Modifying the pom-pom model for extensional viscosity           overshoots

Hawke, Laurence; Huang, Qian; Hassager, Ole; Read, Daniel J.

doi:10.1122/1.4922060

Cited by 29 publications

(33 citation statements)

References 40 publications

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“…Steady stress following the stress overshoot was reported firstly by Rasmussen et al [11] and has been experimentally confirmed by comparing the measurements from the filament stretching rheometer and the cross-slot extensional rheometer [12], as well as by comparing the constant stretch rate and constant stress (creep) experiments [13]. Several models have been developed [12,14,15] for the attempt to understand the physics behind the stress overshoot. However, none of the models can be practically used for predicting the rheological behavior of LDPEs in industry, since the models contain numerous fitting parameters which are not directly related to molecular structures.…”

Section: Introductionmentioning

confidence: 69%

A new look at extensional rheology of low-density polyethylene

et al. 2016

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The nonlinear rheology of three selected commercial low-density polyethylenes (LDPE) is measured in uniaxial extensional flow. The measurements are performed using three different devices including an extensional viscosity fixture (EVF), a home made filament stretching rheometer (DTU-FSR) and a commercial filament stretching rheometer (VADER-1000). We show that the measurements from the EVF are limited by a maximum Hencky strain of 4, while the two filament stretching rheometers are able to probe the nonlinear behavior at larger Hencky strain values where the steady state is reached. With the capability of the filament stretching rheometers, we show that LDPEs with quite different linear viscoelastic properties can have very similar steady extensional viscosity. This points to the potential for independently controlling shear and extensional rheology in certain rate ranges.

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Section: Introductionmentioning

confidence: 69%

A new look at extensional rheology of low-density polyethylene

et al. 2016

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“…When the flow is stopped, the stress evolution from equation (5) is asymptotically equivalent to: (6) with B tr [54,55]. The trace of the auxiliary tensor has no physical significance and can become arbitrarily large.…”

Section: Resultsmentioning

confidence: 99%

Stress growth and relaxation of dendritically branched macromolecules in shear and uniaxial extension

Huang¹,

Costanzo²,

Das³

et al. 2017

Journal of Rheology

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We present unique nonlinear rheological data of well-defined symmetric Cayley-tree poly(methyl methacrylates) in shear and uniaxial extension. Earlier work has shown that their linear viscoelasticity is governed by the hierarchical relaxation of different generations, whereas the segments between branch points are responsible for their substantial strain hardening as compared to linear homopolymers of the same total molar mass at the same value of imposed stretch rate. Here, we extend that work in order to obtain further experimental evidence that will help understanding the molecular origin of the remarkable properties of these highly branched macromolecules. In particular, we address three questions pertinent to the specific molecular structure: (i) is steady state attainable during uniaxial extension? (ii) what is the respective transient response in simple shear? and (iii) how does stress relax upon cessation of extension or shear? To accomplish our goal we utilize state-of-the-art instrumentation, i.e., filament stretching rheometry (FSR) and cone-partitioned plate (CPP) shear rheometry for polymers with 3 and 4 generations, and complement it with state-of-the-art modeling predictions using the Branch-on-Branch (BoB) algorithm. The data indicates that the extensional viscosity reaches a steady state value, whose dependence on extension rate is identical to that of entangled linear and other branched polymer melts. Nonlinear shear is characterized by transient stress overshoots and the validity of the Cox-Merz rule. Remarkably, nonlinear stress relaxation is much broader and slower in extension compared to shear. It is also slower at higher generation, and rate-independent for rates below the Rouse rate of the outer segment. For extension, the relaxation time is longer than that of the linear stress relaxation, suggesting a strong 'elastic memory' of the material. These results are 2 described by BoB semi-quantitatively, both in linear and nonlinear shear and extensional regimes. Given the fact that the segments between branch points are less than 3 entanglements long, this is a very promising outcome that gives confidence in using BoB for understanding the key features. Moreover, the response of the segments between generations controls the rheology of the Cayley trees. Their substantial stretching in uniaxial extension appears responsible for strain hardening, whereas coupling of stretches of different parts of the polymer appears to be the origin of the slower subsequent relaxation of extensional stress. Concerning the latter effect, for which predictions are not available, it is hoped that the present experimental findings and proposed framework of analysis will motivate further developments in the direction of molecular constitutive models for branched and hyperbranched polymers.

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“…An entangled star arm is pinned at one end by its branch point -which is fixed in our simple model (we ignore, for simplicity, branch point withdrawal [12][13][14][15]). Hence, as presented in Figure 1, we consider that the star arm has strictly only two possible states:…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, given the above argument that in practice the relaxation of linear chains shares features with star chains, we might hope that our toy model captures the essence of the non-linear rheology for many linear chain systems. In this sense, we consider our model to be an equivalent of the "pom-pom" model for branched polymers [13,15] it is based on a simplified picture of a representative architecture, and designed to capture the essential physics.…”

Section: Introductionmentioning

confidence: 99%

Stochastic and preaveraged nonlinear rheology models for entangled telechelic star polymers

Boudara

Read

2017

J. Rheol.

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We present a simplified stochastic model designed to exemplify the non-linear rheology of entangled supramolecular polymeric materials. We have developed a simplified stochastic model for the rheology of entangled telechelic star polymers. As a toy model for entanglement effects, we use the Rolie-Poly equations [1] that we decorate with finite extensibility. Additionally, we include a stretch-dependent probability of detachment for the stickers. In both linear and non-linear regimes, we explore the parameter space, indicating the parameter values for which qualitative changes in response to the applied flow are predicted. Theory and results in the linear rheology regime are consistent with previous more detailed work of van Ruymbeke and co-workers [2]. Finally, we develop a pre-averaged version of the stochastic equations described above to obtain a set of non-stochastic coupled equations that produces very similar predictions but requires less computing resources.This pre-averaged model is based on two tensors representing the attached and detached chain populations and a scalar quantity that represents the fraction of these populations. * mmvahb@leeds.ac.uk

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Modifying the pom-pom model for extensional viscosity overshoots

Cited by 29 publications

References 40 publications

A new look at extensional rheology of low-density polyethylene

A new look at extensional rheology of low-density polyethylene

Stress growth and relaxation of dendritically branched macromolecules in shear and uniaxial extension

Stochastic and preaveraged nonlinear rheology models for entangled telechelic star polymers

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