Extensional Rheometry of Entangled Solutions

Bhattacharjee, Pradipto K.; Oberhauser, James P.; McKinley, Gareth H.; Leal, L. Gary; Sridhar, T.

doi:10.1021/ma0118623

Cited by 154 publications

(181 citation statements)

References 64 publications

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“…The material parameters, t d 0 , G N 0 , t R 0 , and λ max shown in Table I were evaluated from the linear viscoelastic data of the PS melts 1,2) and solution, 3) as explained below.…”

Section: Appendixmentioning

confidence: 99%

“…Recent experiments have established the thinning feature of the uniaxial steady state elongational viscosity η E for entangled monodisperse linear polystyrene (PS) melts 1,2) and the thickening feature for equally entangled PS solutions, 3,4) both occurring in the same range of strain rate ε 4 higher than the equilibrium Rouse relaxation frequency, w R . The classical Doi-Edwards tube theory 5) (DE theory) assuming a constant chain length cannot describe the thickening of the solutions, whereas the extended tube theory of Marrucci and Grizzuti 6) considering the chain stretch does not reproduce the monotonic thinning for the melts.…”

Section: Introductionmentioning

confidence: 99%

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Concept of Stretch/Orientation-Induced Friction Reduction Tested with a Simple Molecular Constitutive Equation

Yaoita

Masubuchi

Watanabe

2014

J. Soc. Rheol., Jpn

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Under elongational flow at strain rates higher than the Rouse relaxation frequency, entangled polymer melts exhibit thinning of their elongational viscosity whereas equally entangled solutions show thickening. Yaoita et al. [Yaoita et al., Macromolecules 2012, 45, 2773 related this difference between the melts and solutions to reduction of segmental friction on enhancement of the stretch/orientation averaged for the components therein (that includes the solvent for the case of solutions). They analyzed the stress relaxation data after cessation of elongational flow to propose an empirical equation describing this friction reduction as a function of the stretch/orientation factor. Multi-chain slip-link (PCN) simulations considering this friction reduction described the thinning of melts and the thickening of solutions consistently and semi-quantitatively. This study further tests the molecular concept of the stretch/orientation-induced friction reduction with the aid of a simple molecular constitutive equation, a toy version of the Mead-Larson-Doi model [Mead et al., Macromolecules 1998, 31, 7895] (MLD toy model) being modified to incorporate this empirical equation of the friction reduction. The modified toy model mimicked the behavior of melts and solutions consistently. This consistency vanished when the friction reduction in the model was artificially switched off, even though the finite extensible nonlinear elasticity was still taken into account. These results lend further support to the molecular concept of the stretch/orientation-induced friction reduction.

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“…The material parameters, t d 0 , G N 0 , t R 0 , and λ max shown in Table I were evaluated from the linear viscoelastic data of the PS melts 1,2) and solution, 3) as explained below.…”

Section: Appendixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Concept of Stretch/Orientation-Induced Friction Reduction Tested with a Simple Molecular Constitutive Equation

Yaoita

Masubuchi

Watanabe

2014

J. Soc. Rheol., Jpn

View full text Add to dashboard Cite

show abstract

“…[1][2][3][4][5][6][7][8][9][10][11] Of particular interest is the lack of strain-hardening observed for entangled polymer melts under fast steady elongational flow, [1][2][3][4][5] which makes a contrast to the significant hardening seen for entangled polymer solutions. [4][5][6][7][8] The hardening of the entangled solutions reflects the finite extensibility of the stress-sustaining subchains (entanglement strands) that allows the highly stretched subchain to become non-Gaussian and behave as a stiffened spring. [5][6][7][8] The lack of hardening for the entangled polymer melts is in turn attributable to a decrease of the segmental friction on the subchain orientation/ stretch that tends to reduce the orientation/stretch and suppress the hardening due to stiffening of the stretched subchain.…”

Section: Introductionmentioning

confidence: 99%

“…[4][5][6][7][8] The hardening of the entangled solutions reflects the finite extensibility of the stress-sustaining subchains (entanglement strands) that allows the highly stretched subchain to become non-Gaussian and behave as a stiffened spring. [5][6][7][8] The lack of hardening for the entangled polymer melts is in turn attributable to a decrease of the segmental friction on the subchain orientation/ stretch that tends to reduce the orientation/stretch and suppress the hardening due to stiffening of the stretched subchain. [9][10][11] Regarding the above features of entangled polymer melts and solutions, we note that the essence of strain-hardening is related to the stiffening of the stretched chain irrespective of the entanglement.…”

