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Register a new userDynamics and Rheology of Ring-Linear Blend Semidilute Solutions in Extensional Flow: Single Molecule Experiments
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Ring polymers exhibit unique flow properties due to their closed chain topology. Despite recent progress, we have not yet achieved a full understanding of the nonequilibrium flow behavior of rings in nondilute solutions where intermolecular interactions greatly influence chain dynamics. In this work, we directly observe the dynamics of DNA rings in semidilute ring-linear polymer blends using single molecule techniques. We systematically investigate ring polymer relaxation dynamics from high extension and transient and steady-state stretching dynamics in planar extensional flow for a series of ring-linear blends with varying ring fraction. Our results show multiple molecular sub-populations for ring relaxation in ring-linear blends, as well as large conformational fluctuations for rings in steady extensional flow, even long after the initial transient stretching process has subsided. We further quantify the magnitude and characteristic timescales of ring conformational fluctuations as a function of blend composition. Interestingly, we find that the magnitude of ring conformational fluctuations follows a non-monotonic response with increasing ring fraction, first increasing at low ring fraction and then substantially decreasing at large ring fraction in ring-linear blends. A unique set of ring polymer conformations are observed during the transient stretching process, which highlights the prevalence of molecular individualism and supports the notion of complex intermolecular interactions in ring-linear polymer blends. Together with results from molecular simulations, our results suggest that ring conformational fluctuations arise due to ring-linear threading and intermolecular hydrodynamic interactions (HI). Taken together, our results provide a new molecular understanding of ring polymer dynamics in ring-linear blends in nonequilibrium flow.
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Extensive molecular simulations are applied to characterize the equilibrium dynamics, entanglement topology, and nonlinear extensional rheology of symmetric ring-linear polymer blends with systematically varied ring fraction $phi_R$. Chains with degree of entanglement $Zapprox14$ mixed to produce 10 well-entangled systems with $phi_R$ varying from neat linear to neat ring melts. Primitive path analysis are used to visualize and quantify the structure of the composite ring-linear entanglement network. We directly measure the quantity of ring-linear threading and linear-linear entanglement as a function of $phi_R$, and identify with simple arguments a ring fraction $phi_Rapprox0.4$ where the topological constraints of the entanglement network are maximized. These topological analyses are used to rationalize the $phi_R$-dependence of ring and linear chain dynamics, conformations, and blend viscosity. Complimentary simulations of startup uniaxial elongation flows demonstrate the extensional stress overshoot observed in recent filament stretching experiments, and characterize how it depends on the blend composition and entanglement topology. The overshoot is driven by an overstretching and recoil of ring polymer conformations that is caused by the convective unthreading of rings from linear chains. This produces significant changes in the entanglement structure of blends that we directly visualize and quantify with primitive path analyses during flow.
I review single-molecule experiments (SME) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SME it is possible to: manipulate molecules one at a time and measure distributions describing molecular properties; characterize the kinetics of biomolecular reactions and; detect molecular intermediates. SME provide the additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SME it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level emphasizing the importance of SME to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques. The review discusses SME from an experimental perspective, first exposing the most common experimental methodologies and later presenting various molecular systems where such techniques have been applied. I briefly discuss experimental techniques such as atomic-force microscopy (AFM), laser optical tweezers (LOT), magnetic tweezers (MT), biomembrane force probe (BFP) and single-molecule fluorescence (SMF). I then present several applications of SME to the study of nucleic acids (DNA, RNA and DNA condensation), proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discuss applications of SME to the study of the nonequilibrium thermodynamics of small systems and the experimental verification of fluctuation theorems. I conclude with a discussion of open questions and future perspectives.
Although the behavior of fluid-filled vesicles in steady flows has been extensively studied, far less is understood regarding the shape dynamics of vesicles in time-dependent oscillatory flows. Here, we investigate the nonlinear dynamics of vesicles in large amplitude oscillatory extensional (LAOE) flows using both experiments and boundary integral (BI) simulations. Our results characterize the transient membrane deformations, dynamical regimes, and stress response of vesicles in LAOE in terms of reduced volume (vesicle asphericity), capillary number ($Ca$, dimensionless flow strength), and Deborah number ($De$, dimensionless flow frequency). Results from single vesicle experiments are found to be in good agreement with BI simulations across a wide range of parameters. Our results reveal three distinct dynamical regimes based on vesicle deformation: pulsating, reorienting, and symmetrical regimes. We construct phase diagrams characterizing the transition of vesicle shapes between pulsating, reorienting, and symmetrical regimes within the two-dimensional Pipkin space defined by $De$ and $Ca$. Contrary to observations on clean Newtonian droplets, vesicles do not reach a maximum length twice per strain rate cycle in the reorienting and pulsating regimes. The distinct dynamics observed in each regime result from a competition between the flow frequency, flow time scale, and membrane deformation timescale. By calculating the particle stresslet, we quantify the nonlinear relationship between average vesicle stress and strain rate. Additionally, we present results on tubular vesicles that undergo shape transformation over several strain cycles. Broadly, our work provides new information regarding the transient dynamics of vesicles in time-dependent flows that directly informs bulk suspension rheology.
We investigate the dynamics of nanoparticles in semidilute polymer solutions when the nanoparticles are comparably sized to the polymer coils using explicit- and implicit-solvent simulation methods. The nanoparticle dynamics are subdiffusive on short time scales before transitioning to diffusive motion on long time scales. The long-time diffusivities scale according to theoretical predictions based on full dynamic coupling to the polymer segmental relaxations. In agreement with our recent experiments, however, we observe that the nanoparticle subdiffusive exponents are significantly larger than predicted by the coupling theory over a broad range of polymer concentrations. We attribute this discrepancy in the subdiffusive regime to the presence of an additional coupling mechanism between the nanoparticle dynamics and the polymer center-of-mass motion, which differs from the polymer relaxations that control the long-time diffusion. This coupling is retained even in the absence of many-body hydrodynamic interactions when the long-time dynamics of the colloids and polymers are matched.
The tumbling dynamics of individual polymers in semidilute solution is studied by large-scale non-equilibrium mesoscale hydrodynamic simulations. We find that the tumbling time is equal to the non-equilibrium relaxation time of the polymer end-to-end distance along the flow direction and strongly depends on concentration. In addition, the normalized tumbling frequency as well as the widths of the alignment distribution functions for a given concentration-dependent Weissenberg number exhibit a weak concentration dependence in the cross-over regime from a dilute to a semidilute solution. For semidilute solutions a universal behavior is obtained. This is a consequence of screening of hydrodynamic interactions at polymer concentrations exceeding the overlap concentration.
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