Advertisement

Nanoindentation of circular multilayer graphene allotropes

  • Zhanlei Huo
  • Zhengrong Guo
  • Jiantao Leng
  • Tienchong Chang
Article

Abstract

Nanoindentaion has been proposed as an efficient technique to measure mechanical single-layer two-dimensional (2D) materials via combining the membrane theory with the indentation data. However, for multilayered structures of 2D materials, significant discrepancy exists between the Young’s modulus obtained from the existing membrane model and those from other methods. Here we develop a multilayer indentation model by taking the multilayer effect into account in the previous membrane model. We show that the present model can accurately predict the Young’s modulus of multilayered 2D carbon materials. For few layer graphene and twin graphene structures, the deviation of the Young’s moduli obtained by the present model are both within a reasonable range, while the error caused by the direct use of the previous single-layer membrane model increases with the number of layers. The present model provides an efficient tool to extract the mechanical properties of 2D materials from the nanoindentation data of their multilayered structures.

Keywords

nanoindentaion two-dimensional materials Young’s modulus molecular dynamics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films. Science, 2004, 306: 666–669CrossRefGoogle Scholar
  2. 2.
    Zhang H. Ultrathin two-dimensional nanomaterials. ACS Nano, 2015, 9: 9451–9469CrossRefGoogle Scholar
  3. 3.
    Jiang J W, Leng J, Li J, et al. Twin graphene: A novel two-dimensional semiconducting carbon allotrope. Carbon, 2017, 118: 370–375CrossRefGoogle Scholar
  4. 4.
    Liu H, Du Y, Deng Y, et al. Semiconducting black phosphorus: Synthesis, transport properties and electronic applications. Chem Soc Rev, 2015, 44: 2732–2743CrossRefGoogle Scholar
  5. 5.
    Lin Y, Williams T V, Connell J W. Soluble, exfoliated hexagonal boron nitride nanosheets. J Phys Chem Lett, 2009, 1: 277–283CrossRefGoogle Scholar
  6. 6.
    Mas-Ballesté R, Gómez-Navarro C, Gómez-Herrero J, et al. 2D materials: To graphene and beyond. Nanoscale, 2011, 3: 20–30CrossRefGoogle Scholar
  7. 7.
    Colson J W, Woll A R, Mukherjee A, et al. Oriented 2D covalent organic framework thin films on single-layer graphene. Science, 2011, 332: 228–231CrossRefGoogle Scholar
  8. 8.
    Miyake K, Satomi N, Sasaki S. Elastic modulus of polystyrene film from near surface to bulk measured by nanoindentation using atomic force microscopy. Appl Phys Lett, 2006, 89: 031925CrossRefGoogle Scholar
  9. 9.
    Pradhan S K, Nayak B B, Sahay S S, et al. Mechanical properties of graphite flakes and spherulites measured by nanoindentation. Carbon, 2009, 47: 2290–2292CrossRefGoogle Scholar
  10. 10.
    Zhou L, Xue J, Wang Y, et al. Molecular mechanics simulations of the deformation mechanism of graphene monolayer under free standing indentation. Carbon, 2013, 63: 117–124CrossRefGoogle Scholar
  11. 11.
    Cao G, Chen X. The size effect of nanoindentation on ZnO nanofilms. J Appl Phys, 2007, 102: 123513CrossRefGoogle Scholar
  12. 12.
    Jung Y G, Lawn B R, Martyniuk M, et al. Evaluation of elastic modulus and hardness of thin films by nanoindentation. J Mater Res, 2004, 19: 3076–3080CrossRefGoogle Scholar
  13. 13.
    Zhou L, Wang Y, Cao G. Estimating the elastic properties of few-layer graphene from the free-standing indentation response. J Phys-Condens Matter, 2013, 25: 475301CrossRefGoogle Scholar
  14. 14.
