The dynamic behavior of semi-dilute polymer solutions is governed by an interplay between solvent quality, concentration, molecular weight, and flow type. 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 'self-entangle' in semi-dilute solutions, thereby leading to 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 λ-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 τ ∼ (c/c * ) 0.48 in semi-dilute solutions, where c is polymer concentration and c * is the overlap concentration. Based on these results, an effective excluded volume exponent ν ≈ 0.56 was found, which is in good agreement with recent bulk rheological experiments. We further studied the nonequilibrium stretching dynamics of semi-dilute polymer solutions, including transient (1 c * ) and steady-state (0.2 c * and 1 c * ) 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, a decrease in transient polymer stretch in semidilute solutions at moderate Weissenberg number (W i) compared to dilute solutions is observed.Moreover, our experiments reveal a milder coil-to-stretch transition for semi-dilute polymer solutions at 0.2 c * and 1 c * compared to dilute solutions. Interestingly, a unique set of molecular conformations during the transient stretching process for single polymers in semi-dilute solutions is observed, which suggests transient stretching pathways for polymer chains in semi-dilute solutions are qualitatively different compared to dilute solutions due to intermolecular interactions.Taken together, this work provides a molecular framework for understanding the non-equilibrium stretching dynamics of semi-dilute solutions in strong flows. * cms@illinois.eduThe dynamics of semi-dilute polymer solutions is an intriguing yet particularly challenging problem in soft materials and rheology. Dilute polymer solutions are characterized by the rarity of overlap of single chains, whereas concentrated solutions and melts are governed by topological entanglements and dense polymer phases. Unentangled semi-dilute solutions, however, are characterized by coil-coil interpenetration at equilibrium, albeit in the absence of intermolecular entanglements under quiescent conditions. From this view, the d...

Extensional rheometry and Brownian Dynamics simulations of flexible polymer solutions confirm predictions based on blob concepts that coil-stretch hysteresis in extensional flows increases with concentration, reaching a maximum at the critical overlap concentration c * before progressively vanishing in the semidilute regime. These observations demonstrate that chain stretching strengthens intermolecular hydrodynamic screening in dilute solutions, but weakens it in semidilute solutions. Flow can thus strongly modify the concentration dependence of viscoelastic properties of polymer solutions.

The dynamics of individual DNA molecules in semidilute solutions undergoing planar extensional flow is simulated using a multi-particle Brownian dynamics algorithm, which incorporates hydrodynamic and excluded volume interactions in the context of a coarse-grained bead-spring chain model for DNA. The successive fine-graining protocol [1,2], in which simulation data acquired for bead-spring chains with increasing values of the number of beads N b , is extrapolated to the number of Kuhn steps NK in DNA (while keeping key physical parameters invariant), is used to obtain parameter-free predictions for a range of Weissenberg numbers and Hencky strain units. A systematic comparison of simulation predictions is carried out with the experimental observations of Hsiao et al. [3], who have recently used single molecule techniques to investigate the dynamics of dilute and semidilute solutions of λ-phage DNA in planar extensional flow. In particular, they examine the response of individual chains to step-strain deformation followed by cessation of flow, thereby capturing both chain stretch and relaxation in a single experiment. The successive fine-graining technique is shown to lead to quantitatively accurate predictions of the experimental observations in the stretching and relaxation phases. Additionally, the transient chain stretch following a step strain deformation is shown to be much smaller in semidilute solutions than in dilute solutions, in agreement with experimental observations.

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