Skip to main content

Thank you for visiting nature.com. 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.

  • Letter
  • Published:

Nested self-similar wrinkling patterns in skins

Nature Materials volume 4, pages 293–297 (2005)Cite this article

Abstract

Stiff thin films on soft substrates are both ancient and commonplace in nature; for instance, animal skin comprises a stiff epidermis attached to a soft dermis. Although more recent and rare, artificial skins are increasingly used in a broad range of applications, including flexible electronics1, tunable diffraction gratings2,3, force spectroscopy in cells4, modern metrology methods5, and other devices6,7,8. Here we show that model elastomeric artificial skins wrinkle in a hierarchical pattern consisting of self-similar buckles extending over five orders of magnitude in length scale, ranging from a few nanometres to a few millimetres. We provide a mechanism for the formation of this hierarchical wrinkling pattern, and quantify our experimental findings with both computations and a simple scaling theory. This allows us to harness the substrates for applications. In particular, we show how to use the multigeneration-wrinkled substrate for separating particles based on their size, while simultaneously forming linear chains of monodisperse particles.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Optical microscopy images taken in the transmission mode.
Figure 2: Characterization of the nested hierarchy of buckles.
Figure 3: Results of a finite element simulation of the skin + substrate system.
Figure 4: Scaled buckle amplitude (ζ/Δ½) plotted as a function of the buckle period (λ) on a log–log plot.
Figure 5: Utilization of buckled substrates as microfluidic sieves.

Similar content being viewed by others

References

  1. Hamers, R. J. Flexible electronic futures. Nature 412, 489–490 (2001).

    Article  CAS  Google Scholar 

  2. Lim, J. H., Lee, K. S., Kim, J. C. & Lee, B. H. Tunable fiber gratings fabricated in photonic crystal fiber by use of mechanical pressure. Opt. Lett. 29, 331–333 (2004).

    Article  Google Scholar 

  3. Wong, C. W. et al. Strain-tunable silicon photonic band gap microcavities in optical waveguides. Appl. Phys. Lett. 84, 1242–1244 (2004).

    Article  CAS  Google Scholar 

  4. Harris, A. K., Wild, P. & Stopak, D. Silicone rubber substrata: a new wrinkle in the study of cell locomotion. Science 208, 177 (1980).

    Article  CAS  Google Scholar 

  5. Stafford, C. M. et al. A buckling-based metrology for measuring the elastic moduli of polymeric thin films. Nature Mater. 3, 545–550 (2004).

    Article  CAS  Google Scholar 

  6. Bowden, N., Brittain, S., Evans, A. G., Hutchinson, J. W. & Whitesides, G. W. Spontaneous formation of ordered structures in thin films of metals supported on an elastomeric polymer. Nature 393, 146–149 (1998).

    Article  CAS  Google Scholar 

  7. Bowden, N., Huck, W. T. S, Paul, K. & Whitesides, G. W. The controlled formation of ordered, sinusoidal structures by plasma oxidation of an elastomeric polymer. Appl. Phys. Lett. 75, 2557–2559 (1999).

    Article  CAS  Google Scholar 

  8. Huck, W. T. S., Bowden, N., Onck, P., Pardoen, T., Hutchinson, J. W. & Whitesides, G. W. Ordering of spontaneously formed buckles on planar surfaces. Langmuir 16, 3497–3501 (2000).

    Article  CAS  Google Scholar 

  9. Cerda, E. & Mahadevan, L. Geometry and physics of wrinkling. Phys. Rev. Lett. 90, 074302 (2003).

    Article  CAS  Google Scholar 

  10. Hedden, R. C., Saxena, H. & Cohen, C. Mechanical properties and swelling behavior of end-linked poly(diethylsiloxane) networks. Macromolecules 33, 8676–8684 (2000).

    Article  CAS  Google Scholar 

  11. Genzer, J., Fischer, D. A. & Efimenko, K. Fabricating two-dimensional molecular gradients via asymmetric deformation of uniformly-coated elastomer sheets. Adv. Mater. 15, 1545–1547 (2003).

    Article  CAS  Google Scholar 

  12. Ouyang, M., Yuan, C., Muisener, R. J., Boulares, A. & Koberstein, J. T. Conversion of some siloxane polymers to silicon oxide by UV/ozone photochemical processes. Chem. Mater. 12, 1591–1596 (2000).

    Article  CAS  Google Scholar 

  13. Efimenko, K., Wallace, W. E. & Genzer, J. Surface modification of Sylgard-184 poly(dimethyl siloxane) networks by ultraviolet and ultraviolet/ozone treatment. J. Colloid Interface Sci. 254, 306–315 (2002).