    Deng X, Koopman M, Chawla N, et al. Young’s modulus of (Cu, Ag)- Sn intermetallics measured by nanoindentation. Mater Sci Eng-A, 2004, 364: 240–243CrossRefGoogle Scholar
  15. 15.
    Huang G, Lu H. Measurement of Young’s relaxation modulus using nanoindentation. Mech Time-Depend Mater, 2006, 10: 229–243CrossRefGoogle Scholar
  16. 16.
    Soomro M Y, Hussain I, Bano N, et al. Nanoscale elastic modulus of single horizontal ZnO nanorod using nanoindentation experiment. Nanoscale Res Lett, 2012, 7: 146CrossRefGoogle Scholar
  17. 17.
    Llorente A, Serrano B, Baselga J, et al. Nanoindentation and wear behavior of thermally stable biocompatible polysulfone-alumina nanocomposites. RSC Adv, 2016, 6: 100239–100247CrossRefGoogle Scholar
  18. 18.
    Bamber M J, Cooke K E, Mann A B, et al. Accurate determination of Young’s modulus and Poisson’s ratio of thin films by a combination of acoustic microscopy and nanoindentation. Thin Solid Films, 2001, 398–399: 299–305Google Scholar
  19. 19.
    Tan X, Wu J, Zhang K, et al. Nanoindentation models and Young’s modulus of monolayer graphene: A molecular dynamics study. Appl Phys Lett, 2013, 102: 071908CrossRefGoogle Scholar
  20. 20.
    Petersen K E, Guarnieri C R. Young’s modulus measurements of thin films using micromechanics. J Appl Phys, 1979, 50: 6761–6766CrossRefGoogle Scholar
  21. 21.
    Chen Y, Gao Q, Wang Y, et al. Determination of Young’s modulus of ultrathin nanomaterials. Nano Lett, 2015, 15: 5279–5283CrossRefGoogle Scholar
  22. 22.
    Jiang J W, Wang J S, Li B. Young’s modulus of graphene: A molecular dynamics study. Phys Rev B, 2009, 80: 113405CrossRefGoogle Scholar
  23. 23.
    Zhou L, Wang Y, Cao G. van der Waals effect on the nanoindentation response of free standing monolayer graphene. Carbon, 2013, 57: 357–362Google Scholar
  24. 24.
    Neek-Amal M, Peeters F M. Linear reduction of stiffness and vibration frequencies in defected circular monolayer graphene. Phys Rev B, 2010, 81: 235437CrossRefGoogle Scholar
  25. 25.
    Cadelano E, Palla P L, Giordano S, et al. Nonlinear elasticity of monolayer graphene. Phys Rev Lett, 2009, 102: 235502CrossRefGoogle Scholar
  26. 26.
    Lee C, Wei X, Kysar J W, et al. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science, 2008, 321: 385–388CrossRefGoogle Scholar
  27. 27.
    Natsuki T, Tantrakarn K, Endo M. Prediction of elastic properties for single-walled carbon nanotubes. Carbon, 2004, 42: 39–45CrossRefGoogle Scholar
  28. 28.
    Van Lier G, Van Alsenoy C, Van Doren V, et al. Ab initio study of the elastic properties of single-walled carbon nanotubes and graphene. Chem Phys Lett, 2000, 326: 181–185CrossRefGoogle Scholar
  29. 29.
    Reddy C D, Rajendran S, Liew K M. Equivalent continuum modeling of graphene sheets. Int J Nanosci, 2005, 04: 631–636CrossRefGoogle Scholar
  30. 30.
    Xiao J R, Gama B A, Gillespie Jr. J W. An analytical molecular structural mechanics model for the mechanical properties of carbon nanotubes. Int J Solids Struct, 2005, 42: 3075–3092Google Scholar
  31. 31.
    Kudin K N, Scuseria G E, Yakobson B I. C2FBN, and C nanoshell elasticity from ab initio computations. Phys Rev B, 2001, 64: 235406CrossRefGoogle Scholar
  32. 32.
    Chen X, Yi C, Ke C. Bending stiffness and interlayer shear modulus of few-layer graphene. Appl Phys Lett, 2015, 106: 101907CrossRefGoogle Scholar
  33. 33.
    Wang L, Zhang Q. Elastic behavior of bilayer graphene under in-plane loadings. Curr Appl Phys, 2012, 12: 1173–1177CrossRefGoogle Scholar
  34. 34.
