Dynamics of entanglements: A nonlinear model consistent with the Cox-Merz rule

Marrucci, G.

doi:10.1016/0377-0257(95)01407-1

Cited by 436 publications

(320 citation statements)

References 17 publications

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“…This unique behaviour is intimately related to the uncrossability of chains which effectively leads to topological constraints between chains in the form of entanglements (deGennes, 1980;Doi and Edwards, 1988). The original reptation theory, based on the tube model, and more recent theoretical concepts have captured qualitatively and quantitatively the effect of entanglements on polymer dynamics and rheology (deGennes, 1980;Doi and Edwards, 1988;Kroger, 2004;Likhtman, 2005;Likhtman and McLeish, 2002;Marrucci, 1996;Marrucci and Ianniruberto, 2004;McLeish and Larson, 1998;Ramirez et al, 2007;Stephanou et al, 2011;Wang et al, 2012). Additionally, density is one of the key factors which affect profoundly the static, dynamic and rheological properties of entangled polymers (Daoud et al, 1975;Doi and Edwards, 1988;Edwards, 1966;Fleer et al, 1993).…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

Foteinopoulou

Karayiannis

Laso

2015

Chemical Engineering Science

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HIGHLIGHTS• Identification of the maximally random jammed state for polymer packings.• Molecular simulation of the phase transition in hard-sphere chains.• Molecular modelling of the effect of confinement in densely-packed athermal polymers.• Numerical calculation of the topological constraints in polymeric systems.• First-principles calculation of the scaling regimes in flexible polymers. ABSTRACTWe review the main results from extensive Monte Carlo (MC) simulations on athermal polymer packings in the bulk and under confinement. By employing the simplest possible model of excluded volume, macromolecules are represented as freely-jointed chains of hard spheres of uniform size. Simulations are carried out in a wide concentration range: from very dilute up to very high volume fractions, reaching the maximally random jammed (MRJ) state. We study how factors like chain length, volume fraction and flexibility of bond lengths affect the structure, shape and size of polymers, their packing efficiency and their phase behaviour (disorder-order transition). In addition, we observe how these properties are affected by confinement realized by fiat, impenetrable walls in one dimension. Finally, by mapping the parent polymer chains to primitive paths through direct geometrical algorithms, we analyse the characteristics of the entanglement network as a function of packing density.

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Section: Introductionmentioning

confidence: 99%

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

Foteinopoulou

Karayiannis

Laso

2015

Chemical Engineering Science

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“…It might be that, before a test chain has escaped from its tube, one of the constraining chains moves out of the way, releasing the entanglement constraint. This constraint release process provides a second relaxation mechanism, commonly modeled as a local sideways hop of the tube at each constraint release event [3][4][5][6]. Accounting for constraint release has been essential in understanding the experimental lack of shear banding in strong flows of monodisperse melts [5,6].…”

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confidence: 99%

“…This constraint release process provides a second relaxation mechanism, commonly modeled as a local sideways hop of the tube at each constraint release event [3][4][5][6]. Accounting for constraint release has been essential in understanding the experimental lack of shear banding in strong flows of monodisperse melts [5,6]. It is also crucial in most industrial polymers, where polydispersity of chain length, and chain branching, result in a wide spectrum of constraint release rates.…”

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confidence: 99%

Elongational Flow of Blends of Long and Short Polymers: Effective Stretch Relaxation Time

et al. 2009

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“…The accuracy of fit is remarkable particularly as only a single adjustable parameter is used in the model. Convective Constraint Release (CCR) [21] is incorporated into the model described in reference [20], in a manner that effectively separates elongational and rotational damping functions. The versions preceding the CCR model can be recognized as following the 'separabilty' assumption [20].…”

Section: Introductionmentioning

confidence: 99%

A study of the quadratic molecular stress function constitutive model in simulation

Olley

2005

Journal of Non-Newtonian Fluid Mechanics

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Constitutive models that conform to separable KBKZ specification have been shown to fit steady-state strain hardening rheological data in planar and uniaxial elongational flows, but with inaccuracy in the rate of strain hardening. The single parameter Molecular Stress Function model of Wagner [Rheol. Acta, 39 (2000), 97-109] has been shown to accurately fit the rise-rate in experimental data for a number of strain hardening and strain softening materials. We study this models accuracy against the well characterised IUPAC LDPE data, and present a method for full implementation of this model for flow solution which is suitable for incorporating into existing separable KBKZ software. A new method for particle tracking in arbitrarily aligned meshes, which is efficient and robust, is given. The Quadratic Molecular Stress Function (QMSF) model is compared to existing separable KBKZ based models, including one which is capable of giving planar strain hardening; the QMSF is shown to fit experimental rheological and contraction flow data more convincingly. The issue of 'negative correction pressures' notable in some Doi-Edwards based models is addressed. The cause is identified, and leads to a logical method of calculation which does not give these anomalous results.

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Dynamics of entanglements: A nonlinear model consistent with the Cox-Merz rule

Cited by 436 publications

References 17 publications

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

Elongational Flow of Blends of Long and Short Polymers: Effective Stretch Relaxation Time

A study of the quadratic molecular stress function constitutive model in simulation

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