Skip to main content

Ripples and Wrinkles in Graphene: Beyond Continuum Mechanics

  • Chapter
  • First Online:
Wrinkled Polymer Surfaces

Abstract

Graphene and other low-dimensional materials are a fantastic playground both for fundamental and applied sciences: for the former, to reach beyond the laws of continuum mechanics and expand the realm of bulk materials and, for the latter, to unlock new potential breakthroughs in areas ranging from single-molecule sensors to hydrogen storage and water filtration.

In this review, we explore the physical origins of the unique mechanical properties of mono- and few-layer graphene. For instance, bending resistance builds up in monolayer graphene through pi-orbital misalignment but does not involve any elastic strain, in stark contrast with its bulk counterpart. In addition, thermal fluctuations and physical defects renormalize the effective mechanical behavior of graphene. We then review the various wrinkling processes observed in graphene systems, thermally activated self-tearing, thermal expansion or lattice mismatch, and adsorbate-induced spontaneous curvature, and discuss their relevance in technological applications.

The uniqueness of graphene properties presented here showcases the broad range of disciplines impacted by the (just nucleated) birth of 2D systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183–191 (2007)

    Article  CAS  Google Scholar 

  2. R. Peierls, Ann. IH Poincare 5, 177–222 (1935)

    Google Scholar 

  3. L.D. Landau, E.M. Lifshitz, L. Pitaevskii, Statistical Physics, Part I (Pergamon Press, Oxford/New York, 1980)

    Google Scholar 

  4. K. Novoselov, A.K. Geim, S. Morozov, D. Jiang, M. Katsnelson, I. Grigorieva, S. Dubonos, A. Firsov, Nature 438, 197–200 (2005)

    Article  CAS  Google Scholar 

  5. E. Secchi, S. Marbach, A. Niguès, D. Stein, A. Siria, L. Bocquet, Nature 537, 210–213 (2016)

    Article  CAS  Google Scholar 

  6. L. Lindsay, D. Broido, N. Mingo, Phys. Rev. B 82, 115427 (2010)

    Article  CAS  Google Scholar 

  7. P. Zhang, L. Ma, F. Fan, Z. Zeng, C. Peng, P.E. Loya, Z. Liu, Y. Gong, J. Zhang, X. Zhang, et al., Nat. Commun. 5, 3782 (2014)

    Article  CAS  Google Scholar 

  8. T.R. Nayak, H. Andersen, V.S. Makam, C. Khaw, S. Bae, X. Xu, P.-L.R. Ee, J.-H. Ahn, B.H. Hong, G. Pastorin, et al., ACS Nano 5, 4670–4678 (2011)

    Article  CAS  Google Scholar 

  9. Y.-M. Lin, C. Dimitrakopoulos, K.A. Jenkins, D.B. Farmer, H.-Y. Chiu, A. Grill, P. Avouris, Science 327, 662–662 (2010)

    Article  CAS  Google Scholar 

  10. T.-H. Han, H. Kim, S.-J. Kwon, T.-W. Lee, Mater. Sci. Eng. R. Rep 118, 1–43 (2017)

    Article  Google Scholar 

  11. R.R. Nair, H.A. Wu, P.N. Jayaram, I.V. Grigorieva, A.K. Geim, Science 335, 442–444 (2012)

    Article  CAS  Google Scholar 

  12. The Graphene Flagship General Assembly 2018. (2018). https://graphene-flagship.eu/the-graphene-flagship-general-assembly-2018

  13. J.C. Meyer, A.K. Geim, M.I. Katsnelson, K.S. Novoselov, T.J. Booth, S. Roth, Nature 446, 60–63 (2007)

    Article  CAS  Google Scholar 

  14. A.C. Ferrari, F. Bonaccorso, V. Fal’Ko, K.S. Novoselov, S. Roche, P. Bøggild, S. Borini, F.H. Koppens, V. Palermo, N. Pugno, et al., Nanoscale 7, 4598–4810 (2015)

