous attempts to solve it. Herein, we report what we believe to be the solution: A unique bicontinuous phase that is non-cubic and is made up of orthogonal twisted columns with planar 4-way junctions. While SmQ had only been observed in chiral compounds, we show that this chiral phase forms also in achiral materials through spontaneous symmetry breaking. The results strongly support the idea of a helical substructure of bicontinuous phases and long-range homochirality being sustained by helicity-matching at network junctions. The model also explains the triangular shape of double-gyroid domains growing within a SmQ environment. SmQ-forming materials hold potential for applications such as circularly polarized light emitters that require no alignment or asymmetric synthesis.

A Liquid-Crystalline Phenylene-Based Shape-Persistent Molecular Spoked Wheel.

Molecular spoked wheels with an all-phenylene backbone and different alkoxy side chain substitution patterns were synthesized using a cobalt-catalyzed [2 + 2 + 2] cycloaddition and subsequent template-directed cyclization via Yamamoto coupling. The two-dimensional organization of the molecules at the solid/liquid interface was investigated by means of scanning tunneling microscopy, allowing imaging of the molecular structure with submolecular resolution. With the right proportion of the flexible alkyl corona to the rigid core, mesomorphic behavior of one compound could be observed over a wide temperature range.