Influence of a knot on the strength of a polymer strand

Abstract

Many experiments have been done to determine the relative strength of different knots, and these show that the break in a knotted rope almost invariably occurs at a point just outside the `entrance' to the knot. The influence of knots on the properties of polymers has become of great interest, in part because of their effect on mechanical properties. Knot theory applied to the topology of macromolecules indicates that the simple trefoil or `overhand' knot is likely to be present with high probability in any long polymer strand. Fragments of DNA have been observed to contain such knots in experiments and computer simulations. Here we use {\it ab initio} computational methods 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.