    Article  CAS  Google Scholar 

  14. Allen, H. G. Analysis and Design of Structural Sandwich Panels (Pergamon, New York, 1969).

    Google Scholar 

  15. Landau, L. D. & Lifshitz, L. Theory of Elasticity 3rd edn (Pergamon, New York, 1986).

    Google Scholar 

  16. Cerda, E. & Mahadevan, L. Wrinkling of an elastic sheet under tension. Nature 419, 579–580 (2003).

    Article  Google Scholar 

  17. Babler, W. J. Embryologic development of epidermal ridges and their configurations. Birth Defects Orig. 27, 95–112 (1991).

    CAS  Google Scholar 

  18. Kücken, M. & Newell, A. C. A model for fingerprint formation. Europhys. Lett. 68, 141–146 (2004).

    Article  Google Scholar 

  19. Price, N. J. & Cosgrove, J. W. Analysis of Geological Structures (Cambridge Univ. Press, Cambridge, 1990).

    Google Scholar 

  20. Huddleston, P. J. & Lan, L. Information from fold shapes. J. Struct. Geology 15, 253–264 (1993).

    Article  Google Scholar 

  21. Harrison, C., Stafford, C. M., Zhang, W. & Karim, A. Sinusoidal phase grating created by a tunably buckled surface. Appl. Phys. Lett. 85, 4016–4018 (2004).

    Article  CAS  Google Scholar 

  22. Ulman, A. Formation and structure of self-assembled monolayers. Chem. Rev. 96, 1533–1554 (1996).

    Article  CAS  Google Scholar 

  23. Schreiber, F. Structure and growth of self-assembling monolayers. Prog. Surf. Sci. 65, 151–256 (2000).

    Article  CAS  Google Scholar 

  24. Zhao, B. & Brittain, W. J. Polymer brushes: surface-immobilized macromolecules. Prog. Polym. Sci. 25, 677–710 (2000).

    Article  CAS  Google Scholar 

  25. Edmondson, S., Osborne, V. L. & Huck, W. T. S. Polymer brushes via surface-initiated polymerizations. Chem. Soc. Rev. 33, 14–22 (2004).

    Article  CAS  Google Scholar 

  26. Teixeira, A. I., Abrams, G. A., Bertics, P. J., Murphy, C. J. & Nealey, P. F. Epithelial contact guidance on well-defined micro- and nanostructured substrates. J. Cell. Sci. 116, 1881–1892 (2003).

    Article  CAS  Google Scholar 

  27. Hynes, R. O. & Lander, A. D. Contact and adhesive specificities in the associations, migrations, and targeting of cells and axons. Cell 68, 303–322 (1992).

    Article  CAS  Google Scholar 

  28. Patel, S. K., Malone, S., Cohen, C., Gilmor, K. R. & Colby, R. H. Elastic modulus and equilibrium swelling of poly(dimethylsiloxane) networks. Macromolecules 25, 5241–5251 (1992).

    Article  CAS  Google Scholar 

  29. Manias, E., Chen, J., Fang, N. & Zhang, X. Polymeric MEMS components with tunable stiffness. Appl. Phys. Lett. 79, 1700–1702 (2001).

    Article  CAS  Google Scholar 

  30. Radmacher, M., Fritz, M., Cleveland, J. P., Walters, D. A. & Hansma, P. K. Imaging adhesion forces and elasticity of lysozyme adsorbed on mica with the atomic force microscope. Langmuir 10, 3809–3814 (1994).

    Article  CAS  Google Scholar 

  31. Rotsch, C & Radmacher, M. Mapping local electrostatic forces with the atomic force microscope. Langmuir 13, 2825–2832 (1997).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The work was supported by the grants from the Camille & Henry Dreyfus Foundation (J.G.), the NER Program at the National Science Foundation (J.G., E.M.), and the Office of Naval Research (J.G., L.M.). We thank O.D. Velev for fruitful discussions.

Author information

Author notes

  1. Mindaugas Rackaitis

    Present address: Bridgestone/Firestone Research, Akron, Ohio, 44317, USA

Authors and Affiliations

  1. Department of Chemical Engineering, North Carolina State University, Raleigh, 27695-7905, North Carolina, USA

    Kirill Efimenko & Jan Genzer

  2. Department of Materials Science & Engineering, Pennsylvania State University, University Park, 16802, Pennsylvania, USA

    Mindaugas Rackaitis & Evangelos Manias

  3. Division of Engineering & Applied Sciences, Harvard University, Cambridge, 02138, Massachusetts, USA

    Ashkan Vaziri & L. Mahadevan

Authors
  1. Kirill Efimenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mindaugas Rackaitis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Evangelos Manias
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ashkan Vaziri
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. L. Mahadevan
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jan Genzer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to L. Mahadevan or Jan Genzer.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary text (PDF 54 kb)

Supplementary Information

Supplementary animation (GIF 3769 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Efimenko, K., Rackaitis, M., Manias, E. et al. Nested self-similar wrinkling patterns in skins. Nature Mater 4, 293–297 (2005). https://doi.org/10.1038/nmat1342

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat1342

This article is cited by

Search

Advanced search

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