Supramolecular dendritic liquid quasicrystals

Zeng, Xiangbing; Ungar, Goran; Liu, Yongsong; Percéc, Virgil; Dulcey, Andrés E.; Hobbs, Jamie K.

doi:10.1038/nature02368

Cited by 609 publications

(587 citation statements)

References 29 publications

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“…16,17 The resulting polyelectrolyte-surfactant complexes have been shown to microphase segregate into liquid crystalline mesophases, analogous to those obtained in systems where the mesogenic units are covalently attached to macromolecules. [18][19][20][21][22][23][24] Bioinspired complexes based on ionic complexation of polypeptides and phospholipids have been recently reported using both peptide homopolymers and block copolymers, leading to a rich polymorphism, including lamellar, tetragonal 14,15 or rectangular 14,25 mesophases. Furthermore, in contrast to peptidic polymers covalently modified with mesogenic units, 26,27 polypeptide-surfactant complexes are expected to be pH responsive and thus offer a very promising pathway to design pH-responsive mesostructures.…”

Section: Introductionmentioning

confidence: 99%

Thermotropic Ionic Liquid Crystals via Self-Assembly of Cationic Hyperbranched Polypeptides and Anionic Surfactants

et al. 2007

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This work describes the dilute solution and solid-state structure of polyelectrolyte complexes generated from hyperbranched polylysine (HBPL) and various anionic, sodium alkyl sulfate surfactants. In dilute solution, the radius of gyration (R g ) of the HBPL and HBPL-surfactant complexes was determined in the Guinier regime in good solvent conditions by means of small-angle X-ray scattering (SAXS). With increasing molecular weight of the HBPL, an increase in R g up to a maximum of 3.7 and 4.2 nm was observed for the HBPLs and HBPL-surfactant complexes, respectively. In the solid state, HBPL-surfactant complexes were found to form liquid crystalline (LC) phases, whose thermal stability and structure depended both on the molecular weight of the HBPL as well as on the nature of the anionic surfactant. Depending on the surfactant alkyl chain length, liquid crystalline phases with short range liquid-like order, columnar hexagonal packing or lamellar ordering were observed. By combination of small-angle X-ray scattering, differential scanning calorimetry (DSC), and cross-polarized light optical microscopy (CPOM), the exact structure of the LC phases, as well as their region of thermal stability, could be identified. HBPL-sodium dodecyl sulfate LC phases showed thermotropic behavior and underwent two transitions with increasing temperature. First, at lower temperatures, an order-nematic transition was observed. Upon further temperature increase, a second transition from a nematic to an isotropic phase was observed. Structural models for these different LC phases are proposed.

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Section: Introductionmentioning

confidence: 99%

Thermotropic Ionic Liquid Crystals via Self-Assembly of Cationic Hyperbranched Polypeptides and Anionic Surfactants

et al. 2007

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“…Originally discovered in metallic alloys [23], many alloy quasicrystals are now known, and a handful of quasicrystals have been reported in non-metallic systems. Among them are quasicrystals made from spherical micelles [24], binary nanoparticles [25], and hard tetrahedra [19]. In this Letter, we investigate the phase behavior of hard TBPs and report a degenerate quasicrystal.…”

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Degenerate Quasicrystal of Hard Triangular Bipyramids

2011

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We report a degenerate quasicrystal in Monte Carlo simulations of hard triangular bipyramids each composed of two regular tetrahedra sharing a single face. The dodecagonal quasicrystal is similar to that 1 recently reported for hard tetrahedra [Haji-Akbari et al., Nature (London) 462, 773 (2009)] but degenerate in the pairing of tetrahedra, and self-assembles at packing fractions above 54%. This notion of degeneracy differs from the degeneracy of a quasiperiodic random tiling arising through phason flips. Free energy calculations show that a triclinic crystal is preferred at high packing fractions.Hard disks and spheres order into hexagonal and facecentered cubic crystals, respectively, above a certain packing fraction. A more complex phase behavior is observed if the disks or spheres are rigidly bonded into dimers (dumbbells) [1][2][3][4]. A solid phase, disordered in the orientation of dimers while ordered on the monomer level, forms if the distance between monomers within a dimer is roughly the diameter of a monomer. This equilibrium solid phase can be alternatively understood as a random pairing of neighboring monomers within the native monomer crystal. The resulting thermodynamic ensemble of ground states is degenerate and the structure is therefore called a degenerate crystal. As shown by Wojciechowski et al.[1] for hard disks, the entropy associated with the degeneracy exceeds the entropy from excluded volume effects, which by itself is sufficient to drive the crystallization of hard monomers. Other consequences of the pairing of monomers into dimers include topological defects [5], a restricted, glassy dislocation motion [6,7], and unusual elastic properties [8]. Similar degenerate phases have also been observed for freely-joined chains of hard spheres [9,10].Although degenerate crystals can potentially assemble from dimers of hard shapes other than disks and spheres, few examples have been reported. One reason is the competition between degenerate crystals and the liquid crystalline phases frequently observed for particles with large aspect ratios. For example, elongated tetragonal parallelepipeds, which for an aspect ratio of 2:1 can be viewed as dimers of face-sharing cubes, form a degenerate parquet phase at intermediate densities before transforming into a smectic liquid crystal that eventually crystallizes [11]. Another simple dimer is the triangular bipyramid (TBP), which consists of two face-sharing, regular tetrahedra (Fig. 1a). The TBP is the simplest face-transitive bipyramid and the twelfth of the 92 Johnson solids. The lack of inversion symmetry of the TBP, however, makes lattice packings non-optimal [12], and thus it is potentially more interesting as a dimer than dimers of spheres and cubes. Moreover, the recent synthesis of TBP-shaped nanoparticles and colloids [13][14][15][16] relevance. In both of the known ordered phases of hard, regular tetrahedra, each tetrahedron is in almost-perfect face-to-face contact with at least one other tetrahedron. The densest known packing of tetrahedr...

