Ultrasoft slip-mediated bending in few-layer graphene
Source abstract
Abstract
Continuum scaling laws often break down when materials approach atomic length scales, reflecting changes in their underlying physics and the opportunities to access unconventional properties. These continuum limits are evident in two-dimensional materials, where there is no consensus on their bending stiffnesses or how they scale with thickness. Through combined computational and electron microscopy experiments, we measure the bending stiffness of graphene, obtaining 1.2-1.7 eV for a monolayer. Moreover, we find that the bending stiffness of few-layer graphene decreases sharply as a function of bending angle, tuning by almost 400% for trilayer graphene. This softening results from shear, slip and the onset of superlubricity between the atomic layers and corresponds with a gradual change in scaling power from cubic to linear. Our results provide a unified model for bending in two-dimensional materials and show that their multilayers can be orders of magnitude softer than previously thought, among the most flexible electronic materials currently known.
Source: europepmc · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Graphene research and applications · Nanowire Synthesis and Applications · Diamond and Carbon-based Materials Research
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (56)
Show source-provided references
1. Lee, C., Wei, X., Kysar, J. W. & Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008).10.1126/science.1157996 ↗
2. Shen, Y. & Wu, H. Interlayer shear effect on multilayer graphene subjected to bending. Appl. Phys. Lett. 100, 101904–101909 (2012).10.1063/1.3692108 ↗
3. Song, Y. et al. Robust microscale superlubricity in graphite/hexagonal boron nitride layered heterojunctions. Nat. Mater. 17, 894–899 (2018).10.1038/s41563-018-0144-z ↗
4. Alden, J. S. et al. Strain solitons and topological defects in bilayer graphene. Proc. Natl Acad. Sci. USA 110, 11256–11260 (2013).10.1073/pnas.1309394110 ↗
5. Cumings, J. & Zettl, A. Low-friction nanoscale linear bearing realized from multiwall carbon nanotubes. Science 289, 602–604 (2000).10.1126/science.289.5479.602 ↗
6. Yakobson, B. I., Samsonidze, G. & Samsonidze, G. G. Atomistic theory of mechanical relaxation in fullerene nanotubes. Carbon 38, 1675–1680 (2000).10.1016/S0008-6223(00)00093-2 ↗
7. Zang, J. et al. Multifunctionality and control of the crumpling and unfolding of large-area graphene. Nat. Mater. 12, 321–325 (2013).10.1038/nmat3542 ↗
8. Kang, P., Wang, M. C., Knapp, P. M. & Nam, S. Crumpled graphene photodetector with enhanced, strain-tunable, and wavelength-selective photoresponsivity. Adv. Mater. 28, 4639–4645 (2016).10.1002/adma.201600482 ↗
9. Blees, M. K. et al. Graphene kirigami. Nature 524, 204–207 (2015).10.1038/nature14588 ↗
10. Lee, W. et al. Two-dimensional materials in functional three-dimensional architectures with applications in photodetection and imaging. Nat. Commun. 9, 1417 (2018).
11. Miskin, M. Z. et al. Graphene-based bimorphs for micron-sized, autonomous origami machines. Proc. Natl Acad. Sci. USA 115, 466–470 (2018).10.1073/pnas.1712889115 ↗
12. Chen, X., Yi, C. & Ke, C. Bending stiffness and interlayer shear modulus of few-layer graphene. Appl. Phys. Lett. 106, 101907 (2015).10.1063/1.4915075 ↗
13. Bao, W. et al. Controlled ripple texturing of suspended graphene and ultrathin graphite membranes. Nat. Nanotechnol. 4, 562–566 (2009).10.1038/nnano.2009.191 ↗
14. Brennan, C. J., Nguyen, J., Yu, E. T. & Lu, N. Interface adhesion between 2D materials and elastomers measured by buckle delaminations. Adv. Mater. Interfaces 2, 1500176 (2015).10.1002/admi.201500176 ↗
15. Jiang, T., Huang, R. & Zhu, Y. Interfacial sliding and buckling of monolayer graphene on a stretchable substrate. Adv. Funct. Mater. 24, 396–402 (2013).10.1002/adfm.201301999 ↗
16. Akinwande, D. et al. A review on mechanics and mechanical properties of 2D materials—graphene and beyond. Extreme Mech. Lett. 13, 42–77 (2017).10.1016/j.eml.2017.01.008 ↗
17. Zhang, D. B., Akatyeva, E. & Dumitrică, T. Bending ultrathin graphene at the margins of continuum mechanics. Phys. Rev. Lett. 106, 3–6 (2011).
