Skip to main content
Log in

Self-folding mechanics of graphene tearing and peeling from a substrate

  • Research Article
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

Understanding the underlying mechanism in the tearing and peeling processes of graphene is crucial for the further hierarchical design of origami-like folding and kirigami-like cutting of graphene. However, the complex effects among bending moduli, adhesion, interlayer interaction, and local crystal structure during origami-like folding and kirigami-like cutting remain unclear, resulting in challenges to the practical applications of existing theoretical and experimental findings as well as to potential manipulations of graphene in metamaterials and nanodevices. Toward this end, classical molecular dynamics (MD) simulations are performed with synergetic theoretical analysis to explore the tearing and peeling of self-folded graphene from a substrate driven by external force and by thermal activation. It is found that the elastic energy localized at the small folding ridge plays a significant role in the crack trajectory. Due to the extremely small bending modulus of monolayer graphene, its taper angle when pulled by an external force follows a scaling law distinct from that in case of bilayer graphene. With the increase in the initial width of the folding ridge, the self-folded graphene, motivated by thermal fluctuations, can be self-assembled by spontaneous self-tearing and peeling from a substrate. Simultaneously, the scaling law between the taper angle and adhesive energy is independent of the motivations for thermal activation-induced self-assembly and external force tearing, providing effective insights into the underlying physics for graphene-based origami-like folding and kirigami-like cutting.

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. A. K. Geim and K. S. Novoselov, The rise of graphene, Nat. Mater. 6(3), 183 (2007)

    Article  ADS  Google Scholar 

  2. A. C. Neto, F. Guinea, N. M. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81(1), 109 (2009)

    Article  ADS  Google Scholar 

  3. R. Nair, H. Wu, P. Jayaram, I. Grigorieva, and A. Geim, Unimpeded permeation of water through helium-leak–tight graphene-based membranes, Science 335(6067), 442 (2012)

    Article  ADS  Google Scholar 

  4. S. Hu, M. Lozada-Hidalgo, F. Wang, A. Mishchenko, F. Schedin, R. Nair, E. Hill, D. Boukhvalov, M. Katsnelson, R. Dryfe, I. V. Grigorieva, H. A. Wu, and A. K. Geim, Proton transport through one-atom-thick crystals, Nature 516(7530), 227 (2014)

    Article  ADS  Google Scholar 

  5. R. Joshi, P. Carbone, F. C. Wang, V. G. Kravets, Y. Su, I. V. Grigorieva, H. Wu, A. K. Geim, and R. R. Nair, Precise and ultrafast molecular sieving through graphene oxide membranes, Science 343(6172), 752 (2014)

    Article  ADS  Google Scholar 

  6. X. Liu, F. Wang, H. Wu, and W. Wang, Strengthening metal nanolaminates under shock compression through dual effect of strong and weak graphene interface, Appl. Phys. Lett. 104(23), 231901 (2014)

    Article  ADS  Google Scholar 

  7. M. Yan, F. Wang, C. Han, X. Ma, X. Xu, Q. An, L. Xu, C. Niu, Y. Zhao, X. Tian, P. Hu, H. Wu, and L. Mai, Nanowire templated semihollow bicontinuous graphene scrolls: Designed construction, mechanism, and enhanced energy storage performance, J. Am. Chem. Soc. 135(48), 18176 (2013)

    Google Scholar 

  8. D. Akinwande, C. J. Brennan, J. S. Bunch, P. Egberts, J. R. Felts, H. Gao, R. Huang, J. S. Kim, T. Li, Y. Li, K. M. Liechti, N. Lu, H. S. Park, E. J. Reed, P. Wang, B. I. Yakobson, T. Zhang, Y. W. Zhang, Y. Zhou, and Y. Zhu, A review on mechanics and mechanical properties of 2D materials — Graphene and beyond, Extreme Mechanics Letters 13, 42 (2017)

    Article  Google Scholar 

  9. V. Panchal, C. Giusca, A. Lartsev, R. Yakimova, and O. Kazakova, Local electric field screening in bi-layer graphene devices, Front. Phys. 2, 3 (2014)

    Article  Google Scholar 

  10. G. Algara-Siller, O. Lehtinen, F. Wang, R. Nair, U. Kaiser, H. Wu, A. Geim, and I. Grigorieva, Square ice in graphene nanocapillaries, Nature 519(7544), 443 (2015)

    Article  ADS  Google Scholar 

  11. Y. Zhu, F. Wang, J. Bai, X. C. Zeng, and H. Wu, Compression limit of two-dimensional water constrained in graphene nanocapillaries, ACS Nano 9(12), 12197 (2015)

