Knots in open Polymers

  Disclaimer:   A knot is not mathematically well defined in an open chain,

and its "size" is ambiguous.    Results somewhat depend on operational definitions.

Pulling knots: Knots can be tied by pulling on the ends of a chain.

We used simulations of pulled knots to estimate the size:

  • The presence of the knot introduces a new length scale into the problem,
    • Can we use the lack of scaling to deduce a knot size?

  • Interestingly, the correction to scaling exponent of 0.56 in d=3 is consistent with t=0.4 0.1.
    • However, a recent study claims t=0.75 0.14.
      • B. Marcone, E. Orlandini, A.L. Stella, and F. Zonta, PRE 75, 041105 (2007)

Reducing complexity: To find and localize knots in long open polymers

Model polyethylene: Monte Carlo (MC) simulations of a coarse-grained model for polyethylene

Qualitative results for polymers in   coil (swollen),   globule (compact),  and   confined  sates.


MIT web-server for detection of knots: