Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Self-assembly of graphene ribbons by spontaneous self-tearing and peeling from a substrate


Graphene and related two-dimensional materials have shown unusual and exceptional mechanical properties1,2,3, with similarities to origami-like paper folding4,5 and kirigami-like cutting6,7 demonstrated. For paper analogues, a critical difference between macroscopic sheets and a two-dimensional solid is the molecular scale of the thin dimension of the latter, allowing the thermal activation of considerable out-of-plane motion. So far thermal activity has been shown to produce local wrinkles in a free graphene sheet that help in theoretically understanding its stability8, for example, and give rise to unexpected long-range bending stiffness6. Here we show that thermal activation can have a more marked effect on the behaviour of two-dimensional solids, leading to spontaneous and self-driven sliding, tearing and peeling from a substrate on scales approaching the macroscopic. We demonstrate that scalable nanoimprint-style contact techniques can nucleate and direct the parallel self-assembly of graphene ribbons of controlled shape in ambient conditions. We interpret our observations through a simple fracture-mechanics model that shows how thermodynamic forces drive the formation of the graphene–graphene interface in lieu of substrate contact with sufficient strength to peel and tear multilayer graphene sheets. Our results show how weak physical surface forces can be harnessed and focused by simple folded configurations of graphene to tear the strongest covalent bond. This effect may hold promise for the patterning and mechanical actuating of devices based on two-dimensional materials.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Self assembly of graphene flaps and ribbons.
Figure 2: Fracture mechanics analysis of quasi-static ribbon growth.
Figure 3: Geometry of ribbon growth.
Figure 4: Kinetics of self-assembling graphene ribbons.


  1. 1

    Rasool, H. I., Ophus, C., Klug, W. S., Zettl, A. & Gimzewski, J. K. Measurement of the intrinsic strength of crystalline and polycrystalline graphene. Nat. Commun. 4, 2811 (2013)

    ADS  Article  Google Scholar 

  2. 2

    Zhang, T., Li, X. & Gao, H. Fracture of graphene: a review. Int. J. Fract. 196, 1–31 (2015)

    Article  Google Scholar 

  3. 3

    Ovid’ko, I. A. Mechancial properties of graphene. Rev. Adv. Mater. Sci. 34, 1–11 (2013)

    Google Scholar 

  4. 4

    Cranford, S., Sen, D. & Buehler, M. J. Meso-origami: folding multilayer graphene sheets. Appl. Phys. Lett. 95, 123121 (2009)

    ADS  Article  Google Scholar 

  5. 5

    Ebbesen, T. W. & Hiura, H. Graphene in 3-dimensions: towards graphite origami. Adv. Mater. 7, 582–586 (1995)

    CAS  Article  Google Scholar 

  6. 6

    Blees, M. K. et al. Graphene kirigami. Nature 524, 204–207 (2015)

    CAS  ADS  Article  Google Scholar 

  7. 7

    Castle, T. et al. Making the cut: lattice kirigami rules. Phys. Rev. Lett. 113, 245502 (2014)

    ADS  Article  Google Scholar 

  8. 8

    Fasolino, A., Los, J. H. & Katsnelson, M. I. Intrinsic ripples in graphene. Nat. Mater. 6, 858–861 (2007)

    CAS  ADS  Article  Google Scholar 

  9. 9

    Hamm, E., Reis, P., LeBlanc, M., Roman, B. & Cerda, E. Tearing as a test for mechanical characterization of thin adhesive films. Nat. Mater. 7, 386–390 (2008)

    CAS  ADS  Article  Google Scholar 

  10. 10

    Kendall, K. Thin-film peeling-the elastic term. J. Phys. D 8, 1449 (1975)

    ADS  Article  Google Scholar 

  11. 11

    Sen, D., Novoselov, K. S., Reis, P. M. & Buehler, M. J. Tearing graphene sheets from adhesive substrates produces tapered nanoribbons. Small 6, 1108–1116 (2010)

    CAS  Article  Google Scholar 

  12. 12

    Chopra, N. G. et al. Fully collapsed carbon nanotubes. Nature 337, 135–138 (1995)

