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...

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 molecular dynamics. Here, we report the direct observation of circular DNA dynamics in transient and steady flows for molecular sizes spanning the range of 25.0−114.8 kilobase pairs (kbp). Our results show that the longest relaxation times of the rings follow a power-law scaling relation with molecular weight that differs from that of 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.

Understanding the dynamics of ring polymers is a particularly challenging yet interesting problem in soft materials. Despite recent progress, a complete understanding of the nonequilibrium behavior of ring polymers has not yet been achieved. In this work, we directly observe the flow dynamics of DNA-based rings in semidilute linear polymer solutions using single molecule techniques. Our results reveal strikingly large conformational fluctuations of rings in extensional flow long after the initial transient stretching process has terminated, which is observed even at extremely low concentrations (0.025 c * ) of linear polymers in the background solution. The magnitudes and characteristic timescales of ring conformational fluctuations are determined as functions of flow strength and polymer concentration. Our results suggest that ring conformational fluctuations arise due to transient threading of linear polymers through open ring chains stretching in flow.

The behavior of linear polymer chains in dilute solution flows has an established history. Polymers often possess more complex architectures, however, such as branched, dendritic, or ring structures. A major challenge lies in understanding how these nonlinear chain topologies affect the dynamic properties in nonequilibrium conditions, in both dilute and entangled solutions. In this work, we interrogate the single-chain dynamics of ring polymers using a combination of simulation, theory, and experiment. Inspired by recent experimental results by Li et al., we demonstrate that the presence of architectural constraints has surprising and pronounced effects on the dynamic properties of polymers as they are driven out of equilibrium. Ring constraints lead to two behaviors that contrast from linear chains. First, the coil−stretch transition occurs at larger values of the dimensionless flow strength (Weissenberg number) compared to linear chains, which is driven by coupling between intramolecular hydrodynamic interactions (HI) and chain architecture. Second, a large loop conformation is observed for ring polymers in extensional flow at intermediate to large Weissenberg numbers, and we show that this open loop conformation is driven by intramolecular HI. Our results reveal the emergence of new paradigms in chain architecture− hydrodynamic coupling that may be relevant for solution-based processing of polymeric materials and could provide new opportunities for precise flow-based polymer conformation control to guide material properties.

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.