Influence of a knot on the strength of a polymer strand

Many experiments have been done to determine the relative strengths of diff erent knots, and these show that the break in a knotted rope almost invaria bly occurs at the point just outside the 'entrance' to the knot(1). The inf luence of knots on the properties of polymers has become of great interest, in part because of their effect on mechanical properties(2). Knot theory(3, 4) applied to the topology of macromolecules(5-8) indicates that the simple trefoil or 'overhand' knot is likely to be present in any long polymer str and(9-12). Fragments of DNA have been observed to contain such knots in exp eriments(13,14) and computer simulations(15). Here we use ab initio computa tional methods(16) to investigate the effect of a trefoil knot on the break ing 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 th e entrance to the knot.