Liquid-Crystalline Kagome

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.

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.

Soft self-assembled sub-5 nm scale chessboard and snub-square tilings with oligo(para-phenyleneethynylene) rods

X-Shaped bolapolyphiles, comprising a linear polyaromatic core with glycerol groups at each end and two chemically different and incompatible chains, fixed to it at opposite sides, were synthesized and found to self-assemble into honeycomb-type liquid crystalline phases with square symmetry. The polyaromatic π-conjugated rods form the cell walls and the resulting prismatic cells of sub-5 nm size are alternatively filled with perfluorocarbon (RF) and the carbosilane chains (RSi). The resulting structures can be represented as either a two-colour snub-square tiling with triangular and square cells or as a chessboard tiling of squares.

Heteropore covalent organic frameworks: a new class of porous organic polymers with well-ordered hierarchical porosities

This review highlights the development of heteropore covalent organic frameworks, a new class of porous organic polymers which exhibit well-ordered heterogeneous/hierarchical porosities.

Effects of Lateral and Terminal Chains of X-Shaped Bolapolyphiles with Oligo(phenylene ethynylene) Cores on Self-Assembly Behaviour. Part 1: Transition between Amphiphilic and Polyphilic Self-Assembly in the Bulk

Polyphilic self-assembly leads to compartmentalization of space and development of complex structures in soft matter on different length scales, reaching from the morphologies of block copolymers to the liquid crystalline (LC) phases of small molecules. Whereas block copolymers are known to form membranes and interact with phospholipid bilayers, liquid crystals have been less investigated in this respect. Here, series of bolapolyphilic X-shaped molecules were synthesized and investigated with respect to the effect of molecular structural parameters on the formation of LC phases (part 1), and on domain formation in phospholipid bilayer membranes (part 2). The investigated bolapolyphiles are based on a rod-like π-conjugated oligo(phenylene ethynylene) (OPE) core with two glycerol groups being either directly attached or separated by additional ethylene oxide (EO) units to both ends. The X-shape is provided by two lateral alkyl chains attached at opposite sides of the OPE core, being either linear, branched, or semiperfluorinated. In this report, the focus is on the transition from polyphilic (triphilic or tetraphilic) to binary amphiphilic self-assembly. Polyphilic self-assembly, i.e., segregation of all three or four incorporated units into separate nano-compartments, leads to the formation of hexagonal columnar LC phases, representing triangular honeycombs. A continuous transition from the well-defined triangular honeycomb structures to simple hexagonal columnar phases, dominated by the arrangement of polar columns on a hexagonal lattice in a mixed continuum formed by the lipophilic chains and the OPE rods, i.e., to amphiphilic self-assembly, was observed by reducing the length and volume of the lateral alkyl chains. A similar transition was found upon increasing the length of the EO units involved in the polar groups. If the lateral alkyl chains are enlarged or replaced by semiperfluorinated chains, then the segregation of lateral chains and rod-like cores is retained, even for enlarged polar groups, i.e., the transition from polyphilic to amphiphilic self-assembly is suppressed.

Monte Carlo study of the ordering in a strongly frustrated liquid crystal

We have performed Monte Carlo simulations to investigate the temperature dependence of the ordering of the side chains of the X-shaped liquid crystal molecules which are arranged in a hexagonal array. Each hexagon contains six side chains, one from each side of the hexagon. Each liquid crystal molecule has two, dissimilar, side chains, one that contains silicon and one that contains fluorine. Like chains attract each other more strongly than unlike chains and this drives an order-disorder transition. The system is frustrated because it is not possible to find a configuration in which all the hexagons are occupied by either all silicon or all fluorine chains. There are two phase transitions. If only pairwise interactions are included it is found that there is an interesting fluctuating phase between the disordered phase and the fully ordered ground state. This did not agree with the experiments where an intermediate phase was seen that had long range order on one of the three sublattices. Agreement was found when the calculations were modified to include attractive three-body interactions between the silicon chains.

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.

Hierarchical Self-Assembly of Disc-Rod Shape Amphiphiles Having Hexa-peri-hexabenzocoronene and a Relatively Long Rod

Two disc-rod shape amphiphiles consisting of hexa-peri-hexabenzocoronene (HBC) and a nanosized rodlike mesogen were designed and synthesized. Thermotropic phase behaviors were carefully studied. Despite significant steric mismatch between the discs and rods, hierarchical structures were observed for both disc-rod shape amphiphiles at ambient temperature and upon heating. Molecular packing schemes were proposed and confirmed using the reconstructed electron density maps, molecular dynamics simulation, and direct observation using transmission electron microscope. The results demonstrate that the shape effect is of great importance in the self-assembly of shape amphiphiles.

Construction of two heteropore covalent organic frameworks with Kagome lattices

Two novel covalent organic frameworks (COFs) bearing Kagome lattices have been fabricated through the condensations of a D_2h symmetrical tetraaldehyde and C₂ symmetrical aromatic diamines of various lengths.