    Article  CAS  Google Scholar 

  15. F. Brau, P. Damman, H. Diamant, T.A. Witten, Soft Matter 9, 8177–8186 (2013)

    Article  CAS  Google Scholar 

  16. J.E. Gordon, Structures: Or why Things don’t Fall Down (Da Capo Press, Cambrige, MA, 2003)

    Google Scholar 

  17. F. Scarpa, S. Adhikari, A.S. Phani, Nanotechnology 20, 065709 (2009)

    Article  CAS  Google Scholar 

  18. C. Lee, X. Wei, J.W. Kysar, J. Hone, Science 321, 385–388 (2008)

    Article  CAS  Google Scholar 

  19. G. López-Polín, C. Gómez-Navarro, V. Parente, F. Guinea, M.I. Katsnelson, F. Pérez-Murano, J. Gómez-Herrero, Nat. Phys. 11, 26–31 (2015)

    Article  CAS  Google Scholar 

  20. Q. Lu, M. Arroyo, R. Huang, J. Phys. D. Appl. Phys. 42, 102002 (2009)

    Article  CAS  Google Scholar 

  21. D.-B. Zhang, E. Akatyeva, T. Dumitrică, Phys. Rev. Lett. 106, 255503 (2011)

    Article  CAS  Google Scholar 

  22. A.E.H. Love, Philos. Trans. R. Soc. Lond. A 179, 491–546 (1888)

    Article  Google Scholar 

  23. A. Carlson, T. Dumitrică, Nanotechnology 18, 065706 (2007)

    Article  CAS  Google Scholar 

  24. B. Audoly, Y. Pomeau, Elasticity and Geometry: From Hair Curls to the Nonlinear Response of Shells (Oxford University Press, Oxford/New York, 2010)

    Google Scholar 

  25. Y. Wei, B. Wang, J. Wu, R. Yang, M.L. Dunn, Nano Lett. 13, 26–30 (2013)

    Article  CAS  Google Scholar 

  26. I. Nikiforov, E. Dontsova, R.D. James, T. Dumitrică, Phys. Rev. B 89, 155437 (2014)

    Article  CAS  Google Scholar 

  27. J.H. Los, A. Fasolino, M.I. Katsnelson, npj 2D Mater. Appl. 1, 9 (2017)

    Article  Google Scholar 

  28. J. Los, A. Fasolino, M. Katsnelson, Phys. Rev. Lett. 116, 015901 (2016)

    Article  CAS  Google Scholar 

  29. O. Blakslee, D. Proctor, E. Seldin, G. Spence, T. Weng, J. Appl. Phys. 41, 3373–3382 (1970)

    Article  CAS  Google Scholar 

  30. L. Tapasztó, T. Dumitrică, S.J. Kim, P. Nemes-Incze, C. Hwang, L.P. Biró, Nat. Phys. 8, 739–742 (2012)

    Article  CAS  Google Scholar 

  31. Z. Ni, H. Bu, M. Zou, H. Yi, K. Bi, Y. Chen, Phys. B Condens. Matter 405, 1301–1306 (2010)

    Article  CAS  Google Scholar 

  32. Y. Zhang, L. Liu, N. Xi, Y. Wang, Z. Dong, U.C. Wejinya, Sci. China Phys. Mech. Astron. 57, 663–667 (2014)

    Article  CAS  Google Scholar 

  33. J.S. Choi, J.-S. Kim, I.-S. Byun, D.H. Lee, M.J. Lee, B.H. Park, C. Lee, D. Yoon, H. Cheong, K.H. Lee, et al., Science 333, 607–610 (2011)

    Article  CAS  Google Scholar 

  34. A.K. Geim, I.V. Grigorieva, Nature 499, 419–425 (2013)

    Article  CAS  Google Scholar 

  35. K.S. Novoselov, A. Mishchenko, A. Carvalho, A.H. Castro Neto, Science 353, aac9439 (2016)

    Article  CAS  Google Scholar 

  36. C.N.R. Rao, A.K. Sood, Graphene: Synthesis, Properties, and Phenomena (Wiley, Weinheim, 2013)

    Google Scholar 

  37. D. Akinwande, C.J. Brennan, J.S. Bunch, P. Egberts, J.R. Felts, H. Gao, R. Huang, J.-S. Kim, T. Li, Y. Li, et al., Extreme Mech. Lett. 13, 42–77 (2017)

