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

TL;DR

This study systematically investigates the statistical and hydrodynamic properties of topological polymers with various graph structures, revealing universal ratios and enhanced short-range correlations through simulations.

Contribution

It provides new insights into the universal ratios and correlation enhancements in topological polymers with complex graph structures, using numerical simulations.

Findings

Ratios of radius of gyration to hydrodynamic radius are universal across topologies.

Short-range intrachain correlations are significantly enhanced in complex topological polymers.

Ratios among different topological types are independent of excluded volume for certain vertices.

Abstract

For various polymers with different topological structures we numerically evaluate the mean-square radius of gyration and the hydrodynamic radius systematically through simulation. We call polymers with nontrivial topology topological polymers. We evaluate the two quantities both for ideal and real chain models and show that the ratios of the quantities among different topological types 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 topological polymers expressed with complex graphs.