Statistical and hydrodynamic properties of topological polymers for various graphs showing enhanced short-range correlation.

Abstract

For various polymers with different structures in chemical connectivity expressed by graphs, we numerically evaluate the mean-square radius of gyration and the hydrodynamic radius systematically through simulation. We call polymers with nontrivial structures in chemical connectivity and those of nontrivial topology of spatial graphs as embeddings in three dimensions topological polymers. We evaluate the two quantities both for ideal and real chain models and show that the ratios of the quantities among different structures in chemical connectivity do not depend on the existence of excluded volume if the topological polymers have only up to trivalent vertices, as far as the polymers investigated. We also evaluate the ratio of the gyration radius to the hydrodynamic radius, which we expect to be universal from the viewpoint of renormalization group. Furthermore, we show that the short-distance intrachain correlation is much enhanced for real topological polymers (the Kremer-Grest model) expressed with complex graphs.