Chain topology has a profound impact on the flow behavior of single macromolecules. For circular polymers, the absence of free ends results in a unique chain architecture compared to linear or branched chains, thereby generating distinct dynamics. In this work, we use single molecule techniques to investigate the dynamics of ring polymers in dilute and semi-dilute solutions in planar extensional flow, including polymer relaxation from high stretch, transient stretching dynamics in step-strain experiments, and steady-state stretching in flow. In this work, we use fluorescently labeled circular DNA as ring polymers, which naturally provides monodisperse rings for single molecule experiments. In the first set of studies, we preformed a series of controlled strain-rate experiments on ring polymers in ultra-dilute solutions in planar extensional flow using precision microfluidics. [1,2]
Our results show that the longest relaxation times of rings follow a power-law scaling relation with molecular weight that differs from linear chains. Also, relative to their linear counterparts, circular DNA molecules show a shifted coil-to-stretch transition and less diverse "molecular individualism" behavior as evidenced by their conformational stretching pathways. These results show the impact of chain topology on dynamics and reveal commonalities in the steady state behavior of circular and linear DNA that extends beyond chain architecture. We further compared our experimental results with Brownian dynamics (BD) simulations, and we confirmed the shifted coil-to-stretch transition is due to coupling of intra-molecular hydrodynamic interactions in the presence of architectural constraints. In a second set of studies, we extended single polymer experiments to study the dynamics of ring polymers in background solutions of semi-dilute linear polymers and semi-dilute ring polymers. This work represents the first single molecule measurement and direct observation of ring polymer dynamics in semi-dilute solutions under flow. Interestingly, we observe distinct "threading behavior" of single ring polymers in a sea of semi-dilute linear polymers, which results in qualitatively different dynamics compared to linear chains. We observe strong inhibition of polymer extension and strikingly large fluctuations
in steady-state polymer extension for ring polymers in flow, demonstrating the strong interplay between polymer topology and polymer concentration. Taken together, our work aims to provide a molecular-level understanding of the role of polymer concentration and topology in non-dilute polymer solutions via direct observation of single chain dynamics in strong flow.
 Y. Li, K. Hsiao, C. A. Brockman, D. Y. Yates, R. M. Robertson-Anderson, J. A. Kornfield,
M. J. San Francisco, C. M. Schroeder, and G. B. McKenna, "When ends meet: Circular DNA stretches differently in elongational flows," Macromolecules, 48, 5997-6001 (2015).
 K. Hsiao, C. M. Schroeder, and C. E. Sing, "Ring polymer dynamics are governed by a coupling between architecture and hydrodynamic interactions," Macromolecules, 49, 1961-1971 (2016).