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Influence of a knot on the strength of a polymer strand

Nature volume 399, pages 4648 (06 May 1999) | Download Citation

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Abstract

Many experiments have been done to determine the relative strengths of different knots, and these show that the break in a knotted rope almost invariably occurs at the point just outside the ‘entrance’ to the knot1. The influence of knots on the properties of polymers has become of great interest, in part because of their effect on mechanical properties2. Knot theory3,4 applied to the topology of macromolecules5,6,7,8 indicates that the simple trefoil or ‘overhand’ knot is likely to be present in any long polymer strand9,10,11,12. Fragments of DNA have been observed to contain such knots in experiments13,14 and computer simulations15. Here we use ab initio computational methods16 to investigate the effect of a trefoil knot on the breaking strength of a polymer strand. We find that the knot weakens the strand significantly, and that, like a knotted rope, it breaks under tension at the entrance to the knot.

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References

  1. 1.

    The Ashley Book of Knots(Doubleday, New York, (1993).

  2. 2.

    Structure transfer from a polymeric melt to the solid state. Part III: Influence of knots on structure and mechanical properties of semicrystalline polymers. Colloid Polym. Sci. 272, 910–932 (1994).

  3. 3.

    The Geometry and Physics of Knots(Cambridge Univ. Press, (1990).

  4. 4.

    Geometry and physics of knots. Nature 383, 142–145 (1996); Properties of ideal composite knots. Nature 388, 148–151 (1997).

  5. 5.

    & Chemical topology, J. Am. Chem. Soc. 83, 3789–3795 (1961).

  6. 6.

    Introduction to Stereochemistry(Benjamin, New York, (1965).

  7. 7.

    Catenanes, Rotaxanes, and Knots(Academic, New York, (1971).

  8. 8.

    Topological stereochemistry. Tetrahedron 41, 3161–3212 (1985).

  9. 9.

    , & Statistical mechanics and topology of polymer chains. Nature 258, 398–402 (1975).

  10. 10.

    Macromolecular topology—Metastable isomers from pseudo interpenetrating polymer networks. New J. Chem. 17, 697–701 (1993).

  11. 11.

    Knots in hamiltonian cycles. Macromolecules 27, 5924–5926 (1994).

  12. 12.

    , , & Entanglement complexity of self-avoiding walks. J. Phys. A 25, 6557–6566 (1992).

  13. 13.

    & Biochemical topology: applications to DNA recombination and replication. Science 232, 951–960 (1986).

  14. 14.

    & Knotting of a DNA chain during ring closure. Science 260, 533–536 (1993).

  15. 15.

    & Trefoil knotting revealed by molecular dynamics simulations of supercoiled DNA. Science 257, 1110–1115 (1992).

  16. 16.

    & Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55, 2471–2474 (1985).

  17. 17.

    Tight knots. Macromolecules 17, 703–704 (1984).

  18. 18.

    , & Simulating the critical-behaviour of complex fluids. Nature 365, 330–332 (1993).

  19. 19.

    , , , & Equilibrium and non-equilibrium simulation studies of fluid alkanes in bulk and at interfaces. Faraday Discuss. 104, 17–36 (1996).

  20. 20.

    , & Mechanical properties and force-field parameters for polyethylene crystal. J. Phys. Chem. US 95, 2260–2272 (1991).

  21. 21.

    , , & Dissociation of methane into hydrocarbons at extreme (planetary) pressure and temperature. Science 275, 1288–1290 (1997).

  22. 22.

    & Density functional study of crystalline polyethylene. Chem. Phys. Lett. 272, 347–352 (1997).

  23. 23.

    PINY Code. Comp. Phys. Comm.(in the press).

  24. 24.

    Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 38, 3098–3100 (1988).

  25. 25.

    , & Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 37, 785–789 (1988).

  26. 26.

    Tying a molecular knot with optical tweezers. Nature(in the press).

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Acknowledgements

This work was supported in part by the National Science Foundation.

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Affiliations

  1. *Center for Molecular Modeling, Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6202, USA

    • A. Marco Saitta
    •  & Michael L. Klein
  2. †DuPont Central Research and Development, Expt. Station, Wilmington, Delaware 19880-0328, USA

    • Paul D. Soper
    •  & E. Wasserman

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Correspondence to Michael L. Klein.

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https://doi.org/10.1038/19935

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