A differential constitutive equation for polymer melts

Wiest, John M.

doi:10.1007/bf01354763

Cited by 46 publications

(35 citation statements)

References 19 publications

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“…These results are supposed to resolve the long-time standing issue in the field whether or not the tension-thickening behavior exhibited by many branched polymers in elongational flows is true; it is clearly true! Even for the short, unentangled branched H_78_25 PE melt studied here, the NEMD data demonstrate that chain branching results in an increase of the dominant viscosity ͑ 1 ͒ with extension rate, a phenomenon which, in fact, is also predicted by several existing macroscopic models 24,41,42 in a certain range of their parameter space. This is considered as an important finding ͑especially from the point of view of theoretical modeling͒, since it proves that it is not only mechanisms ͑such as arm withdrawal and backbone stretching͒ of relevance to entangled state that cause ͑both transient and steady-state͒ stress thickening: Given that the phenomenon shows up even in unentangled systems, we understand that it is more generic thereby calling for a clearer conception of the role of chain branching on polymer dynamics.…”

Section: Simulation Detailssupporting

confidence: 70%

Tension thickening, molecular shape, and flow birefringence of an H-shaped polymer melt in steady shear and planar extension

Baig

Mavrantzas

2010

The Journal of Chemical Physics

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Articles you may be interested in Nonequilibrium molecular dynamics simulation of dendrimers and hyperbranched polymer melts undergoing planar elongational flow J. Rheol. 58, 281 (2014) Despite recent advances in the design of extensional rheometers optimized for strain and stress controlled operation in steady, dynamic, and transient modes, obtaining reliable steady-state elongational data for macromolecular systems is still a formidable task, limiting today's approach to trial-and-error efforts rather than based on a deep understanding of the deformation processes occurring under elongation. Guided, in particular, by the need to understand the special rheology of branched polymers, we studied a model, unentangled H-shaped polyethylene melt using nonequilibrium molecular dynamics simulations based on a recently developed rigorous statistical mechanics algorithm. The melt has been simulated under steady shear and steady planar extension, over a wide range of deformation rates. In shear, the steady-state shear viscosity is observed to decrease monotonically as the shear rate increases; furthermore, the degree of shear thinning of the viscosity and of the first-and second-normal stress coefficients is observed to be similar to that of a linear analog of the same total chain length. By contrast, in planar extension, the primary steady-state elongational viscosity 1 is observed to exhibit a tension-thickening behavior as the elongation rate increases, which we analyze here in terms of ͑a͒ perturbations in the instantaneous intrinsic chain shape and ͑b͒ differences in the stress distribution along chain contour. The maximum in the plot of 1 with occurs when the arm-stretching mode becomes active and is followed by a rather abrupt tension-thinning behavior. In contrast, the second elongational viscosity 2 shows only a tension-thinning behavior. As an interesting point, the simulations predict the same value for the stress optical coefficient in the two flows, revealing an important rheo-optical characteristic. In agreement with experimental indications on significantly longer systems, our results confirm the importance of chain branching on the unique rheological properties of polymer melts in extension.

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Section: Simulation Detailssupporting

confidence: 70%

Tension thickening, molecular shape, and flow birefringence of an H-shaped polymer melt in steady shear and planar extension

Baig

Mavrantzas

2010

The Journal of Chemical Physics

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“…Such a constitutive model was developed by Wiest [53]. Unfortunately, the use of a nonzero nonlinearity parameter (α > 0) in the Wiest model significantly reduces the predicted extensional strain hardening of the fluid.…”

Section: Extensional Rheologymentioning

confidence: 99%

Flow of a wormlike micelle solution past a falling sphere

Chen

Rothstein

2004

Journal of Non-Newtonian Fluid Mechanics

108

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“…They represent a family of models widely used by rheologists in order to analyze complicated polymer flow problems with considerable success, since they are easy to solve numerically as they do not require tracking fluid elements. Typical examples include the upper-convected Maxwell ͑UCM͒, 8 the Giesekus, 14 the Phan-Thien/Tanner ͑PTT͒, 15,16 and the Leonov 17,18 models, as well as modifications accounting for finite extensibility with nonlinear molecular stretching, 8,[19][20][21][22][23] nonaffine deformation, 24,25 variation in the longest chain relaxation time with chain conformation, 26,27 and bounded free energy, 28 either separately or all together. 29 Of course, in addition to a single conformation tensor, one can envision higher-mode conformation tensor viscoelastic equations corresponding to the Rouse or bead-spring chain model.…”

Section: Introductionmentioning

confidence: 99%

Multiscale simulation of polymer melt viscoelasticity: Expanded-ensemble Monte Carlo coupled with atomistic nonequilibrium molecular dynamics

Baig

Mavrantzas

2009

Phys. Rev. B

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We present a powerful framework for computing the viscoelastic properties of polymer melts based on an efficient coupling of two different atomistic models: the first is represented by the nonequilibrium molecular dynamics method and is considered as the microscale model. The second is represented by a Monte Carlo ͑MC͒ method in an expanded statistical ensemble and is free from any long time scale constraints. Guided by recent developments in nonequilibrium thermodynamics, the expanded ensemble incorporates appropriately defined "field" variables driving the corresponding structural variables to beyond equilibrium steady states. The expanded MC is considered as the macroscale solver for the family of all viscoelastic models built on the given structural variable͑s͒. The explicit form of the macroscopic model is not needed; only its structure in the context of the general equation for the nonequilibrium reversible irreversible coupling or generalized bracket formalisms of nonequilibrium thermodynamics is required. We illustrate the method here for the case of unentangled linear polymer melts, for which the appropriate structural variable to consider is the conformation tensor c. The corresponding Lagrange multiplier is a tensorial field ␣. We have been able to compute modelindependent values of the tensor ␣, which for a wide range of strain rates ͑covering both the linear and the nonlinear viscoelastic regimes͒ bring results for the overall polymer conformation from the two models ͑mi-croscale and macroscale͒ on top of each other. In a second step, by comparing the computed values of ␣ with those suggested by the macroscopic model addressed by the chosen structural variable͑s͒, we can identify shortcomings in the building blocks of the model. How to modify the macroscopic model in order to be consistent with the results of the coupled micro-macro simulations is also discussed. From a theoretical point of view, the present multiscale modeling approach provides a solid framework for the design of improved, more accurate macroscopic models for polymer melts.

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A differential constitutive equation for polymer melts

Cited by 46 publications

References 19 publications

Tension thickening, molecular shape, and flow birefringence of an H-shaped polymer melt in steady shear and planar extension

Tension thickening, molecular shape, and flow birefringence of an H-shaped polymer melt in steady shear and planar extension

Flow of a wormlike micelle solution past a falling sphere

Multiscale simulation of polymer melt viscoelasticity: Expanded-ensemble Monte Carlo coupled with atomistic nonequilibrium molecular dynamics

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