Influence of a knot on the strength of a polymer strand
arXiv:cond-mat/9905129 · doi:10.1038/19935
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.
3 pages, 4 figures
Cited by in corpus (21)
- Polymers with spatial or topological constraints: theoretical and computational results
- Topological jamming of spontaneously knotted polyelectrolyte chains driven through a nanopore
- Spontaneous knotting and unknotting of flexible linear polymers: equilibrium and kinetic aspects
- Sequence-specific size, structure, and stability of tight protein knots
- Knots in Charged Polymers
- Polyethylene under tensile load: strain energy storage and breaking of linear and knotted alkanes probed by first-principles molecular dynamics calculations
- How molecular knots can pass through each other
- Matched asymptotic expansions for twisted elastic knots: a self-contact problem with non- trivial contact topology
- Periodic motion of sedimenting flexible knots
- The shapes of physical trefoil knots
- Stiff knots
- Activity-driven polymer knotting for macromolecular topology engineering
- Chirality modifies the interaction between knots
- Inner topological structure of Hopf invariant
- On the factorization of composite polymer knots into separated prime components
- Knotlike Cosmic Strings in The Early Universe
- A principle for ideal torus knots
- How cooperatively folding are homopolymer molecular knots?
- Twist deformation of physical trefoil knots
- Novel Topological Invariant in the U(1) Gauge Field Theory
- Hydrodynamic Inflation of Ring Polymers under Shear