Origin of Stress Overshoot during Startup Shear of Entangled Polymer Melts

Lu, Yuyuan; An, Lijia; Wang, Shi‐Qing; Wang, Zhen‐Gang

doi:10.1021/mz500260h

Cited by 43 publications

(94 citation statements)

References 34 publications

(48 reference statements)

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“…We have revisited the stress-optical rule of flexible polymers to examine if the shear component of the orientational anisotropy of the subchain, S xy (t ), can grow monotonically with t when the squared stretch ratio l (t ) 2 exhibits the overshoot as claimed by Lu et al 3,4) Expanding l(t ) 2 and the segmental shear orientational anisotropy O xy (t ) with respect to the shear rate g 4 , we found that the overshoot of S xy (t ) is a nonlinearity of the order of g 4 3 and emerges at lower g 4 compared to the overshoot of l(t ) 2 (that is a nonlinearity of the order of g 4 4 ), as long as SOR is valid. In other words, l(t ) 2 can monotonically grow even when S xy (t ) exhibits the overshoot, but the overshoot of l(t ) 2 is always accompanied by the overshoot of S xy (t ).…”

Section: Resultsmentioning

confidence: 96%

“…Fig.2c. Thus, the claim by Lu et al 3,4) 3,4) as long as SOR is valid at those g 4 in the moderately nonlinear regime.…”

Section: Orientational Anisotropy and Stretch Of Subchain In The Linementioning

confidence: 84%

“…(8) is rewritten as (10) The overshoot of the shear stress s xy is equivalent to the overshoot of O xy = 〈u x u y 〉, as noted from Eq.(7). Thus, if s xy overshoots but the shear component of the orientational anisotropy of the subchain S xy does not (as claimed by Lu et al 3,4) ) and if SOR is valid, the overshoot of segmental O xy should be canceled by an overshoot of l Nevertheless, analysis of S and l 2 in the linear regime and moderately nonlinear regime suggests that such cancellation does not occur, and thus the claim by Lu et al 3,4) has no sound basis. Details of this analysis are described below.…”

Section: Stress-optical Rulementioning

confidence: 98%

“…6) In fact, the internal equilibration is a pre-requisite for the subchain to behave as the stress-sustaining unit to satisfy Eq.(1). 3,4) ) Obviously, the end-to-end vector r of this subchain is expressed as a sum of the bond-vectors b j of the monomeric segments therein (cf. Fig.1):…”

Section: Stress-optical Rulementioning

confidence: 99%

“…In relation to this anisotropy/deformation of the subchains, Lu et al 3,4) recently conducted Brownian dynamics simulation on start-up of relatively slow shear flow at rates g 4 above the terminal relaxation frequency, w d , but below the Rouse relaxation frequency of the chain backbone, w R . They claimed that the overshoot of shear stress at such g 4 is mostly due to the overshoot of chain length (total length of the subchains) whereas the subchain orientation monotonically grows (no overshoot) at such g 4 .…”

Section: Introductionmentioning

confidence: 99%

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Revisit the Stress-Optical Rule for Entangled Flexible Chains: Overshoot of Stress, Segmental Orientation, and Chain Stretch on Start-up of Flow

Watanabe

Inoue

2015

J. Soc. Rheol., Jpn

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For flexible polymers, the deviatoric parts of the stress and optical anisotropy tensors, with the latter reflecting the orientational anisotropy of the monomeric segments, are proportional to each other. This proportionality, known as the stress-optical rule (SOR), is valid not only in the linear viscoelastic regime but also in the moderately nonlinear regime, given that the chain is not highly stretched and is free from the finite extensible nonlinear elasticity (FENE) effect. On start-up of flow in such a moderately nonlinear regime, the chain exhibits an overshoot of the shear stress and thus of the shear component of the segmental orientational anisotropy. Nevertheless, it was not clearly understood whether this overshoot is associated with an overshoot of chain stretch. This study revisited SOR to conduct a simple analysis for this problem. It turned out that the orientational anisotropy of subchains overshoots but the subchain stretch (identical to the chain stretch) does not when the shear stress overshoots in the moderately nonlinear regime.

