Mean-square radius of gyration and hydrodynamic radius for topological polymers evaluated through the quaternionic algorithm

We evaluate numerically the mean-square (MS) radius of gyration and the diffusion coefficient for topological polymers such as ring, tadpole, double-ring, and caged polymers and catenanes. We consider caged polymers with any given number of subchains, and catenanes consisting of two linked ring polymers with a fixed linking number. Through Kirkwood's approximation we evaluate the hydrodynamic radius, which is proportional to the inverse of the diffusion coefficient, for various topological polymers. Here we take the statistical averages over configurations of topological polymers constructed through the quaternionic algorithm, which generates uniform random walks connecting given two points. It gives ideal chains with no excluded volume. We evaluate numerically the ratio of the square root of the MS radius of gyration to the hydrodynamic radius for several topological polymers, and show for them that the ratio decreases as the topology becomes more complex.