18. Koskinen, P. & Kit, O. O. Approximate modeling of spherical membranes. Phys. Rev. B 82, 1–5 (2010).
19. Bunch, J. S. et al. Impermeable atomic membranes from graphene sheets. Nano Lett. 8, 2458–2462 (2008).10.1021/nl801457b ↗
20. Lopez-Polin, G. et al. Increasing the elastic modulus of graphene by controlled defect creation. Nat. Phys. 11, 26–31 (2014).10.1038/nphys3183 ↗
21. Tapasztó, L. et al. Breakdown of continuum mechanics for nanometre-wavelength rippling of graphene. Nat. Phys. 8, 739–742 (2012).10.1038/nphys2389 ↗
22. Nikiforov, I., Tang, D. M., Wei, X., Dumitrică, T. & Golberg, D. Nanoscale bending of multilayered boron nitride and graphene ribbons: experiment and objective molecular dynamics calculations. Phys. Rev. Lett. 109, 1–5 (2012).10.1103/PhysRevLett.109.025504 ↗
23. Yang, Z. et al. Mechanical properties of atomically thin boron nitride and the role of interlayer interactions. Nat. Commun. 8, 15815 (2017).
24. Rooney, A. P. et al. Anomalous twin boundaries in two dimensional materials. Nat. Commun. 9, 3597 (2018).10.1038/s41467-018-06074-8 ↗
25. Poot, M. & van der Zant, H. S. J. Nanomechanical properties of few-layer graphene membranes. Appl. Phys. Lett. 92, 063111 (2008).10.1063/1.2857472 ↗
26. Booth, T. J. et al. Macroscopic graphene membranes and their extraordinary stiffness. Nano Lett. 8, 2442–2446 (2008).10.1021/nl801412y ↗
27. Lindahl, N. et al. Determination of the bending rigidity of graphene via electrostatic actuation of buckled membranes. Nano Lett. 12, 3526–3531 (2012).10.1021/nl301080v ↗
28. Zhao, J. et al. Two-dimensional membrane as elastic shell with proof on the folds revealed by three-dimensional atomic mapping. Nat. Commun. 6, 8935 (2015).10.1038/ncomms9935 ↗
29. Kvashnin, D. G. & Sorokin, P. B. Effect of ultrahigh stiffness of defective graphene from atomistic point of view. J. Phys. Chem. Lett. 6, 2384–2387 (2015).10.1021/acs.jpclett.5b00740 ↗
30. Ertekin, E., Chrzan, D. C. & Daw, M. S. Topological description of the Stone–Wales defect formation energy in carbon nanotubes and graphene. Phys. Rev. B 79, 155421 (2009).10.1103/PhysRevB.79.155421 ↗
31. Guo, Y., Qiu, J. & Guo, W. Mechanical and electronic coupling in few-layer graphene and hBN wrinkles: a first-principles study. Nanotechnology 27, 505702 (2016).10.1088/0957-4484/27/50/505702 ↗
32. Wei, Y., Wang, B., Wu, J., Yang, R. & Dunn, M. L. Bending rigidity and Gaussian bending stiffness of single-layered graphene. Nano Lett. 13, 26–30 (2013).10.1021/nl303168w ↗
33. Iijima, S., Brabec, C., Maiti, A. & Bernholc, J. Structural flexibility of carbon nanotubes. J. Chem. Phys. 104, 2089–2092 (1996).10.1063/1.470966 ↗
34. Warner, J. H. et al. Dislocation-driven deformations in graphene. Science 337, 209–212 (2012).10.1126/science.1217529 ↗
35. Kim, K. et al. Ripping graphene: preferred directions. Nano Lett. 12, 293–297 (2012).10.1021/nl203547z ↗
36. Casillas, G., Liao, Y., Jose-Yacaman, M. & Marks, L. D. Monolayer transfer layers during sliding at the atomic scale. Tribol. Lett. 59, 45 (2015).10.1007/s11249-015-0563-9 ↗