    Article  Google Scholar 

  38. G. Wang, Z. Dai, Y. Wang, P. Tan, L. Liu, Z. Xu, Y. Wei, R. Huang, Z. Zhang, Phys. Rev. Lett. 119, 036101 (2017)

    Article  Google Scholar 

  39. X. Chen, C. Yi, C. Ke, Appl. Phys. Lett. 106, 101907 (2015)

    Article  CAS  Google Scholar 

  40. L. Ruiz, W. Xia, Z. Meng, S. Keten, Carbon 82, 103–115 (2015)

    Article  CAS  Google Scholar 

  41. M. Yamamoto, O. Pierre-Louis, J. Huang, M.S. Fuhrer, T.L. Einstein, W.G. Cullen, Phys. Rev. X 2, 041018 (2012)

    Google Scholar 

  42. A. Kŏsmrlj, D.R. Nelson, Phys. Rev. E 88, 012136 (2013)

    Article  CAS  Google Scholar 

  43. J.A. Aronovitz, T.C. Lubensky, Phys. Rev. Lett. 60, 2634 (1988)

    Article  CAS  Google Scholar 

  44. K. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich, S. Morozov, A. Geim, Proc. Natl. Acad. Sci. U. S. A. 102, 10451–10453 (2005)

    Article  CAS  Google Scholar 

  45. J. Venables, G. Spiller, M. Hanbucken, Rep. Prog. Phys. 47, 399 (1984)

    Article  Google Scholar 

  46. J. Evans, P. Thiel, M.C. Bartelt, Surf. Sci. Rep. 61, 1–128 (2006)

    Article  CAS  Google Scholar 

  47. A. Fasolino, J. Los, M.I. Katsnelson, Nat. Mater. 6, 858–861 (2007)

    Article  CAS  Google Scholar 

  48. R.J. Nicholl, H.J. Conley, N.V. Lavrik, I. Vlassiouk, Y.S. Puzyrev, V.P. Sreenivas, S.T. Pantelides, K.I. Bolotin, Nat. Commun. 6, 8789 (2015)

    Article  CAS  Google Scholar 

  49. E.V. Castro, H. Ochoa, M.I. Katsnelson, R.V. Gorbachev, D.C. Elias, K.S. Novoselov, A.K. Geim, F. Guinea, Phys. Rev. Lett. 105, 266601 (2010)

    Article  CAS  Google Scholar 

  50. P. Partovi-Azar, N. Nafari, M.R.R. Tabar, Phys. Rev. B 83, 165434 (2011)

    Article  CAS  Google Scholar 

  51. M.B. Amar, Y. Pomeau, Proc. Math. Phys. Eng. Sci. 453, 729–755 (1997)

    Article  Google Scholar 

  52. P. Grandgeorge, N. Krins, A. Hourlier-Fargette, C. Laberty-Robert, S. Neukirch, A. Antkowiak, Science 360, 296–299 (2018)

    Article  CAS  Google Scholar 

  53. T.M.G. Mohiuddin, A. Lombardo, R.R. Nair, A. Bonetti, G. Savini, R. Jalil, N. Bonini, D.M. Basko, C. Galiotis, N. Marzari, et al. Phys. Rev. B 79, 205433 (2009)

    Article  CAS  Google Scholar 

  54. A.C. Ferrari, D.M. Basko, Nat. Nanotechnol. 8, 235 (2013)

    Article  CAS  Google Scholar 

  55. N. Colthup, Introduction to Infrared and Raman Spectroscopy (Elsevier, Burlington, 2012)

    Google Scholar 

  56. D. Yoon, Y.-W. Son, H. Cheong, Nano Lett. 11, 3227–3231 (2011)

    Article  CAS  Google Scholar 

  57. L. Malard, M. Pimenta, G. Dresselhaus, M. Dresselhaus, Phys. Rep. 473, 51–87 (2009)

    Article  CAS  Google Scholar 

  58. F. Yavari, C. Kritzinger, C. Gaire, L. Song, H. Gulapalli, T. Borca-Tasciuc, P.M. Ajayan, N. Koratkar, Small 6, 2535–2538 (2010)