    ADS  Article  Google Scholar 

  13. 13

    Mikata, Y. New and improved analytical solutions for the self-folding problem of carbon nanotubes. J. Nanomech. Micromech. 3, 04013004 (2013)

    Article  Google Scholar 

  14. 14

    Meng, X., Li, M., Kang, Z., Zhang, X. & Xiao & J. Mechanics of self-folding of single-layer graphene. J. Phys. D 46, 055308 (2013)

    ADS  Article  Google Scholar 

  15. 15

    Cox, B. J., Baowan, D., Bacsa, W. & Hill, J. M. Relating elasticity and graphene folding conformation. RSC Adv. 5, 57515–57520 (2015)

    CAS  Article  Google Scholar 

  16. 16

    Chen, X., Yi, C. & Ke, C. Bending stiffness and interlayer shear modulus of few-layer graphene. Appl. Phys. Lett. 106, 101907 (2015)

    ADS  Article  Google Scholar 

  17. 17

    Chen, X., Zhang, L., Zhao, Y., Wang, X. & Ke, C. Graphene folding on flat substrates. J. Appl. Phys. 116, 164301 (2014)

    ADS  Article  Google Scholar 

  18. 18

    Lawn, B. R. Fracture of Brittle Solids (Cambridge Univ. Press, 1993)

  19. 19

    Dietzel, D., Feldmann, M., Schwarz, U. D., Fuchs, H. & Schirmeisen, A. Scaling laws of structural lubricity. Phys. Rev. Lett. 111, 235502 (2013)

    ADS  Article  Google Scholar 

  20. 20

    Feng, X., Kwon, S., Park, J. Y. & Salmeron, M. Superlubric sliding of graphene nanoflakes on graphene. ACS Nano 7, 1718–1724 (2013)

    CAS  Article  Google Scholar 

  21. 21

    Liu, Z. et al. Observation of microscale superlubricity in graphite. Phys. Rev. Lett. 108, 205503 (2012)

    ADS  Article  Google Scholar 

  22. 22

    Yang, J. et al. Observation of high-speed microscale superlubricity in graphite. Phys. Rev. Lett. 110, 255504 (2013)

    ADS  Article  Google Scholar 

  23. 23

    Li, P., You, Z. & Cui, T. Adhesion energy of few layer graphene characterized by atomic force microscope. Sens. Actuator. A 217, 56–61 (2014)

    CAS  Article  Google Scholar 

  24. 24

    Vahdat, A. S. & Cetinkaya, C. Adhesion energy characterization of monolayer graphene by vibrational spectroscopy. J. Appl. Phys. 114, 143502 (2013)

    ADS  Article  Google Scholar 

  25. 25

    He, Y., Chen, W. F., Yu, W. B., Ouyang, G. & Yang, G. W. Anomalous interface adhesion of graphene membranes. Sci. Rep. 3, 2660 (2013)

    CAS  ADS  Article  Google Scholar 

  26. 26

    Bunch, J. S. & Dunn, M. L. Adhesion mechanics of graphene membranes. Solid State Commun. 152, 1359–1364 (2012)

    CAS  ADS  Article  Google Scholar 

  27. 27

    Huang, X., Yang, H., van Duin, A. C. T., Hsia, K. J. & Zhang, S. Chemomechanics control of tearing paths in graphene. Phys. Rev. B 85, 195453 (2012)

    ADS  Article  Google Scholar 

  28. 28

    Slotman, G. J. et al. Effect of structural relaxation on the electronic structure of graphene on hexagonal boron nitride. Phys. Rev. Lett. 115, 186801 (2015)

    CAS  ADS  Article  Google Scholar 

  29. 29

    Ferrari, A. C. et al. Raman spectrum of graphene and graphene layers. Phys. Rev. Lett. 97, 187401 (2006)

    CAS  ADS  Article  Google Scholar 

  30. 30

    Ni, Z., Wang, Y., Yu, T., You, Y. & Shen, Z. Reduction of Fermi velocity in folded graphene observed by resonance Raman spectroscopy. Phys. Rev. B 77, 235403 (2008)

