(291i) Single Polymer Dynamics of Linear and Circular Chains in Semi-Dilute Solutions

Semi-dilute polymer solutions are commonly encountered in a wide array of applications, including inkjet printing and advanced 3D printing technologies. Semi-dilute solutions are characterized by large fluctuations in polymer concentration, wherein polymer coils interpenetrate but may not be topologically entangled at equilibrium. In non-equilibrium flows, it is generally thought that polymer chains can â??self-entangleâ?? in semi-dilute solutions, thereby leading to topological entanglements in solutions that are nominally unentangled at equilibrium. Despite recent progress in the field, we still lack a complete molecular-level understanding of the dynamics of polymer chains in semi-dilute solutions. In this work, we use single molecule techniques to investigate the dynamics of dilute and semi-dilute solutions of lambda-phage DNA in planar extensional flow, including polymer relaxation from high stretch, transient stretching dynamics in step-strain experiments, and steady-state stretching in flow. Our results are consistent with a power-law scaling of the longest polymer relaxation time (c/c*)^0.48 in semi-dilute solutions, where c is polymer concentration and c* is the overlap concentration. Based on these results, we found an effective excluded volume exponent ν = 0.56, which is in good agreement with recent bulk rheological experiments on semi-dilute DNA solutions.

We also studied the non-equilibrium stretching dynamics of semi-dilute polymer solutions, including transient and steady-state stretching dynamics in planar extensional flow using an automated microfluidic trap. Our results show that polymer stretching dynamics in semi-dilute solutions is a strong function of concentration. In particular, we observe a decrease in transient polymer stretch in semi-dilute solutions at moderate Weissenberg number Wi compared to dilute solutions, with the difference in polymer stretch between dilute and semi-dilute solutions decreasing for Wi > 1. Moreover, our experiments reveal a milder coil-to-stretch transition for semi-dilute polymer solutions compared to dilute solutions, which is interpreted in the context of a critical Wi at the coil-to-stretch transition. Interestingly, we observe a unique set of molecular conformations during the transient stretching process for single polymers in semi-dilute solutions, which suggests that the transient stretching pathways for polymer chains in semi-dilute solutions is qualitatively different compared to dilute solutions due to intermolecular interactions. ^[1,2]

We further extended single polymer experiments to study the dynamics of ring polymers in ultra-dilute solutions^[3] and in background solutions of semi-dilute linear 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. Using fluorescently labeled circular DNA as ring polymers, we preformed a series of controlled strain-rate experiments on ring polymers in unlabeled semi-dilute linear background in planar extensional flow using precision microfluidics. 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. ^[3,4]

[1] K. Hsiao, C. Sasmal, J. R. Prakash, and C. M. Schroeder, "Direct observation of DNA dy�namics in semi-dilute solutions in extensional flow," submitted (2016).

[2] C. Sasmal, K. Hsiao, J. R. Prakash, and C. M. Schroeder, "Stretch relaxation of DNA molecules in semi-dilute solutions," submitted (2016).

[3] 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).

[4] 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).