    Article  CAS  Google Scholar 

  59. Z.H. Ni, T. Yu, Z.Q. Luo, Y.Y. Wang, L. Liu, C.P. Wong, J. Miao, W. Huang, Z.X. Shen, ACS Nano 3, 569–574 (2009)

    Article  CAS  Google Scholar 

  60. L.G. Cançado, A. Jorio, E.M. Ferreira, F. Stavale, C. Achete, R. Capaz, M. Moutinho, A. Lombardo, T. Kulmala, A. Ferrari, Nano Lett. 11, 3190–3196 (2011)

    Article  CAS  Google Scholar 

  61. R. Roldán, A. Fasolino, K.V. Zakharchenko, M.I. Katsnelson, Phys. Rev. B 83, 174104 (2011)

    Article  CAS  Google Scholar 

  62. G. López-Polín, M. Jaafar, F. Guinea, R. Roldán, C. Gómez-Navarro, J. Gómez-Herrero, Carbon 124, 42–48 (2017)

    Article  CAS  Google Scholar 

  63. R.J.T. Nicholl, N.V. Lavrik, I. Vlassiouk, B.R. Srijanto, K.I. Bolotin, Phys. Rev. Lett. 118, 266101 (2017)

    Article  Google Scholar 

  64. Y. Huang, J. Wu, K.-C. Hwang, Phys. Rev. B 74, 245413 (2006)

    Article  CAS  Google Scholar 

  65. A. Kŏsmrlj, D.R. Nelson, Phys. Rev. X 7, 011002 (2017)

    Google Scholar 

  66. P. Le Doussal, L. Radzihovsky, Phys. Rev. Lett. 69, 1209 (1992)

    Article  Google Scholar 

  67. D. Nelson, L. Peliti, J. Phys. 48, 1085–1092 (1987)

    Article  CAS  Google Scholar 

  68. P. Flory, M. Volkenstein, et al., Statistical Mechanics of Chain Molecules (Hanser Publishers, Munich, 1969)

    Book  Google Scholar 

  69. P.-G. De Gennes, P.-G. Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca/London, 1979)

    Google Scholar 

  70. M.J. Bowick, A. Kŏsmrlj, D.R. Nelson, R. Sknepnek, Phys. Rev. B 95, 104109 (2017)

    Article  Google Scholar 

  71. 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, et al., Nature 524, 204 (2015)

    Article  CAS  Google Scholar 

  72. W. CAN, O. LOG, Bioscience 51, 341–352 (2001)

    Article  Google Scholar 

  73. N. Lindahl, D. Midtvedt, J. Svensson, O.A. Nerushev, N. Lindvall, A. Isacsson, E.E. Camp- bell, Nano Lett. 12, 3526–3531 (2012)

    Article  CAS  Google Scholar 

  74. S. Scharfenberg, D. Rocklin, C. Chialvo, R.L. Weaver, P.M. Goldbart, N. Mason, Appl. Phys. Lett. 98, 091908 (2011)

    Article  CAS  Google Scholar 

  75. P.L. De Andres, F. Guinea, M.I. Katsnelson, Phys. Rev. B 86, 144103 (2012)

    Article  CAS  Google Scholar 

  76. G. López-Polín, M. Ortega, J. Vilhena, I. Alda, J. Gomez-Herrero, P.A. Serena, C. Gomez- Navarro, R. Pérez, Carbon 116, 670–677 (2017)

    Article  CAS  Google Scholar 

  77. X. Hu, P. Yasaei, J. Jokisaari, S. Öğüt, A. Salehi-Khojin, R.F. Klie, Phys. Rev. Lett. 120, 055902 (2018)

    Article  Google Scholar 

  78. W. Bao, F. Miao, Z. Chen, H. Zhang, W. Jang, C. Dames, C.N. Lau, Nat. Nanotechnol. 4, 562–566 (2009)

    Article  CAS  Google Scholar 

  79. C. Moreno, M. Vilas-Varela, B. Kretz, A. Garcia-Lekue, M.V. Costache, M. Paradinas, M. Panighel, G. Ceballos, S.O. Valenzuela, D. Peña, et al., Science 360, 199–203 (2018)

