Buckling of graphene layers supported by rigid substrates

Journal of Computational and Theoretical Nanoscience

Volumn 7, Issue 11, 2010, Pages 2338-2348

  Wilber, J Patrick ^a  

^a UNIVERSITY OF AKRON   (United States)

Author keywords

Elastic foundation; Elastica; Graphene; Mechanical behavior; Van der waals forces

Indexed keywords

BIFURCATION THEORY; ELASTIC FOUNDATION; ELASTICA; ELEMENTARY TECHNIQUES; GRAPHENE LAYERS; GRAPHENE SHEETS; MECHANICAL BEHAVIOR; NONLINEAR CONTINUUM MODEL; NUMERICAL RESULTS; OPPOSITE EDGES; RIGID SUBSTRATES; VAN DER WAALS;

BIFURCATION (MATHEMATICS); CONTINUUM MECHANICS; GRAPHENE; MECHANICAL ENGINEERING; VAN DER WAALS FORCES;

SUBSTRATES;

EID: 79955452165     PISSN: 15461955     EISSN: None     Source Type: Journal    
DOI: 10.1166/jctn.2010.1617     Document Type: Article

References (47)

1. S. S. Amman, Nonlinear Problems of Elasticity, Springer, New York (2005).
2. P. Blake, E. W. Hill, A. H. C. Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, Appl. Phys. Lett. 91, 063124 (2007).
3. J. S. Bunch, A. M. van der Zande, S. S. Verbridge, I. W. Frank, D. M. Tanenbaum, J. M. Parpia, H. G. Craighead, and P. L. McEuen, Science 315, 490 (2007).
4. A. Deshpande, W. Bao, F. Miao, C. N. Lau, and B. J. LeRoy, Phys. Rev. B (Condens. Matter and Mater. Phys.) 79, 205411 (2009).
5. E. Doedel, A. R. Champneys, T. Fairgrieve, Y. Kuznetsov, B. Oldeman, R. Paffenroth, B. Sandstede, X. Wang, and C. Zhang, Auto-07p: Continuation and bifurcation software for ordinary differential equations. Technical report, Concordia University, http://indy.cs.concordia.ca/auto/(2006).
6. A. Fasolino, J. H. Los, and M. I. Katsnelson, Nat. Mater. 6, 858 (2007).
7. D. Gazit, Phys. Rev. B (Condens. Matter and Mater. Phys.) 79, 113411 (2009).
8. A. K. Geim and K. S. Novoselov, Nat. Mater. 6, 183 (2007).
9. V. Geringer, M. Liebmann, T. Echtermeyer, S. Runte, M. Schmidt, R. Riickamp, M. C. Lemme, and M. Morgenstern, Phys. Rev. Lett. 102, 076102 (2009).
10. L. A. Girifalco and R. A. Lad, J. Chem. Phys. 25, 693 (1956).
11. M. Ishigami, J. H. Chen, W. G. Cullen, M. S. Fuhrer, and E. D. Williams, Nano Lett. 7, 1643 (2007).
12. E.-A. Kim and A. H. C. Neto, EPL 84, 57007 (2008).
13. K. R. Knox, S. Wang, A. Morgante, D. Cvetko, A. Locatelli, T. O. Mentes, M. A. Nino, P. Kim, and R. M. Osgood, Jr., Phys. Rev. B (Condens. Matter Mater. Phys.) 78, 201408 (2008).
14. T. Lenosky, X. Gonze, M. Teter, and V. Elser, Nature 355, 333 (1992).
15. C. Li and T.-W Chou, International Journal of Solids and Structures 40, 2487 (2003).
16. T. Li and Z. Zhang, Nanoscale Research Letters 5, 169 (2010).
17. Q. Lu and R. Huang, Int. J. Applied Mechanics 1, 443 (2009).
18. X. Lu, M. Yu, H. Huang, and R. S. Ruoff, Nanotechnology 10, 269 (1999).
19. J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth, Nature 446, 60 (2007).
