Single molecule visualization of single ring polymers in the flow-gradient plane of shear flow*

The lack of free ends on ring polymers yields a unique topology that has fascinated polymer physicists and chemists for decades. Despite recent progress, we still lack a clear understanding of the molecular-level dynamics of ring polymers. Here, we use single-molecule imaging to directly visualize individual ring polymers in shear flow. We have built a custom shear flow apparatus to be used in conjunction with single-molecule fluorescence microscopy to study the dynamics of individual ring polymers in the flow-gradient shear flow. Using this device, we are able to characterize the fractional extension and orientation angle of ring polymers under steady shear, and compare the responses to their linear counterparts. We report the steady-shear fractional extension, orientation angle, and temporal-averaged spatial conformations of ring polymers in shear flow as a function of the applied dimensionless flow strength (Wi, Weissenberg number), and compare the results to their linear polymer counterparts. We also report observations of tumbling and tank-treading-like behavior of ring polymers in shear flow. Overall, these results provide new molecular-level insights into the dynamics of ring polymers in flow.