Nonlinear Elongational Rheology of Unentangled Polystyrene and Poly(p-tert-butylstyrene) Melts

Yumi Matsumiya, Hiroshi Watanabe, Yuichi Masubuchi, Qian Huang, Ole Hassager

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Abstract

Nonlinear rheological behavior under uniaxial elongation was examined for unentangled melts of polystyrene (PS27; molecular weight M = 27k) and poly(p-tert-butylstyrene) (PtBS53; M = 53k) having nearly the same number of Kuhn segments per chain (nK = 30 and 35for PS27 and PtBS53, respectively). For both materials, the steady state elongational viscosity, ηE, exhibited strain-rate-hardening and then strain-rate-softening on an increase of the Weissenberg number Wi ≥ 0.3 (Wi = ε̇τ1eq, with τ1eq and ε̇ being the longest relaxation time in the linear viscoelastic regime and the Hencky strain rate, respectively). For the unentangled melts, the hardening and softening were free from any entanglement nonlinearity, so that the hardening was unequivocally related to the finite extensible nonlinear elasticity (FENE) of the chain, and the softening, to the suppression of the FENE effect due to reduction of the segment friction ζ occurring for the highly stretched and oriented chain. Thus, the ζ reduction, speculatively discussed for entangled melts so far, was experimentally confirmed, for the first time, for unentangled melts. Quantitatively, the hardening at intermediate Wi was stronger and the softening at higher Wi was weaker for PtBS53 than for PS27 despite the similarity of their nK values, which suggested that the magnitude of ζ reduction depends on the chemical structure of the chains. For estimation of this magnitude, the FENE-PM model (a FENE bead–springmodel with a pre-averaged FENE spring strength) was modified for the ζ reduction in an empirical way with an assumption that ζ at a given time is fully determined by the chain stretch and orientation and, thus, by the tensile stress σE at that time.This modified model was able to mimic the steady state ηE data excellently, and the ζ reduction utilized in the modification was weaker for PtBS53 than for PS27 to confirm the dependenc eof the magnitude of ζ reduction on the chemical structure of the chain. Nevertheless, the same modified model failed to mimic the transient stress growth and relaxation data on start-up and cessation of fast flow (at Wi ≥ 4) despite its success for the steady state ηE data in the entire range of Wi. Specifically, changes of ζ in the unentangled melts with time during the relaxation for large Wi were delayed compared to the model calculation. This result suggests, as one possibility, that ζ in those melts is determined not only by the chain stretch and orientation (i.e., by σE) at respective times but also by the transient changes of the stretch and orientation (by σ̇E), with those changes vanishing in the steady state thereby allowing the model to mimic the ηE data. The origin of this change of ζ with the transient changes of the stretch and orientation is discussed in relation to the local motion of the chain necessary for adjusting its friction to the changes of the stretch/orientation environment.
Original languageEnglish
JournalMacromolecules
Volume51
Issue number23
Pages (from-to)9710-9729
Number of pages20
ISSN0024-9297
DOIs
Publication statusPublished - 2018