    Google Scholar 

  12. H. Yin, H. J. Qi, F. Fan, T. Zhu, B. Wang, and Y. Wei, Griffith criterion for brittle fracture in graphene, Nano Lett. 15(3), 1918 (2015)

    Article  ADS  Google Scholar 

  13. Z. Song, Y. Ni, and Z. Xu, Geometrical distortion leads to Griffith strength reduction in graphene membranes, Extreme Mechanics Letters 14, 31 (2017)

    Article  Google Scholar 

  14. J. W. Jiang and H. S. Park, Negative Poisson’s ratio in single-layer graphene ribbons, Nano Lett. 16(4), 2657 (2016)

    Article  ADS  Google Scholar 

  15. J. W. Jiang, T. Chang, X. Guo, and H. S. Park, Intrinsic negative Poisson’s ratio for single-layer graphene, Nano Lett. 16(8), 5286 (2016)

    Article  ADS  Google Scholar 

  16. G. Wang, Z. Dai, Y. Wang, P. Tan, L. Liu, Z. Xu, Y. Wei, R. Huang, and Z. Zhang, Measuring interlayer shear stress in bilayer graphene, Phys. Rev. Lett. 119(3), 036101 (2017)

    Article  ADS  Google Scholar 

  17. J. Annett and G. L. Cross, Self-assembly of graphene ribbons by spontaneous self-tearing and peeling from a substrate, Nature 535(7611), 271 (2016)

    Article  ADS  Google Scholar 

  18. Y. Zhang, F. Zhang, Z. Yan, Q. Ma, X. Li, Y. Huang, and J. A. Rogers, Printing, folding and assembly methods for forming 3D mesostructures in advanced materials, Nature Reviews Materials 2(4), 17019 (2017)

    Google Scholar 

  19. X. Meng, M. Li, Z. Kang, X. Zhang, and J. Xiao, Mechanics of self-folding of single-layer graphene, J. Phys. D Appl. Phys. 46(5), 055308 (2013)

    Article  ADS  Google Scholar 

  20. X. Chen, L. Zhang, Y. Zhao, X. Wang, and C. Ke, Graphene folding on flat substrates, J. Appl. Phys. 116(16), 164301 (2014)

    Article  ADS  Google Scholar 

  21. X. Liu, F. Wang, and H. Wu, Anisotropic growth of buckling-driven wrinkles in graphene monolayer, Nanotechnology 26(6), 065701 (2015)

    Article  ADS  Google Scholar 

  22. M. K. Blees, A. W. Barnard, P. A. Rose, S. P. Roberts, K. L. McGill, P. Y. Huang, A. R. Ruyack, J. W. Kevek, B. Kobrin, D. A. Muller, and P. L. McEuen, Graphene kirigami, Nature 524(7564), 204 (2015)

    Article  ADS  Google Scholar 

  23. T. Zhang, S. Wu, R. Yang, and G. Zhang, Graphene: Nanostructure engineering and applications, Front. Phys. 12(1), 127206 (2017)

    Article  Google Scholar 

  24. E. Hamm, P. Reis, M. LeBlanc, B. Roman, and E. Cerda, Tearing as a test for mechanical characterization of thin adhesive films, Nat. Mater. 7(5), 386 (2008)

    Article  ADS  Google Scholar 

  25. E. Bayart, A. Boudaoud, and M. Adda-Bedia, Finitedistance singularities in the tearing of thin sheets, Phys. Rev. Lett. 106(19), 194301 (2011)

    Article  ADS  Google Scholar 

  26. O. Kruglova, F. Brau, D. Villers, and P. Damman, How geometry controls the tearing of adhesive thin films on curved surfaces, Phys. Rev. Lett. 107(16), 164303 (2011)

    Article  ADS  Google Scholar 

  27. F. Brau, Tearing of thin sheets: cracks interacting through an elastic ridge, Phys. Rev. E 90(6), 062406 (2014)

    Article  ADS  Google Scholar 

  28. B. Roman, Fracture path in brittle thin sheets: a unifying review on tearing, Int. J. Fract. 182(2), 209 (2013)

    Article  Google Scholar 

  29. A. Ibarra, B. Roman, and F. Melo, The tearing path in a thin anisotropic sheet from two pulling points: Wulff’s view, Soft Matter 12(27), 5979 (2016)