    Article  CAS  Google Scholar 

  80. J.D. Eshelby, Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 241, 376–396 (1957)

    Google Scholar 

  81. R.W. Style, R. Boltyanskiy, B. Allen, K.E. Jensen, H.P. Foote, J.S. Wettlaufer, E.R. Dufresne, Nat. Phys. 11, 82–87 (2015)

    Article  CAS  Google Scholar 

  82. N. Fleck, G. Muller, M. Ashby, J. Hutchinson, Acta Metall. Mater. 42, 475–487 (1994)

    Article  CAS  Google Scholar 

  83. J. GREER, W. OLIVER, W. NIX, Acta Mater. 54, 1705–1705 (2006)

    Article  CAS  Google Scholar 

  84. T. Zhang, X. Li, H. Gao, Extreme Mech. Lett 1, 3–8 (2014)

    Article  Google Scholar 

  85. T. Zhang, H. Gao, J. Appl. Mech. 82, 051001 (2015)

    Article  CAS  Google Scholar 

  86. N.P. Mitchell, V. Koning, V. Vitelli, W.T.M. Irvine, Nat. Mater. 16, 89–93 (2017)

    Article  CAS  Google Scholar 

  87. G. López-Polín, J. Gómez-Herrero, C. Gómez-Navarro, Nano Lett. 15, 2050–2054 (2015)

    Article  CAS  Google Scholar 

  88. A.A. Griffith, M. Eng, Philos. Trans. R. Soc. Lond. A 221, 163–198 (1921)

    Article  Google Scholar 

  89. J.N. Grima, S. Winczewski, L. Mizzi, M.C. Grech, R. Cauchi, R. Gatt, D. Attard, K.W. Wojciechowski, J. Rybicki, Adv. Mater. 27, 1455–1459 (2014)

    Article  CAS  Google Scholar 

  90. H. Qin, Y. Sun, J.Z. Liu, M. Li, Y. Liu, Nanoscale 9, 4135–4142 (2017)

    Article  CAS  Google Scholar 

  91. C. Wang, L. Lan, Y. Liu, H. Tan, Comput. Mater. Sci. 77, 250–253 (2013)

    Article  CAS  Google Scholar 

  92. T. Zhang, X. Li, H. Gao, J. Mech. Phys. Solids 67, 2–13 (2014)

    Article  CAS  Google Scholar 

  93. I. Gornyi, V.Y. Kachorovskii, A. Mirlin, Phys. Rev. B 92, 155428 (2015)

    Article  CAS  Google Scholar 

  94. J. Annett, G.L. Cross, Nature 535, 271–275 (2016)

    Article  CAS  Google Scholar 

  95. E. Hamm, P. Reis, M. LeBlanc, B. Roman, E. Cerda, Nat. Mater. 7, 386–390 (2008)

    Article  CAS  Google Scholar 

  96. X. Chen, L. Zhang, Y. Zhao, X. Wang, C. Ke, J. Appl. Phys. 116, 164301 (2014)

    Article  CAS  Google Scholar 

  97. Z. Budrikis, S. Zapperi, Nano Lett. 16, 387–391 (2015)

    Article  CAS  Google Scholar 

  98. J. Bunch, M. Dunn, Solid State Commun. 152, 1359–1364 (2012)

    Article  CAS  Google Scholar 

  99. S.P. Koenig, N.G. Boddeti, M.L. Dunn, J.S. Bunch, Nat. Nanotechnol. 6, 543–546 (2011)

    Article  CAS  Google Scholar 

  100. D. Sen, K.S. Novoselov, P.M. Reis, M.J. Buehler, Small 6, 1108–1116 (2010)

    Article  CAS  Google Scholar 

  101. O.C. Compton, S.T. Nguyen, Small 6, 711–723 (2010)

    Article  CAS  Google Scholar 

  102. M.J. Allen, V.C. Tung, R.B. Kaner, Chem. Rev. 110, 132–145 (2009)

    Article  CAS  Google Scholar 

  103. M. Yi, Z. Shen, Carbon 78, 622–626 (2014)

    Article  CAS  Google Scholar 

  104. D.H. Seo, S. Pineda, J. Fang, Y. Gozukara, S. Yick, A. Bendavid, S.K.H. Lam, A.T. Murdock, A.B. Murphy, Z.J. Han, et al. Nat. Commun. 8, 14217 (2017)

