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A torsional potential for graphene derived from fitting to DFT results

  • Georgios D. Chatzidakis
  • George Kalosakas
  • Zacharias G. Fthenakis
  • Nektarios N. LathiotakisEmail author
Regular Article

Abstract

We present a simple torsional potential for graphene to accurately describe its out-of-plane deformations. The parameters of the potential are derived through appropriate fitting with suitable DFT calculations regarding the deformation energy of graphene sheets folded around two different folding axes, along an armchair or along a zig-zag direction. Removing the energetic contribution of bending angles, using a previously introduced angle bending potential, we isolate the purely torsional deformation energy, which is then fitted to simple torsional force fields. The presented out-of-plane torsional potential can accurately fit the deformation energy for relatively large torsional angles up to 0.5 rad. To test our proposed potential, we apply it to the problem of the vertical displacement of a single carbon atom out of the graphene plane and compare the obtained deformation energy with corresponding DFT calculations. The dependence of the deformation energy on the vertical displacement of the pulled carbon atom is indistinguishable in these two cases, for displacements up to about 0.5 Å. The presented potential is applicable to other sp2 carbon structures.

Keywords

Solid State and Materials 

References

  1. 1.
    K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666 (2004) ADSCrossRefGoogle Scholar
  2. 2.
    A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009) ADSCrossRefGoogle Scholar
  3. 3.
    L. Chen, Y. Hernandez, X. Feng, K. Mullen, Angew. Chem. Int. Ed. 51, 7640 (2012) CrossRefGoogle Scholar
  4. 4.
    A.C. Ferrari et al., Nanoscale 7, 4598 (2015) ADSCrossRefGoogle Scholar
  5. 5.
    C. Daniels, A. Horning, A. Phillips, D.V.P. Massote, L. Liang, Z. Bullard, B.G. Sumpter, V. Meunier, J. Phys.: Condens. Matter 27, 373002 (2015) Google Scholar
  6. 6.
    Y.-M. Lin et al., Science 332, 1294 (2011) ADSCrossRefGoogle Scholar
  7. 7.
    F.V. Kusmartsev, W.M. Wu, M.P. Pierpoint, K.C. Yung, in Applied spectroscopy and the science of nanomaterials, edited by P. Misra, (Springer, Singapore, 2015) Google Scholar
  8. 8.
    K. Celebi et al., Science 344, 289 (2014) ADSCrossRefGoogle Scholar
  9. 9.
    M.F. El-Kady, Y. Shao, R.B. Kaner, Nat. Rev. Mater. 1, 16033 (2016) ADSCrossRefGoogle Scholar
  10. 10.
    C. Lee, X. Wei, J.W. Kysar, J. Hone, Science 321, 385 (2008) ADSCrossRefGoogle Scholar
  11. 11.
    G. Tsoukleri, J. Parthenios, K. Papagelis, R. Jalil, A.C. Ferrari, A.K. Geim, K.S. Novoselov, C. Galiotis, Small 21, 2397 (2009) CrossRefGoogle Scholar
  12. 12.
    G. Kalosakas, N.N. Lathiotakis, C. Galiotis, K. Papagelis, J. Appl. Phys. 113, 134307 (2013) ADSCrossRefGoogle Scholar
  13. 13.
    A. Fasolino, J.H. Los, M.I. Katsnelson, Nat. Mater. 6, 858 (2007) ADSCrossRefGoogle Scholar
  14. 14.
    K.V. Zakharchenko, M.I. Katsnelson, A. Fasolino, Phys. Rev. Lett. 102, 046808 (2009) ADSCrossRefGoogle Scholar
  15. 15.
    P. Liu, Y.W. Zhang, Appl. Phys. Lett. 94, 231912 (2009) ADSCrossRefGoogle Scholar
  16. 16.
    Z. Xu, M.J. Buechler, ACS Nano 4, 3869 (2010) CrossRefGoogle Scholar
  17. 17.
    M. Neek-Amal, F.M. Peeters, Phys. Rev. B 82, 085432 (2010) ADSCrossRefGoogle Scholar
  18. 18.
    M. Neek-Amal, F.M. Peeters, Appl. Phys. Lett. 97, 153118 (2010) ADSCrossRefGoogle Scholar
  19. 19.
    X. Tan, J. Wu, K. Zhang, X. Peng, L. Sun, J. Zhong, Appl. Phys. Lett. 102, 071908 (2013) ADSCrossRefGoogle Scholar
  20. 20.
    Z. Qi, D.A. Bahamon, V.M. Pereira, H.S. Park, D.K. Campbell, A.H. Castro Neto, Nano Lett. 13, 2692 (2013) ADSCrossRefGoogle Scholar
  21. 21.
    A.P. Sgouros, G. Kalosakas, M.M. Sigalas, K. Papagelis, RSC Adv. 5, 39930 (2015) CrossRefGoogle Scholar
  22. 22.
    E.N. Koukaras, G. Kalosakas, C. Galiotis, K. Papagelis, Sci. Rep. 5, 12923 (2015) ADSCrossRefGoogle Scholar
  23. 23.
    A.P. Sgouros, G. Kalosakas, C. Galiotis, K. Papagelis, 2D Mater. 3, 025033 (2016) CrossRefGoogle Scholar
  24. 24.
    J. Tersoff, Phys. Rev. Lett. 61, 2879 (1988) ADSCrossRefGoogle Scholar
  25. 25.
    J. Tersoff, Phys. Rev. B 37, 6991 (1988) ADSCrossRefGoogle Scholar
  26. 26.
    D.W. Brenner, Phys. Rev. B 42, 9458 (1990) ADSCrossRefGoogle Scholar
  27. 27.
    L. Lindsay, D.A. Broido, Phys. Rev. B 81, 205441 (2010) ADSCrossRefGoogle Scholar
  28. 28.
    J.H. Los, A. Fasolino, Phys. Rev. B 68, 024107 (2003) ADSCrossRefGoogle Scholar
  29. 29.
    J.H. Los, L.M. Ghiringhelli, E.J. Meijer, A. Fasolino, Phys. Rev. B 72, 214102 (2005) ADSCrossRefGoogle Scholar
  30. 30.
    S.J. Stuart, A.B. Tutein, J.A. Harrison, J. Chem. Phys. 112, 6472 (2000) ADSCrossRefGoogle Scholar
  31. 31.
    D. Wei, Y. Song, F. Wang, J. Chem. Phys. 134, 184704 (2011) ADSCrossRefGoogle Scholar
  32. 32.
    Z.G. Fthenakis, G. Kalosakas, G.D. Chatzidakis, C. Galiotis, K. Papagelis, N.N. Lathiotakis, Phys. Chem. Chem. Phys. 19, 30925 (2017) CrossRefGoogle Scholar
  33. 33.
    P. Giannozzi et al., J. Phys.: Condens. Matter 21, 395502 (2009) Google Scholar
  34. 34.

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsNational Technical University of AthensAthensGreece
  2. 2.Materials Science Department, University of PatrasRioGreece
  3. 3.Crete Center for Quantum Complexity and Nanotechnology (CCQCN), Physics Department, University of CreteHeraklionGreece
  4. 4.Institute of Electronic Structure and Laser, FORTHHeraklionGreece
  5. 5.Department of PhysicsUniversity of South FloridaTampaUSA
  6. 6.Theoretical and Physical Chemistry Institute, National Hellenic Research FoundationAthensGreece

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