Origin of Stress Overshoot during Startup Shear of Entangled Polymer Melts

Nonlinear Actin Deformations Lead to Network Stiffening, Yielding, and Nonuniform Stress Propagation

We use optical tweezers microrheology and fluorescence microscopy to apply nonlinear microscale strains to entangled and cross-linked actin networks, and measure the resulting stress and actin filament deformations. We couple nonlinear stress response and relaxation to the velocities and displacements of individual fluorescent-labeled actin segments, at varying times throughout the strain and varying distances from the strain path, to determine the underlying molecular dynamics that give rise to the debated nonlinear response and stress propagation of cross-linked and entangled actin networks at the microscale. We show that initial stress stiffening arises from acceleration of strained filaments due to molecular extension along the strain, while softening and yielding is coupled to filament deceleration, halting, and recoil. We also demonstrate a surprising nonmonotonic dependence of filament deformation on cross-linker concentration. Namely, networks with no cross-links or substantial cross-links both exhibit fast initial filament velocities and reduced molecular recoil while intermediate cross-linker concentrations display reduced velocities and increased recoil. We show that these collective results are due to a balance of network elasticity and force-induced cross-linker unbinding and rebinding. We further show that cross-links dominate entanglement dynamics when the length between cross-linkers becomes smaller than the length between entanglements. In accord with recent simulations, we demonstrate that post-strain stress can be long-lived in cross-linked networks by distributing stress to a small fraction of highly strained connected filaments that span the network and sustain the load, thereby allowing the rest of the network to recoil and relax.

Correction: Finite cohesion due to chain entanglement in polymer melts

Correction for 'Finite cohesion due to chain entanglement in polymer melts' by Shiwang Cheng et al., Soft Matter, 2016, 12, 3340-3351.

Correction: Nonlinear rheology of entangled polymers at turning point

Correction for 'Nonlinear rheology of entangled polymers at turning point' by Shi-Qing Wang et al., Soft Matter, 2015, 11, 1454-1458.

DNA as a Model for Probing Polymer Entanglements: Circular Polymers and Non-Classical Dynamics

Double-stranded DNA offers a robust platform for investigating fundamental questions regarding the dynamics of entangled polymer solutions. The exceptional monodispersity and multiple naturally occurring topologies of DNA, as well as a wide range of tunable lengths and concentrations that encompass the entanglement regime, enable direct testing of molecular-level entanglement theories and corresponding scaling laws. DNA is also amenable to a wide range of techniques from passive to nonlinear measurements and from single-molecule to bulk macroscopic experiments. Over the past two decades, researchers have developed methods to directly visualize and manipulate single entangled DNA molecules in steady-state and stressed conditions using fluorescence microscopy, particle tracking and optical tweezers. Developments in microfluidics, microrheology and bulk rheology have also enabled characterization of the viscoelastic response of entangled DNA from molecular levels to macroscopic scales and over timescales that span from linear to nonlinear regimes. Experiments using DNA have uniquely elucidated the debated entanglement properties of circular polymers and blends of linear and circular polymers. Experiments have also revealed important lengthscale and timescale dependent entanglement dynamics not predicted by classical tube models, both validating and refuting new proposed extensions and alternatives to tube theory and motivating further theoretical work to describe the rich dynamics exhibited in entangled polymer systems.

Flow of DNA in micro/nanofluidics: From fundamentals to applications

Thanks to direct observation and manipulation of DNA in micro/nanofluidic devices, we are now able to elucidate the relationship between the polymer microstructure and its rheological properties, as well as to design new single-molecule platforms for biophysics and biomedicine. This allows exploration of many new mechanisms and phenomena, which were previously unachievable with conventional methods such as bulk rheometry tests. For instance, the field of polymer rheology is at a turning point to relate the complex molecular conformations to the nonlinear viscoelasticity of polymeric fluids (such as coil-stretch transition, shear thinning, and stress overshoot in startup shear). In addition, nanofluidic devices provided a starting point for manipulating single DNA molecules by applying basic principles of polymer physics, which is highly relevant to numerous processes in biosciences. In this article, we review recent progress regarding the flow and deformation of DNA in micro/nanofluidic systems from both fundamental and application perspectives. We particularly focus on advances in the understanding of polymer rheology and identify the emerging research trends and challenges, especially with respect to future applications of nanofluidics in the biomedical field.

