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

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.

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.

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.

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.

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.

Liquid Crystals: Versatile Self-Organized Smart Soft Materials

Smart soft materials are envisioned to be the building blocks of the next generation of advanced devices and digitally augmented technologies. In this context, liquid crystals (LCs) owing to their responsive and adaptive attributes could serve as promising smart soft materials. LCs played a critical role in revolutionizing the information display industry in the 20th century. However, in the turn of the 21st century, numerous beyond-display applications of LCs have been demonstrated, which elegantly exploit their controllable stimuli-responsive and adaptive characteristics. For these applications, new LC materials have been rationally designed and developed. In this Review, we present the recent developments in light driven chiral LCs, i.e., cholesteric and blue phases, LC based smart windows that control the entrance of heat and light from outdoor to the interior of buildings and built environments depending on the weather conditions, LC elastomers for bioinspired, biological, and actuator applications, LC based biosensors for detection of proteins, nucleic acids, and viruses, LC based porous membranes for the separation of ions, molecules, and microbes, living LCs, and LCs under macro- and nanoscopic confinement. The Review concludes with a summary and perspectives on the challenges and opportunities for LCs as smart soft materials. This Review is anticipated to stimulate eclectic ideas toward the implementation of the nature's delicate phase of matter in future generations of smart and augmented devices and beyond.

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.