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Influence of a knot on the strength of a polymer strand

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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Figure 1: Strain energy distribution in a knotted polymer strand.
Figure 2: Analysis of chain rupture.
Figure 3: Schematic electron charge density immediately after the break.
Figure 4: Relaxation of the strain energy distribution.

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Acknowledgements

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

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Correspondence to Michael L. Klein.

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Saitta, A., Soper, P., Wasserman, E. et al. Influence of a knot on the strength of a polymer strand. Nature 399, 46–48 (1999). https://doi.org/10.1038/19935

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