Finite cohesion due to chain entanglement in polymer melts

Three different types of experiments, quiescent stress relaxation, delayed rate-switching during stress relaxation, and elastic recovery after step strain, are carried out in this work to elucidate the existence of a finite cohesion barrier against free chain retraction in entangled polymers. Our experiments show that there is little hastened stress relaxation from step-wise shear up to γ = 0.7 and step-wise extension up to the stretching ratio λ = 1.5 at any time before or after the Rouse time. In contrast, a noticeable stress drop stemming from the built-in barrier-free chain retraction is predicted using the GLaMM model. In other words, the experiment reveals a threshold magnitude of step-wise deformation below which the stress relaxation follows identical dynamics whereas the GLaMM or Doi-Edwards model indicates a monotonic acceleration of the stress relaxation dynamics as a function of the magnitude of the step-wise deformation. Furthermore, a sudden application of startup extension during different stages of stress relaxation after a step-wise extension, i.e. the delayed rate-switching experiment, shows that the geometric condensation of entanglement strands in the cross-sectional area survives beyond the reptation time τd that is over 100 times the Rouse time τR. Our results point to the existence of a cohesion barrier that can prevent free chain retraction upon moderate deformation in well-entangled polymer melts.

Torsional Linearity in Nonlinear Stress-Optical Regimes for Polymeric Materials

The birefringence on anisotropic materials under flow has been tremendously useful for understanding the physical states of nonequilibrium materials. It is, however, well-known that the linear relationship between the anisotropy of the stress and that of the birefringence breaks down above a certain flow strength, severely limiting its practical applicability. Here we present an encouraging result which helps overcome this limitation and extends our knowledge beyond the conventional the stress-optical rule regime. Through a detailed molecular-level analysis of the stress-optical behaviors of various polyethylene melts under shear via direct atomistic nonequilibrium molecular dynamics simulations, we found a universal feature in the stress-optical behaviors of polymeric materials that there exists a strictly linear relationship between the birefringence tensor and the stress tensor contributed solely by the bond-torsional interaction in the whole range of flow strength. While a limited range of chain length and architecture (unentangled and moderately entangled linear and H-shaped polymer melts) under shear flow was investigated in this study, the main features and conclusions as drawn are considered to be general and valid regardless of (i) the chain length and molecular architecture, (ii) flow types, and (iii) force fields of polymeric materials. They are further useful as guidance in developing an accurate coarse-grained polymer model.

In-chain functionalized polymer induced assembly of nanoparticles: toward materials with tailored properties

We adopt a molecular dynamics simulation method to describe the self-assembly of nanoparticles in in-chain functionalized polymers. In such novel systems, the organization of nanoparticles is governed by the interplay of the intrinsic attractions between nanoparticles and the entropy of redistributing the functionalized polymers that are adsorbed on the nanoparticles. Our simulations also demonstrate that this approach to nanoparticle assembly enables considerable control for the creation of polymer nanocomposites with tailored properties.

Tube Dynamics Works for Randomly Entangled Rings

The tube model is the cornerstone of molecular theory for polymer rheology. We test its microscopic assumptions by simulating topologically equilibrated ring polymers, whose dynamics is free from end segment relaxation. We show that a closed-form expression derived from the tube model adapted to ring polymers quantitatively predicts the segmental mean squared displacements over the entire range of time scales from local motion to complete equilibration, with a time-independent local friction factor.

Simulating Startup Shear of Entangled Polymer Melts

Start-up shear rheology is a standard experiment used for characterizing polymer flow, and to test various models of polymer dynamics. A rich phenomenology is developed for behavior of entangled monodisperse linear polymers in such tests, documenting shear stress overshoots as a function of shear rates and molecular weights. A tube theory does a reasonable qualitative job at describing these phenomena, although it involves several drastic approximations and the agreement can be fortuitous. Recently, Lu and co-workers published several papers [e.g., Lu ACS Macro Lett. 2014, 3, 569-573] reporting results from molecular dynamics simulations of linear entangled polymers, which contradict both theory and experiment. On the basis of these observations, they made very serious conclusions about the tube theory, which seem to be premature. In this letter, we repeat simulations of Lu et al. and systematically show that neither their simulation results nor their comparison with theory is confirmed.

Perspectives on the viscoelasticity and flow behavior of entangled linear and branched polymers

We briefly review the recent advances in the rheology of entangled polymers and identify emerging research trends and outstanding challenges, especially with respect to branched polymers. Emphasis is placed on the role of well-characterized model systems, as well as the synergy of synthesis-characterization, rheometry and modeling/simulations. The theoretical framework for understanding the observed linear and nonlinear rheological phenomena is the tube model, which is critically assessed in view of its successes and shortcomings, and alternative approaches are briefly discussed. Finally, intriguing experimental findings and controversial issues that merit consistent explanation, such as shear banding instabilities, multiple stress overshoots in transient simple shear and enhanced steady-state elongational viscosity in polymer solutions, are discussed, and future directions such as branch point dynamics and anisotropic monomeric friction are outlined.

Entangled F-actin displays a unique crossover to microscale nonlinearity dominated by entanglement segment dynamics

We drive optically trapped microspheres through entangled F-actin at constant speeds and distances well beyond the linear regime, and measure the microscale force response of the entangled filaments during and following strain. Our results reveal a unique crossover to appreciable nonlinearity at a strain rate of [small gamma, Greek, dot above]c ≈ 3 s(-1) which corresponds remarkably well with the theoretical rate of relaxation of entanglement length deformations 1/τent. Above [small gamma, Greek, dot above]c, we observe stress stiffening which occurs over very short time scales comparable to the predicted timescale over which mesh size deformations relax. Stress softening then takes over, yielding to an effectively viscous regime over a timescale comparable to the entanglement length relaxation time, τent. The viscous regime displays shear thinning but with a less pronounced viscosity scaling with strain rate compared to flexible polymers. The relaxation of induced force on filaments following strain shows that the relative relaxation proceeds more quickly for increasing strain rates; and for rates greater than [small gamma, Greek, dot above]c, the relaxation displays a complex power-law dependence on time. Our collective results reveal that molecular-level nonlinear viscoelasticity is driven by non-classical dynamics of individual entanglement segments that are unique to semiflexible polymers.

Nonlinear rheology of entangled polymers at turning point

Thanks to extensive observations of strain localization upon startup or after stepwise shear, a conceptual framework for nonlinear rheology of entangled polymers appears to have emerged that has led to discovery of many new phenomena, which were not previously predicted by the standard tube model. On the other hand, the published theoretical and experimental attempts to test the limits of the tube model have largely demonstrated that the most experimental data appear consistent with the tube-model based theoretical calculations. Therefore, the field of nonlinear rheology of entangled polymers is at a turning point and is thus a rather crucial area in which further examinations are needed. In particular, more molecular dynamics simulations are needed to delineate the detailed molecular mechanisms for the various nonlinear rheological phenomena.

Origin of Stress Overshoot under Start-up Shear in Primitive Chain Network Simulation

Birefringence measurement demonstrates that the segment orientation of entangled polymers overshoots on start-up of fast shear [Pearson et al. J. Rheol. 1989 33, 517-535]. The stress-optical rule holds for those polymers, so that the overshoot of orientation results in the overshoot of shear stress. On the other hand, an opposite result was deduced from the recent molecular dynamics simulation for bead-spring chain [Lu et al. ACS Macro Lett. 2014 3, 569-573]: the evolution of segment orientation does not overshoot but the chain stretch induces the stress overshoot, even at the shear rate γ̇ smaller than the reciprocal Rouse time, 1/τ_R. In this study, we performed the primitive chain network simulation to find that our simulation reproduces the overshoot of both stress and orientation and the chain stretch exhibits a slight, monotonic increase but no overshoot. Our result is thus fully consistent with the experiment.

Nonlinear microrheology reveals entanglement-driven molecular-level viscoelasticity of concentrated DNA

We optically drive a trapped microscale probe through entangled DNA at rates up to 100× the disentanglement rate (Wi≈100), then remove the trap and track subsequent probe recoil motion. We identify a unique crossover to the nonlinear regime at Wi≈20. Recoil dynamics display rate-dependent dilation and complex power-law healing of the reptation tube. The force response during strain exhibits key nonlinear features such as shear thinning and yielding with power-law rate dependence. Our results, distinctly nonclassical and in accord with recent theoretical predictions, reveal molecular dynamics governed by individual stress-dependent entanglements rather than chain stretching.