Mean-Square Radius of Gyration and Scattering Function of Semiflexible Ring Polymers of the Trefoil Knot

A Monte Carlo study of the mean-square radius of gyration R g 2 and scattering function P ( k ) with k the magnitude of the scattering vector for semiflexible ring polymers of the trefoil knot was conducted by the use of the discrete version of the Kratky⁻Porod (KP) wormlike ring model. The behavior of R g 2 and P ( k ) as functions of the reduced contour length λ L , defined as the total contour length L divided by the stiffness parameter λ - 1 , is clarified. A comparison is made of the results for the KP ring of the trefoil knot with those for the KP ring of the trivial knot and for the phantom KP ring without the topological constraints.