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.

Nonlinear control of high-frequency phonons in spider silk

Abstract

Spider dragline silk possesses superior mechanical properties1,2 compared with synthetic polymers with similar chemical structure due to its hierarchical structure comprised of partially crystalline oriented nanofibrils3,4. To date, silk’s dynamic mechanical properties have been largely unexplored. Here we report an indirect hypersonic phononic bandgap and an anomalous dispersion of the acoustic-like branch from inelastic (Brillouin) light scattering experiments under varying applied elastic strains. We show the mechanical nonlinearity of the silk structure generates a unique region of negative group velocity, that together with the global (mechanical) anisotropy provides novel symmetry conditions for gap formation5,6,7,8. The phononic bandgap and dispersion show strong nonlinear strain-dependent behaviour. Exploiting material nonlinearity along with tailored structural anisotropy could be a new design paradigm to access new types of dynamic behaviour.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Access to the mechanical properties along and normal to the spider dragline fibre.
Figure 2: The effect of strain on the dispersion diagram and the mechanical anisotropy of native and supercontracted fibres.
Figure 3: BLS spectra and dispersion diagrams of the native spider dragline silk and regenerated silk.

References

  1. Giesa, T., Arslan, M., Pugno, N. M. & Buehler, M. J. Nanoconfinement of spider silk fibrils begets superior strength, extensibility, and toughness. Nano Lett. 11, 5038–5046 (2011).

    CAS  Article  Google Scholar 

  2. Sapede, D. et al. Nanofibrillar structure and molecular mobility in spider dragline silk. Macromolecules 38, 8447–8453 (2005).

    CAS  Article  Google Scholar 

  3. Vollrath, F., Madsen, B. & Shao, Z. The effect of spinning conditions on the mechanics of a spider’s dragline silk. Proc. R. Soc. B 268, 2339–2346 (2001).

    CAS  Article  Google Scholar 

  4. Agnarsson, I., Kuntner, M. & Blackledge, T. A. Bioprospecting finds the toughest biological material: extraordinary silk from a giant riverine orb spider. PLoS ONE 5, e11234 (2010).

    Article  Google Scholar 

  5. Cheng, W., Wang, J., Jonas, U., Fytas, G. & Stefanou, N. Observation and tuning of hypersonic bandgaps in colloidal crystals. Nature Mater. 5, 830–836 (2006).

    CAS  Article  Google Scholar 

  6. Schneider, D. et al. Defect-controlled hypersound propagation in hybrid superlattices. Phys. Rev. Lett. 111, 164301 (2013).

    Article  Google Scholar 

  7. Still, T. et al. Simultaneous occurrence of structure-directed and particle-resonance-induced phononic gaps in colloidal films. Phys. Rev. Lett. 100, 194301 (2008).

    CAS  Article  Google Scholar 

  8. Lemoult, F., Kaina, N., Fink, M. & Lerosey, G. Wave propagation control at the deep subwavelength scale in metamaterials. Nature Phys. 9, 55–60 (2013).

    CAS  Article  Google Scholar 

  9. Miller, L. D., Putthanarat, S., Eby, R. & Adams, W. Investigation of the nanofibrillar morphology in silk fibers by small angle X-ray scattering and atomic force microscopy. Int. J. Biol. Macromol. 24, 159–165 (1999).

    CAS  Article  Google Scholar 

  10. Poza, P., Pérez-Rigueiro, J., Elices, M. & LLorca, J. Fractographic analysis of silkworm and spider silk. Eng. Fract. Mech. 69, 1035–1048 (2002).

    Article  Google Scholar 

  11. Gould, S. A. C., Tran, K. T., Spagna, J. C., Moore, A. M. F. & Shulman, J. B. Short and long range order of the morphology of silk from Latrodectus hesperus (Black Widow) as characterized by atomic force microscopy. Int. J. Biol. Macromol. 24, 151–157 (1999).

    CAS  Article  Google Scholar 

  12. Yang, Y. et al. Toughness of spider silk at high and low temperatures. Adv. Mater. 17, 84–88 (2005).

    Article  Google Scholar 

  13. Savage, K. N., Guerette, P. A. & Gosline, J. M. Supercontraction stress in spider webs. Biomacromolecules 5, 675–679 (2004).

    CAS  Article  Google Scholar 

  14. Guinea, G. V., Elices, M., Péez-Rigueiro, J. & Plaza, G. R. Stretching of supercontracted fibers: a link between spinning and the variability of spider silk. J. Exp. Biol. 208, 25–30 (2005).

    CAS  Article  Google Scholar 

  15. Ene, R., Papadopoulos, P. & Kremer, F. Supercontraction in Nephila spider dragline silk—relaxation into equilibrium state. Polymer 52, 6056–6060 (2011).

    CAS  Article  Google Scholar 

  16. Ebenstein, D. M. & Wahl, K. J. Anisotropic nanomechanical properties of Nephila clavipes dragline silk. J. Mater. Res. 21, 2035–2044 (2011).

    Article  Google Scholar 

  17. Glišović, A., Vehoff, T., Davies, R. J. & Salditt, T. Strain dependent structural changes of spider dragline silk. Macromolecules 41, 390–398 (2008).

    Article  Google Scholar 

  18. Mortimer, B. et al. The speed of sound in silk: linking material performance to biological function. Adv. Mater. 26, 5179–5183 (2014).

    CAS  Article  Google Scholar 

  19. Cusack, S. Variation of longitudinal acoustic velocity at gigahertz frequencies with water content in rat-tail tendon fibers. Biopolymers 23, 337–351 (1984).

    CAS  Article  Google Scholar 

  20. Koski, K. J., Akhenblit, P., McKiernan, K. & Yarger, J. L. Non-invasive determination of the complete elastic moduli of spider silks. Nature Mater. 12, 262–267 (2013).

    CAS  Article  Google Scholar 

  21. LeféIvre, T., Boudreault, S., Cloutier, C. & Pézolet, M. Conformational and orientational transformation of silk proteins in the major ampullate gland of Nephila clavipes spiders. Biomacromolecules 9, 2399–2407 (2008).

    Article  Google Scholar 

  22. Davydov, S. L., Zaretskii-Feoktistov, G. G. & Sudakov, V. V. Propagation of axially symmetric elastic vibrations along a waveguide in an elastic medium. Polym. Mech. 10, 90–94 (1974).

    Article  Google Scholar 

  23. Pérez-Rigueiro, J., Elices, M. & Guinea, G. V. Controlled supercontraction tailors the tensile behaviour of spider silk. Polymer 44, 3733–3736 (2003).

    Article  Google Scholar 

  24. Keten, S., Xu, Z., Ihle, B. & Buehler, M. J. Nanoconfinement controls stiffness, strength and mechanical toughness of β-sheet crystals in silk. Nature Mater. 9, 359–367 (2010).

    CAS  Article  Google Scholar 

  25. Cranford, S. W., Tarakanova, A., Pugno, N. M. & Buehler, M. J. Nonlinear material behaviour of spider silk yields robust webs. Nature 482, 72–76 (2012).

    CAS  Article  Google Scholar 

  26. Parnes, R. Dispersion relations of waves in a rod embedded in an elastic medium. J. Sound Vib. 76, 65–75 (1981).

    Article  Google Scholar 

  27. Askar, A. Dispersion relation and wave solution for anharmonic lattices and Korteweg De Vries continua. Proc. R. Soc. Lond. A 334, 83–94 (1973).

    CAS  Article  Google Scholar 

  28. Alonso-Redondo, E. et al. A new class of tunable hypersonic phononic crystals based on polymer-tethered colloids. Nature Commun. 6, 8309 (2015).

    CAS  Article  Google Scholar 

  29. Teyssier, J., Saenko, S. V., van der Marel, D. & Milinkovitch, M. C. Photonic crystals cause active colour change in chameleons. Nature Commun. 6, 6368 (2015).

    CAS  Article  Google Scholar 

  30. Lee, S.-M. et al. Greatly increased toughness of infiltrated spider silk. Science 324, 488–492 (2009).

    CAS  Article  Google Scholar 

  31. Ayzenberg-Stepanenko, M. V. Non-steady state wave propagation in composite structures. Proc. 24th Israeli Conf. Mech. Eng. 4.8.2, 1–3 (1992).

    Google Scholar 

  32. Eringen, A.C. Theory of nonlocal elasticity and some applications. Res. Mech. 21, 313–342 (1987).

    Google Scholar 

  33. Polyzos, D. & Fotiadis, D.I. Derivation of Mindlins first and second strain gradient elastic theory via simple lattice and continuum models. Int. J. Solids Struct. 49, 470–480 (2012).

    Article  Google Scholar 

  34. Koh, C. Y. Generalized Phononic Networks: of Length Scales, Symmetry-breaking and (Non) Locality PhD thesis, Massachusetts Institute of Technology (2011).

  35. Economou, E.N. & Sigalas, M.M. Classical wave propagation in periodic structures: cermet versus network topology. Phys. Rev. B 48, 13434–13438 (1993).

    CAS  Article  Google Scholar 

  36. Gomopoulos, N., Cheng, W., Efremov, M., Nealey, P.F. & Fytas, G. Out of plane longitudinal elastic modulus of supported polymer thin films. Macromolecules 42, 7164–7167 (2009).

    CAS  Article  Google Scholar 

Download references

Acknowledgements

The work was partially supported by Aristeia Program-285 (EU, GSRT-Greece), ERC-AdG-694977, SFB TRR102 and the DFG (Grant No. BU 1556/27).

Author information

Authors and Affiliations

Authors

Contributions

D.S. and N.G. contributed equally to the BLS measurements. P.P. fabricated the samples. C.Y.K. developed the theoretical description of the dispersion diagrams. G.F. planned the project and wrote most of the article; C.Y.K., P.P., F.K. and E.L.T. corrected and finalized it. All authors have discussed the results and commented on the manuscript.

Corresponding author

Correspondence to George Fytas.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary information (PDF 2980 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Schneider, D., Gomopoulos, N., Koh, C. et al. Nonlinear control of high-frequency phonons in spider silk. Nature Mater 15, 1079–1083 (2016). https://doi.org/10.1038/nmat4697

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat4697

Further reading

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