Skip to main content
Log in

Mechanical buckling induced periodic kinking/stripe microstructures in mechanically peeled graphite flakes from HOPG

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

Mechanical exfoliation is a widely used method to isolate high quality graphene layers from bulk graphite. In our recent experiments, some ordered microstructures, consisting of a periodic alternation of kinks and stripes, were observed in thin graphite flakes that were mechanically peeled from highly oriented pyrolytic graphite. In this paper, a theoretical model is presented to attribute the formation of such ordered structures to the alternation of two mechanical processes during the exfoliation: (1) peeling of a graphite flake and (2) mechanical buckling of the flake being subjected to bending. In this model, the width of the stripes L is determined by thickness h of the flakes, surface energy \(\gamma \), and critical buckling strain \(\varepsilon _{\mathrm{cr}}\). Using some appropriate values of \(\gamma \) and \(\varepsilon _{\mathrm{cr}}\) that are within the ranges determined by other independent experiments and simulations, the predicted relations between the stripe width and the flake thickness agree reasonably well with our experimental measurements. Conversely, measuring the Lh relations of the periodic microstructures in thin graphite flakes could help determine the critical mechanical buckling strain \(\varepsilon _{\mathrm{cr}}\) and the interface energy \(\gamma \).

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Poncharal, P., Wang, Z., Ugarte, D., et al.: Electrostatic deflections and electromechanical resonances of carbon nanotubes. Science 283, 1513 (1999)

  2. Hwang, E., Adam, S., Sarma, S.D.: Carrier transport in two-dimensional graphene layers. Phys. Rev. Lett. 98, 186806 (2007)

    Article  Google Scholar 

  3. Kim, S., Nah, J., Jo, I., et al.: Realization of a high mobility dual-gated graphene field-effect transistor with \({\rm Al}_{2}{\rm O}_{3}\) dielectric. Appl. Phys. Lett. 94, 062103–062107 (2009)

  4. Pirkle, A., Wallace, R.M., Colombo, L.: In situ studies of \({\rm Al}_{2}{\rm O}_{3}\) and \({\rm HfO}_2\) dielectrics on graphite. Appl. Phys. Lett. 95, 133103–133106 (2009)

  5. Ghosh, S., Calizo, I., Teweldebrhan, D., et al.: Extremely high thermal conductivity of graphene: prospects for thermal management applications in nanoelectronic circuits. Appl. Phys. Lett. 92, 151911–151913 (2008)

    Article  Google Scholar 

  6. Zheng, Q., Jiang, B., Liu, S., et al.: Self-retracting motion of graphite microflakes. Phys. Rev. Lett. 100, 067205 (2008)

    Article  MATH  Google Scholar 

  7. Bunch, J.S., Van Der Zande, A.M., Verbridge, S.S., et al.: Electromechanical resonators from graphene sheets. Science 315, 490–493 (2007)

    Article  Google Scholar 

  8. Chen, C., Rosenblatt, S., Bolotin, K.I., et al.: Performance of monolayer graphene nanomechanical resonators with electrical readout. Nat. Nanotechnol. 4, 861–867 (2009)

    Article  Google Scholar 

  9. Zheng, Q., Liu, J.Z., Jiang, Q.: Excess van der Waals interaction energy of a multiwalled carbon nanotube with an extruded core and the induced core oscillation. Phys. Rev. B 65, 245409 (2002)

    Article  Google Scholar 

  10. Rogers, G.W., Liu, J.Z.: Graphene actuators: quantum-mechanical and electrostatic double-layer effects. J. Am. Chem. Soc. 133, 10858–10863 (2011)

    Article  Google Scholar 

  11. Rogers, G.W., Liu, J.Z.: High-performance graphene oxide electromechanical actuators. J. Am. Chem. Soc. 134, 1250–1255 (2011)

    Article  Google Scholar 

  12. Rogers, G.W., Liu, J.Z.: Monolayer graphene oxide as a building block for artificial muscles. Appl. Phys. Lett. 102, 021903 (2013)

    Article  Google Scholar 

  13. Xie, X., Qu, L., Zhou, C., et al.: An asymmetrically surface-modified graphene film electrochemical actuator. ACS Nano 4, 6050–6054 (2010)

    Article  MATH  Google Scholar 

  14. Liang, J., Huang, Y., Oh, J., et al.: Electromechanical actuators based on graphene and graphene/\(\text{ Fe }_{3}\text{ O }_{4}\) hybrid paper. Adv. Funct. Mater. 21, 3778–3784 (2011)

  15. Chang, Z., Yan, W., Shang, J., et al.: Piezoelectric properties of graphene oxide: a first-principles computational study. Appl. Phys. Lett. 105, 023103 (2014)

    Article  Google Scholar 

  16. Ong, M.T., Reed, E.J.: Engineered piezoelectricity in graphene. ACS Nano 6, 1387–1394 (2012)

    Article  Google Scholar 

  17. Xie, X., Bai, H., Shi, G., et al.: Load-tolerant, highly strain-responsive graphene sheets. J. Mater. Chem. 21, 2057–2059 (2011)

    Article  Google Scholar 

  18. Joshi, R., Carbone, P., Wang, F., et al.: Precise and ultrafast molecular sieving through graphene oxide membranes. Science 343, 752–754 (2014)

    Article  MATH  Google Scholar 

  19. Falk, K., Sedlmeier, F., Joly, L., et al.: Molecular origin of fast water transport in carbon nanotube membranes: Superlubricity versus curvature dependent friction. Nano Lett. 10, 4067–4073 (2010)

