Highly branched bolapolyphilic liquid crystals with a cubic A15 network at the triangle-square transition.

Rod-like bolapolyphiles with highly branched carbosilane-based side-chains self-assemble into several honeycomb structures if the oligo(p-phenylene ethynylene) core is polyfluorinated, whereas for the non-fluorinated series an A15 type cubic network of rod-bundles was observed instead, suggesting a brand new pathway for the transition between triangular and square honeycomb phases.

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.

A columnar liquid quasicrystal with a honeycomb structure that consists of triangular, square and trapezoidal cells.

Quasicrystals are intriguing structures that have long-range positional correlations but no periodicity in real space, and typically with rotational symmetries that are 'forbidden' in conventional periodic crystals. Here, we present a two-dimensional columnar liquid quasicrystal with dodecagonal symmetry. Unlike previous dodecagonal quasicrystals based on random tiling, a honeycomb structure based on a strictly quasiperiodic tessellation of tiles is observed. The structure consists of dodecagonal clusters made up of triangular, square and trapezoidal cells that are optimal for local packing. To maximize the presence of such dodecagonal clusters, the system abandons periodicity but adopts a quasiperiodic structure that follows strict packing rules. The stability of random-tiling dodecagonal quasicrystals is often attributed to the entropy of disordering when strict tiling rules are broken, at the sacrifice of the long-range positional order. However, our results demonstrate that quasicrystal stability may rest on energy minimization alone, or with only minimal entropic intervention.

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.

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.

The rhombic honeycomb - a new mode of self-assembly in liquid crystalline soft matter.

Rod-like liquid crystalline (LC) polyphilic compounds with a linear oligo(phenyleneethynylene) core, sticky glycerol groups at each end and two long alkyl side chains (C20-C32) at opposite sides form rhombic honeycombs with inner angles around 60/120°, occurring between triangular and square tiling patterns.

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.

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.

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.

2,6-Dibromogallates as a new building block for controlling π-stacking, network formation and mirror symmetry breaking.

Achiral multi-chain (polycatenar) compounds based on the 2,7-diphenyl substituted [1]benzothieno[3,2-b]benzothiophene (BTBT) unit and a 2,6-dibromo-3,4,5-trialkoxybenzoate end group lead to materials forming bicontinuous cubic liquid crystalline phases with helical network structures over wide temperature ranges.

Emergence of uniform tilt and π-stacking in triangular liquid crystalline honeycombs.

The synclinic tilted organization of specifically designed polyphilic oligo(p-phenylene ethynylene) rods in cylindrical shells around triangular prismatic cells on the <5 nm scale leads to a new kind of liquid crystalline honeycomb composed of helical shells with alternating helix sense. Core fluorination at the outer ring modifies the core-core interactions, thus resulting in triangular arrays with face-to-face π-stacking along the honeycomb.

Different Modes of Deformation of Soft Triangular Honeycombs at the Sub-5 nm Scale.

Patterning on the sub-5 nm length scale is a contemporary challenge for further miniaturization of microelectronic circuits. Here, the first soft self-assembled triangular patterns are reported showing transitions between regular and two different kinds of isosceles (acute and obtuse angled) triangles on this length scale, formed by liquid crystalline honeycombs of polyphilic block molecules involving a fluorinated oligo(para-phenylene ethynylene) core. The type of formed triangular pattern depends on the degree and position of fluorination and on temperature. They are the first soft honeycombs combining tilted and nontilted organizations in a uniform nanostructure, where the tilted molecules in only one or two sides of the triangular prismatic cells dominate the shape and the size of the morphology.

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.

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.

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.

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.

A periodic dodecagonal supertiling by self-assembly of star-shaped molecules in the liquid crystalline state.

Molecular tessellations are known in solid state systems and their formation is often induced or supported by a periodic surface lattice. Here we discover a complex tessellation on the 10 nm length scale, spontaneously formed in the highly dynamic liquid crystalline state. It is composed of overlapping dodecagonal supertiles combining prismatic cells with triangular and square cross sections. This complex honeycomb occurs between a triangular honeycomb at high and a square at low temperature, being opposite to the sequence expected for a thermal expansion of the side chains in the prismatic cells. Formation of the supertiles is supported by the segregation of alkyl chains with different length. The emergent behaviour of this complex soft matter structure is demonstrated, and intriguing connections between self-assembly on surfaces, in liquid crystals, and in block copolymers are drawn. Moreover, the tessellation represents a close approximant of the elusive columnar liquid quasicrystal with dodecagonal symmetry.

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.

Controlling spontaneous mirror symmetry breaking in cubic liquid crystalline phases by the cycloaliphatic ring size.

Rod-like molecules combining a fork-like triple chain end and a cycloaliphatic apex are introduced as a new design concept for materials with broad ranges of bicontinuous cubic (Cubbi) phases. By ring expansion from n = 4 to 12 a sequence of three Cubbi phases is observed; the achiral double gyroid la3[combining macron]d phase, a chiral "Im3m" phase and an achiral re-entrant la3[combining macron]d phase. The chiral "Im3m" phase is formed if the helical twist between the molecules along the networks is in the range of 8.6°-9.5°, either for the individual compounds or their mixtures.