20. Z. H. Ni, W. Chen, X. F. Fan, J. L. Kuo, T. Yu, A. T. S. Wee, and Z. X. Shen, Phys. Rev. B (Condens. Matter Mater. Phys.) 77, 115416 (2008).
21. Z. H. Ni, T. Yu, Y. H. Lu, Y. Y. Wang, Y. P. Feng, and Z. X. Shen, ACS Nano 2, 2301 (2008).
22. R. Nicklow, N. Wakabayashi, and H. G. Smith, Phys. Rev. B 5, 4951 (1972).
23. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004).
24. K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, Proceedings of the National Academy of Sciences 102, 10451 (2005).
25. V. M. Pereira and A. H. C. Neto, Phys. Rev. Lett. 103, 046801 (2009).
26. S. C. Pradhan and T. Murmu, Comput. Mater. Sci. 47, 268 (2009).
27. M. A. Raifiee, J. Raifiee, Z.-Z. Yu, and N. Koratkar, Appl. Phy. Lett. 95, 223103 (2009).
28. D. H. Robertson, D. W. Brenner, and J. W. Mintmire, Phys. Rev. B 45, 12592 (1992).
29. H.-V. Roy, C. Kallinger, B. Marsen, and K. Sattler, J. Appl. Phys. 83, 4695 (1998).
30. C. Q. Ru. Phys. Rev. B 62, 16962 (2000).
31. C. Q. Ru, J. Mech. Phys. Solids 49, 1265 (2001).
32. J. Gallagher, Y. Milman, S. Ryan, D. G. Golovaty, J. P. Wilber, and A. Buldum, A buckling problem for graphene sheets, Proceedings of CMDS 11, the 11th International Symposium on Continuum Models and Discrete Systems (2007).
33. J. Sabio, C. Seoánez, S. Fratini, F. Guinea, A. H. C. Neto, and F. Sols, Phys. Rev. B (Condens. Matter and Mater. Phys.) 77, 195409 (2008).
34. A. Sakhaee-Pour, Comput. Mater. Sci. 45, 266 (2009).
35. H. C. Schniepp, K. N. Kudin, J.-L. Li, R. K. Prudehomme, R. Car, D. A. Saville, and I. A. Aksay, ACS Nana 2, 2577 (2008).
36. H. C. Schniepp, J.-L. Li, M. J. McAllister, H. Sai, M. Herrera-Alonso, D. H. Adamson, R. K. Prud'homme, R. Car, D. A. Saville, and I. A. Aksay, J. Phys. Chem. B 110, 8535 (2006).
37. H.-S. Shen, Int. J. Solids Struct. 41, 2643 (2004).
38. G. J. Simitses and D. H. Hodges, Fundamentals of Structural Stability, Elsevier, Amsterdam (2006).
39. S. Stankovich, D. A. Dikin, G. H. B. Dommett, K. M. Kohlhaas, E. J. Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, and R. S. Ruoff, Nature 442, 282 (2006).
40. E. Stolyarova, K. T. Rim, S. Ryu, J. Maultzsch, P. Kim, L. E. Brus, T. F. Heinz, M. S. Hybertsen, and G. W. Flynn, Proceedings of the National Academy of Sciences 104, 9209 (2007).
41. J. Tersoff, Phys. Rev. B 46, 15546 (1992).
42. R. C. Thompson-Flagg, M. J. B. Moura, and M. Marder, EPL (Europhysics Letters) 85, 46002 (2009).
43. S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability, Mcgraw-Hill, New York (1961).
44. Z.-C. Tu and Z.-C. Ou-Yang, Phys. Rev. B 65, 233407 (2002).
45. J. P. Wilber, A. Buldum, C. B. Clemons, D. D. Quinn, and G. W. Young, Phys. Rev. B 75, 045418 (2007).
46. B. I. Yakobson, C. J. Brabec, and J. Bernholc, Phys. Rev. Lett. 76, 2511 (1996).
47. J. Zhou, Z. Shen, S. Hou, X. Zhao, Z. Xue, Z. Shi, and Z. Gu, Appl. Surf. Sci. 253, 3237 (2007).