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“…1 A-C): the snub hexagonal tiling (four triangles and one hexagon at each vertex, labeled 3.3.3.3.6), the elongated triangular tiling (three triangles and two squares join at each vertex in a 3.3.3.4.4 sequence), and the snub square tiling (three triangles and two squares at each vertex; labeled 3.3.4.3.4). They have been identified in bulk materials, such as layered crystalline structures of complex metallic alloys (4,(16)(17)(18), supramolecular dendritic liquids (19), liquid crystals (20), special star-branched polymers (21,22), and binary nanoparticle superlattices (23). Moreover, recent experiments with colloids at a quasicrystalline substrate potential induced by five interfering laser beams, conceived to specifically address the surface tiling problem, yielded a distorted, 2D Archimedeanlike architecture (24).…”

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confidence: 99%

Five-vertex Archimedean surface tessellation by lanthanide-directed molecular self-assembly

Écija

Urgel

Papageorgiou

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

127

109

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The tessellation of the Euclidean plane by regular polygons has been contemplated since ancient times and presents intriguing aspects embracing mathematics, art, and crystallography. Significant efforts were devoted to engineer specific 2D interfacial tessellations at the molecular level, but periodic patterns with distinct five-vertex motifs remained elusive. Here, we report a direct scanning tunneling microscopy investigation on the ceriumdirected assembly of linear polyphenyl molecular linkers with terminal carbonitrile groups on a smooth Ag(111) noble-metal surface. We demonstrate the spontaneous formation of fivefold Celigand coordination motifs, which are planar and flexible, such that vertices connecting simultaneously trigonal and square polygons can be expressed. By tuning the concentration and the stoichiometric ratio of rare-earth metal centers to ligands, a hierarchic assembly with dodecameric units and a surface-confined metalorganic coordination network yielding the semiregular Archimedean snub square tiling could be fabricated.T he tiling of surfaces is relevant for pure art (1), mathematics (2, 3), material physics (4), and molecular science (5). Johannes Kepler's pertaining, rigorous analysis revealed four centuries ago that in the Euclidean plane 11 tessellations based on symmetric polygonal units exist (6): three consist of a specific polygon (so-called regular tilings with squares, triangles, or hexagons, respectively), whereas eight require the combination of two or more different polygons (named semiregular or Archimedean tilings from triangles, squares, hexagons, octagons, and dodecagons).Manifestations of regular tessellations at the atomic and molecular level are ubiquitous, including crystalline planes and surfaces of elemental or molecular crystals, and honeycomb structures encountered, e.g., for graphene sheets, strain relief and supramolecular lattices. In addition, the family of semiregular Archimedean tilings features intriguing characteristics. They may represent geometrically frustrated magnets (7) or provide novel routes for constructing photonic crystals (8). However, with the exception of the frequently realized trihexagonal tiling (also known as the Kagomé lattice) (9-15), the other semiregular Archimedean tiling patterns remain largely unexplored.Three of the semiregular Archimedean tilings correspond to five-vertex configurations (Fig. 1 A-C): the snub hexagonal tiling (four triangles and one hexagon at each vertex, labeled 3.3.3.3.6), the elongated triangular tiling (three triangles and two squares join at each vertex in a 3.3.3.4.4 sequence), and the snub square tiling (three triangles and two squares at each vertex; labeled 3.3.4.3.4). They have been identified in bulk materials, such as layered crystalline structures of complex metallic alloys (4, 16-18), supramolecular dendritic liquids (19), liquid crystals (20), special star-branched polymers (21, 22), and binary nanoparticle superlattices (23). Moreover, recent experiments with colloids at a quasicrystalline substra...

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Supramolecular dendritic liquid quasicrystals

Cited by 609 publications

References 29 publications

Thermotropic Ionic Liquid Crystals via Self-Assembly of Cationic Hyperbranched Polypeptides and Anionic Surfactants

Thermotropic Ionic Liquid Crystals via Self-Assembly of Cationic Hyperbranched Polypeptides and Anionic Surfactants

Degenerate Quasicrystal of Hard Triangular Bipyramids

Five-vertex Archimedean surface tessellation by lanthanide-directed molecular self-assembly

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