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Section: Resultsmentioning

confidence: 96%

“…Fig.2c. Thus, the claim by Lu et al 3,4) 3,4) as long as SOR is valid at those g 4 in the moderately nonlinear regime.…”

Section: Orientational Anisotropy and Stretch Of Subchain In The Linementioning

confidence: 84%

Section: Stress-optical Rulementioning

confidence: 98%

Section: Stress-optical Rulementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Revisit the Stress-Optical Rule for Entangled Flexible Chains: Overshoot of Stress, Segmental Orientation, and Chain Stretch on Start-up of Flow

Watanabe

Inoue

2015

J. Soc. Rheol., Jpn

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Coupled Orientation and Stretching of Chains in Mesoscale Models of Polydisperse Linear Polymers in Startup of Steady Shear Flow Simulations

Gooneie

Schuschnigg

Holzer

2016

Macro Theory & Simulations

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behavior of the polymer melt. [ 5 ] Fujiyama et al. [ 6 ] provide a comprehensive experimental work on the rheological properties of poly(propylene)s with different molecular weight distributions. According to their results many of the rheological properties depend on the polydispersity including the end correlation coeffi cient in capillary fl ow, the die swell ratio, the critical shear-rate and shear stress for the onset of melt fracture, the zero-shear viscosity, the characteristic relaxation time, and the oscillatory storage and loss moduli. The infl uence of polydispersity is not only limited to these properties. It also affects the fl ow patterns of the melt even in the simplest geometries. Studies have shown that a highly monodisperse sample partitions into two fractions with different local shear-rates in a sliding plate rheometer. [ 7 ] The polydisperse sample possesses a smooth spatial variation of the local shear-rates in the same experimental setup. Other reports on the polydisperse Polydisperse linear polymers are studied in startup of steady shear fl ow simulations using dissipative particle dynamics. The results show that with an increase in polydispersity the stress overshoot declines while the steady-state stress increases. Various physical characteristics of the systems are studied including frequency of nonbonded interactions, gyration radius data, fl ow alignment angles, and average bond lengths. The patterns in the data suggest higher forces are necessary to orient and stretch long chain fractions in the fl ow direction. Relaxation modulus data prove the broad range of relaxation mechanisms in polydisperse systems. Linear viscoelasticity theory is used to quantify the relaxation spectrum. The results indicate an increase in the longest relaxation time in systems with higher polydispersity. The steady-state shear viscosity results show higher viscosities with an increase in polydispersity at all shear-rates. The good agreement of the characteristic behaviors of modeled polydisperse polymers with experiments is encouraging for future work.

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Nonlinear shear of entangled polymers from nonequilibrium molecular dynamics

Anwar

Graham

2019

J Polym Sci B Polym Phys

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This study aims to use molecular dynamics (MD) simulations of Kremer–Grest (KG) chains to inform future developments of models of entangled polymer dynamics. We perform nonequilibrium MD simulations, under shear flow, for well‐entangled KG chains. We study chains of 512 and 1000 KG beads, corresponding to 8 and 15 entanglements, respectively. We compute the linear rheological properties from equilibrium simulations of the stress autocorrelation and obtain from these data the tube model parameters. Under nonlinear shear flow, we compute the shear viscosity, the first and second normal stress differences, and chain contour length. For chains of 512 monomers, we obtain agreement with the results of Cao and Likhtman (ACS Macro. Lett. 2015, 4, 1376). We also compare our nonlinear results with the Graham, Likhtman and Milner‐McLeish (GLaMM) model. We identify some systematic disagreement that becomes larger for the longer chains. We made a comparison of the transient shear stress maximum from our simulations, two nonlinear models and experiments on a wide range of melts and solutions, including polystyrene (PS), polybutadiene, and styrene–butadiene rubber. This comparison establishes that the PS melt data show markedly different behavior to all other melts and solutions and KG simulations reproduce the PS data more closely than either the GLaMM or Xie and Schweizer models. We discuss the performance of these models against the data and simulations. Finally, by imposing a rapid reversing flow, we produce a method to extract the recoverable strain from MD simulations, valid for sufficiently entangled monodisperse polymers. We explore how the resulting data can probe the melt state just before the reversing flow. © 2019 The Authors. Journal of Polymer Science Part B: Polymer Physics published by Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1692–1704

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Origin of Stress Overshoot during Startup Shear of Entangled Polymer Melts

Cited by 43 publications

References 34 publications

Revisit the Stress-Optical Rule for Entangled Flexible Chains: Overshoot of Stress, Segmental Orientation, and Chain Stretch on Start-up of Flow

Revisit the Stress-Optical Rule for Entangled Flexible Chains: Overshoot of Stress, Segmental Orientation, and Chain Stretch on Start-up of Flow

Coupled Orientation and Stretching of Chains in Mesoscale Models of Polydisperse Linear Polymers in Startup of Steady Shear Flow Simulations

Nonlinear shear of entangled polymers from nonequilibrium molecular dynamics

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