Section: Introductionmentioning

confidence: 99%

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Revisit the Elongational Viscosity of FENE Dumbbell Model

Watanabe

2017

J. Soc. Rheol., Jpn

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It is well known that the elongational viscosity η E of the Hookean dumbbell model increases with increasing elongational strain rate ε and finally diverges to infinite on approach of ε to 1/2τ H eq , where τ H eq is the viscoelastic relaxation time of the Hookean dumbbell that does not change with ε. This divergence of η E reflects infinite extensibility of the Hookean dumbbell. Real polymer chains obviously have the maximum stretch limit, so that the dumbbell model with a finite extensibility was developed almost a half century ago as a model for those chains under strong flow. This model exhibits the finite extensible nonlinear elasticity (FENE) effect under strong flow to provide η E with the strain-hardening feature but without any divergence. This FENE dumbbell model has been mathematically analyzed in detail and is now well established. Nevertheless, in a naive expectation, stiffening of the FENE dumbbell could/should largely increase the viscosity. Thus, it is still desired to explain, on an intuitive physical basis, how the stiffening suppresses the divergence of η E . From this point of view, this study focuses on the effective relaxation time τ eff allows the FENE dumbbell to change its conformation just slightly even for a large increase of ε from 1/2τ H eq to any higher value, which naturally leads to the lack of divergence of η E .

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Rheological Measurements

2013

Encyclopedia of Polymer Science and Technology

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Rheology is the science to study the flow and deformation of matter. It becomes an important field in material science and engineering, food, biotechnology, and so on. The objects in rheological study are not the ideal solid and ideal fluid, which can be described by the Hookean elastic model and the Newtonian viscous model, respectively. Instead, the rheological study often focuses on materials that can exhibit viscous, elastic, and plastic behavior under different flow conditions. They are often termed as complex fluids or soft matter, which include polymers, gels, suspensions, emulsions, biofluids, foods, inks (1). In contrast to hydrodynamics, which often accounts for the complex flow behavior of simple fluids, simple geometry is utilized in rheological measurements to understand the rather complicated relationship between the mechanical input and output of complex fluids. The real flow fields encountered in many applications (such as polymer extrusion, injection molding, blow molding, fiber spinning, inkjet printing, coating) are rather complicated (2). It becomes a problem whether the rheological measurements that performed under simple flow fields are useful in understanding the complicated flow behaviors of complex fluids. Fortunately, it has been proved in many examples that the properties determined from simple rheological measurements are sufficient to quantify the material parameters in various constitutive equations, which have been used widely and successfully to simulate the flow behaviors in polymer processing (3-11). The most frequently used simple flow fields are simple shear flow and simple extensional flow.The simplest geometry that defines the simple shear is two infinite parallel plates separated by a distance h. The liquid is set between two plates with one plate moving parallel to the other (Fig. 1). In reality, when the length L and the width B are much larger than the gap h, the flow in the center regime resembles the flow between two infinite plates. It means that the edge effects are ignored in most experimental shear geometries. In rheological measurements, the flow between two plates should be laminar. Moreover, it is usually assumed that the velocity across the gap satisfies a linear profile. As shown in Fig. 1, if the bottom plate is fixed and the upper plate moves horizontally with the velocity V, the fluid velocity varies linearly from 0 at the bottom plate to V at the upper plate if the no-slip boundary condition is satisfied. The linear velocity profile generates a constant velocity gradient, which is known as the shear rate. Then, the flow field between two parallel plates is homogeneous in the shear rate. The homogeneous assumption is nontrivial in the rheological tests since the actual velocity

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Extensional Rheometry of Entangled Solutions

Cited by 154 publications

References 64 publications

Concept of Stretch/Orientation-Induced Friction Reduction Tested with a Simple Molecular Constitutive Equation

Concept of Stretch/Orientation-Induced Friction Reduction Tested with a Simple Molecular Constitutive Equation

Revisit the Elongational Viscosity of FENE Dumbbell Model

Rheological Measurements

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