We derive an effective Maxwell-London equation for entangled polymer complex under the topological constraint, borrowing the theoretical framework from the topological field theory. We find that the transverse current flux of the test polymer chain, surrounded with entangled chains, decays exponentially from its average position with finite penetration depth, which is analogous to the magnetic-field decay in a superconductor (SC). Like as the mass acquirement of photons in SC is the origin of the magnetic-field decay, the polymer earns uncrossible intersections along the chain due to the preserved linking number, which restricts the deviation of the transverse polymer current in the normal direction. Interestingly, this picture is well incorporated with the most successful phenomenological theory of the so called tube model, of which researchers have long pursued its microscopic origin. The correspondence of our equation of motion to the tube model claims that the confining tube potential is a consequence of the topological constraint (linking number). The tube radius is attributed to the decay length, and increasing the retracting force at intersections or increasing the number of intersections (linking number), the tube becomes narrow and tighter. It further shows that the probability of the tube leakage decays exponentially with the decay length of tube radius.
We present a new reduced-order computational method for the molecular dynamics simulation of entangled polymer systems. The polymer chains are modeled as continuous Gaussian chains. Our algorithm is based on the application of the molecular dynamics simulation method to the pseudospectral representation of the Fourier modes of the chains.
Entanglement of polymer chains is ubiquitous in elastomers, gels, and biological tissues. While the effects of chain entanglement on elasticity and viscoelasticity of polymer networks have been intensively studied, it remains elusive how chain entanglement affects fracture and fatigue of polymer networks. In this paper, using polyacrylamide hydrogels as a model material, we systematically compare fracture toughness and fatigue threshold of polymer networks with various levels of chain entanglement. We find that the fracture toughness and fatigue threshold of an unentangled polymer network are …
Equilibration of polymer melts containing highly entangled long polymer chains in confinement or with free surfaces is a challenge for computer simulations. We approach this problem by first studying polymer melts based on the soft-sphere coarse-grained model confined between two walls with periodic boundary conditions in two directions parallel to the walls. Then we apply backmapping to reinsert the microscopic details of the underlying bead-spring model. Tuning the strength of the wall potential, the monomer density of confined polymer melts in equilibrium is kept at the bulk density even ne…
We investigated the elongational flows of the weakly entangled linear polymer melt using a coarse-grained molecular dynamics simulation. We extended the uniform extensional flow (UEF) method developed by Nicholson and Rutledge (D. A. Nicholson and G. C. Rutledge, J. Chem. Phys., 145, 244903 (2016)) for application to Langevin dynamics. We succeeded in observing the elongational viscosity of the weakly entangled linear polymer melt from the equilibrium state to the steady state using the extended UEF method, whereas the conventional rectangular parallelepiped shape technique for extensional flo…
The spatial correlations of entangled polymer dynamics are examined by molecular dynamics simulations and neutron spin-echo spectroscopy. Due to the soft nature of topological constraints, the initial spatial decays of intermediate scattering functions of entangled chains are, to the first approximation, surprisingly similar to those of an unentangled system in the functional forms. However, entanglements reveal themselves as a long tail in the reciprocal-space correlations, implying a weak but persistent dynamic localization in real space. Comparison with a number of existing theoretical mode…
We analyze the capillarity-driven thinning dynamics of entangled polymer solutions described by the Doi-Edwards-Marrucci-Grizzuti (DEMG) model and the Rolie-Poly (RP) model. Both models capture polymer reptation, finite rates of chain retraction and finite extensibility of single polymer molecules, while differing slightly in their final form regarding to the convective constraint release. We calculate numerically the filament thinning profiles predicted by the two models with realistic entanglement densities, assuming cylindrical filament shapes and no fluid inertia. Both results reveal an ea…
Nonlinear extensional flows are common in polymer processing but remain challenging theoretically because dramatic stretching of chains deforms the entanglement network far from equilibrium. Here, we present coarse-grained simulations of extensional flows in entangled polymer melts for Rouse-Weissenberg numbers $Wi_R=0.06$-$52$ and Hencky strains $ε\geq6$. Simulations reproduce experimental trends in extensional viscosity with time, rate and molecular weight. Studies of molecular structure reveal an elongation and thinning of the confining tube with increasing $Wi_R$. The rising stress is quan…
Single-filament tracing has been a valuable tool to directly determine geometrical and mechanical properties of entangled polymer networks. However, systematically verifying how the stiffness of the tracer filament or its molecular interactions with the surrounding network impacts the measurement of these parameters has not been possible with the established experimental systems. Here, we use mechanically programmable DNA nanotubes embedded in crosslinked and entangled F-actin networks, as well as in synthetic DNA networks, in order to measure fundamental, structural network properties like tu…
The classical rheological theories of entangled polymeric liquids are built upon two pillars: Gaussian statistics of entanglement strands and the assumption that the stress arises exclusively from the change of intramolecular configuration entropy. We show that these two hypotheses are not supported by molecular dynamics simulations of polymer melts. Specifically, the segment distribution functions at the entanglement length scale and below deviate considerably from the theoretical predictions, in both the equilibrium and deformed states. Further conformational analysis reveals that the intrac…
Based on non-equilibrium molecular dynamics simulations of entangled polymer melts, a recent Letter [Phys. Rev. Lett. $\textbf{121}$, 047801 (2018), arXiv:1806.09509] claims that the rising extensional stress is quantitatively consistent with the decreasing entropy of chains at the equilibrium entanglement length. We point out that exactly the opposite is true: the intrachain entropic stress arising from individual entanglement strands generally does not agree with the total "macroscopic" stress. The conclusion of the Letter is based on an incomplete and questionable analysis of a limited rang…
We use computer simulations to study the relaxation of strongly deformed highly entangled polymer melts in the non-linear viscoelastic regime, focusing on anisotropic chain conformations after isochoric elongation. The Doi-Edwards tube model and its GLaMM extension, incorporating contour length fluctuation and convective constraint release, predict a retraction of the polymer chain extension in all directions, setting in immediately after deformation. This prediction has been challenged by experiment, simulation, and other theoretical studies, questioning the general validity of the tube conce…
We report observations of a remarkable scaling behavior with respect to concentration in the passive microbead rheology of two highly entangled polymeric solutions, polyethylene oxide (PEO) and hyaluronic acid (HA). This behavior was reported previously [Hill et al., PLOS ONE (2014)] for human lung mucus, a complex biological hydrogel, motivating the current study for synthetic polymeric solutions PEO and HA. The strategy is to identify, and focus within, a wide range of lag times $τ$ for which passive micron diameter beads exhibit self-similar (fractional, power law) mean-squared-displacement…
In this paper we study a system of entangled chains that bear reversible cross-links in a melt state. The cross-links are tethered uniformly on the backbone of each chain. A slip-link type model for the system is presented and solved for the relaxation modulus. The effects of entanglements and reversible cross-linkers are modelled as discrete form of constraints that influence the motion of the primitive path. In contrast to a non-associating entangled system the model calculations demonstrate that the elastic modulus has a much higher first plateau and a delayed terminal relaxation. These eff…
The widely used double-bridging hybrid (DBH) method for equilibrating simulated entangled polymer melts [R. Auhl et al., J. Chem. Phys. v. 119, p. 12718, 2003] loses its effectiveness as chain stiffness increases into the semiflexible regime because the energy barriers associated with double-bridging Monte Carlo moves become prohibitively high. Here we overcome this issue by combining DBH with the use of core-softened pair potentials. This reduces the energy barriers substantially, allowing us to equilibrate melts with $N \simeq 40 N_e$ and chain stiffnesses all the way up to the isotropic-nem…
Single Chain Slip-Spring Model for Fast Rheology Simulations of Entangled Polymers on GPU
本文在Likhtman [A. E. Likhtman，Macromolecules，38，6128（2005）]，用于在GPU上缠结聚合物的快速流变学模拟。为了在GPU上进行有效的计算，我们稍微修改了原始的滑动弹簧模型。我们的模型被设计成满足细致平衡条件，这使我们能够很容易地分析其静态或线性响应特性。我们从理论上分析了模型的一些统计特性，如线性响应，这将有助于分析模拟数据。我们表明，我们的模型可以重现几个流变特性，如线性粘弹性或粘度增长定性。我们还表明，使用GPU可以大大提高性能。
In this work, we explore the dynamics of active entangled chains using molecular dynamics simulations of a modified Kremer-Grest model. The active chains are diluted in a mesh of very long passive linear chains, to avoid constraint release effects, and an active force is applied to the monomers in a way that it imparts a constant polar drift velocity along the primitive path. The simulation results show that, over a wide range of activity values, the conformational properties of the chains and the tubes are not affected, but the dynamics of the chains are severely modified. Despite not having …
Understanding how entanglements affect the behaviour of polymeric complex fluids is an open challenge in many fields. To elucidate the nature and consequence of entanglements in dense polymer solutions, we propose a novel method: a "dynamical entanglement analysis" (DEA) to extract spatio-temporal entanglement structures from the pair-wise displacement correlation of entangled chains. By applying this method to large-scale Molecular Dynamics simulations of linear and unknotted, nonconcatenated ring polymers, we find a strong and unexpected cooperative dynamics: the footprint of mutual entrainm…
Optical tweezers microrheology (OTM) offers a powerful approach to probe the nonlinear response of complex soft matter systems, such as networks of entangled polymers, over wide-ranging spatiotemporal scales. OTM can also uniquely characterize the microstructural dynamics that lead to the intriguing nonlinear rheological properties that these systems exhibit. However, the strain in OTM measurements, applied by optically forcing a micro-probe through the material, induces network inhomogeneities in and around the strain path, and the resultant flow field complicates the measured response of the…
The Monte Carlo carbyne model is modified to investigate the glass transition of the semi-flexible entangled polymer chains. The stochastic bombardment between monomers are monitored by Metropolis algorithm with help of the consideration of hard potential while the mobility of monomers is governed by its mass, scattering rate and temperature. Our model is capable to show that the glass transition temperature reduces with decreasing film thickness and the formation of critical voids in the thinner polymer contributing to the glass transition that is much easier than the bulk polymer.
