Local Strain Relaxation Dictates Polymer Melt Viscosity

柔性和半柔性环状熔体的粘度——分子起源与流动诱导的分离

Viscosity of flexible and semiflexible ring melts -- molecular origins and flow-induced segregation

该研究通过数值模拟对比了柔性与半柔性环状熔体与线性链系统的粘度分子起源，发现环刚度增加导致缠结簇形成并在剪切下解体，引发剪切变稀与非牛顿行为，且流动会使柔性/半柔性环共混物分离，可用于微流控分离。

Shear viscosity of a crosslinked polymer melt

We investigate the static shear viscosity on the sol side of the vulcanization transition within a minimal mesoscopic model for the Rouse-dynamics of a randomly crosslinked melt of phantom polymers. We derive an exact relation between the viscosity and the resistances measured in a corresponding random resistor network. This enables us to calculate the viscosity exactly for an ensemble of crosslinks without correlations. The viscosity diverges logarithmically as the critical point is approached. For a more realistic ensemble of crosslinks amenable to the scaling description of percolation, we …

Universal collapse of the viscosity of supercooled fluids

All liquids in nature can be supercooled to form a glass. Surprisingly, although this phenomenon has been employed for millennia, it still remains ill-understood. Perhaps the most puzzling feature of supercooled liquids is the dramatic increase in their viscosity as the temperature ($T$) is lowered. This precipitous rise has long posed a fundamental theoretical challenge. Numerous approaches currently attempt to explain this phenomenon. When present, data collapse points to an underlying simplicity in various branches of science. In this Letter, we report on a 16 decade data collapse of the vi…

Variational bounds for the shear viscosity of gelling melts

We study shear stress relaxation for a gelling melt of randomly crosslinked, interacting monomers. We derive a lower bound for the static shear viscosity $η$, which implies that it diverges algebraically with a critical exponent $k\ge 2ν-β$. Here, $ν$ and $β$ are the critical exponents of percolation theory for the correlation length and the gel fraction. In particular, the divergence is stronger than in the Rouse model, proving the relevance of excluded-volume interactions for the dynamic critical behaviour at the gel transition. Precisely at the critical point, our exact results imply a Mark…

阐明聚合物熔体在稳态剪切流下的分子构象与剪切粘度之间的相关性

Elucidation of the Correlation between Molecular Conformation and Shear Viscosity of Polymer Melts under Steady-State Shear Flow

研究通过分子动力学模拟探讨聚合物熔体中分子构象与剪切稀化行为的关系，发现分子构象的各向异性与剪切粘度存在明确的标度关系，揭示链伸展方向控制有效摩擦力。

基于振动模式的非仿射理论计算聚合物熔体的粘度

Viscosity of polymer melts using non-affine theory based on vibrational modes

本研究应用非仿射晶格动力学（NALD）和瞬态简正模分析方法计算Kremer-Grest聚合物系统在不同温度下的粘度，发现所有振动模式均对粘度有贡献，为玻璃化转变附近等系统提供了高效粘度计算框架。

On the nonlocal viscosity kernel of mixtures

In this report we investigate the multiscale hydrodynamical response of a liquid as a function of mixture composition. This is done via a series of molecular dynamics simulations where the wave vector dependent viscosity kernel is computed for three mixtures each with 7-15 different compositions. We observe that the nonlocal viscosity kernel is dependent on composition for simple atomic mixtures for all the wave vectors studied here, however, for a model polymer melt mixture the kernel is independent of composition for large wave vectors. The deviation from ideal mixing is also studied. Here i…

Relating Chain Conformations to Extensional Stress In Entangled Polymer Melts

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…

Viscosity Overshoot in Biaxial Elongational Flow: Coarse-Grained Molecular Dynamics Simulation of Ring-Linear Polymer Mixtures

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…

Temperature-Controlled Slip of Polymer Melts on Ideal Substrates

The temperature dependence of the hydrodynamic boundary condition between a PDMS melt and two different non-attractive surfaces made of either an OTS (octadecyltrichlorosilane) self-assembled monolayer (SAM) or a grafted layer of short PDMS chains has been characterized. A slip length proportional to the fluid viscosity is observed on both surfaces. The slip temperature dependence is deeply influenced by the surfaces. The viscous stress exerted by the polymer liquid on the surface is observed to follow exactly the same temperature dependences as the friction stress of a cross-linked elastomer …

长链支化、短链支化和多分散性对聚合物熔体压敏流变学的影响

Effects of long-chain branching, short-chain branching, and polydispersity on pressure sensitive rheology of polymer melts

研究长链支化、短链支化和多分散性对聚乙烯熔体压敏流变学的影响，用高压滑动板流变仪表征四种聚乙烯熔体，发现分子支链是控制流变响应的主要结构参数，为高压聚合物加工预测模型提供见解。

Rheology of Ring Polymer Melts: From Linear Contaminants to Ring/Linear Blends

Ring polymers remain a major challenge to our current understanding of polymer dynamics. Experimental results are difficult to interpret because of the uncertainty in the purity and dispersity of the sample. Using both equilibrium and non-equilibrium molecular dynamics simulations we have systematically investigated the structure, dynamics and rheology of perfectly controlled ring/linear polymer blends with chains of such length and flexibility that the number of entanglements is up to about 14 per chain, which is comparable to experimental systems examined in the literature. The smallest conc…

The rigidity transition in polymer melts with van der Waals interactions

We study the onset of rigidity near the glass transition (GT) in a short-chain polymer melt modelled by a bead-spring model, where all beads interact with Lennard-Jones potentials. The properties of the system are examined above and below the GT. In order to minimize high cooling-rate effects and computational times, equilibrium configurations are reached via isothermal compression. We monitor quantities such as the heat capacity C_P, the short-time diffusion constants D, the viscosity η, and the shear modulus; the time-dependent shear modulus G(t) is compared with the shear modulus μobtained …

Friction of polymers: from PDMS melts to PDMS elastomers

The slip behavior of polydimethylsiloxane (PDMS) polymer melts flowing on non-adsorbing surfaces made of short non-entangled PDMS chains densely end-grafted to silica has been characterized. For high enough shear rates, constant slip lengths proportional to the bulk fluid viscosity have been observed, in agreement with Navier's interfacial equation, and demonstrating that the interfacial Navier's friction coefficient is a local quantity, independent of the polymer molecular weight. Comparing the interfacial shear stresses deduced from these measured slip lengths to available friction stress me…

链刚度对线形和环形聚合物熔体中Cox-Merz规则失效的影响

Effects of chain stiffness on the breakdown of the Cox-Merz rule in linear and ring polymer melts

本研究通过分子动力学模拟发现，Cox-Merz规则在线形聚合物熔体中的失效随链长和链刚度增加而加剧，而环形聚合物保持较好一致性，表明其适用性依赖链长、刚度和分子拓扑。

Rheology of a Supercooled Polymer Melt

Molecular dynamics simulations are performed for a polymer melt composed of short chains in quiescent and sheared conditions. The stress relaxation function $G(t)$ exhibits a stretched exponential form in a relatively early stage and ultimately follows the Rouse function in quiescent supercooled state. Transient stress evolution after application of shear obeys the linear growth $\int_0^t dt'G(t')$ for strain less than 0.1 and then saturates into a non-Newtonian viscosity. In steady states, strong shear-thinning and elongation of chains into ellipsoidal shapes are found at extremely small shea…

Temperature dependence of the slip length in polymer melts at attractive surfaces

Using Couette and Poiseuille flow, we extract the temperature dependence of the slip length, $δ$, from molecular dynamics simulations of a coarse-grained polymer model in contact with an attractive, corrugated surface. $δ$ is dictated by the ratio of bulk viscosity and surface mobility. At weakly attractive surfaces, a lubrication layer forms, $δ$ is large and increases upon cooling. Close to the glass transition temperature, $T_ g$, very large slip lengths are observed. At a more attractive surface, a``stick y surface layer" is build up, which gives rise to a small slip length. Upon cool ing,…

Dynamics and Rheology of a Supercooled Polymer Melt in Shear Flow

Using molecular dynamics simulations, we study dynamics of a model polymer melt composed of short chains with bead number N=10 in supercooled states. In quiescent conditions, the stress relaxation function $G(t)$ is calculated, which exhibits a stretched exponential relaxation on the time scale of the $α$ relaxation time $τ_α$ and ultimately follows the Rouse dynamics characterized by the time $τ_{\rm R} \sim N^2 τ_α$. After application of shear $\gdot$, transient stress growth $σ_{xy}(t)/\gdot$ first obeys the linear growth $\int_0^t dt'G(t')$ for strain less than 0.1 but saturates into a non…

Polymer threadings and rigidity dictate the viscoelasticity and nonlinear relaxation dynamics of entangled ring-linear blends and their composites with rigid rod microtubules

Mixtures of polymers of varying topologies and stiffnesses display complex emergent rheological properties that often cannot be predicted from their single-component counterparts. For example, entangled blends of ring and linear polymers have been shown to exhibit enhanced shear thinning and viscosity, as well as prolonged relaxation timescales, compared to pure solutions of rings or linear chains. These emergent properties arise in part from the synergistic threading of rings by linear polymers. Topology has also been shown to play an important role in composites of flexible (e.g., DNA) and s…

Slip boundary conditions for shear flow of polymer melts past atomically flat surfaces

Molecular dynamics simulations are carried out to investigate the dynamic behavior of the slip length in thin polymer films confined between atomically smooth thermal surfaces. For weak wall-fluid interactions, the shear rate dependence of the slip length acquires a distinct local minimum followed by a rapid growth at higher shear rates. With increasing fluid density, the position of the local minimum is shifted to lower shear rates. We found that the ratio of the shear viscosity to the slip length, which defines the friction coefficient at the liquid/solid interface, undergoes a transition fr…

Molecular Dynamics Simulation Study of Nonconcatenated Ring Polymers in a Melt: II. Dynamics

Molecular dynamics simulations were conducted to investigate the dynamic properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers. The longest rings were composed of N=1600 monomers per chain which corresponds to roughly 57 entanglement lengths for comparable linear polymers. The ring melts were found to diffuse faster than their linear counterparts, with the self-diffusion coefficient for both architectures scaling as approximately N to the -2.4 power for large N. The mean-square displacement of the center-of-mass of the rings follows a sub-diffusive behav…

Crystal nucleation mechanism in melts of short polymer chains under quiescent conditions and under shear flow

We present a molecular dynamics simulation study of crystal nucleation from undercooled melts of n-alkanes, and we identify the molecular mechanism of homogeneous crystal nucleation under quiescent conditions and under shear flow. We compare results for n-eicosane(C20) and n-pentacontahectane(C150), i.e. one system below the entanglement length and one above. Under quiescent conditions, we observe that entanglement does not have an effect on the nucleation mechanism. For both chain lengths, the chains first align and then straighten locally. Then the local density increases and finally positio…

未缠结聚合物熔体中非线性剪切流变的取向起源

Orientational origin of nonlinear shear rheology in unentangled polymer melts

本文通过拉伸-取向分解构建本构模型，揭示未缠结聚合物熔体非线性剪切流变的取向起源，模型再现稳态剪切标度并预测有限第二法向应力系数。

Static and dynamic properties of the interface between a polymer brush and a melt of identical chains

Molecular dynamics simulations of a short-chain polymer melt between two brush-covered surfaces under shear have been performed. The end-grafted polymers which constitute the brush have the same chemical properties as the free chains in the melt and provide a soft deformable substrate. Polymer chains are described by a coarse-grained bead-spring model with Lennard-Jones interactions between the beads and a FENE potential between nearest neighbors along the backbone of the chains. The grafting density of the brush layer offers a way of controlling the behavior of the surface without altering th…

Breakdown of time-temperature superposition in a bead-spring polymer melt near the glass transition temperature

The breakdown of the time-temperature superposition (TTS) near its glass transition temperature (Tg) in simple bead-spring polymer melts with and without the chain angle potential was numerically investigated. The stress relaxation modulus at different temperatures G(t,T) was calculated by the Green-Kubo relation. The TTS of G(t,T) of bead-spring polymer melts worked well at temperatures sufficiently higher than its Tg. However, when the system temperature is approaching the glass transition regime, the breakdown of TTS is observed. At temperatures near the Tg, the temperature dependence of th…

Slip-controlled thin film dynamics

In this study, we present a novel method to assess the slip length and the viscosity of thin films of highly viscous Newtonian liquids. We quantitatively analyse dewetting fronts of low molecular weight polystyrene melts on Octadecyl- (OTS) and Dodecyltrichlorosilane (DTS) polymer brushes. Using a thin film (lubrication) model derived in the limit of large slip lengths, we can extract slip length and viscosity. We study polymer films with thicknesses between 50 nm and 230 nm and various temperatures above the glass transition. We find slip lengths from 100 nm up to 1 micron on OTS and between …

Understanding the dynamics of rings in the melt in terms of annealed tree model

Dynamical properties of a long polymer ring in a melt of unknotted and unconcatenated rings are calculated. We re-examine and generalize the well known model of a ring confined to a lattice of topological obstacles in the light of the recently developed Flory theory of unentangled rings which maps every ring on an annealed branched polymer and establishes that the backbone associated with each ring follows self-avoiding rather than Gaussian random walk statistics. We find the scaling of ring relaxation time and diffusion coefficient with ring length, as well as time dependence of stress relaxa…

玻璃物理的2/3规则暗示了晶体熔化的普遍性

The 2/3 Rule of Glass Physics Implies Universalities in Crystal Melting

本文基于玻璃物理的2/3规则，揭示了晶体熔化过程中液体粘度和弛豫时间的差异源于协同性，挑战了传统林德曼准则的主导地位。

单轴拉伸流中对称与非对称星形聚合物缠结熔体的Primitive Chain Network模拟

Primitive Chain Network Simulations of Entangled Melts of Symmetric and Asymmetric Star Polymers in Uniaxial Elongational Flows

本研究通过多链滑结模拟探究对称与非对称星形聚合物缠结熔体的拉伸行为，结合Rouse时间计算与SORF效应，揭示了不同结构下拉伸粘度相近的多重作用机制，半定量复现了实验结果。

Dynamic rheology of a supercooled polymer melt in non-uniform oscillating flows in rapidly oscillating plates

The dynamic rheology of a polymer melt composed of short chains with ten beads between rapidly oscillating plates is investigated for various oscillation frequencies by using the hybrid simulation of the molecular dynamics and computational fluid dynamics. In the rapidly oscillating plates, non-uniform boundary layer flows are generated over the plate due to inertia of the fluid, and the local rheological properties of the melt are spatially varied according to the local flow fields. Far from the plate, the local strain decreases as the oscillation frequency increases such that the dynamic rhe…

Capillary leveling of stepped films with inhomogeneous molecular mobility

A homogeneous thin polymer film with a stepped height profile levels due to the presence of Laplace pressure gradients. Here we report on studies of polymeric samples with precisely controlled, spatially inhomogeneous molecular weight distributions. The viscosity of a polymer melt strongly depends on the chain length distribution; thus, we learn about thin-film hydrodynamics with viscosity gradients. These gradients are achieved by stacking two films with different molecular weights atop one another. After a sufficient time these samples can be well described as having one dimensional viscosit…

幂律分子量分布决定高度多分散聚合物溶液中的普遍行为

Power-law molecular-weight distributions dictate universal behaviors in highly polydisperse polymer solutions

研究发现，幂律分子量分布指数a控制聚合物溶液的集体行为，揭示了多分散系统中粘度、重叠浓度和纠缠浓度的显著变化。

i-Rheo-Tempo：一种无需四则运算的复杂粘度到剪切松弛模量重建方法

i-Rheo-Tempo: A Model-Free, Quadrature-Free Reconstruction of the Shear Relaxation Modulus from Complex Viscosity

本文提出一种无需四则运算的模型无关方法，通过复杂粘度的二阶导数表示直接从动态测量中重建剪切松弛模量，验证了其在多种复杂流体中的有效性。

Self-organising Dissipative Polymer Structures

In frameworks of the scaling theory of phase transitions and critical phenomena the quantitative dependence of macroscopic properties on nanostructural parameters in a polymeric material is revealed. The draw ratios at neck and at break are referred to the macroscopic properties. The structure is characterized by an average thickness of amorphous layers in isotropic melt-crystallized linear high density polyethylene which is chosen as an example. The square of the neck draw ratio is equal to the product of the square of the draw ratio at break and the chain ends collision probability. This pro…

Shear Induced Pressure Determines a Reduction in Polymer Radius

Shear induced particle pressure has been measured and modelled for concentrated suspensions of particles. Importantly, the significance of the shear induced particle pressure has not been recognized in polymer rheology. The shear induced particle pressure results in an inward pressure on the polymer chains resulting in a shear dependent compressive force. The analytical form of the force balance equations that incorporate the effect of shear induced particle pressure predict a reduced polymer blob size and reducing viscosity with increasing shear rate as has been observed experimentally. Power…

Thermodynamic scaling of dynamics in polymer melts: Predictions from the generalized entropy theory

Many glass-forming fluids exhibit a remarkable thermodynamic scaling in which dynamic properties, such as the viscosity, the relaxation time, and the diffusion constant, can be described under different thermodynamic conditions in terms of a unique scaling function of the ratio rho^gamma/T, where rho is the density, T is the temperature, and gamma is a material dependent constant. Given the successes of the generalized entropy theory in elucidating the influence of molecular details on the universal properties of glass-forming polymers, this theory is extended here to investigate the thermodyn…