37. Yakobson, B. I., Brabec, C. J. & Bernolc, J. Nanomechanics of carbon tubes: instabilities beyond linear response. Phys. Rev. Lett. 76, 2511–2514 (1996).10.1103/PhysRevLett.76.2511 ↗
38. Ru, C. Q. Effective bending stiffness of carbon nanotubes. Phys. Rev. B 62, 9973–9976 (2000).10.1103/PhysRevB.62.9973 ↗
39. Sanchez, D. A. et al. Mechanics of spontaneously formed nanoblisters trapped by transferred 2D crystals. Proc. Natl Acad. Sci. USA 115, 7884–7889 (2018).10.1073/pnas.1801551115 ↗
40. Woods, C. R. et al. Commensurate–incommensurate transition in graphene on hexagonal boron nitride. Nat. Phys. 10, 451–456 (2014).10.1038/nphys2954 ↗
41. Nicklow, R., Wakabayashi, N. & Smith, H. G. Lattice dynamics of pyrolytic graphite. Phys. Rev. B 5, 4951–4962 (1972).10.1103/PhysRevB.5.4951 ↗
42. Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. B 136, 864–871 (1964).10.1103/PhysRev.136.B864 ↗
43. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. A 140, 1133–1138 (1965).10.1103/PhysRev.140.A1133 ↗
44. Nye, J. F. Some geometrical relations in dislocated crystals. Acta Metall. 1, 153–162 (1953).10.1016/0001-6160(53)90054-6 ↗
45. Shinjo, K. & Hirano, M. Dynamics of friction: superlubric state. Surf. Sci. 293, 473–478 (1993).10.1016/0039-6028(93)91022-H ↗
46. Sangid, M. D., Ezaz, T., Sehitoglu, H. & Robertson, I. M. Energy of slip transmission and nucleation at grain boundaries. Acta Mater. 59, 283–296 (2011).10.1016/j.actamat.2010.09.032 ↗
47. Son, J. et al. Atomically precise graphene etch stops for three dimensional integrated systems from two dimensional material heterostructures. Nat. Commun. 9, 3988 (2018).10.1038/s41467-018-06524-3 ↗
48. Pizzocchero, F. et al. The hot pick-up technique for batch assembly of van der Waals heterostructures. Nat. Commun. 7, 11894 (2016).10.1038/ncomms11894 ↗
49. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).10.1016/0927-0256(96)00008-0 ↗
50. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).10.1103/PhysRevB.50.17953 ↗
51. Klimeš, J., Bowler, D. R. & Michaelides, A. Van der Waals density functionals applied to solids. Phys. Rev. B 83, 195131 (2011).10.1103/PhysRevB.83.195131 ↗
52. Brenner, D. W. et al. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys. Condens. Matter 14, 783–802 (2002).10.1088/0953-8984/14/4/312 ↗
53. Kolmogorov, A. N. & Crespi, V. H. Registry-dependent interlayer potential for graphitic systems. Phys. Rev. B 71, 235415 (2005).10.1103/PhysRevB.71.235415 ↗
54. Ouyang, W., Mandelli, D., Urbakh, M. & Hod, O. Nanoserpents: graphene nanoribbon motion on two-dimensional hexagonal materials. Nano Lett. 18, 6009–6016 (2018).10.1021/acs.nanolett.8b02848 ↗
55. Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).10.1006/jcph.1995.1039 ↗
56. Bitzek, E., Koskinen, P., Gähler, F., Moseler, M. & Gumbsch, P. Structural relaxation made simple. Phys. Rev. Lett. 97, 170201 (2006).10.1103/PhysRevLett.97.170201 ↗