title: Finite-size and asymptotic behaviors of the gyration radius of knotted cylindrical self-avoiding polygons.
abstract: Several nontrivial properties are shown for the mean-square radius of gyration R2(K) of ring polymers with a fixed knot type K. Through computer simulation, we discuss both finite size and asymptotic behaviors of the gyration radius under the topological constraint for self-avoiding polygons consisting of N cylindrical segments with radius r. We find that the average size of ring polymers with the knot K can be much larger than that of no topological constraint. The effective expansion due to the topological constraint depends strongly on the parameter r that is related to the excluded volume. The topological expansion is particularly significant for the small r case, where the simulation result is associated with that of random polygons with the knot K.
authors.affiliation: Department of Applied Physics, Graduate School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
authors.forename: Miyuki K
authors.initials: MK
authors.lastname: Shimamura
authors.forename: Tetsuo
authors.initials: T
authors.lastname: Deguchi