Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Elastic coupling between layers in two-dimensional materials

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 Young’s 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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Modulated nanoindentation experiments.
Figure 2: Experimental, SAM-simulated and Hertz indentation curves.
Figure 3: DFT and experimental results for conventional GO films.

References

  1. 1

    Park, J. Y., Kwon, S. & Kim, J. H. Nanomechanical and charge transport properties of two-dimensional atomic sheets. Adv. Mater. Interfaces 1, 130089 (2014).

    Google Scholar 

  2. 2

    Berger, C. et al. Electronic confinement and coherence in patterned epitaxial graphene. Science 312, 1191–1196 (2006).

    CAS  Google Scholar 

  3. 3

    Zhu, Y. et al. Microwave assisted exfoliation and reduction of graphite oxide for ultracapacitors. Carbon 48, 2118–2122 (2010).

    CAS  Google Scholar 

  4. 4

    Lin, Y-M. et al. Operation of graphene transistors at gigahertz frequencies. Nano Lett. 9, 422–426 (2008).

    Google Scholar 

  5. 5

    Wang, X., Zhi, L. & Müllen, K. Transparent, conductive graphene electrodes for dye-sensitized solar cells. Nano Lett. 8, 323–327 (2008).

    CAS  Google Scholar 

  6. 6

    Yu, W. J. et al. Vertically stacked multi-heterostructures of layered materials for logic transistors and complementary inverters. Nature Mater. 12, 246–252 (2013).

    CAS  Google Scholar 

  7. 7

    Pesin, D. & MacDonald, A. H. Spintronics and pseudospintronics in graphene and topological insulators. Nature Mater. 11, 409–416 (2012).

    CAS  Google Scholar 

  8. 8

    Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).

    CAS  Google Scholar 

  9. 9

    De Heer, W. A. et al. Epitaxial graphene. Solid State Commun. 143, 92–100 (2007).

    CAS  Google Scholar 

  10. 10

    Lee, C., Wei, X., Kysar, J. W. & Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008).

    CAS  Google Scholar 

  11. 11

    Baringhaus, J. et al. Exceptional ballistic transport in epitaxial graphene nanoribbons. Nature 506, 349–354 (2014).

    CAS  Google Scholar 

  12. 12

    Bolotin, K. I. et al. Ultrahigh electron mobility in suspended graphene. Solid State Commun. 146, 351–355 (2008).

    CAS  Google Scholar 

  13. 13

    Balandin, A. A. et al. Superior thermal conductivity of single-layer graphene. Nano Lett. 8, 902–907 (2008).

    CAS  Google Scholar 

  14. 14

    Chiu, H. C., Kim, S., Klinke, C. & Riedo, E. Morphology dependence of radial elasticity in multiwalled boron nitride nanotubes. Appl. Phys. Lett. 101, 103109 (2012).

    Google Scholar 

  15. 15

    Loh, K. P., Bao, Q., Eda, G. & Chhowalla, M. Graphene oxide as a chemically tunable platform for optical applications. Nature Chem. 2, 1015–1024 (2010).

    CAS  Google Scholar 

  16. 16

    Eda, G., Fanchini, G. & Chhowalla, M. Large-area ultrathin films of reduced graphene oxide as a transparent and flexible electronic material. Nature Nanotech. 3, 270–274 (2008).

    CAS  Google Scholar 

  17. 17

    Wei, Z. et al. Nanoscale tunable reduction of graphene oxide for graphene electronics. Science 328, 1373–1376 (2010).

    CAS  Google Scholar 

  18. 18

    Ci, L. et al. Atomic layers of hybridized boron nitride and graphene domains. Nature Mater. 9, 430–435 (2010).

    CAS  Google Scholar 

  19. 19

    Ramakrishna Matte, H. S. S. et al. MoS2 and WS2 analogues of graphene. Angew. Chem. 122, 4153–4156 (2010).

    Google Scholar 

  20. 20

    Castellanos-Gomez, A. et al. Mechanical properties of freely suspended semiconducting graphene-like layers based on MoS2 . Nanoscale Res. Lett. 7, 1–4 (2012).