Complex liquid-crystal nanostructures in semiflexible ABC linear triblock copolymers: A self-consistent field theory

We show that two series of ABC linear triblock copolymers possess sequences of order-to-order phase transitions between microphase-separated states, as the degree of flexibility of the semiflexible middle B-blocks varies. The spatial and orientational symmetries of these phases, some of them containing liquid-crystal ordering, are analysed in comparison with related structures previously determined experimentally and theoretically. A theoretical framework based on the self-consistent field treatment of the wormlike-chain model, which incorporates the Flory-Huggins and Maier-Saupe interactions in the free energy, is used here as a basic foundation for numerical calculations. We suggest that tuning the flexibility parameter, which reduces to the concept of degree of polymerization in the coil-like limit and characterizes the chain-persistency in the rod-like limit, provides a promising approach that can be used to design the resulting microphase-separated structures in semiflexible copolymer melts.

Zeolite-like liquid crystals

Zeolites represent inorganic solid-state materials with porous structures of fascinating complexity. Recently, significant progress was made by reticular synthesis of related organic solid-state materials, such as metal-organic or covalent organic frameworks. Herein we go a step further and report the first example of a fluid honeycomb mimicking a zeolitic framework. In this unique self-assembled liquid crystalline structure, transverse-lying π-conjugated rod-like molecules form pentagonal channels, encircling larger octagonal channels, a structural motif also found in some zeolites. Additional bundles of coaxial molecules penetrate the centres of the larger channels, unreachable by chains attached to the honeycomb framework. This creates a unique fluid hybrid structure combining positive and negative anisotropies, providing the potential for tuning the directionality of anisotropic optical, electrical and magnetic properties. This work also demonstrates a new approach to complex soft-matter self-assembly, by using frustration between space filling and the entropic penalty of chain extension.

Zeolites with regular porous structures are widely used as gas adsorbents and scaffolding for catalysts. Poppe et al. report a liquid crystal with zeolite-like structure by self-assembly of polyphilic molecules with π-conjugated rod-like cores into a honeycomb formed by pentagonal/octagonal channels.

Dendritic domains with hexagonal symmetry formed by x-shaped bolapolyphiles in lipid membranes

A novel class of bolapolyphile (BP) molecules are shown to integrate into phospholipid bilayers and self-assemble into unique sixfold symmetric domains of snowflake-like dendritic shapes. The BPs comprise three philicities: a lipophilic, rigid, π-π stacking core; two flexible lipophilic side chains; and two hydrophilic, hydrogen-bonding head groups. Confocal microscopy, differential scanning calorimetry, XRD, and solid-state NMR spectroscopy confirm BP-rich domains with transmembrane-oriented BPs and three to four lipid molecules per BP. Both species remain well organized even above the main 1,2-dipalmitoyl-sn-glycero-3-phosphocholine transition. The BP molecules only dissolve in the fluid membrane above 70 °C. Structural variations of the BP demonstrate that head-group hydrogen bonding is a prerequisite for domain formation. Independent of the head group, the BPs reduce membrane corrugation. In conclusion, the BPs form nanofilaments by π stacking of aromatic cores, which reduce membrane corrugation and possibly fuse into a hexagonal network in the dendritic domains.

Tolane-based bent bolaamphiphiles forming liquid crystalline hexagonal honeycombs with trigonal symmetry

Fluorescent bent bolaamphiphiles self-assemble into non-centrosymmetric honeycombs with p3m1 symmetry, which can be solvent-stabilized to form lyotropic LC phases.

Honeycombs in honeycombs: complex liquid crystal alumina composite mesostructures

Small-angle X-ray scattering (SAXS) and atomic force microscopy (AFM) were used to study orientation patterns of two polyphilic liquid crystals (LC) confined to cylindrical pores of anodic aluminum oxide (AAO). The hierarchical hybrid systems had the LC honeycomb (lattice parameter 3.5-4 nm) inside the pores of the AAO honeycomb (diameters 60 and 400 nm). By conducting complete reciprocal space mapping using SAXS, we conclude that the columns of both compounds align in planes normal to the AAO pore axis, with a specific crystallographic direction of the LC lattice aligning strictly parallel to the pore axis. AFM of LC-containing AAO fracture surfaces further revealed that the columns of the planar anchoring LC (compound 1) formed concentric circles in the plane normal to the pore axis near the AAO wall. Toward the pore center, the circles become anisometric "racetrack" loops consisting of two straight segments and two semicircles. This mode compensates for slight ellipticity of the pore cross section. Indications are, however, that for perfectly circular pores, circular shape is maintained right to the center of the pore, the radius coming down to the size of a molecule. For the homeotropically anchoring compound 2, the columns are to the most part straight and parallel to each other, arranged in layers normal to the AAO pore axis, like logs in an ordered pile. Only near the pore wall the columns splay somewhat. In both cases, columns are confined to layers strictly perpendicular to the AAO pore axis, and there is no sign of escape to the third dimension or of axial orientation, the latter having been reported previously for some discotic LCs. The main cause of the two new LC configurations, the "racetrack" and the "logpile", and of their difference from those of confined nematic LC, is the very high splay energy and low bend energy of columnar phases.

