L. Tubiana, A. Rosa, F. Fragiacomo and C. Micheletti
Spontaneous knotting and unknotting of flexible linear polymers:\\equilibrium and kinetic aspects
Macromol., 2013, 46 3669-3678
Link to arXiv preprint ,
Link to online article
Abstract
We report on a computational study of the statics and dynamics of long
flexible linear polymers that spontaneously knot and unknot.
Specifically, the equilibrium self-entanglement properties, such as the
knotting probability, knot length and position, are investigated with
extensive Monte Carlo sampling of chains of up to 15,000 beads. Tens of
such equilibrated chains of up to $\sim 4,000$ beads are next used as
starting points for Langevin dynamics simulations. The complex interplay
of chain dynamics and self-knotting is addressed by monitoring the time
evolution of various metric and entanglement properties. In particular,
the extensive duration of the simulations allows for observing the
spontaneous formation and disappearance of prime and composite physical knots in
linear chains. Notably, a sizeable fraction of self-knotting and
unknotting events is found to involve regions that are far away from the
chain termini. To the best of our knowledge this represents the first
instance where spontaneous changes in knotting for linear homopolymers are
systematically characterized using unbiased dynamics
simulations.