    Google Scholar 

  21. 21

    Radisavljevic, B., Radenovic, A., Brivio, J., Giacometti, V. & Kis, A. Single-layer MoS2 transistors. Nature Nanotech. 6, 147–150 (2011).

    CAS  Google Scholar 

  22. 22

    Kelly, B. T. Physics of Graphite (Applied Science, 1981).

    Google Scholar 

  23. 23

    Kwon, S. et al. Probing nanoscale conductance of monolayer graphene under pressure. Appl. Phys. Lett. 99, 013110 (2011).

    Google Scholar 

  24. 24

    Lee, C. et al. Frictional characteristics of atomically thin sheets. Science 328, 76–80 (2010).

    CAS  Google Scholar 

  25. 25

    Lee, C. et al. Elastic and frictional properties of graphene. Phys. Status Solidi B 246, 2562–2567 (2009).

    CAS  Google Scholar 

  26. 26

    Stewart, J. A. & Spearot, D. E. Atomistic simulations of nanoindentation on the basal plane of crystalline molybdenum disulfide (MoS2). Modelling Simul. Mater. Sci. Eng. 21, 045003 (2013).

    Google Scholar 

  27. 27

    Suk, J. W., Piner, R. D., An, J. & Ruoff, R. S. Mechanical properties of monolayer graphene oxide. ACS Nano 4, 6557–6564 (2010).

    CAS  Google Scholar 

  28. 28

    Hajgató, B. et al. Out-of-plane shear and out-of plane Young’s modulus of double-layer graphene. Chem. Phys. Lett. 564, 37–40 (2013).

    Google Scholar 

  29. 29

    Nakamura, N., Ogi, H. & Hirao, M. Resonance ultrasound spectroscopy with laser-Doppler interferometry for studying elastic properties of thin films. Ultrasonics 42, 491–494 (2004).

    CAS  Google Scholar 

  30. 30

    Chiritescu, C. et al. Ultralow thermal conductivity in disordered, layered WSe2 crystals. Science 315, 351–353 (2007).

    CAS  Google Scholar 

  31. 31

    Riedl, C., Coletti, C. & Starke, U. Structural and electronic properties of epitaxial graphene on SiC(0 0 0 1): A review of growth, characterization, transfer doping and hydrogen intercalation. J. Phys. D 43, 374009 (2010).

    Google Scholar 

  32. 32

    Lucas, M. et al. Hindered rolling and friction anisotropy in supported carbon nanotubes. Nature Mater. 8, 876–881 (2009).

    CAS  Google Scholar 

  33. 33

    Tan, P. H. et al. The shear mode of multilayer graphene. Nature Mater. 11, 294–300 (2012).

    CAS  Google Scholar 

  34. 34

    Lucas, M., Mai, W., Yang, R., Wang, Z. L. & Riedo, E. Aspect ratio dependence of the elastic properties of ZnO nanobelts. Nano Lett. 7, 1314–1317 (2007).

    CAS  Google Scholar 

  35. 35

    Palaci, I. et al. Radial elasticity of multiwalled carbon nanotubes. Phys. Rev. Lett. 94, 175502 (2005).

    CAS  Google Scholar 

  36. 36

    Kim, S. et al. Room-temperature metastability of multilayer graphene oxide films. Nature Mater. 11, 544–549 (2012).

    CAS  Google Scholar 

  37. 37

    Hummers, W. S. Jr & Offeman, R. E. Preparation of graphitic oxide. J. Am. Chem. Soc. 80, 1339–1339 (1958).

    CAS  Google Scholar 

  38. 38

    Lantz, M., O’Shea, S., Welland, M. & Johnson, K. Atomic-force-microscope study of contact area and friction on NbSe2 . Phys. Rev. B 55, 10776–10785 (1997).

    CAS  Google Scholar 

  39. 39

    Carpick, R. W., Ogletree, D. & Salmeron, M. Lateral stiffness: A new nanomechanical measurement for the determination of shear strengths with friction force microscopy. Appl. Phys. Lett. 70, 1548–1550 (1997).