Cite this

Matsumiya, Yumi ; Watanabe, Hiroshi ; Masubuchi, Yuichi ; Huang, Qian ; Hassager, Ole. / Nonlinear Elongational Rheology of Unentangled Polystyrene and Poly(p-tert-butylstyrene) Melts. In: Macromolecules. 2018 ; Vol. 51, No. 23. pp. 9710-9729.
@article{21aec216fe4948389dd25795b215e57f,
title = "Nonlinear Elongational Rheology of Unentangled Polystyrene and Poly(p-tert-butylstyrene) Melts",
abstract = "Nonlinear rheological behavior under uniaxial elongation was examined for unentangled melts of polystyrene (PS27; molecular weight M = 27k) and poly(p-tert-butylstyrene) (PtBS53; M = 53k) having nearly the same number of Kuhn segments per chain (nK = 30 and 35for PS27 and PtBS53, respectively). For both materials, the steady state elongational viscosity, ηE, exhibited strain-rate-hardening and then strain-rate-softening on an increase of the Weissenberg number Wi ≥ 0.3 (Wi = ε̇τ1eq, with τ1eq and ε̇ being the longest relaxation time in the linear viscoelastic regime and the Hencky strain rate, respectively). For the unentangled melts, the hardening and softening were free from any entanglement nonlinearity, so that the hardening was unequivocally related to the finite extensible nonlinear elasticity (FENE) of the chain, and the softening, to the suppression of the FENE effect due to reduction of the segment friction ζ occurring for the highly stretched and oriented chain. Thus, the ζ reduction, speculatively discussed for entangled melts so far, was experimentally confirmed, for the first time, for unentangled melts. Quantitatively, the hardening at intermediate Wi was stronger and the softening at higher Wi was weaker for PtBS53 than for PS27 despite the similarity of their nK values, which suggested that the magnitude of ζ reduction depends on the chemical structure of the chains. For estimation of this magnitude, the FENE-PM model (a FENE bead–springmodel with a pre-averaged FENE spring strength) was modified for the ζ reduction in an empirical way with an assumption that ζ at a given time is fully determined by the chain stretch and orientation and, thus, by the tensile stress σE at that time.This modified model was able to mimic the steady state ηE data excellently, and the ζ reduction utilized in the modification was weaker for PtBS53 than for PS27 to confirm the dependenc eof the magnitude of ζ reduction on the chemical structure of the chain. Nevertheless, the same modified model failed to mimic the transient stress growth and relaxation data on start-up and cessation of fast flow (at Wi ≥ 4) despite its success for the steady state ηE data in the entire range of Wi. Specifically, changes of ζ in the unentangled melts with time during the relaxation for large Wi were delayed compared to the model calculation. This result suggests, as one possibility, that ζ in those melts is determined not only by the chain stretch and orientation (i.e., by σE) at respective times but also by the transient changes of the stretch and orientation (by σ̇E), with those changes vanishing in the steady state thereby allowing the model to mimic the ηE data. The origin of this change of ζ with the transient changes of the stretch and orientation is discussed in relation to the local motion of the chain necessary for adjusting its friction to the changes of the stretch/orientation environment.",
author = "Yumi Matsumiya and Hiroshi Watanabe and Yuichi Masubuchi and Qian Huang and Ole Hassager",
year = "2018",
doi = "10.1021/acs.macromol.8b01954",
language = "English",
volume = "51",
pages = "9710--9729",
journal = "Macromolecules",
issn = "0024-9297",
publisher = "American Chemical Society",
number = "23",

}

Nonlinear Elongational Rheology of Unentangled Polystyrene and Poly(p-tert-butylstyrene) Melts. / Matsumiya, Yumi; Watanabe, Hiroshi; Masubuchi, Yuichi; Huang, Qian; Hassager, Ole.

In: Macromolecules, Vol. 51, No. 23, 2018, p. 9710-9729.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Nonlinear Elongational Rheology of Unentangled Polystyrene and Poly(p-tert-butylstyrene) Melts

AU - Matsumiya, Yumi

AU - Watanabe, Hiroshi

AU - Masubuchi, Yuichi

AU - Huang, Qian

AU - Hassager, Ole

PY - 2018

Y1 - 2018

N2 - Nonlinear rheological behavior under uniaxial elongation was examined for unentangled melts of polystyrene (PS27; molecular weight M = 27k) and poly(p-tert-butylstyrene) (PtBS53; M = 53k) having nearly the same number of Kuhn segments per chain (nK = 30 and 35for PS27 and PtBS53, respectively). For both materials, the steady state elongational viscosity, ηE, exhibited strain-rate-hardening and then strain-rate-softening on an increase of the Weissenberg number Wi ≥ 0.3 (Wi = ε̇τ1eq, with τ1eq and ε̇ being the longest relaxation time in the linear viscoelastic regime and the Hencky strain rate, respectively). For the unentangled melts, the hardening and softening were free from any entanglement nonlinearity, so that the hardening was unequivocally related to the finite extensible nonlinear elasticity (FENE) of the chain, and the softening, to the suppression of the FENE effect due to reduction of the segment friction ζ occurring for the highly stretched and oriented chain. