Dynamics and Rheology of Ring-Linear Blend Semidilute Solutions in Extensional Flow: Modeling and Molecular Simulations.

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). The streamlines determined from BD simulation are qualitatively comparable to elastic instabilities in cross-slot flow of polymer solutions, and we speculate that the dynamics of solution blends may be understood by deviations of the flow from planar extension. 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. Comparing 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.