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 [Formula: see text] and scattering function [Formula: see text] 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 [Formula: see text] and [Formula: see text] as functions of the reduced contour length [Formula: see text] , defined as the total contour length L divided by the stiffness parameter [Formula: see text] , 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.