title: Gyration radius of a circular polymer under a topological constraint with excluded volume.
abstract: It is nontrivial whether the average size of a ring polymer should become smaller or larger under a topological constraint. Making use of some knot invariants, we numerically evaluate the mean-square radius of gyration for ring polymers having a fixed knot type, where the ring polymers are given by self-avoiding polygons consisting of freely jointed hard cylinders. We obtain plots of the gyration radius versus the number of polygonal nodes for the trivial, trefoil, and figure-eight knots. We discuss possible asymptotic behaviors of the gyration radius under the topological constraint. In the asymptotic limit, the size of a ring polymer with a given knot is larger than that of no topological constraint when the polymer is thin, and the effective expansion becomes weak when the polymer is thick enough.
authors.affiliation: Department of Physics, Faculty of Science and Graduate School of Humanities and Sciences, Ochanomizu University 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan.
authors.forename: M K
authors.initials: MK
authors.lastname: Shimamura
authors.forename: T
authors.initials: T
authors.lastname: Deguchi