Research ArticleChemistry

Metal-organic framework based on hinged cube tessellation as transformable mechanical metamaterial

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Science Advances  10 May 2019:
Vol. 5, no. 5, eaav4119
DOI: 10.1126/sciadv.aav4119
  • Fig. 1 Schematic representation of Poisson’s ratio.

    (A) Conformation of conventional material (Poisson’s ratio, >0). (B) Conformation of NPR material (Poisson’s ratio, <0). The gray-colored cubes represent the original geometry of the materials.

  • Fig. 2 Description of UPF-1 structure.

    (A) Three building blocks of UPF-1: 3-TCPP, BPY, and [Zn2(COO)3]2O. Zn, green; C, gray; N, blue; O, red; all hydrogen and solvents are omitted for clarity. (B) A nanocage of UPF-1 consists of three constituents and is represented by rhombicuboctahedron. The nanocage has 10 linkages, BPY as its pillars and oxo ligands. The oxygen of oxo ligands and BPY are represented by balls (yellow) and rods (orange), respectively. The rhombicuboctahedron and 10 linkages of the structure are simplified to a cuboid form. The vertex of the cuboid is the oxygen of the oxo ligands. (C) Packing system of rhombicuboctahedra and cuboids in UPF-1. The oxo ligands were bent to a clockwise direction. The rods connect between cages in the picture showing the sides of the structure. The connection by rods is omitted because packing of the cuboid emphasizes the connectivity of oxo ligands.

  • Fig. 3 Thermal response of UPF-1.

    (A) PXRD pattern depending on temperature. Immovable peak of the (002) plane represents that the value of the c parameter is not changed with temperature. Shifted peak of the (220) plane signifies that connected parts are changed by temperature. (B) The relative change of the normalized a and c parameters from SCXRD (193 to 313 K; red dashed lines) and PXRD data (100 to 313 K; black dashed lines).

  • Fig. 4 Definition of space-filling in UPF-1.

    (A) Three main classes, divided from simplified cuboid form. Cuboid, blue; another cuboid, gray; hexahedron with rhombus face, yellow. (B) Filled UPF-1 using four cuboids and a hexahedron in a unit cell. (C) Space-filled UPF-1 in 2 by 2 unit cells from the c axis. (D) Comparison with normalized volume of cuboid (red) and hexahedron (black). The volume of the cuboid is rarely changed, while the hexahedron is largely changed depending on temperature.

  • Fig. 5 Transition of two factors following corotating mechanism.

    (A) Schematic representation of the relation between θ and (x, y) coordinates showing rotating squares in geometry model. (B) Comparison with θ transition of calculation and SCXRD data depending on temperature. (C) Movement of the coordinates in accordance with the change of θ. The points, x coordinate (red) and y coordinate (black), are experimental data and matched well with the calculated dotted lines.

  • Fig. 6 Poisson’s ratio of UPF-1.

    (A) Schematic representation of rotating mechanisms based on square tessellation. (B) Simulated UPF-1, which has an applied uniaxial strain along the x (or y) direction. The red skeleton (A) rotates counterclockwise, and the blue part (B) rotates clockwise based on the hinged point (Zn─O─Zn). The skeletons rotate, and the colored area (green) becomes wider as strain is increased. The cell parameters increased as well, from 29.835 to 30.026 Å and then 30.412 Å. (C) Optimized b for different a value. The value b is optimized, while a and c are fixed. The dotted line shows the line a = b. The optimized crystal structure remains in tetragonal symmetry. (D) The calculated Poisson’s ratio is close to −1 with respect to various unit cell parameters.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/5/eaav4119/DC1

    Scheme S1. Synthetic procedure of 3-TCPP.

    Fig. S1. Characterization of BPY as a pillar in UPF-1.

    Fig. S2. Coordination environment of Zn2+ ion of new SBU, [(Zn(COO)32−O)Zn(COO)3].

    Fig. S3. Packing of rhombicuboctahedron and cuboid of UPF-1.

    Fig. S4. Thermogravimetric analysis data for UPF-1.

    Fig. S5. 1H NMR data for trace of solvent content in the UPF-1.

    Fig. S6. Simulated and experimental PXRD patterns of UPF-1 from 100 to 313 K.

    Fig. S7. Perspective view of the (002) and (220) planes in UPF-1.

    Fig. S8. Thermal expansion coefficients of UPF-1.

    Fig. S9. Transformation of a cuboid in UPF-1.

    Fig. S10. Schematic representation in a corotating model.

    Fig. S11. Calculated θ values from temperature-dependent PXRD data of UPF-1.

    Fig. S12. Schematic illustration of the corotating model.

    Fig. S13. Calculated (x, y) coordinates from 0° to 90°, derived from equation.

    Fig. S14. Energy as a function of deformations Di’s.

    Table S1. Temperature-dependent cell parameters (Å) and unit cell volume (Å3) data from synchrotron PXRD.

    Table S2. Temperature-dependent SCXRD of UPF-1.

    Table S3. Thermal expansion coefficients from the a and c parameters and cell volume of SCXRD.

    Table S4. Thermal expansion coefficients from the a and c parameters and cell volume of PXRD.