    Article  CAS  Google Scholar 

  105. C. Mattevi, H. Kim, M. Chhowalla, J. Mater. Chem. 21, 3324–3334 (2011)

    Article  CAS  Google Scholar 

  106. D. Bandurin, I. Torre, R.K. Kumar, M.B. Shalom, A. Tomadin, A. Principi, G. Auton, E. Khestanova, K. Novoselov, I. Grigorieva, et al., Science 351, 1055–1058 (2016)

    Article  CAS  Google Scholar 

  107. W. Yang, G. Chen, Z. Shi, C.-C. Liu, L. Zhang, G. Xie, M. Cheng, D. Wang, R. Yang, D. Shi, et al. Nat. Mater. 12, 792–797 (2013)

    Article  CAS  Google Scholar 

  108. P. Sutter, J.T. Sadowski, E. Sutter, Phys. Rev. B 80, 245411 (2009)

    Article  CAS  Google Scholar 

  109. C.H. Lui, L. Liu, K.F. Mak, G.W. Flynn, T.F. Heinz, Nature 462, 339 (2009)

    Article  CAS  Google Scholar 

  110. A.L.V. de Parga, F. Calleja, B. Borca, M.C.G. Passeggi, J.J. Hinarejos, F. Guinea, R. Miranda, Phys. Rev. Lett. 100, 056807 (2008)

    Article  CAS  Google Scholar 

  111. S. Goler, C. Coletti, V. Tozzini, V. Piazza, T. Mashoff, F. Beltram, V. Pellegrini, S. Heun, J. Phys. Chem. C 117, 11506–11513 (2013)

    Article  CAS  Google Scholar 

  112. S.J. Chae, F. Güneş, K.K. Kim, E.S. Kim, G.H. Han, S.M. Kim, H.-J. Shin, S.-M. Yoon, J.-Y. Choi, M.H. Park, et al. Adv. Mater. 21, 2328–2333 (2009)

    Article  CAS  Google Scholar 

  113. N. Liu, Z. Pan, L. Fu, C. Zhang, B. Dai, Z. Liu, Nano Res. 4, 996–1004 (2011)

    Article  CAS  Google Scholar 

  114. C.T. Cherian, F. Giustiniano, I. Martin-Fernandez, H. Andersen, J. Balakrishnan, B. Ӧzyilmaz, Small 11, 189–194 (2015)

    Article  CAS  Google Scholar 

  115. L. Gao, G.-X. Ni, Y. Liu, B. Liu, A.H.C. Neto, K.P. Loh, Nature 505, 190–194 (2014)

    Article  CAS  Google Scholar 

  116. X. Liang, B.A. Sperling, I. Calizo, G. Cheng, C.A. Hacker, Q. Zhang, Y. Obeng, K. Yan, H. Peng, Q. Li, et al., ACS Nano 5, 9144–9153 (2011)

    Article  CAS  Google Scholar 

  117. N. Levy, S. Burke, K. Meaker, M. Panlasigui, A. Zettl, F. Guinea, A.C. Neto, M. Crommie, Science 329, 544–547 (2010)

    Article  CAS  Google Scholar 

  118. S. Bӧttcher, H. Vita, M. Weser, F. Bisti, Y.S. Dedkov, K. Horn, J. Phys. Chem. Lett. 8, 3668–3672 (2017)

    Article  CAS  Google Scholar 

  119. Q. Pei, Y. Zhang, V. Shenoy, Carbon 48, 898–904 (2010)

    Article  CAS  Google Scholar 

  120. P. Poulin, R. Jalili, W. Neri, F. Nallet, T. Divoux, A. Colin, S.H. Aboutalebi, G. Wallace, C. Zakri, Proc. Natl. Acad. Sci. 201605121 (2016)