    Article  Google Scholar 

  20. Xiong, W., Liu, J.Z., Ma, M., et al.: Strain engineering water transport in graphene nanochannels. Phys. Rev. E 84, 056329 (2011)

  21. Schwierz, F.: Graphene transistors. Nat. Nanotechnol. 5, 487–496 (2010)

    Article  Google Scholar 

  22. Bae, S., Kim, H., Lee, Y., et al.: Roll-to-roll production of 30-inch graphene films for transparent electrodes. Nat. Nanotechnol. 5, 574–578 (2010)

    Article  Google Scholar 

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

  24. Sutter, P.W., Flege, J.-I., Sutter, E.A.: Epitaxial graphene on ruthenium. Nat. Mater. 7, 406–411 (2008)

    Article  Google Scholar 

  25. Park, S., Ruoff, R.S.: Chemical methods for the production of graphenes. Nat. Nanotechnol. 4, 217–224 (2009)

    Article  Google Scholar 

  26. Deng, D., Pan, X., Zhang, H., et al.: Freestanding graphene by thermal splitting of silicon carbide granules. Adv. Mater. 22, 2168–2171 (2010)

    Article  MATH  Google Scholar 

  27. Li, D., Müller, M.B., Gilje, S., et al.: Processable aqueous dispersions of graphene nanosheets. Nat. Nanotechnol. 3, 101–105 (2008)

    Article  Google Scholar 

  28. Liu, Z., Zheng, Q., Liu, J.Z.: Stripe/kink microstructures formed in mechanical peeling of highly orientated pyrolytic graphite. Appl. Phys. Lett. 96, 201903–201909 (2010)

    Article  Google Scholar 

  29. Kelly, B.T.: Physics of Graphite. Applied Science Publisher, London (1981)

    Google Scholar 

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

    Article  Google Scholar 

  31. Girifalco, L., Lad, R.: Energy of cohesion, compressibility, and the potential energy functions of the graphite system. J. Chem. Phys. 25, 693–697 (1956)

    Article  MATH  Google Scholar 

  32. Benedict, L.X., Chopra, N.G., Cohen, M.L., et al.: Microscopic determination of the interlayer binding energy in graphite. Chem. Phys. Lett. 286, 490–496 (1998)

    Article  Google Scholar 

  33. Zacharia, R., Ulbricht, H., Hertel, T.: Interlayer cohesive energy of graphite from thermal desorption of polyaromatic hydrocarbons. Phys. Rev. B 69, 155406 (2004)

    Article  Google Scholar 

  34. Spanu, L., Sorella, S., Galli, G.: Nature and strength of interlayer binding in graphite. Phys. Rev. Lett. 103, 196401 (2009)

    Article  Google Scholar 

  35. Liu, Z., Liu, J.Z., Cheng, Y., et al.: Interlayer binding energy of graphite: a mesoscopic determination from deformation. Phys. Rev. B 85, 205418 (2012)

    Article  Google Scholar 

  36. Gould, T., Liu, Z., Liu, J.Z., et al.: Binding and interlayer force in the near-contact region of two graphite slabs: Experiment and theory. J. Chem. Phys. 139, 224704 (2013)

    Article  Google Scholar 

  37. Liu, J.Z., Zheng, Q., Jiang, Q.: Effect of a rippling mode on resonances of carbon nanotubes. Phys. Rev. Lett. 86, 4843–4846 (2001)

    Article  Google Scholar 

  38. Liu, J.Z., Zheng, Q., Jiang, Q.: Effect of bending instabilities on the measurements of mechanical properties of multiwalled carbon nanotubes. Phys. Rev. B 67, 075414 (2003)

    Article  Google Scholar 

  39. Arroyo, M., Belytschko, T.: Nonlinear mechanical response and rippling of thick multiwalled carbon nanotubes. Phys. Rev. Lett. 91, 215505 (2003)

    Article  MATH  Google Scholar 

  40. Ren, M., Liu, J.Z., Wang, L., et al.: Anomalous elastic buckling of hexagonal layered crystalline materials in the absence of structure slenderness. arXiv preprint arXiv:1405.4086 (2014)

  41. Liu, Z., Yang, J., Grey, F., et al.: Observation of microscale superlubricity in graphite. Phys. Rev. Lett. 108, 205503 (2012)

    Article  Google Scholar 

  42. Zang, J., Ryu, S., Pugno, N., et al.: Multifunctionality and control of the crumpling and unfolding of large-area graphene. Nat. Mater. 12, 321–325 (2013)

    Article  Google Scholar 

  43. Koo, W.H., Jeong, S.M., Araoka, F., et al.: Light extraction from organic light-emitting diodes enhanced by spontaneously formed buckles. Nat. Photonics 4, 222–226 (2010)

    Article  Google Scholar 

  44. Efimenko, K., Rackaitis, M., Manias, E., et al.: Nested self-similar wrinkling patterns in skins. Nat. Mater. 4, 293–297 (2005)

    Article  Google Scholar 

Download references

Acknowledgments

Q.S.Z. acknowledges the financial support from NSFC (Grant 10832005), the National Basic Research Program of China (Grant 2007CB936803), and the National 863 Project (Grant 2008AA03Z302). Jefferson Zhe Liu acknowledges the support from the engineering faculty of Monash University through seed grant 2014.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Quan-shui Zheng or Jefferson Zhe Liu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ren, M., Liu, Z., Zheng, Qs. et al. Mechanical buckling induced periodic kinking/stripe microstructures in mechanically peeled graphite flakes from HOPG. Acta Mech. Sin. 31, 494–499 (2015). https://doi.org/10.1007/s10409-015-0417-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-015-0417-6

Keywords

Navigation