(284e) Direct Observation of Linear and Circular Polymers in Non-Equilibrium Flows: Single Molecule Studies of Topology and Entanglements

Over the past two decades, advances in fluorescence imaging and particle manipulation have enabled the direct observation of single polymer dynamics. The vast majority of studies, however, has focused on dilute linear chain dynamics under simple model flow fields. There is a critical need to study the dynamics of single polymers with complex chain topologies in densely entangled solutions and under non-idealized flow fields. In one experiment, we investigate the transient dynamics of ring-shaped (or circular) polymers in semi-dilute unentangled solutions of linear chains (c* < c < c_e) in extensional flow.¹ Interestingly, our results show that ring polymer exhibit markedly less molecular individualism compared to their linear counterparts during transient stretching in extensional flow, which is attributed to circular topological constraints. Moreover, our results show that ring polymers drastically fluctuate in chain extension, even at steady-state, which has not observed for steady-state stretching of linear polymers in semi-dilute unentangled solutions. We hypothesize that these fluctuations arise due to “threading” of linear polymers through open ring polymer chains in flow. The fluctuation frequency as a function of strain rate and concentration is further quantified. In a second experiment, we directly observe the relaxation dynamics of linear tracer polymers in a background of linear entangled polymers (c_e < c < c**).² Our results reveal a fundamentally new behavior through the emergence of multiple relaxation modes upon increasing concentration in the lightly entangled regime. It is known that concentrated polymer solutions exhibit complex dynamic behavior due to an interplay between topological entanglements and non-equilibrium effects in flow, and our single molecule experiments directly reveal the emergence of molecular sub-populations in the entangled regime. Our results show that single polymer relaxation trajectories exhibit either a single-mode or double-mode exponential decay, which starkly contrasts relaxation behaviors from dilute and semi-dilute unentangled solutions. As polymer concentration is increased from 2.8 c* to 15.3 c*, the fraction of molecules that exhibit single-mode exponential decay behavior decreases, whereas the fraction of double-mode exponential trajectories increases, with nearly all relaxation modes showing a double exponential response at high concentrations. In all cases, we interpret the power law scalings of these relaxation times as a function of concentration. Taken together, these results reveal fundamentally new information regarding the behavior of polymer chain relaxation for lightly entangled solutions. Finally, we discuss related work on the first experimental study of single polymer dynamics in large amplitude oscillatory extensional flow (LAOE).^3-4 Here, we study dynamics in both small amplitude and large amplitude sinusoidal oscillatory extensional flow in a cross-slot microfluidic device, while imaging the conformational dynamics of single DNA polymers as a function of the Weissenberg number (Wi, flow strength) and Deborah number (De, probing frequency). Interestingly, we characterize transient chain dynamics by constructing single molecule Lissajous curves, which are defined based on chain conformation and stretching in flow. In addition, we further extend this study to circular polymers under LAOE, which reveals a rich set of dynamics due to the circular chain topology.

[1]. Y. Zhou, K.-W. Hsiao, K. E. Regan, G. B. McKenna, R. M. R. Anderson and C. M. Schroeder, “Single circular polymer dynamics in semi-dilute solutions”, in preparation (2018)

[2]. Y. Zhou and C. M. Schroeder, “Dynamically heterogeneous relaxation of entangled polymer chains”, submitted (2018)

[3]. Y. Zhou and C. M. Schroeder, “Single polymer dynamics under large amplitude oscillatory extension”, Physical Review Fluids, 1(5), 053301 (2016)

[4]. Y. Zhou and C. M. Schroeder, “Transient and average unsteady dynamics of single polymers in large-amplitude oscillatory extension”, Macromolecules, 49(20), 8018-8030 (2016)