We have developed a new multiscale simulation technique to investigate history-dependent flow behavior of entangled polymer melt, using a smoothed particle hydrodynamics simulation with microscopic simulators that account for the dynamics of entangled polymers acting on each fluid element. The multiscale simulation technique is applied to entangled polymer melt flow around a circular obstacle in a two-dimensional periodic system. It is found that the strain-rate history-dependent stress of the entangled polymer melt affects its flow behavior, and the memory in the stress causes nonlinear behavior even in the regions where ${\rm Wi} \le 1$. The spatial distribution of the entanglements $<Z>$ is also investigated. The slightly low entanglement region is observed around the obstacle and is found to be broaden in the downstream region.
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 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.
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）
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…
The Kremer-Grest (KG) polymer model is a standard model for studying generic polymer properties in Molecular Dynamics simulations. It owes its popularity to its simplicity and computational efficiency, rather than its ability to represent specific polymers species and conditions. Here we show, that by tuning the chain stiffness it is possible to adapt the KG model to model melts of real polymers. In particular, we provide mapping relations from KG to SI units for a wide range of commodity polymers. The connection between the experimental and the KG melts is made at the Kuhn scale, i.e. at the …
We present computer simulations of a dynamic Monte Carlo algorithm for polymer chains on the FCC lattice which takes explicitly into account the possibility to overcome topological constraints by controlling the rate at which nearby polymer strands may cross through each other. By applying the method to systems of interacting ring polymers at melt conditions, we characterize their structure and dynamics by measuring, in particular, the amounts of knots and links which are formed during the relaxation process. In comparison to standard melts of unknotted and unconcatenated rings, our simulation…
The dynamics of ring polymer melts are studied via molecular dynamics simulations of the Kremer-Grest bead-spring model. Rouse mode analysis is performed in comparison with linear polymers by changing the chain length. Rouse-like behavior is observed in ring polymers by quantifying the chain length dependence of the Rouse relaxation time, whereas a crossover from Rouse to reptation behavior is observed in linear polymers. Furthermore, the non-Gaussian parameters of the monomer bead displacement and chain center-of-mass displacement are analyzed. It is found that the non-Gaussianity of ring pol…
We present a computationally efficient multiscale method for preparing equilibrated, isotropic long chain model polymer melts. As an application we generate Kremer-Grest melts of $1000$ chains with $200$ entanglements and $25000$-$2000$ beads per chain, which cover the experimentally relevant bending rigidities up to and beyond the limit of the isotropic-nematic transition. In the first step, we employ Monte Carlo simulations of a lattice model to equilibrate the large-scale chain structure above the tube scale while ensuring a spatially homogeneous density distribution. We then use theoretica…
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…
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…
In this work we developed a theoretical model to describe the polymerization of very long macromolecules with simultaneous precipitation. As a reference system for our model we consider UHMWPE polymerization process, via homogeneous catalysis and with molecular weight above $10^6$ monomers. We derived time dependency of the entanglement length in the system, and assessed how polymerization rate and fraction of initiators affects this dependency. We show that decrease of the fraction of initiators leads to increase of the average entanglement length in the melt after complete polymerization. Th…
The isothermal, isobaric spontaneous crystallization of a supercooled polymer melt is investigated by MD simulation of an ensemble of fully-flexible linear chains. Frustration is introduced via two incommensurate length scales set by the bond length and the position of the minimum of the non-bonding potential. Marked polymorphism with considerable bond disorder, distortions of both the local packing and the global monomer arrangements is observed. The analyses in terms of: i) orientational order parameters characterizing the global and the local order and ii) the angular distribution of the ne…
