Finite-size and asymptotic behaviors of the gyration radius of knotted cylindrical polygons

Several nontrivial properties are shown for the mean square radius of gyration $R_K^2$ 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 a 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 which 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.