Viscoelastic properties of polymer melts are particularly challenging to compute due to the intrinsic stress fluctuations in molecular dynamics (MD). We compared equilibrium and non-equilibrium MD approaches for extracting the storage (G') and loss moduli (G") over a wide frequency range from a bead-spring chain model, in both unentangled and entangled regimes. We found that, with properly chosen data processing and noise reduction procedures, different methods render quantitatively equivalent results. In equilibrium MD (EMD), applying the Green-Kubo relation with a multi-tau correlator method for noise filtering generates smooth stress relaxation modulus profiles, from which accurate G' and G" can be obtained. For unentangled chains, combining the Rouse model with a short-time correction provides a convenient option that circumvents the stress fluctuation challenge altogether. For non-equilibrium MD (NEMD), we found that combining a stress pre-averaging treatment with discrete Fourier transform analysis reliably computes G' and G" with much shorter simulation length than previously reported. Comparing the efficiency and statistical accuracy of these methods, we concluded that EMD is both reliable and efficient, and is suitable when the whole spectrum of linear viscoelastic properties is desired, whereas NEMD offers flexibility when only some frequency ranges are of interest.
We investigate previously unclarified effects of fluid elasticity on shear-thickening in dilute suspensions in an Oldroyd-B viscoelastic fluid using a novel direct numerical simulation based on the smoothed profile method. Fluid elasticity is determined by the Weissenberg number Wi and by viscosity ratio $1-β=η_p/(η_s+η_p)$ which measures the coupling between the polymer stress and flow: $η_p$ and $η_s$ are the polymer and solvent viscosity, respectively.As $1-β$ increases, while the stresslet does not change significantly compared to that in the $β\to 1$ limit, the growth rate of the normaliz…
The progressive onset of slip at the wall, which corresponds to a slip length increasing with the solicitation time before reaching a plateau, has been investigated for model viscoelastic polymer solutions, allowing one to vary the longest relaxation time while keeping constant solid - fluid interactions. A hydrodynamic model based on a Maxwell fluid and the classical Navier's hypothesis of a linear response for the friction stress at the interface fully accounts for the data, without any adjustable parameter. No viscoelastic response needs be postulated for the friction, reflecting the local …
We investigate the linear viscoelasticity of polymer gels produced by the dispersion of gluten proteins in water:ethanol binary mixtures with various ethanol contents, from pure water to 60% v/v ethanol. We show that the complex viscoelasticity of the gels exhibits a time/solvent composition superposition principle, demonstrating the self-similarity of the gels produced in different binary solvents. All gels can be regarded as near critical gels with characteristic rheological parameters, elastic plateau and characteristic relaxation time, which are related one to another, as a consequence of …
We present a theoretical framework for the linear and nonlinear visco-elastic properties of reversibly crosslinked networks of semiflexible polymers. In contrast to affine models where network strain couples to the polymer end-to-end distance, in our model strain rather serves to locally distort the network structure. This induces bending modes in the polymer filaments, the properties of wich are slaved to the surrounding network structure. Specifically, we investigate the frequency-dependent linear rheology, in particular in combination with crosslink binding/unbinding processes. We also deve…
We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear chains. We investigate the rheology of polymeric chains entangled into weaves with varying topologies and levels of chain density. To investigate viscoelastic responses, we perform non-equilibrium molecular simulations over a range of frequencies using sheared Lees-Edwards boundary conditions. We show how our topological characteristics can be used to capture k…
We consider models for elastic liquids, such as solutions of flexible polymers. They introduce a relaxation time $λ$ into the system, over which stresses relax. We study the kinematics of the problem, and clarify the relationship between Lagrangian and Eulerian descriptions, thereby showing which polymer models correspond to a nonlinear elastic deformation in the limit $λ\rightarrow\infty$. This allows us to split the change in elastic energy into reversible and dissipative parts, and thus to write an equation for the total energy, the sum of kinetic and elastic energies. As an illustration, w…
The effects of viscoelasticity on the dynamics and break-up of fluid threads in microfluidic T-junctions are investigated using numerical simulations of dilute polymer solutions at changing the Capillary number ($\mbox {Ca}$), i.e. at changing the balance between the viscous forces and the surface tension at the interface, up to $\mbox{Ca} \approx 3 \times 10^{-2}$. A Navier-Stokes (NS) description of the solvent based on the lattice Boltzmann models (LBM) is here coupled to constitutive equations for finite extensible non-linear elastic dumbbells with the closure proposed by Peterlin (FENE-P …
The evolution over time of the non-linear slip behavior of a polydimethylsiloxane (PDMS) polymer melt on a weakly adsorbing surface made of short non-entangled PDMS chains densely end-grafted to the surface of a fused silica prism has been measured. The critical shear rate at which the melt enters the nonlinear slip regime has been shown to increase with time. The adsorption kinetics of the melt on the same surface has been determined independently using ellipsometry. We show that the evolution of slip can be explained by the slow adsorption of melt chains using the Brochard-de Gennes's model.
We investigate the structure of gluten polymer-like gels in a binary mixture of water/ethanol, $50/50$ v/v, a good solvent for gluten proteins. Gluten comprises two main families of proteins, monomeric gliadins and polymer glutenins. In the semi-dilute regime, scattering experiments highlight two classes of behavior, akin to standard polymer solution and polymer gel, depending on the protein composition. We demonstrate that these two classes are encoded in the structural features of the proteins in very dilute solution, and are correlated with the presence of proteins assemblies of typical siz…
An extended Molecular-Dynamics study of the short-time "glassy" elasticity exhibited by a polymer melt of linear fully-flexible chains above the glass transition is presented. The focus is on the infinite-frequency shear modulus $G_\infty$ manifested in the picosecond time scale and the relaxed plateau $G_p$ reached at later times and terminated by the structural relaxation. The local stiffness of the interactions with the first neighbours of each monomer exhibits marked distribution with average value given by $G_\infty$. In particular, the neighbourhood of the end monomers of each chain are …
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…
Atomistic Framework for Glassy Polymer Viscoelasticity Across Twenty Frequency Decades
University of Milan（米兰大学）；University of Göttingen（哥廷根大学）；Graz University of Technology（格拉茨工业大学）；Polymer Competence Center Leoben GmbH（莱奥本聚合物能力中心有限公司）；US Army DEVCOM Army Research Laboratory（美国陆军DEVCOM陆军研究实验室）
Polymer gels behave as soft viscoelastic solids and exhibit a generic nonlinear mechanical response characterized by pronounced stiffening prior to irreversible failure, most often through macroscopic fractures. Here, we aim at capturing the latter scenario for a protein gel using a nonlinear integral constitutive equation built upon ($i$) the linear viscoelastic response of the gel, here well described by a power-law relaxation modulus, and ($ii$) the nonlinear viscoelastic properties of the gel, encoded into a "damping function". Such formalism predicts quantitatively the gel mechanical resp…
X-ray particle tracking velocimetry for steady-state rheological characterization: Case study of a complex polymer melt flow in material extrusion additive manufacturing
University of Stuttgart（斯图加特大学）；University of Milan（米兰大学）；CNR – Consiglio Nazionale delle Ricerche, Istituto di Chimica della Materia Condensata e di Tecnologie per l’Energia（意大利国家研究委员会凝聚态材料与能源技术研究所）
Orientational origin of nonlinear shear rheology in unentangled polymer melts
Department of Chemical Science and Engineering, Kyoto University（京都大学化学工程系）；Advanced Manufacturing Technology Institute, Kanazawa University（金泽大学先进制造技术研究所）
The effect of viscoelasticity on sprays produced from agricultural flat fan nozzles is investigated experimentally using dilute aqueous solutions of polyethylene oxide (PEO). Measurements of the droplet size distribution using laser diffraction reveal that polymer addition to water results in the formation of overall bigger droplets with a broader size distribution. The median droplet size $D_{50}$ is found to increase linearly with the extensional relaxation time of the liquid. The non-dimensional median droplet sizes of different polymer solutions, sprayed at different operating pressures fr…
Hydrodynamic slip of a liquid at a solid surface represents a fundamental phenomenon in fluid dynamics that governs liquid transport at small scales. For polymeric liquids, de Gennes predicted that the Navier boundary condition together with the theory of polymer dynamics imply extraordinarily large interfacial slip for entangled polymer melts on ideal surfaces; this Navier-de Gennes model was confirmed using dewetting experiments on ultra-smooth, low-energy substrates. Here, we use capillary leveling - surface tension driven flow of films with initially non-uniform thickness - of polymeric fi…
Polymer melts undergoing large deformation by uniaxial elongation are studied by molecular dynamics simulations of bead-spring chains in melts. Applying a primitive path analysis to strongly deformed polymer melts, the role of topological constrains in highly entangled polymer melts is investigated and quantified. We show that the over-all, large scale conformations of the primitive paths (PPs) of stretched chains follow affine deformation while the number and the distribution of entanglement points along the PPs do not. Right after deformation, PPs of chains retract in both directions paralle…
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…
The generalized entropy theory (GET) offers many insights into how molecular parameters influence polymer glass-formation. Given the fact that chain rigidity often plays a critical role in understanding the glass-formation of polymer materials, the GET was originally developed based on models of semiflexible chains. Consequently, all previous calculations within the GET considered polymers with some degree of chain rigidity. Motivated by unexpected results from computer simulations of fully flexible polymer melts concerning the dependence of thermodynamic and dynamic properties on the cohesive…
The calculation of discrete or continuous relaxation time spectra from rheometric measurables of polydisperse polymers is an ill-posed problem. In this paper, a curve fitting method for solving this problem is presented and compared to selected models from the literature. It is shown that the new method is capable of correctly predicting the molecular mass distributions of linear polydisperse polymer melts as well as their relaxation time spectra.
Linear Viscoelasticity of Semidilute Unentangled Flexible Polymer Solutions
IITB-Monash Research Academy, Indian Institute of Technology Bombay（IITB-莫纳什研究学院，印度理工学院孟买分校）；Department of Chemical Engineering, Indian Institute of Technology Bombay（印度理工学院孟买分校化学工程系）；Department of Chemical and Biological Engineering, Monash University（莫纳什大学化学与生物工程系）
Plateau moduli of Kremer-Grest models for commodity polymer melts
University of Southern Denmark（南丹麦大学）；ENSL, CNRS, Laboratoire de Physique (UMR 5672) and Centre Blaise Pascal de l’École Normale Supérieure de Lyon（里昂高等师范学院、法国国家科学研究中心物理实验室（UMR 5672）及里昂高等师范学院布莱兹·帕斯卡中心）
In polymer physics it is typically assumed that excluded volume interactions are effectively screened in polymer melts. Hence, chains could be described by an effective random walk without excluded volume interactions. In this letter, we show that this mapping is problematic by analyzing the occurrence of knots, their spectrum and sizes in polymer melts, corresponding random walks and chains in dilute solution. The effective random walk severely overrates the occurrence of knots and their complexity, particularly when compared to melts of flexible chains, indicating that non-trivial effects du…
We use non-equilibrium atomistic molecular dynamics simulations of unentangled melts of linear and star polymers ($\mathrm{C_{25}H_{52}}$) to study the steady-state viscoelastic response under confinement within nanoscale hematite $\left ( \mathrm{α-Fe_2O_3} \right )$ channels. We report (i) the negative (positive) first (second) normal stress difference and (ii) the presence of viscoelastic tension at low shear rates. We link these effects to bond alignment such that chains near the surface can carry the elastic force exerted on the walls, which decays as the chains become more aligned in the…
We perform molecular-dynamics simulations for polymer melts of the coarse-grained polyvinyl alcohol model that crystallizes upon slow cooling. To establish the properties of its high temperature liquid state as a reference point, we characterize in detail the structural features of equilibrated polymer melts with chain lengths $5\le N \le 1000$ at a temperature slightly above their crystallization temperature. We find that the conformations of sufficiently long polymers with $N >50$ obey essentially the Flory's ideality hypothesis. The chain length dependence of the end-to-end distance and the…
The Kremer-Grest (KG) model is a standard for studying generic polymer properties. Here we have equilibrated KG melts up to and beyond $200$ entanglements per chain for varying chain stiffness. We present methods for estimating the Kuhn length corrected for incompressibility effects, for estimating the entanglement length corrected for chain stiffness, for estimating bead frictions and Kuhn times taking into account entanglement effects. These are the key parameters for enabling quantitative, accurate, and parameter free comparisons between theory, experiment and simulations of KG polymer mode…
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 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…