    Article  ADS  Google Scholar 

  30. T. Zhang, X. Li, and H. Gao, Fracture of graphene: A review, Int. J. Fract. 196(1–2), 1 (2015)

    Article  Google Scholar 

  31. M. J. Moura and M. Marder, Tearing of free-standing graphene, Phys. Rev. E 88(3), 032405 (2013)

    Article  ADS  Google Scholar 

  32. Y. Guo, C. Liu, Q. Yin, C. Wei, S. Lin, T. B. Hoffman, Y. Zhao, J. H. Edgar, Q. Chen, S. P. Lau, J. Dai, H. Yao, H. S. Wong, and Y. Chai, Distinctive in-plane cleavage behaviors of two-dimensional layered materials, ACS Nano 10(9), 8980 (2016)

    Google Scholar 

  33. J. Yang, Y. Wang, Y. Li, H. Gao, Y. Chai, and H. Yao, Edge orientations of mechanically exfoliated anisotropic two-dimensional materials, J. Mech. Phys. Solids 112, 157 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  34. D. Sen, K. S. Novoselov, P. M. Reis, and M. J. Buehler, Tearing graphene sheets from adhesive substrates produces tapered nanoribbons, Small 6(10), 1108 (2010)

    Article  Google Scholar 

  35. A. F. Fonseca and D. S. Galvao, Self-driven graphene tearing and peeling: A fully atomistic molecular dynamics investigation, arXiv: 1801.05354 (2018)

    Google Scholar 

  36. S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 117(1), 1 (1995)

    Article  ADS  MATH  Google Scholar 

  37. S. J. Stuart, A. B. Tutein, and J. A. Harrison, A reactive potential for hydrocarbons with intermolecular interactions, J. Chem. Phys. 112(14), 6472 (2000)

    Article  ADS  Google Scholar 

  38. Y. Wei, J. Wu, H. Yin, X. Shi, R. Yang, and M. Dresselhaus, The nature of strength enhancement and weakening by pentagon-heptagon defects in graphene, Nat. Mater. 11(9), 759 (2012)

    Article  ADS  Google Scholar 

  39. A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool, Model. Simul. Mater. Sci. Eng. 18(1), 015012 (2010)

    Article  ADS  Google Scholar 

  40. J. Zhang, J. Xiao, X. Meng, C. Monroe, Y. Huang, and J. M. Zuo, Free folding of suspended graphene sheets by random mechanical stimulation, Phys. Rev. Lett. 104(16), 166805 (2010)

    Article  ADS  Google Scholar 

  41. T. Kawai, S. Okada, Y. Miyamoto, and H. Hiura, Selfredirection of tearing edges in graphene: Tight-binding molecular dynamics simulations, Phys. Rev. B 80(3), 033401 (2009)

    Article  ADS  Google Scholar 

  42. B. Lawn, Fracture of Brittle Solids, Cambridge: Cambridge University Press, 1993

    Book  Google Scholar 

  43. Y. Wang and Z. Liu, The fracture toughness of graphene during the tearing process, Model. Simul. Mater. Sci. Eng. 24(8), 085002 (2016)

    Article  ADS  Google Scholar 

  44. Y. Y. Zhang and Y. Gu, Mechanical properties of graphene: Effects of layer number, temperature and isotope, Comput. Mater. Sci. 71, 197 (2013)

    Article  ADS  Google Scholar 

  45. V. Hakim and A. Karma, Laws of crack motion and phase-field models of fracture, J. Mech. Phys. Solids 57(2), 342 (2009)

    Article  ADS  MATH  Google Scholar 

  46. S. P. Koenig, N. G. Boddeti, M. L. Dunn, and J. S. Bunch, Ultrastrong adhesion of graphene membranes, Nat. Nanotechnol. 6(9), 543 (2011)

    Article  ADS  Google Scholar 

  47. R. Huang, Graphene: Show of adhesive strength, Nat. Nanotechnol. 6(9), 537 (2011)

    Article  ADS  Google Scholar 

  48. N. Lindahl, D. Midtvedt, J. Svensson, O. A. Nerushev, N. Lindvall, A. Isacsson, and E. E. Campbell, Determination of the bending rigidity of graphene via electrostatic actuation of buckled membranes, Nano Lett. 12(7), 3526 (2012)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was jointly supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB22040402), the National Natural Science Foundation of China (Grant Nos. 11525211, 11472263, and 11572307), the Anhui Provincial Natural Science Foundation (Grant No. 1808085QA07), and the National Postdoctoral Program for Innovative Talents (Grant No. BX201700225). The authors declare no competing financial interest.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Heng-An Wu.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, ZZ., Zhu, YB. & Wu, HA. Self-folding mechanics of graphene tearing and peeling from a substrate. Front. Phys. 13, 138111 (2018). https://doi.org/10.1007/s11467-018-0755-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11467-018-0755-5

Keywords

Navigation