    Yi L, Zhang Y, Feng X, et al. Mechanical properties of graphynes under shearing and bending. J Appl Phys, 2016, 119: 204304CrossRefGoogle Scholar
  35. 35.
    Tsai J L, Tu J F. Characterizing mechanical properties of graphite using molecular dynamics simulation. Mater Des, 2010, 31: 194–199CrossRefGoogle Scholar
  36. 36.
    Tan P H, Han W P, Zhao W J, et al. The shear mode of multilayer graphene. Nat Mater, 2012, 11: 294–300CrossRefGoogle Scholar
  37. 37.
    Ohta T, Bostwick A, Seyller T, et al. Controlling the electronic structure of bilayer graphene. Science, 2006, 313: 951–954CrossRefGoogle Scholar
  38. 38.
    Zhang Y, Pan C. Measurements of mechanical properties and number of layers of graphene from nano-indentation. Diamond Related Mater, 2012, 24: 1–5CrossRefGoogle Scholar
  39. 39.
    Neek-Amal M, Peeters F M. Nanoindentation of a circular sheet of bilayer graphene. Phys Rev B, 2010, 81: 235421CrossRefGoogle Scholar
  40. 40.
    Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J Comput Phys, 1995, 117: 1–19CrossRefzbMATHGoogle Scholar
  41. 41.
    Stuart S J, Tutein A B, Harrison J A. A reactive potential for hydrocarbons with intermolecular interactions. J Chem Phys, 2000, 112: 6472–6486CrossRefGoogle Scholar
  42. 42.
    Brenner D W, Shenderova O A, Harrison J A, et al. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J Phys-Condens Matter, 2002, 14: 783–802CrossRefGoogle Scholar
  43. 43.
    Vodenitcharova T, Zhang L C. Mechanism of bending with kinking of a single-walled carbon nanotube. Phys Rev B, 2004, 69: 115410CrossRefGoogle Scholar
  44. 44.
    Xiang L, Ma S Y, Wang F, et al. Nanoindentation models and Young’s modulus of few-layer graphene: A molecular dynamics simulation study. J Phys D-Appl Phys, 2015, 48: 395305CrossRefGoogle Scholar
  45. 45.
    Han J, Pugno N M, Ryu S. Nanoindentation cannot accurately predict the tensile strength of graphene or other 2D materials. Nanoscale, 2015, 7: 15672–15679CrossRefGoogle Scholar
  46. 46.
    Costescu B I, Gräter F. Graphene mechanics: II. Atomic stress distribution during indentation until rupture. Phys Chem Chem Phys, 2014, 16: 12582–12590Google Scholar
  47. 47.
    Wan K T, Guo S, Dillard D A. A theoretical and numerical study of a thin clamped circular film under an external load in the presence of a tensile residual stress. Thin Solid Films, 2003, 425: 150–162CrossRefGoogle Scholar
  48. 48.
    Komaragiri U, Begley M R, Simmonds J G. The mechanical response of freestanding circular elastic films under point and pressure loads. J Appl Mech, 2005, 72: 203CrossRefzbMATHGoogle Scholar
  49. 49.
    Mueggenburg K E, Lin X M, Goldsmith R H, et al. Elastic membranes of close-packed nanoparticle arrays. Nat Mater, 2007, 6: 656–660CrossRefGoogle Scholar
  50. 50.
    Lee J U, Yoon D, Cheong H. Estimation of Young’s modulus of graphene by Raman spectroscopy. Nano Lett, 2012, 12: 4444–4448CrossRefGoogle Scholar
  51. 51.
    Yoon J, Ru C Q, Mioduchowski A. Surface instability of a bilayer elastic film due to surface van der Waals forces. J Appl Phys, 2005, 98: 113503CrossRefGoogle Scholar
  52. 52.
    Lee C, Wei X, Li Q, et al. Elastic and frictional properties of graphene. Phys Status Solidi B, 2009, 246: 2562–2567CrossRefGoogle Scholar

Copyright information

© Science in China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Zhanlei Huo
    • 1
  • Zhengrong Guo
    • 1
  • Jiantao Leng
    • 1
  • Tienchong Chang
    • 1
  1. 1.Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghai UniversityShanghaiChina

Personalised recommendations