    CAS  Google Scholar 

  40. 40

    Grierson, D., Flater, E. & Carpick, R. Accounting for the JKR–DMT transition in adhesion and friction measurements with atomic force microscopy. J. Adhes. Sci. Technol. 19, 291–311 (2005).

    CAS  Google Scholar 

  41. 41

    Derjaguin, B. V., Muller, V. M. & Toporov, Y. P. Effect of contact deformations on the adhesion of particles. J. Colloid Interface Sci. 53, 314–326 (1975).

    CAS  Google Scholar 

  42. 42

    Johnson, K. L. Contact Mechanics (Cambridge Univ. Press, 1987).

    Google Scholar 

  43. 43

    Turner, J. Contact on a transversely isotropic half-space, or between two transversely isotropic bodies. Int. J. Solids Struct. 16, 409–419 (1980).

    Google Scholar 

  44. 44

    Bagault, C., Nelias, D., Baietto, M-C. & Ovaert, T. C. Contact analyses for anisotropic half-space coated with an anisotropic layer: Effect of the anisotropy on the pressure distribution and contact area. Int. J. Solids Struct. 50, 743–754 (2013).

    Google Scholar 

  45. 45

    Bagault, C., Nelias, D. & Baietto, M-C. Contact analyses for anisotropic half space: Effect of the anisotropy on the pressure distribution and contact area. J. Tribol. 134, 031401 (2012).

    Google Scholar 

  46. 46

    Jacq, C., Nelias, D., Lormand, G. & Girodin, D. Development of a three-dimensional semi-analytical elastic–plastic contact code. J. Tribol. 124, 653–667 (2002).

    Google Scholar 

  47. 47

    Palacio, I. et al. Atomic structure of epitaxial graphene sidewall nanoribbons: Flat graphene, miniribbons, and the confinement gap. Nano Lett. 15, 182–189 (2014).

    Google Scholar 

  48. 48

    Zhou, S. & Bongiorno, A. Origin of the chemical and kinetic stability of graphene oxide. Sci. Rep. 3, 2484 (2013).

    Google Scholar 

  49. 49

    Zhou, S. et al. Film structure of epitaxial graphene oxide on SiC: Insight on the relationship between interlayer spacing, water content, and intralayer structure. Adv. Mater. Interface 1, 1300106 (2014).

    Google Scholar 

  50. 50

    Giannozzi, P. et al. QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).

    Google Scholar 

  51. 51

    Carroll, K. M. et al. Parallelization of thermochemical nanolithography. Nanoscale 6, 1299–1304 (2014).

    CAS  Google Scholar 

  52. 52

    Troullier, N. & Martins, J. L. Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B 43, 1993–2006 (1991).

    CAS  Google Scholar 

  53. 53

    Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    CAS  Google Scholar 

  54. 54

    Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 27, 1787–1799 (2006).

    CAS  Google Scholar 

Download references

Acknowledgements

Y.G., S.K., H-C.C. and E.R., acknowledge the support of the Office of Basic Energy Sciences of the US Department of Energy (DE-FG02-06ER46293). S.Z. and A.B. acknowledge the support of the National Science Foundation (NSF) grant CMMI 1436375. S.Z., A.B., C.B. and W.d.H. acknowledge the support of the NSF grant DMR-0820382. C.B. acknowledges partial financial support from the European Flagship Graphene. A.B. acknowledges the support of the NSF grant CHE-0946869. R.S. acknowledges the support of the Italian Cariplo Foundation, project No. 2011-0373. We thank J-P. Turmaud for the EG on Si sample.

Author information

Affiliations

Authors

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.

Corresponding authors

Correspondence to Angelo Bongiorno or Elisa Riedo.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 9188 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gao, Y., Kim, S., Zhou, S. et al. Elastic coupling between layers in two-dimensional materials. Nature Mater 14, 714–720 (2015). https://doi.org/10.1038/nmat4322

Download citation

Further reading

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing