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 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.

• Received 7 February 2002

DOI:https://doi.org/10.1103/PhysRevE.65.051802