    Google Scholar 

  121. S.A. Svatek, O.R. Scott, J.P. Rivett, K. Wright, M. Baldoni, E. Bichoutskaia, T. Taniguchi, K. Watanabe, A.J. Marsden, N.R. Wilson, et al., Nano Lett. 15, 159–164 (2014)

    Article  CAS  Google Scholar 

  122. J.H. Lee, A. Avsar, J. Jung, J.Y. Tan, K. Watanabe, T. Taniguchi, S. Natarajan, G. Eda, S. Adam, A.H. Castro Neto, et al., Nano Lett. 15, 319–325 (2014)

    Article  CAS  Google Scholar 

  123. F. Schedin, A.K. Geim, S.V. Morozov, E.W. Hill, P. Blake, M.I. Katsnelson, K.S. Novoselov, Nat. Mater. 6, 652–655 (2007)

    Article  CAS  Google Scholar 

  124. Z. Gao, H. Xia, J. Zauberman, M. Tomaiuolo, J. Ping, Q. Zhang, P. Ducos, H. Ye, S. Wang, X. Yang, et al., Nano Lett. 18, 3509–3515 (2018)

    Article  CAS  Google Scholar 

  125. C. Py, P. Reverdy, L. Doppler, J. Bico, B. Roman, C.N. Baroud, Phys. Rev. Lett. 98, 156103 (2007)

    Article  CAS  Google Scholar 

  126. M. Boudot, H. Elettro, D. Grosso, ACS Nano 10, 10031–10040 (2016)

    Article  CAS  Google Scholar 

  127. J. Kim, J.A. Hanna, M. Byun, C.D. Santangelo, R.C. Hayward, Science 335, 1201–1205 (2012)

    Article  CAS  Google Scholar 

  128. Y. Zhang, F. Zhang, Z. Yan, Q. Ma, X. Li, Y. Huang, J.A. Rogers, Nature Reviews Materials 2, 17019 (2017)

    Article  CAS  Google Scholar 

  129. B. Florijn, C. Coulais, M. van Hecke, Phys. Rev. Lett. 113, 175503 (2014)

    Article  CAS  Google Scholar 

  130. J. Zang, S. Ryu, N. Pugno, Q. Wang, Q. Tu, M.J. Buehler, X. Zhao, Nat. Mater. 12, 321–325 (2013)

    Article  CAS  Google Scholar 

  131. M.Z. Miskin, K.J. Dorsey, B. Bircan, Y. Han, D.A. Muller, P.L. McEuen, I. Cohen, Proc. Natl. Acad. Sci. 115, 466–470 (2018)

    Article  CAS  Google Scholar 

  132. M. Poot, H.S. van der Zant, Appl. Phys. Lett. 92, 063111 (2008)

    Article  CAS  Google Scholar 

  133. K.S. Novoselov, V.I. Falko, L. Colombo, P.R. Gellert, M.G. Schwab, K. Kim, Nature 490, 192–200 (2012)

    Article  CAS  Google Scholar 

  134. Y. Liu, Z. Xu, Q. Zheng, J. Mech. Phys. Solids 59, 1613–1622 (2011)

    Article  CAS  Google Scholar 

  135. C. Chen, S. Rosenblatt, K.I. Bolotin, W. Kalb, P. Kim, I. Kymissis, H.L. Stormer, T.F. Heinz, J. Hone, Nat. Nanotechnol. 4, 861–867 (2009)

    Article  CAS  Google Scholar 

  136. J.S. Bunch, A.M. van der Zande, S.S. Verbridge, I.W. Frank, D.M. Tanenbaum, J.M. Parpia, H.G. Craighead, P.L. McEuen, Science 315, 490–493 (2007)