Using high-resolution confocal rheometry, we study the shear profiles of well-entangled DNA solutions under large amplitude oscillatory shear (LAOS) in a rectilinear planar shear cell. With increasing Weissenberg number (Wi), we observe successive transitions from normal Newtonian linear shear profiles to wall-slip dominant shear profiles and finally to shear-banding profiles at high Wi. To investigate the microscopic origin of the observed shear banding, we study the dynamics of micron-sized tracers embedded in DNA solutions. Surprisingly, tracer particles in the shear frame exhibit transient…
Stress relaxation following deformation of an entangled polymeric liquid is thought to be affected by transient reforming of chain entanglements. In this work, we use single molecule techniques to study the relaxation of individual polymers in the transition regime from unentangled to entangled solutions. Our results reveal the emergence of dynamic heterogeneity underlying polymer relaxation behavior, including distinct molecular sub-populations described by a single-mode and a double-mode exponential relaxation process. The slower double-mode timescale $τ_{d,2}$ is consistent with a character…
Dynamics of semi-flexible polymer solutions in the highly entangled regime
我们提出的实验证据表明，由D. C. Morse [Phys. Rev. E { \bf 63}，031502，（2001）]提出的有效介质近似（EMA）提供了宏观平台模量$G^{0}\proptoρ^{4/3}L^{-1/3}_{p}$的正确标度律（其中$ρ$是每单位体积的轮廓长度，$L_{p}$是持久长度），在高度纠缠的浓度范围内。竞争的理论，包括自洽的二元碰撞近似（BCA），而不是预测$G^{0}\proptoρ^{7/5}L^{-1/5}_{p}$。我们已经测试了EMA和BCA缩放预测使用肌动蛋白丝（F-肌动蛋白）的解决方案，允许实验控制$L_p$独立于其他参数。被动视频粒子跟踪微流变学和动态光散射的组合产生的弹性模量$G$和$L_{p}$分别独立的测量。因此，我们可以区分这两个建议的法律，在以前的实验研究，重点是（歧视性较低）的浓度功能的$G$。
A Force-Level Theory of the Rheology of Entangled Rod and Chain Polymer Liquids. I. Tube Deformation, Microscopic Yielding and the Nonlinear Elastic Limit
Polydispersity is inevitable in industrially produced polymers. Established theories of polymer dynamics and rheology, however, were mostly built on monodisperse linear polymers. Dynamics of polydisperse polymers is yet to be fully explored -- especially how chains of different lengths affect the dynamics of one another in a mixture. This study explored the dynamics of bidisperse polymer melts using molecular dynamics and a bead-spring chain model. Binary mixtures between a moderately entangled long-chain species and an unentangled or marginally entangled short-chain species were investigated.…
Polymer composites are ideal candidates for next generation biomimetic soft materials because of their exquisite bottom-up designability. However, the richness of behaviours comes at a price: the need for precise and extensive characterisation of material properties over a highly-dimensional parameter space, as well as a quantitative understanding of the physical principles underlying desirable features. Here we couple large-scale Molecular Dynamics simulations with optical tweezers microrheology to characterise the viscoelastic response of DNA-actin composites. We discover that the previously…
Non-equilibrium tube length fluctuations of entangled polymers
我们研究了初始拉伸的缠结高分子链在松弛过程中的非平衡管长涨落。管长度的时间依赖性方差$σ^2$在早期状态下遵循起源于聚合物链段的扩散运动的简单通用幂律$σ^2 = A \sqrt{t}$。从标准蠕动理论和精确可解的格子气蠕动模型中解析计算了振幅$A$，并讨论了振幅与初始管长和平衡管长的关系。非普遍性表明测量的波动（例如，使用荧光显微镜）作为爬行动物模型的测试。
