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

The present research is dedicated to provide deeper understanding of the impact of complex architecture of branched polymers on their behaviour in solvents. The folding dynamics of macromolecules and hydrodynamics of polymer fluids are strongly dependent on size and shape measures of single macromolecules, which in turn are determined by their topology. For this aim, we use combination of analytical theory, based on path integration method, and molecular dynamics simulations to study structural properties of complex Gaussian polymers containing $f^c$ linear branches and $f^r$ closed loops grafted to the central core. Using theory we determine the size measures such as gyration radius $R_g$ and the hydrodynamic radii $R_H$, and obtain the estimates for the size ratio $R_g /R_H$ with its dependence on the functionality $f=f^c+f^r$ of grafted polymers. In particular, we obtain the quantitative estimate of compactification (decrease of size measure) of such complex polymer architectures with increasing number of closed loops $f^r$ as compared with linear or star-shape molecules of the same total molecular weight. Numerical simulations corroborate theoretical prediction that $R_g /R_H$ decreases towards unity with increasing $f$. These findings provide qualitative description of complex polymers with different arm architecture in $\theta$ solutions.