Elastic coupling between layers in two-dimensional materials

Journal name:
Nature Materials
Volume:
14,
Pages:
714–720
Year published:
DOI:
doi:10.1038/nmat4322
Received
Accepted
Published online

Abstract

Two-dimensional materials, such as graphene and MoS2, are films of a few atomic layers in thickness with strong in-plane bonds and weak interactions between the layers. The in-plane elasticity has been widely studied in bending experiments where a suspended film is deformed substantially; however, little is known about the films elastic modulus perpendicular to the planes, as the measurement of the out-of-plane elasticity of supported 2D films requires indentation depths smaller than the films interlayer distance. Here, we report on sub-ångström-resolution indentation measurements of the perpendicular-to-the-plane elasticity of 2D materials. Our indentation data, combined with semi-analytical models and density functional theory, are then used to study the perpendicular elasticity of few-layer-thick graphene and graphene oxide films. We find that the perpendicular Youngs modulus of graphene oxide films reaches a maximum when one complete water layer is intercalated between the graphitic planes. This non-destructive methodology can map interlayer coupling and intercalation in 2D films.

At a glance

Figures

  1. Modulated nanoindentation experiments.
    Figure 1: Modulated nanoindentation experiments.

    a, Schematic diagram of the experimental set-up, where a spherical AFM tip vibrates while indenting a few-layer-thick film of graphene or GO. b, Experimentally measured indentation curves for single-crystal SiC, 10-layer-thick EG, and 10-layer-thick EGO. All three curves were obtained with the same AFM tip, R = 114 nm.

  2. Experimental, SAM-simulated and Hertz indentation curves.
    Figure 2: Experimental, SAM-simulated and Hertz indentation curves.

    a, Experimentally measured indentation curves in HOPG (filled circles), semi-analytical model simulations of indentation in graphite (open circles), and Hertzian fitting (continuum line) of the indentation curves on HOPG. The indenting tip radius was 100 nm. b, Contact-pressure distribution profiles for Hertz contacts and SAM simulations of indentation in graphite. Note that for bulk graphite and for a graphite film 50 nm thick, the SAM simulations and the contact distribution profiles almost overlap. c, Experimental indentation curves on 10-layer-thick EG, 1-layer-thick EG, buffer-layer EG, and SiC. d, Statistical analysis of exponent number b in the fitting function Fz = Czindentb. For EGO and GO, the RH is indicated. baverage is 1.40.

  3. DFT and experimental results for conventional GO films.
    Figure 3: DFT and experimental results for conventional GO films.

    a, The DFT-calculated Fz versus displacement curves for different water contents in graphene fully oxidized with hydroxyl groups. b, Experimental Fz versus indentation depth curves at different RHs in conventional GO. All of the curves were obtained with the same AFM tip. c,d, Experimental and DFT results of E of GO as a function of water content and RH, respectively. The insets are schematic diagrams of the corresponding atomistic structures showing how water molecules fill the interlayer spacing. Each experimental point of E is an average value of more than 30 different measurements.

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Author information

  1. These authors contributed equally to this work.

    • Yang Gao &
    • Suenne Kim

Affiliations

  1. School of Physics, Georgia Institute of Technology, 837 State Street Atlanta, Georgia 30332-0430, USA

    • Yang Gao,
    • Si Zhou,
    • Claire Berger,
    • Walt de Heer,
    • Angelo Bongiorno &
    • Elisa Riedo
  2. Advanced Science Research Center and City College New York, City University of New York, 85 St Nicholas Terrace New York, New York 10031, USA

    • Yang Gao &
    • Elisa Riedo
  3. Department of Applied Physics, Hanyang University, Ansan 426-791, South Korea

    • Suenne Kim
  4. Department of Physics, National Taiwan Normal University, 88, Sec.4, Ting-Chou Road Taipei 116, Taiwan

    • Hsiang-Chih Chiu
  5. Université de Lyon, CNRS, INSA-Lyon, LaMCoS UMR5259, Villeurbanne F69621, France

    • Daniel Nélias
  6. Institut Néel, Université Grenoble Alpes-CNRS, BP 166 38042 Grenoble, France

    • Claire Berger
  7. King Abdulaziz University, Department of Physics, Jeddah 21589, Saudi Arabia

    • Walt de Heer
  8. L-NESS, Department of Physics, Politecnico di Milano, Via Anzani 42 22100 Como, Italy

    • Laura Polloni &
    • Roman Sordan
  9. Department of Chemistry, College of Staten Island, City University of New York, New York, New York 10314, USA

    • Angelo Bongiorno

Contributions

Y.G., S.K. and H-C.C. performed nanomechanics experiments and data analysis. S.Z. carried out DFT calculations. D.N. performed the SAM calculations. C.B., and W.d.H. synthesized the EG and EGO samples. L.P. and R.S. synthesized the GO samples. A.B. conceived and designed the theory and analysed the data. E.R. conceived and designed the experiments and analysed the data. All authors contributed to write the article.

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The authors declare no competing financial interests.

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