Glassy polymers show strain hardening: at constant extensional load, their flow first accelerates, then arrests. Recent experiments under such loading have found this to be accompanied by a striking dip in the segmental relaxation time. This can be explained by a minimal nonfactorable model combining flow-induced melting of a glass with the buildup of stress carried by strained polymers. Within this model, liquefaction of segmental motion permits strong flow that creates polymer-borne stress, slowing the deformation enough for the segmental (or solvent) modes to then re-vitrify. Here we present new results for the corresponding behavior under step-stress shear loading, to which very similar physics applies. To explain the unloading behavior in the extensional case requires introduction of a crinkle factor describing a rapid loss of segmental ordering. We discuss in more detail here the physics of this, which we argue involves non-entropic contributions to the polymer stress, and which might lead to some important differences between shear and elongation. We also discuss some fundamental and possibly testable issues concerning the physical meaning of entropic elasticity in vitrified polymers. Finally we present new results for the startup of steady shear flow, addressing the possible role of transient shear banding.
Viscosity overshoot of entangled polymer melts has been observed under shear flow and uniaxial elongational flow, but has never been observed under biaxial elongational flow. We confirmed the presence of viscosity overshoot under biaxial elongational flows observed in a mixed system of ring and linear polymers expressed by coarse-grained molecular dynamics simulations. The overshoot was found to be more pronounced in weakly entangled melts. Furthermore, the threshold strain rate $\dot{\varepsilon}_{\rm th}$ distinguishing linear and nonlinear behaviors was found to be dependent on the linear c…
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…
Blends of multicyclic and linear polymers under biaxial elongational flow were analyzed using coarse-grained molecular dynamics simulations. The multicyclic/linear blends displayed overshoot in the normal stress difference at the start-up of biaxial elongational flow. This overshoot was steeper for multicyclic/linear blends than for our previously reported monocyclic/linear blends [T. Murashima, K. Hagita, and T. Kawakatsu, Macromolecules, 2021, 54, 7210]. Investigation of the origin of the overshoot in the multicyclic/linear blends revealed a different mechanism than that previously observed …
We show that in monomeric supercooled liquids and glasses that are plastically flowing at a constant shear stress $σ$ while being deformed with strain rate $\dotε$, the microscopic structural relaxation time $τ_{\rm str}$ is given by the universal relation $σ/G_\infty\dotε$ with $G_\infty$ a modulus. This equality holds for all rheological regimes from temperatures above the glass transition all the way to the athermal limit, and arises from the competing effects of elastic loading and viscous dissipation. In macromolecular (polymeric) glasses, however, the stress decouples from this relaxatio…
The excess low-frequency vibrational spectrum, called boson peak, and non-affine elastic response are the most important particularities of glasses. Herein, the vibrational and mechanical properties of polymeric glasses are examined by using coarse-grained molecular dynamics simulations, with particular attention to the effects of the bending rigidity of the polymer chains. As the rigidity increases, the system undergoes a glass transition at a higher temperature (under a constant pressure), which decreases the density of the glass phase. The elastic moduli, which are controlled by the decreas…
Amorphous materials exhibit peculiar mechanical and vibrational properties, including non-affine elastic responses and excess vibrational states, i.e., the so-called boson peak. For polymer glasses, these properties are considered to be affected by the bending rigidity of the constituent polymer chains. In our recent work [Tomoshige, et al., Sci. Rep. 9 19514 (2019)], we have revealed simple relationships between the variations of vibrational properties and the global elastic properties: the response of the boson peak scales only with that of the global shear modulus. This observation suggests…
Semiflexible polymer glasses (SPGs), including those formed by the recently synthesized semiflexible conjugated polymers (SCPs), are expected to be brittle because classical formulas for their craze extension ratio $λ_{\rm craze}$ and fracture stretch $λ_{\rm frac}$ predict that systems with $N_e = C_\infty$ have $λ_{\rm craze} = λ_{\rm frac} = 1$ and hence cannot be deformed to large strains. Using molecular dynamics simulations, we show that in fact such glasses can form stable crazes with $λ_{\rm craze} \simeq N_e^{1/4} \simeq C_\infty^{1/4}$, and that they fracture at $λ_{\rm frac} = (3N_e…
Elucidating the physics of a concentrated suspension of ring polymers, or of an ensemble of ring polymers in a complex environment, is an important outstanding question in polymer physics. Many of the characteristic features of these systems arise due to topological interactions between polymers, or between the polymers and the environment, and it is often challenging to describe this quantitatively. Here we review recent research which suggests that a key role is played by inter-ring threadings (or penetrations), which become more abundant as the ring size increases. As we discuss, the physic…
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；School of Science, Constructor University（康斯坦茨大学理学院）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）
Tunneling dynamics of side chains and defects in proteins, polymer glasses, and OH-doped network glasses
在Lennard-Jones计算机玻璃上进行模拟，以研究低温下玻璃中的缺陷所产生的影响。数值分析表明，已经低浓度的缺陷可能会显着改变的低温性能，引起外在的双阱电位（DWP的）。这些非本征DWP的主要特征是（i）高势垒高度，（ii）高概率的缺陷确实与非本征DWP连接，（iii）高度本地化的动力学围绕这个缺陷，和（iv）较小的变形势耦合到声子。设计一个扩展的标准隧道模型（STM）参数化这张照片和比较与超声实验的湿网络$a$ O $_3$表明，OH-杂质的影响是准确的。然后将该模型应用于有机聚合物玻璃和蛋白质。有人建议，侧基可能会像掺杂杂质一样起作用，因为外在DWP的诱导，它具有一个分布的障碍，峰值周围的高势垒高度。这与内在DWP的，这是与骨干动力学的无结构分布的势垒高度相比。结果表明，这一图像是一致的聚合物的弹性测量，并可以解释异常的非对数线加宽最近在PMMA烧孔实验中观察到的。
Focusing on simulated polymer glasses well below the glass transition, we confirm the validity and the efficiency of the recently proposed simple-average expression $G(t) = μ_A - h(t)$ for the computational determination of the shear stress relaxation modulus $G(t)$. Here, $μ_A = G(0)$ characterizes the affine shear transformation of the system at $t=0$ and $h(t)$ the mean-square displacement of the instantaneous shear stress as a function of time $t$. This relation is seen to be particulary useful for systems with quenched or sluggish transient shear stresses which necessarily arise below the…
Using molecular dynamics simulation of a standard coarse-grained polymer glass model we investigate by means of the stress-fluctuation formalism the shear modulus $μ$ as a function of temperature $T$ and sampling time $Δt$. While the ensemble-averaged modulus $μ(T)$ is found to decrease continuously for all $Δt$ sampled, its standard deviation $δμ(T)$ is non-monotonous with a striking peak at the glass transition. Confirming the effective time-translational invariance of our systems, $μ(Δt)$ can be understood using a weighted integral over the shear-stress relaxation modulus $G(t)$. While the …
The relaxation of polymers around and below their glass transition temperature is governed by a range of correlated unit processes with a wide range of timescales. The fast deformation rates of shock loading can negate a significant fraction of these processes resulting in the dynamical glass transition in rubbers. In this letter we report the inverse, a transient melting of glassy polymer under shock loading. The large deviatoric stresses near the shock front induce fast transitions in backbone dihedral angles and a stress relaxation characteristic of polymer melts. This is followed by the sl…
The linear and nonlinear rheological behavior of two rod-like particle suspensions as a function of concentration is studied using small amplitude oscillatory shear, steady shear and capillary breakup extensional rheometry. The rod-like suspensions are composed of fd virus and its mutant fdY21M, which are perfectly monodisperse, with a length on the order of 900 nm. The particles are semi flexible yet differ in their persistence length. The effect of stiffness on the rheological behavior in both, shear and extensional flow, is investigated experimentally. The linear viscoelastic shear data is …
We investigate by means of molecular dynamics simulation a coarse-grained polymer glass model focusing on (quasi-static and dynamical) shear-stress fluctuations as a function of temperature T and sampling time $Δt$. The linear response is characterized using (ensemble-averaged) expectation values of the contributions (time-averaged for each shear plane) to the stress-fluctuation relation $μ_{sf}$ for the shear modulus and the shear-stress relaxation modulus $G(t)$. Using 100 independent configurations we pay attention to the respective standard deviations. While the ensemble-averaged modulus $…
The relation between elasticity and yielding is investigated in a model polymer solid by Molecular-Dynamics simulations. By changing the bending stiffness of the chain and the bond length, semicrystalline and disordered glassy polymers - both with bond disorder - as well as nematic glassy polymers with bond ordering are obtained. It is found that in systems with bond disorder the ratio Ty/G between the shear yield strength Ty and the shear modulus G is close to the universal value of the atomic metallic glasses. The increase of the local nematic order in glasses leads to the increase of the sh…
