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Approximations of the discrete slip-link model and their effect on nonlinear rheology predictions
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10.1122/1.4788909
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    Affiliations:
    1 Department of Physics, Illinois Institute of Technology, 3101 S. Dearborn Street, Chicago, Illinois 60616 and Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 3440 S. Dearborn Street, Chicago, Illinois 60616
    2 Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 3440 S. Dearborn Street, Chicago, Illinois 60616 and Department of Chemical and Biological Engineering, Illinois Institute of Technology, 10 W. 33rd Street, Chicago, Illinois 60616
    3 Department of Physics, Illinois Institute of Technology, 3101 S. Dearborn Street, Chicago, Illinois 60616; Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 3440 S. Dearborn Street, Chicago, Illinois 60616; and Department of Chemical and Biological Engineering, Illinois Institute of Technology, 10 W. 33rd Street, Chicago, Illinois 60616
    a) Present address: Ludwig Institute for Cancer Research, 9500 Gilman Dr. CMM-East rm 3071G, La Jolla, California 92093.
    b) Author to whom correspondence should be addressed; electronic mail: schieber@iit.edu
    J. Rheol. 57, 535 (2013); http://dx.doi.org/10.1122/1.4788909
/content/sor/journal/jor2/57/2/10.1122/1.4788909
http://aip.metastore.ingenta.com/content/sor/journal/jor2/57/2/10.1122/1.4788909
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Approximations to the inverse Langevin function.

Image of FIG. 2.
FIG. 2.

Symbols are experimental data by Schweizer et al. (2004) : Polystyrene melt 200 kDa, , and lines are DSM prediction:

Image of FIG. 3.
FIG. 3.

Symbols are experimental data by Auhl et al. (2008) : Polyisoprene Melt 90 kDa, , and lines are DSM prediction:

Image of FIG. 4.
FIG. 4.

DSM shear flow predictions: Polystyrene melt 200 kDa, .

Image of FIG. 5.
FIG. 5.

DSM and GLaMM shear flow predictions: Polyisoprene melt 90 kDa, .

Image of FIG. 6.
FIG. 6.

Effects of the DSM approximations on shear flow predictions: Polystyrene melt 200 kDa, . Shown: Effect of convective constraint release (CCR), effect of DED, and effect of combined finite extensibility and DED (Cohen & DED).

Image of FIG. 7.
FIG. 7.

Effects of the DSM approximations on shear flow predictions: Polyisoprene melt 90 kDa, . Shown: Effect of CCR, effect of DED, and effect of combined finite extensibility and DED (Cohen & DED).

Image of FIG. 8.
FIG. 8.

DSM shear flow prediction, transient : Polyisoprene melt 90 kDa, . Marked points correspond to peaks in transient viscosity.

Image of FIG. 9.
FIG. 9.

DSM elongational flow prediction: Polystyrene melt 200 kDa, .

Image of FIG. 10.
FIG. 10.

Effect of CCR on DSM elongational flow prediction: Polystyrene melt 200 kDa, .

Image of FIG. 11.
FIG. 11.

Effect of DED on DSM elongational flow prediction: Polystyrene melt 200 kDa, . (DSM w/DED)—DSM prediction with dangling end dynamics, all strands contribute to stress tensor; (DE stress = 0)—DSM prediction with dangling end dynamics, but dangling ends do not contribute to stress tensor.

Image of FIG. 12.
FIG. 12.

Left: DSM shear flow prediction, transient : Polystyrene melt 200 kDa, . Right: DSM elongational flow prediction, transient : Polystyrene melt 200 kDa, .

Image of FIG. 13.
FIG. 13.

Effects of the DSM approximations on elongational flow prediction, steady-state viscosity: Polystyrene melt 200 kDa, . Shown: Original DSM, effect of CCR, effect of DED, and effect of combined finite extensibility and DED (Cohen & DED).

Image of FIG. 14.
FIG. 14.

Effect of finite extensibility on DSM elongational flow prediction: Polystyrene melt 200 kDa, .

Image of FIG. 15.
FIG. 15.

Strand stretch distribution, DSM elongational flow prediction: Polystyrene melt 200 kDa, , steady state,

Image of FIG. 16.
FIG. 16.

DSM elongational flow prediction: Polystyrene melt 200 kDa, .

Image of FIG. 17.
FIG. 17.

DSM stress-optical rule prediction: Polystyrene melt 200 kDa, . Straight (black) line is fit to linear region, color points are experimental data, color lines are DSM predictions with DED and Cohen-Padé free energy.

Image of FIG. 18.
FIG. 18.

Constraint dynamics creation. New entanglement splits strand , into two strands and .

Image of FIG. 19.
FIG. 19.

Cross-section of Cohen-Padé CD creation in plane of strand. Here . The volume where the new entanglement can be created (the dark shaded region) depends on . Possible shapes: lens—both existing entanglements can be inside or outside this volume, spheres—at least one of the existing entanglements is inside this volume.

Image of FIG. 20.
FIG. 20.

Points: as function of Ni (left), Qi (middle), and N (right). Lines: corresponding rational function approximation.

Image of FIG. 21.
FIG. 21.

Cohen-Padé tension distribution for a strand and its dependence on the number of Kuhn steps, N.

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/content/sor/journal/jor2/57/2/10.1122/1.4788909
2013-01-31
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Approximations of the discrete slip-link model and their effect on nonlinear rheology predictions
http://aip.metastore.ingenta.com/content/sor/journal/jor2/57/2/10.1122/1.4788909
10.1122/1.4788909
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