Skip to main content
Log in

Nanoindentation of circular multilayer graphene allotropes

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films. Science, 2004, 306: 666–669

    Article  Google Scholar 

  2. Zhang H. Ultrathin two-dimensional nanomaterials. ACS Nano, 2015, 9: 9451–9469

    Article  Google Scholar 

  3. Jiang J W, Leng J, Li J, et al. Twin graphene: A novel two-dimensional semiconducting carbon allotrope. Carbon, 2017, 118: 370–375

    Article  Google Scholar 

  4. Liu H, Du Y, Deng Y, et al. Semiconducting black phosphorus: Synthesis, transport properties and electronic applications. Chem Soc Rev, 2015, 44: 2732–2743

    Article  Google Scholar 

  5. Lin Y, Williams T V, Connell J W. Soluble, exfoliated hexagonal boron nitride nanosheets. J Phys Chem Lett, 2009, 1: 277–283

    Article  Google Scholar 

  6. Mas-Ballesté R, Gómez-Navarro C, Gómez-Herrero J, et al. 2D materials: To graphene and beyond. Nanoscale, 2011, 3: 20–30

    Article  Google Scholar 

  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: 228–231

    Article  Google Scholar 

  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: 031925

    Article  Google Scholar 

  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: 2290–2292

    Article  Google Scholar 

  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: 117–124

    Article  Google Scholar 

  11. Cao G, Chen X. The size effect of nanoindentation on ZnO nanofilms. J Appl Phys, 2007, 102: 123513

    Article  Google Scholar 

  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: 3076–3080

    Article  Google Scholar 

  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: 475301

    Article  Google Scholar 

  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: 240–243

    Article  Google Scholar 

  15. Huang G, Lu H. Measurement of Young’s relaxation modulus using nanoindentation. Mech Time-Depend Mater, 2006, 10: 229–243

    Article  Google Scholar 

  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: 146

    Article  Google Scholar 

  17. Llorente A, Serrano B, Baselga J, et al. Nanoindentation and wear behavior of thermally stable biocompatible polysulfone-alumina nanocomposites. RSC Adv, 2016, 6: 100239–100247

    Article  Google Scholar 

  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: 299–305

    Article  Google Scholar 

  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: 071908

    Article  Google Scholar 

  20. Petersen K E, Guarnieri C R. Young’s modulus measurements of thin films using micromechanics. J Appl Phys, 1979, 50: 6761–6766

    Article  Google Scholar 

  21. Chen Y, Gao Q, Wang Y, et al. Determination of Young’s modulus of ultrathin nanomaterials. Nano Lett, 2015, 15: 5279–5283

    Article  Google Scholar 

  22. Jiang J W, Wang J S, Li B. Young’s modulus of graphene: A molecular dynamics study. Phys Rev B, 2009, 80: 113405

    Article  Google Scholar 

  23. Zhou L, Wang Y, Cao G. van der Waals effect on the nanoindentation response of free standing monolayer graphene. Carbon, 2013, 57: 357–362

    Article  Google Scholar 

  24. Neek-Amal M, Peeters F M. Linear reduction of stiffness and vibration frequencies in defected circular monolayer graphene. Phys Rev B, 2010, 81: 235437

    Article  Google Scholar 

  25. Cadelano E, Palla P L, Giordano S, et al. Nonlinear elasticity of monolayer graphene. Phys Rev Lett, 2009, 102: 235502

    Article  Google Scholar 

  26. Lee C, Wei X, Kysar J W, et al. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science, 2008, 321: 385–388

    Article  Google Scholar 

  27. Natsuki T, Tantrakarn K, Endo M. Prediction of elastic properties for single-walled carbon nanotubes. Carbon, 2004, 42: 39–45

    Article  Google Scholar 

  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: 181–185

    Article  Google Scholar 

  29. Reddy C D, Rajendran S, Liew K M. Equivalent continuum modeling of graphene sheets. Int J Nanosci, 2005, 04: 631–636

    Article  Google Scholar 

  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: 3075–3092

    Article  MATH  Google Scholar 

  31. Kudin K N, Scuseria G E, Yakobson B I. C2FBN, and C nanoshell elasticity from ab initio computations. Phys Rev B, 2001, 64: 235406

    Article  Google Scholar 

  32. Chen X, Yi C, Ke C. Bending stiffness and interlayer shear modulus of few-layer graphene. Appl Phys Lett, 2015, 106: 101907

    Article  Google Scholar 

  33. Wang L, Zhang Q. Elastic behavior of bilayer graphene under in-plane loadings. Curr Appl Phys, 2012, 12: 1173–1177

    Article  Google Scholar 

  34. Yi L, Zhang Y, Feng X, et al. Mechanical properties of graphynes under shearing and bending. J Appl Phys, 2016, 119: 204304

    Article  Google Scholar 

  35. Tsai J L, Tu J F. Characterizing mechanical properties of graphite using molecular dynamics simulation. Mater Des, 2010, 31: 194–199

    Article  Google Scholar 

  36. Tan P H, Han W P, Zhao W J, et al. The shear mode of multilayer graphene. Nat Mater, 2012, 11: 294–300

    Article  Google Scholar 

  37. Ohta T, Bostwick A, Seyller T, et al. Controlling the electronic structure of bilayer graphene. Science, 2006, 313: 951–954

    Article  Google Scholar 

  38. Zhang Y, Pan C. Measurements of mechanical properties and number of layers of graphene from nano-indentation. Diamond Related Mater, 2012, 24: 1–5

    Article  Google Scholar 

  39. Neek-Amal M, Peeters F M. Nanoindentation of a circular sheet of bilayer graphene. Phys Rev B, 2010, 81: 235421

    Article  Google Scholar 

  40. Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J Comput Phys, 1995, 117: 1–19

    Article  MATH  Google Scholar 

  41. Stuart S J, Tutein A B, Harrison J A. A reactive potential for hydrocarbons with intermolecular interactions. J Chem Phys, 2000, 112: 6472–6486

    Article  Google Scholar 

  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: 783–802

    Article  Google Scholar 

  43. Vodenitcharova T, Zhang L C. Mechanism of bending with kinking of a single-walled carbon nanotube. Phys Rev B, 2004, 69: 115410

    Article  Google Scholar 

  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: 395305

    Article  Google Scholar 

  45. Han J, Pugno N M, Ryu S. Nanoindentation cannot accurately predict the tensile strength of graphene or other 2D materials. Nanoscale, 2015, 7: 15672–15679

    Article  Google Scholar 

  46. Costescu B I, Gräter F. Graphene mechanics: II. Atomic stress distribution during indentation until rupture. Phys Chem Chem Phys, 2014, 16: 12582–12590

    Google Scholar 

  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: 150–162

    Article  Google Scholar 

  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: 203

    Article  MATH  Google Scholar 

  49. Mueggenburg K E, Lin X M, Goldsmith R H, et al. Elastic membranes of close-packed nanoparticle arrays. Nat Mater, 2007, 6: 656–660

    Article  Google Scholar 

  50. Lee J U, Yoon D, Cheong H. Estimation of Young’s modulus of graphene by Raman spectroscopy. Nano Lett, 2012, 12: 4444–4448

    Article  Google Scholar 

  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: 113503

    Article  Google Scholar 

  52. Lee C, Wei X, Li Q, et al. Elastic and frictional properties of graphene. Phys Status Solidi B, 2009, 246: 2562–2567

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to TienChong Chang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huo, Z., Guo, Z., Leng, J. et al. Nanoindentation of circular multilayer graphene allotropes. Sci. China Technol. Sci. 62, 269–275 (2019). https://doi.org/10.1007/s11431-018-9297-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-018-9297-y

Keywords

Navigation