    Article  CAS  Google Scholar 

  137. F. Xia, D.B. Farmer, Y.-m. Lin, P. Avouris, Nano Lett. 10, 715–718 (2010)

    Article  CAS  Google Scholar 

  138. J. Berashevich, T. Chakraborty, Phys. Rev. B 80, 033404 (2009)

    Article  CAS  Google Scholar 

  139. D.C. Elias, R.R. Nair, T. Mohiuddin, S. Morozov, P. Blake, M. Halsall, A. Ferrari, D. Boukhvalov, M. Katsnelson, A. Geim, et al., Science 323, 610–613 (2009)

    Article  CAS  Google Scholar 

  140. R. Phillipson, C.J. Lockhart de la Rosa, J. Teyssandier, P. Walke, D. Waghray, Y. Fujita, J. Adisoejoso, K.S. Mali, I. Asselberghs, C. Huyghebaert, et al. Nanoscale 8, 20017–20026 (2016)

    Article  CAS  Google Scholar 

  141. X. Wang, Y. Ouyang, X. Li, H. Wang, J. Guo, H. Dai, Phys. Rev. Lett. 100, 206803 (2008)

    Article  CAS  Google Scholar 

  142. M.I. Katsnelson, Mater. Today 10, 20–27 (2007)

    Article  CAS  Google Scholar 

  143. G. Gui, J. Li, J. Zhong, Phys. Rev. B 78, 075435 (2008)

    Article  CAS  Google Scholar 

  144. F. Guinea, M. Katsnelson, A. Geim, Nat. Phys. 6, 30 (2010)

    Article  CAS  Google Scholar 

  145. V.M. Pereira, A.H. Castro Neto, H.Y. Liang, L. Mahadevan, Phys. Rev. Lett. 105, 156603 (2010)

    Article  CAS  Google Scholar 

  146. J. Martin, N. Akerman, G. Ulbricht, T. Lohmann, J.v. Smet, K. Von Klitzing, A. Yacoby, Nat. Phys. 4, 144 (2008)

    Article  CAS  Google Scholar 

  147. V. Tozzini, V. Pellegrini, Phys. Chem. Chem. Phys. 15, 80–89 (2013)

    Article  CAS  Google Scholar 

  148. C. Ataca, E. Aktu¨rk, S. Ciraci, H. Ustunel, Appl. Phys. Lett. 93, 043123 (2008)

    Article  CAS  Google Scholar 

  149. A. Tapia, C. Acosta, R. Medina-Esquivel, G. Canto, Comput. Mater. Sci. 50, 2427–2432 (2011)

    Article  CAS  Google Scholar 

  150. V. Tozzini, V. Pellegrini, J. Phys. Chem. C 115, 25523–25528 (2011)

    Article  CAS  Google Scholar 

  151. Y. Han, Z. Xu, C. Gao, Adv. Funct. Mater. 23, 3693–3700 (2013)

    Article  CAS  Google Scholar 

  152. R. Joshi, P. Carbone, F.-C. Wang, V.G. Kravets, Y. Su, I.V. Grigorieva, H. Wu, A.K. Geim, R.R. Nair, Science 343, 752–754 (2014)

    Article  CAS  Google Scholar 

  153. M. Ma, G. Tocci, A. Michaelides, G. Aeppli, Nat. Mater. 15, 66–71 (2016)

    Article  CAS  Google Scholar 

Download references

Acknowledgment

We acknowledge the financial support from FONDECYT/CONICYT-Chile through the postdoctoral project N° 3160152 and from H2020 through the Marie Skłodowska-Curie Individual Fellowship N° 750802. F.M. is grateful to FONDECYT/Anillo Act-1410. We thank P. Reis, A. Kŏsmrlj, J-C. Géminard, J. Bico, B. Roman, E. Katifori, and L. Gordillo for enlightening discussions.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Hervé Elettro or Francisco Melo .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Elettro, H., Melo, F. (2019). Ripples and Wrinkles in Graphene: Beyond Continuum Mechanics. In: González-Henríquez, C., Rodríguez-Hernández, J. (eds) Wrinkled Polymer Surfaces. Springer, Cham. https://doi.org/10.1007/978-3-030-05123-5_10

Download citation

Publish with us

Policies and ethics