    ADS  Article  Google Scholar 

  31. 31

    Hao, Y. et al. Probing layer number and stacking order of few-layer graphene by Raman spectroscopy. Small 6, 195–200 (2010)

    CAS  Article  Google Scholar 

  32. 32

    van den Ende, J. A., De Wijn, A. S. & Fasolino, A. The effect of temperature and velocity on superlubricity. J. Phys. Condens. Matter 24, 445009 (2012)

    ADS  Article  Google Scholar 

Download references


We thank H. Nolan, N. McEvoy and G. Duesberg for discussions and assistance with the Raman spectroscopy. We thank A. Fasolino, A. Schirmeisen, J. Coleman and P. McCormack for discussions and J. Sader and J. Pethica for critical reviews of the manuscript. We acknowledge financial support from the Science Foundation of Ireland (SFI) under CRANN CSET 08/CE/I1432 and PI 08/IN/I1932. We also recognize assistance from Horizon 2020 COST Action MP1303.

Author information




J.A. observed the phenomena and performed all experiments. J.A. and G.L.W.C. designed experiments, analysed the data and constructed the static and kinetic models. G.L.W.C. wrote the manuscript.

Corresponding author

Correspondence to Graham L. W. Cross.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Ribbon growth and collision with visible contaminants.

The growth pattern recorded by AFM imaging shows ribbon pinning and release as contamination defects are pushed aside (insets a and b), followed by rapid growth until next contaminant reached at point c. Final ribbon pinning occurs by encounter with sliver fracture in the flake that exposes the underlying substrate d. In a, a bulge in the fold (yellow arrow) has been disappeared by b as the defect has moved to a lower position along the ribbon head indicated by the green arrow. Ribbon growth direction is to the left. Horizontal error bars indicate uncertainty in exact time of AFM image acquisition used to extract ribbon length values, whereas vertical error bars are omitted as the uncertainty range is too small to see at this scale.

Extended Data Figure 2 Scanning Raman analysis of commensurate stacked layers in a mechanically exfoliated graphene flake with no self-assembled structures present.

a, Optical micrograph of a mechanically exfoliated graphene sheet. The red box indicates the area that was analysed, comprising three- and four-layer-thick graphene sheets. bd, Maps of the G band intensity (b), 2D band intensity (c) and the FWHM of the 2D band (d). e, Plot of the average Raman spectra within the three- and four-layer areas. f, Comparative plot of the 2D bands within the three- and four-layer areas.

Extended Data Figure 3 Scanning Raman analysis of the self-assembled bilayer graphene ribbons shown in

Fig. 1l. a, Optical micrograph of the mechanically exfoliated bilayer graphene sheet. The red box indicates a single indentation from which the three folded ribbons grew. bd, Maps of the G band intensity (b), 2D band intensity (c) and the FWHM of the 2D band (d). e, Plot of the average Raman spectra within the folded ribbons (four-layer) and the bilayer sheet. f, Comparative plot of the 2D bands within the folded ribbons four-layer) and the bilayer sheet.

Extended Data Figure 4 Fits to the ribbon head position.

ac, Ribbon length (a), velocity (b) and width (c) versus time for the self-assembling ribbon system presented in Fig. 4, as extracted from the sequence of AFM images shown below. See Methods for an explanation of the fitting functions. Scale bars, 1 μm.

Supplementary information

Video 1: Growth of three ribbons nucleated from single indentation into bilayer graphene

An animation of successive images of the growth of three ribbons shown in Figure 1. The video consists of images captured by AFM over a 14 day period. The ribbon in the lower left is able to grow over a subsurface defect before stopping, while the ribbon growing towards the right of the image halts upon encountering the edge of the host graphene sheet. (WMV 2167 kb)

PowerPoint slides

Source data

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Annett, J., Cross, G. Self-assembly of graphene ribbons by spontaneous self-tearing and peeling from a substrate. Nature 535, 271–275 (2016).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing