Research ArticleMATERIALS SCIENCE

The mechanics and design of a lightweight three-dimensional graphene assembly

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Science Advances  06 Jan 2017:
Vol. 3, no. 1, e1601536
DOI: 10.1126/sciadv.1601536
  • Fig. 1 Computational synthesis of the 3D graphene assembly.

    (A) Initial model composed of 500 randomly distributed rectangular graphene flakes and spherical inclusions. (B) Schematics of the graphene with L dimensions that follows a lognormal distribution as given below and spherical inclusion with uniform d in diameter. (C) The targeting temperature T as a function of simulation time in the alternative NPT-NVT ensemble during each equilibration cycle. (D) The targeting pressure p as a function of simulation time in the alternative NPT-NVT ensemble during each equilibration cycle, which is only applicable to the first stage from 0 to 25 ps. (E) The closely packed graphene-inclusion structure obtained after cyclic equilibrations. (F) The equilibrated structure of the 3D graphene assembly after removing the spherical inclusions with dimensions of 11 nm × 11 nm × 11 nm, and the SEM image of a graphene assembly [reproduced from Wu et al. (8)]. Scale bar, 20 μm (inset). (G) The total number of covalent bonds counted at the end of each anneal cycle, averaged by the total number of carbon atoms in the system.

  • Fig. 2 Mechanical tests on the 3D graphene assembly.

    (A) Simulation snapshots of the full atomic graphene structure in tension and compressive tests that are taken at εx = −0.5, 0.0, 0.6, and 1.0 for (i) to (iv), respectively. The atomic stress and its distribution at different strain states are computed and included in fig. S3. The symmetric distribution of positive and negative stress suggests that the graphene is largely bent under deformation. Insets show schematics for the different mechanisms of the material behavior under compression and tension. (B) Full stress-strain curve of the material under compression and tension force. (C) The average strains in the two directions other than the loading direction as a function of εx; for |εx| < 0.02, the slope of the curve is measured to be −0.3. For larger deformations, the three linear fits on the plot have slopes of 0.03, −0.6, and 0.04 from left to right of the curve.

  • Fig. 3

    The normalized Young’s modulus (A), tensile strength (B), and compressive strength (C) of the 3D graphene assembly as a function of its mass density.The data points include mechanical test results of the full atomic 3D graphene assembly (PG), the full atomic gyroid graphene (GG), and the 3D-printed polymer samples (3D-printed). The solid curves are plotted according to scaling laws obtained in the study with slopes of 2.73, 2.01, and 3.01 for (A), (B), and (C), respectively. ρs = 2300 mg/cm3, ES = 1.02 TPa, and σTs = 130 GPa correspond to the density, Young’s modulus, and tensile strength of graphene for its in-plane mechanics, which are used to normalize the properties of graphene materials (PG, GG, and references mentioned). ρs = 1175 mg/cm3, ES = 2.45 GPa, and σTs = 50 MPa correspond to the density, Young’s modulus, and tensile strength of the bulk material properties of polymer material for 3D printing, which are used to normalize the results of 3D-printed samples.

  • Fig. 4 Different atomistic and 3D-printed models of gyroid geometry for mechanical tests.

    (A) Simulation snapshots taken during the modeling of the atomic 3D graphene structure with gyroid geometry, representing key procedures including (i) generating the coordinate of uniformly distributed carbon atoms based on the fcc structure, (ii) generating a gyroid structure with a triangular lattice feature, and (iii) refinement of the modified geometry from a gyroid with a triangular lattice to one with a hexagonal lattice. (B) Five models of gyroid graphene with different length constants of L = 3, 5, 10, 15, and 20 nm from left to right. Scale bar, 2.5 nm. (C) 3D-printed samples of the gyroid structure of various L values and wall thicknesses. Scale bar, 2.5 cm. The tensile and compressive tests on the 3D-printed sample are shown in (D) and (E), respectively.

  • Fig. 5 Comparison between the mechanics of the 3D graphene assembly and a polymeric foam as functions of mass density.

    Young’s modulus (A) and tensile strength (B) of the 3D graphene assembly compared to those of porous polystyrene with a woven and foam structure with ρs = 1065 mg/cm3, ES = 3.67 GPa, and σTs = 100 MPa; its scaling laws, Embedded Image and Embedded Image , were obtained from previous studies (20, 21).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/1/e1601536/DC1

    Supplementary Methods

    fig. S1. Material density of the graphene assembly as a function of elevated pressure.

    fig. S2. The total volume of the 3D graphene assembly as functions of the applied strain.

    fig. S3. The atomic stress (σxx) distribution in the 3D graphene assembly under a tensile loading test.

    fig. S4. The processes of building a gyroid graphene structure from three steps.

    fig. S5. Stress-strain curves of tensile and compressive tests on gyroid graphene.

    fig. S6. Snapshots of tensile and compressive tests with different strains on gyroid graphene.

    fig. S7. Stress-strain curves of tensile and compressive tests for 3D-printed gyroid samples.

    fig. S8. Experimental snapshots of the tensile and compressive tests on 3D-printed samples.

    table S1. Summary of the mechanical properties of different 3D graphene assemblies.

    table S2. Summary of the mechanical properties of different gyroid graphene structures.

    table S3. Summary of the mechanical properties of different 3D-printed gyroid structures obtained from experiments.

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Methods
    • fig. S1. Material density of the graphene assembly as a function of elevated pressure.
    • fig. S2. The total volume of the 3D graphene assembly as functions of the applied strain.
    • fig. S3. The atomic stress (σxx) distribution in the 3D graphene assembly under a tensile loading test.
    • fig. S4. The processes of building a gyroid graphene structure from three steps.
    • fig. S5. Stress-strain curves of tensile and compressive tests on gyroid graphene.
    • fig. S6. Snapshots of tensile and compressive tests with different strains on gyroid graphene.
    • fig. S7. Stress-strain curves of tensile and compressive tests for 3D-printed gyroid samples.
    • fig. S8. Experimental snapshots of the tensile and compressive tests on 3D-printed samples.
    • table S1. Summary of the mechanical properties of different 3D graphene assemblies.
    • table S2. Summary of the mechanical properties of different gyroid graphene structures.
    • table S3. Summary of the mechanical properties of different 3D-printed gyroid structures obtained from experiments.

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