What is the length of a knot in a polymer?

B. Marcone, E. Orlandini, A. L. Stella, F. Zonta

Published 2004-05-12, updated 2005-01-11Version 3

We give statistical definitions of the length, l, of a loose prime knot tied into a long, fluctuating ring macromolecule. Monte Carlo results for the equilibrium, good solvent regime show that < l > ~ N^t, where N is the ring length and t ~ 0.75 is independent of the knot topology. In the collapsed regime below the theta temperature, length determinations based on the entropic competition of different knots within the same ring show delocalization (t~1).