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Register a new userRelating Chain Conformations to Extensional Stress In Entangled Polymer Melts
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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 $epsilongeq6$. 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 quantitatively consistent with the decreasing entropy of chains at the equilibrium entanglement length. Molecular weight dependent trends in viscosity are related to a crossover from the Newtonian limit to a high rate limit that scales differently with chain length.
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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 range of the simulation trajectory. The opposite conclusion should have been drawn from their data, had they examined the full simulation trajectory in a proper way.
We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts. The data allow us to explore the chain dynamics and the shear relaxation modulus, $G(t)$, into the plateau regime for chains with $Z=40$ entanglements and into the terminal relaxation regime for $Z=10$. Using the known (Rouse) mobility of unentangled chains and the melt entanglement length determined via the primitive path analysis of the microscopic topological state of our systems, we have performed parameter -free tests of several different tube models. We find excellent agreement for the Likhtman-McLeish theory using the double reptation approximation for constraint release, if we remove the contribution of high-frequency modes to contour length fluctuations of the primitive chain.
In addition to the terminal flow (the region I) and the shear thinning (the region II), we discover two new flow regions in capillary flow at the wall stress higher than the plateau modulus of the polymer. The region III violates the empirical Cox-Merz rule with a significantly weaker shear thinning than the region II, and the region IV exhibits unexpected shear thickening. Moreover, the crossover shear rates between the regions II and III and between the regions III and IV scale with the number of entanglement per chain, Z=M_w/M_e, as Z^(-2.0) and Z^(-1.2) respectively. We attribute the weakening in shear thinning and the emergence of shear thickening to the deformation-induced non-Gaussian stretching of polymers. These observations offer the first experimental quantification of the deformation behaviors of polymer melts at high-stress shear.
Following the Flory ideality hypothesis intrachain and interchain excluded volume interactions are supposed to compensate each other in dense polymer systems. Multi-chain effects should thus be neglected and polymer conformations may be understood from simple phantom chain models. Here we provide evidence against this phantom chain, mean-field picture. We analyze numerically and theoretically the static correlation function of the Rouse modes. Our numerical results are obtained from computer simulations of two coarse-grained polymer models for which the strength of the monomer repulsion can be varied, from full excluded volume (`hard monomers) to no excluded volume (`phantom chains). For nonvanishing excluded volume we find the simulated correlation function of the Rouse modes to deviate markedly from the predictions of phantom chain models. This demonstrates that there are nonnegligible correlations along the chains in a melt. These correlations can be taken into account by perturbation theory. Our simulation results are in good agreement with these new theoretical predictions.
We present an effective and simple multiscale method for equilibrating Kremer Grest model polymer melts of varying stiffness. In our approach, we progressively equilibrate the melt structure above the tube scale, inside the tube and finally at the monomeric scale. We make use of models designed to be computationally effective at each scale. Density fluctuations in the melt structure above the tube scale are minimized through a Monte Carlo simulated annealing of a lattice polymer model. Subsequently the melt structure below the tube scale is equilibrated via the Rouse dynamics of a force-capped Kremer-Grest model that allows chains to partially interpenetrate. Finally the Kremer-Grest force field is introduced to freeze the topological state and enforce correct monomer packing. We generate $15$ melts of $500$ chains of $10.000$ beads for varying chain stiffness as well as a number of melts with $1.000$ chains of $15.000$ monomers. To validate the equilibration process we study the time evolution of bulk, collective and single-chain observables at the monomeric, mesoscopic and macroscopic length scales. Extension of the present method to longer, branched or polydisperse chains and/or larger system sizes is straight forward.
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