A strongly emitting liquid-crystalline derivative of Y(3)N@C(80): bright and long-lived near-IR luminescence from a charge transfer state

Great balls of fire: C60 and Y3 N@C80 were connected to the same oligo(phenyleneethynylene) unit to investigate their structural and photophysical properties. NMR investigations revealed a fulleroid structure for the Y3 N@C80 derivative, and both dyads gave rise to columnar phases with core-shell cylinders. The black and gray spheres represent the fullerene core units of the Y3 N@C80 derivative, which is an ideal candidate to be involved in energy and electron transfer processes.

Development of structural complexity by liquid-crystal self-assembly

Since the discovery of the liquid-crystalline state of matter 125 years ago, this field has developed into a scientific area with many facets. This Review presents recent developments in the molecular design and self-assembly of liquid crystals. The focus is on new exciting soft-matter structures distinct from the usually observed nematic, smectic, and columnar phases. These new structures have enhanced complexity, including multicompartment and cellular structures, periodic and quasiperiodic arrays of spheres, and new emergent properties, such as ferroelctricity and spontaneous achiral symmetry-breaking. Comparisons are made with developments in related fields, such as self-assembled monolayers, multiblock copolymers, and nanoparticle arrays. Measures of structural complexity used herein are the size of the lattice, the number of distinct compartments, the dimensionality, and the logic depth of the resulting supramolecular structures.

Complex tiling patterns in liquid crystals

In this account recent progress in enhancing the complexity of liquid crystal self-assembly is highlighted. The discussed superstructures are formed mainly by polyphilic T-shaped and X-shaped molecules composed of a rod-like core, tethered with glycerol units at both ends and flexible non-polar chain(s) in lateral position, but also related inverted molecular structures are considered. A series of honeycomb phases composed of polygonal cylinders ranging from triangular to hexagonal, followed by giant cylinder honeycombs is observed for ternary T-shaped polyphiles on increasing the size of the lateral chain(s). Increasing the chain size further leads to new modes of lamellar organization followed by three-dimensional and two-dimensional structures incorporating branched and non-branched axial rod-bundles. Grafting incompatible chains to opposite sides of the rod-like core leads to quaternary X-shaped polyphiles. These form liquid crystalline honeycombs where different cells are filled with different material. Projected on an Euclidian plane, all honeycomb phases can be described either by uniformly coloured Archimedean and Laves tiling patterns (T-shaped polyphiles) or as multi-colour tiling patterns (X-shaped polyphiles). It is shown that geometric frustration, combined with the tendency to segregate incompatible chains into different compartments and the need to find a periodic tiling pattern, leads to a significant increase in the complexity of soft self-assembly. Mixing of different chains greatly enhances the number of possible 'colours' and in this way, periodic structures comprising up to seven distinct compartments can be generated. Relations to biological self-assembly are discussed shortly.

Thermotropic organization of hydrogen-bond-bridged bolaform amphiphiles

A series of quaternary ammonium amphiphiles (A-n) bearing carboxylic acid groups were designed and synthesized. The branched bolaform structures can be constructed by dimerizations of carboxylic acid groups through intermolecular hydrogen bonding, as demonstrated by the Fourier transform infrared (FT-IR) spectra and the temperature-dependent FT-IR spectra. The thermotropic organizations of branched bolaform ammonium dimer complexes were characterized by differential scanning calorimetry, polarized optical microscopy, and X-ray diffraction. We investigated the influence of the spacer between the cationic group and the benzene ring on the thermotropic organization. A-6 with short lateral alkyl chains formed a simple layered structure at room temperature and exhibited smectic A mesophase above 145 °C, whereas A-8 with intermediate lateral chain length organized into smectic A phase over a wide temperature range. A further increase of the length (n = 10, 12) of the lateral chains resulted in the formation of lamellar structure with in-plane layered periodicity, which is rare in the organization of ionic compounds. A packing model of the quasi-2D lamellar was proposed on the basis of the experimental data of X-ray diffraction results. Notably, the quasi-2D lamellar structure could evolve into a simple layer with the increase of temperature. The present results showed a direct relationship in which the branched architecture can be applied to tune the self-assembly behavior of ionic amphiphiles and is allowed to construct new layered superstructure.

Dissipative particle dynamics simulation of quaternary bolaamphiphiles: multi-colour tiling in hexagonal columnar phases

We use dissipative particle dynamics simulations to examine the phase behaviour of X-shaped quaternary bolaamphiphiles. These molecules are composed of a rod-shaped core, with polar groups at each end and two different lateral chains. We show that, as for ternary bolaamphiphiles, square and hexagonal columnar phases are observed. The micro-phase segregation in the four-block systems leads to neighbouring columns containing different types of chain. For a square columnar phase, this does not present a problem. For hexagonal systems, however, this necessarily leads to frustration, and we discuss how the molecular structure can influence the way this frustration is relieved.