Universal size ratios of Gaussian polymers with complex architecture: radius of gyration vs hydrodynamic radius

We study the impact of arm architecture of polymers with a single branch point on their structure in solvents. Many physical properties of polymer liquids strongly dependent on the size and shape measures of individual macromolecules, which in turn are determined by their topology. Here, we use combination of analytical theory, based on path integration method, and molecular dynamics simulations to study structural properties of complex Gaussian polymers containing fc linear branches and fr closed loops grafted to the central core. We determine size measures such as the gyration radius Rg and the hydrodynamic radii RH, and obtain the estimates for the size ratio Rg/RH with its dependence on the functionality f=fc+fr of grafted polymers. In particular, we obtain the quantitative estimate of the degree of compactification of these polymers with increasing number of closed loops fr as compared to linear or star-shape molecules of the same total molecular weight. Numerical simulations corroborate theoretical prediction that Rg/RH decreases towards unity with increasing f. These findings provide qualitative description of polymers with complex architecture in theta solvents.