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 L–h relations of the periodic microstructures in thin graphite flakes could help determine the critical mechanical buckling strain \(\varepsilon _{\mathrm{cr}}\) and the interface energy \(\gamma \).
Similar content being viewed by others
References
Poncharal, P., Wang, Z., Ugarte, D., et al.: Electrostatic deflections and electromechanical resonances of carbon nanotubes. Science 283, 1513 (1999)
Hwang, E., Adam, S., Sarma, S.D.: Carrier transport in two-dimensional graphene layers. Phys. Rev. Lett. 98, 186806 (2007)
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)
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)
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)
Zheng, Q., Jiang, B., Liu, S., et al.: Self-retracting motion of graphite microflakes. Phys. Rev. Lett. 100, 067205 (2008)
Bunch, J.S., Van Der Zande, A.M., Verbridge, S.S., et al.: Electromechanical resonators from graphene sheets. Science 315, 490–493 (2007)
Chen, C., Rosenblatt, S., Bolotin, K.I., et al.: Performance of monolayer graphene nanomechanical resonators with electrical readout. Nat. Nanotechnol. 4, 861–867 (2009)
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)
Rogers, G.W., Liu, J.Z.: Graphene actuators: quantum-mechanical and electrostatic double-layer effects. J. Am. Chem. Soc. 133, 10858–10863 (2011)
Rogers, G.W., Liu, J.Z.: High-performance graphene oxide electromechanical actuators. J. Am. Chem. Soc. 134, 1250–1255 (2011)
Rogers, G.W., Liu, J.Z.: Monolayer graphene oxide as a building block for artificial muscles. Appl. Phys. Lett. 102, 021903 (2013)
Xie, X., Qu, L., Zhou, C., et al.: An asymmetrically surface-modified graphene film electrochemical actuator. ACS Nano 4, 6050–6054 (2010)
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)
Chang, Z., Yan, W., Shang, J., et al.: Piezoelectric properties of graphene oxide: a first-principles computational study. Appl. Phys. Lett. 105, 023103 (2014)
Ong, M.T., Reed, E.J.: Engineered piezoelectricity in graphene. ACS Nano 6, 1387–1394 (2012)
Xie, X., Bai, H., Shi, G., et al.: Load-tolerant, highly strain-responsive graphene sheets. J. Mater. Chem. 21, 2057–2059 (2011)
Joshi, R., Carbone, P., Wang, F., et al.: Precise and ultrafast molecular sieving through graphene oxide membranes. Science 343, 752–754 (2014)
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)
Xiong, W., Liu, J.Z., Ma, M., et al.: Strain engineering water transport in graphene nanochannels. Phys. Rev. E 84, 056329 (2011)
Schwierz, F.: Graphene transistors. Nat. Nanotechnol. 5, 487–496 (2010)
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)
Novoselov, K.S., Geim, A.K., Morozov, S., et al.: Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004)
Sutter, P.W., Flege, J.-I., Sutter, E.A.: Epitaxial graphene on ruthenium. Nat. Mater. 7, 406–411 (2008)
Park, S., Ruoff, R.S.: Chemical methods for the production of graphenes. Nat. Nanotechnol. 4, 217–224 (2009)
Deng, D., Pan, X., Zhang, H., et al.: Freestanding graphene by thermal splitting of silicon carbide granules. Adv. Mater. 22, 2168–2171 (2010)
Li, D., Müller, M.B., Gilje, S., et al.: Processable aqueous dispersions of graphene nanosheets. Nat. Nanotechnol. 3, 101–105 (2008)
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)
Kelly, B.T.: Physics of Graphite. Applied Science Publisher, London (1981)
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)
Girifalco, L., Lad, R.: Energy of cohesion, compressibility, and the potential energy functions of the graphite system. J. Chem. Phys. 25, 693–697 (1956)
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)
Zacharia, R., Ulbricht, H., Hertel, T.: Interlayer cohesive energy of graphite from thermal desorption of polyaromatic hydrocarbons. Phys. Rev. B 69, 155406 (2004)
Spanu, L., Sorella, S., Galli, G.: Nature and strength of interlayer binding in graphite. Phys. Rev. Lett. 103, 196401 (2009)
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)
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)
Liu, J.Z., Zheng, Q., Jiang, Q.: Effect of a rippling mode on resonances of carbon nanotubes. Phys. Rev. Lett. 86, 4843–4846 (2001)
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)
Arroyo, M., Belytschko, T.: Nonlinear mechanical response and rippling of thick multiwalled carbon nanotubes. Phys. Rev. Lett. 91, 215505 (2003)
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)
Liu, Z., Yang, J., Grey, F., et al.: Observation of microscale superlubricity in graphite. Phys. Rev. Lett. 108, 205503 (2012)
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)
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)
Efimenko, K., Rackaitis, M., Manias, E., et al.: Nested self-similar wrinkling patterns in skins. Nat. Mater. 4, 293–297 (2005)
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
Corresponding authors
Rights and permissions
About this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10409-015-0417-6