  We use Brownian dynamics (BD) simulations and single molecule experiments to
investigate the influence of topological constraints and hydrodynamic
interactions on the dynamics and rheology of solutions of ring-linear polymer
blends at the overlap concentration. We find agreement between simulation and
experiment in that rings in solution blends exhibit large conformational
fluctuations, including extension overshoots in the startup of flow and
tumbling and tank-treading at steady state. Ring polymer fluctuations increase
with blend fraction of linear polymers and are peaked at a ring Weissenberg
number $\textrm{Wi}_R \approx 1.5$. On the contrary, linear and ring polymers
in pure solutions show a peak in fluctuations at the critical coil-stretch
Weissenberg number $\textrm{Wi} = 0.5$. BD simulations show that extension
overshoots on startup of flow are due to flow-induced intermolecular
ring-linear polymer hooks, whereas fluctuations at steady state are dominated
by intermolecular hydrodynamic interactions (HI). This is supported by
simulations of bidisperse linear polymer solution blends, which show similar
trends in conformational dynamics between rings and linear polymers with a
matched contour length. Compared to BD simulations, single molecule experiments
show quantitatively larger fluctuations, which could arise because experiments
are performed on higher molecular weight polymers with stronger topological
constraints. To this end, we have advanced the understanding of the effects of
topological interactions and intermolecular HI on the dynamics of semidilute
ring-linear polymer blend solutions.