    Table S5. Thermal expansion coefficient of reported solid-state structures.

    Table S6. The values of d1, d2 and volume of cuboid depending on temperature.

    Table S7. Optimized lattice parameters Ly (Ly*) and bond angles Zn─O─Zn projected on the xy plane with respect to strained Lx’s.

    Table S8. Stiffness tensor components (Cij’s) of UPF-1 in GPa.

    Table S9. Elastic constants of UPF-1.

    Table S10. Poisson’s ratio of a variety of materials.

    Data file S1. Crystallographic data for UPF-1_193K.

    Data file S2. Crystallographic data for UPF-1_213K.

    Data file S3. Crystallographic data for UPF-1_233K.

    Data file S4. Crystallographic data for UPF-1_253K.

    Data file S5. Crystallographic data for UPF-1_273K.

    Data file S6. Crystallographic data for UPF-1_293K.

    Data file S7. Crystallographic data for UPF-1_313K.

    Data file S8. checkCIF for crystal structures of UPF-1_193K.

    Data file S9. checkCIF for crystal structures of UPF-1_213K.

    Data file S10. checkCIF for crystal structures of UPF-1_233K.

    Data file S11. checkCIF for crystal structures of UPF-1_253K.

    Data file S12. checkCIF for crystal structures of UPF-1_273K.

    Data file S13. checkCIF for crystal structures of UPF-1_293K.

    Data file S14. checkCIF for crystal structures of UPF-1_313K.

    Movie S1. Animation of hinged cube tessellation.

    Movie S2. Rotating movement of UPF-1 structure depending on temperature.

    Reference (5376)

  • Supplementary Materials

    The PDF file includes:

    • Scheme S1. Synthetic procedure of 3-TCPP.
    • Fig. S1. Characterization of BPY as a pillar in UPF-1.
    • Fig. S2. Coordination environment of Zn2+ ion of new SBU, (Zn(COO)32−O)Zn(COO)3.
    • Fig. S3. Packing of rhombicuboctahedron and cuboid of UPF-1.
    • Fig. S4. Thermogravimetric analysis data for UPF-1.
    • Fig. S5. 1H NMR data for trace of solvent content in the UPF-1.
    • Fig. S6. Simulated and experimental PXRD patterns of UPF-1 from 100 to 313 K.
    • Fig. S7. Perspective view of the (002) and (220) planes in UPF-1.
    • Fig. S8. Thermal expansion coefficients of UPF-1.
    • Fig. S9. Transformation of a cuboid in UPF-1.
    • Fig. S10. Schematic representation in a corotating model.
    • Fig. S11. Calculated θ values from temperature-dependent PXRD data of UPF-1.
    • Fig. S12. Schematic illustration of the corotating model.
    • Fig. S13. Calculated (x, y) coordinates from 0° to 90°, derived from equation.
    • Fig. S14. Energy as a function of deformations Di’s.
    • Table S1. Temperature-dependent cell parameters (Å) and unit cell volume (Å3) data from synchrotron PXRD.
    • Table S2. Temperature-dependent SCXRD of UPF-1.
    • Table S3. Thermal expansion coefficients from the a and c parameters and cell volume of SCXRD.
    • Table S4. Thermal expansion coefficients from the a and c parameters and cell volume of PXRD.
    • Table S5. Thermal expansion coefficient of reported solid-state structures.
    • Table S6. The values of d1, d2 and volume of cuboid depending on temperature.
    • Table S7. Optimized lattice parameters Ly ( Ly*) and bond angles Zn─O─Zn projected on the xy plane with respect to strained Lx’s.
    • Table S8. Stiffness tensor components (Cij’s) of UPF-1 in GPa.
    • Table S9. Elastic constants of UPF-1.
    • Table S10. Poisson’s ratio of a variety of materials.
    • Reference (5376)

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • Data file S1 (.cif format). Crystallographic data for UPF-1_193K.
    • Data file S2 (.cif format). Crystallographic data for UPF-1_213K.
    • Data file S3 (.cif format). Crystallographic data for UPF-1_233K.
    • Data file S4 (.cif format). Crystallographic data for UPF-1_253K.
    • Data file S5 (.cif format). Crystallographic data for UPF-1_273K.
    • Data file S6 (.cif format). Crystallographic data for UPF-1_293K.
    • Data file S7 (.cif format). Crystallographic data for UPF-1_313K.
    • Data file S8 (.pdf format). checkCIF for crystal structures of UPF-1_193K.
    • Data file S9 (.pdf format). checkCIF for crystal structures of UPF-1_213K.
    • Data file S10 (.pdf format). checkCIF for crystal structures of UPF-1_233K.
    • Data file S11 (.pdf format). checkCIF for crystal structures of UPF-1_253K.
    • Data file S12 (.pdf format). checkCIF for crystal structures of UPF-1_273K.
    • Data file S13 (.pdf format). checkCIF for crystal structures of UPF-1_293K.
    • Data file S14 (.pdf format). checkCIF for crystal structures of UPF-1_313K.
    • Movie S1 (.avi format). Animation of hinged cube tessellation.
    • Movie S2 (.mp4 format). Rotating movement of UPF-1 structure depending on temperature.

    Files in this Data Supplement:

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