Universality of dilute solutions of ring polymers in the thermal crossover region between θ and athermal solvents

Abstract

Due to their unique topology of having no chain ends, dilute solutions of ring polymers exhibit behavior distinct from their linear chain counterparts. The universality of their static and dynamic properties, as a function of solvent quality [Formula: see text] in the thermal crossover regime between [Formula: see text] and athermal solvents, is studied here using Brownian dynamics simulations. The universal ratio [Formula: see text] of the radius of gyration [Formula: see text] to the hydrodynamic radius [Formula: see text] is determined, and a comparative study of the swelling ratio [Formula: see text] of the radius of gyration, the swelling ratio [Formula: see text] of the hydrodynamic radius, and the swelling ratio [Formula: see text] of the mean polymer stretch [Formula: see text] along the [Formula: see text]-axis, for linear and ring polymers, is carried out. The ratio [Formula: see text] for dilute ring polymer solutions is found to converge asymptotically to a constant value as [Formula: see text], which is a major difference from the behavior of solutions of linear chains, where no such asymptotic limit exists. Additionally, the ratio of the mean stretch along the [Formula: see text]-axis to the hydrodynamic radius, [Formula: see text], is found to be independent of [Formula: see text] for polymeric rings, unlike in the case for linear polymers. These results indicate a fundamental difference in the scaling of static and dynamic properties of rings and linear chains in the thermal crossover regime.