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Frank-Kasper and related quasicrystal spherical phases in macromolecules

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  • ReceivedJul 25, 2017
  • AcceptedSep 11, 2017
  • PublishedDec 13, 2017

Abstract

Creation of diverse ordered nanostructures via self-assembly of macromolecules is a promising “bottom-up” approach towards next-generation nanofabrication technologies. It is therefore of critical importance to explore the possibilities to form new self-assembled phases in soft matter systems. In this review, we summarized recent advances on the identification of several unconventional spherical phases in the self-assembly of functional macromolecules, including Frank-Kasper (F-K) phases and quasicrystals originally observed in metal alloys. We believe that these results provide a new strategy towards the rational design of novel functional materials with hierarchically ordered structures.


Acknowledgment

This work was supported by the Pearl River Talents Scheme (2016ZT06C322), the National Key R&D Program of China (2017YFC11050003), and the Fundamental Research Funds for the Central Universities (2017JQ001). K. Yue thanks the Youth Thousand Talents Program of China for support.


Interest statement

The authors declare that they have no conflict of interest.


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  • Figure 1

    Coordination environments of the central atom in polyhedra shapes of (a) cuboctahedron in FCC, twinned cuboctahedron in HCP, and icosahedron in TCP, and (b) the distorted icosahedra with CN=12, and three Kasper polyhedra with CN=14, 15 and 16, respectively (color online).

  • Figure 2

    Unit cells of (a) Frank-Kasper A15, σ, and Z phases; (b) packing of spheres in A15, σ, and Z phases viewed along the z axis and their corresponding tiling patterns; (c) unit cells of Lavas C14, Lavas C15, and Lavas C36 phases; (d) triangle diagram that includes all the F-K phases experimentally observed so far. Three corners of this triangle are defined by the A15, Z, and C15 phases. The horizontal axis is the average coordination number of a specific F-K phase, and the vertical axis indicates the fraction of the Kasper polyhedra with CN=15 in that phase. Each filled dot represents a known F-K phase. Superimposing phases are drawn as open circles outside the filled dots (color online).

  • Figure 3

    (a) Chemical structure of a low-generation, tapered dendron and its self-assembly into a supramolecular hexagonal cylindrical liquid crystal phase. (b) Chemical structure of a high-generation dendron and its self-assembly into a supramolecular A15 phase. Panels (a) and (b) are adapted with permission from Ref. [15], copyright 1997 American Association for the Advancement of Science. (c) Chemical structure of a dendron exhibiting a supramolecular σ phase with its characteristic small-angle X-ray scattering (SAXS) profile and tetragonal unit cell. Adapted with permission from Ref. [55], copyright 2003 American Association for the Advancement of Science. (d) Chemical structure of a dendron resulting in a DQC structure. Three basic decorated tiles combine to generate the model of the DQC. Single-domain diffraction pattern showed a 12-fold symmetry. Adapted with permission from Ref. [31], copyright 2004 Nature Publishing Group (color online).

  • Figure 4

    (a) Chemical structure of an SISO-3 tetrablock terpolymer exhibiting σ and DQC phases upon temperature change. As shown in the middle scheme, contact between I and O blocks is unfavorable, resulting the avoided I/O interface in the supramolecular sphere. Adapted with permission from Ref. [18], copyright 2012 American Chemical Society. (b) Chemical structures of PEP-b-PLA, PI-b-PLA, and PEE-b-PLA diblock copolymers with different degrees of conformational asymmetry. Experimental phase diagrams of PEP-b-PLA, PI-b-PLA, and PEE-b-PLA block polymers. Adapted with permission from Ref. [58], copyright 2017 American Physical Society (color online).

  • Figure 5

    (A) Scheme illustration of the two macromolecular topologies for comparison. At different volume fractions, the interface adopts different shapes. At asymmetrical compositions the spherical interface is favored, while at relatively symmetrical compositions the shape of the Voronoi cell dominates. (B) Phase diagram of linear diblock copolymer melt (a) and branched diblock copolymer melt (b) calculated by SCFT. Panels (A) and (B) are adapted with permission from Ref. [37], copyright 2003 American Physical Society. (C) Phase diagrams of conformational asymmetric AB diblock copolymers with ε=1.5 (a) and ε=2.0 (b) calculated by SCFT. (D) Phase diagrams of AB2 (a) and AB3 (b) diblock copolymers calculated by SCFT. Panels (C) and (D) are adapted with permission from Ref. [61], copyright 2014 American Chemical Society (color online).

  • Figure 6

    (a) Chemical structures of the DPOSS-NPSm giant surfactants with topological variations; (b) SAXS patterns and TEM images of five representative DPOSS-4PSm samples showing (from left to right) HEX, A15, σ, DQC, and BCC phases; (c) phase boundary diagrams of the four series of giant surfactants with different molecular topology. Black dots represent experimentally accessed data points. Adapted with permission from Ref. [65], copyright 2017 National Academy of Sciences (color online).

  • Figure 7

    Summary of self-assembly behaviors of a set of DPOSS-BPOSSn dendron-like giant molecules. Structural evolution is directed by variations of molecular geometric factors. Adapted with permission from Ref [67], copyright 2017 American Chemical Society (color online).

  • Figure 8

    (a) Chemical structures and cartoon illustrations of four giant tetrahedra with different molecular symmetry. Blue spheres represent hydrophilic POSS cages and red spheres hydrophobic BPOSS cages. (b) SAXS pattern and TEM images of 2a after thermal annealing at 140 °C. Fourier filtering and color inversion revealed a clear view of the 2D 44 tiling along the <100> direction. (c) Proposed mechanism of the selective assembly and molecular packing model in the A15 superlattice. Adapted with permission from Ref. [25], copyright 2017 American Association for the Advancement of Science (color online).

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