Simple constitutive equation for linear polymer melts derived from molecular theory: Rolie–Poly equation

Likhtman, Alexei E.; Graham, Richard S.

doi:10.1016/s0377-0257(03)00114-9

Cited by 326 publications

(355 citation statements)

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“…(ii) Second, we perform a multimode fit to the linear and nonlinear data using the Rolie-Poly model [8], and define the effective stretch relaxation time from that of the slowest mode in the fit. Because of the noise in the elongational data, especially at the greatest dilutions, there remains some uncertainty in this value, but this gives tighter error bounds than the first method.…”

Section: Prl 103 136001 (2009) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

“…At greater dilutions (smaller L ) there is some deviation. Equation (8) gives two bounds for the predicted power law behavior. We estimate the constraint release rate from the short chains as S ¼ c = dS , where c ¼ 0:1 is a parameter describing the effectiveness of constraint release events in inducing tube hops [6] and dS is the reptation time of the short chains (3:04 Â 10 À3 s at 25 C).…”

Section: Prl 103 136001 (2009) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

“…Stretches in the thin and fat tubes are defined as t ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hr r i=a 2 p and f ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hR R i=a 2 f q , respectively [6,8], so taking the trace of Eq. (4) and averaging over fat tube segments gives…”

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confidence: 99%

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

et al. 2009

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Section: Prl 103 136001 (2009) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

Section: Prl 103 136001 (2009) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

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

et al. 2009

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“…An attractive feature of these is that they embody awareness of molecular architecture. Examples are the PomPom model (McLeish and Larson, 1998) for branched molecules and the Rolie-Poly model (Likhtman and Graham, 2003) for linear molecules. However these do not yet capture accurately the highly elastic extensional flows of interest here, without empirical extensions.…”

Section: Introductionmentioning

confidence: 99%

On the modelling of highly elastic flows of amorphous thermoplastics

Figiel

Buckley

2009

International Journal of Non-Linear Mechanics

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International audienceTwo approaches to the kinematic structuring of constitutive models for highly elastic flows of polymer melts have been examined systematically, assuming either: (1) additivity of elastic and viscous velocity gradients, or (2) multiplicability of elastic and viscous deformation gradients. A series of constitutive models was compared, with differing kinematic structure but the same linear responses in elastic and viscous limits. They were solved numerically and their predictions compared, and they were also compared to those of the Giesekus model. Several variants, previously proposed as separate models, are shown to be equivalent and qualitatively in agreement with experiment, and therefore a sound basis for construction of models. But the assignment of viscous spin is critical: if it is assumed equal to the total spin with approach (1), or equal to zero with approach (2), then unphysical viscoelastic behaviour is predicted

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“…The …rst method has been most successfully pursued by the group of Wim Briels, who suggested either preventing chain crossing geometrically [9], or maintaining information about entanglements by re-introducing slow variables such as the number of entanglements between two coils [10]. On the other hand, a one chain model can eventually lead to the tube model, which can be simpli…ed to a constitutive equation [11]. Our new group at the University of Reading is pursuing this second approach.…”

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confidence: 99%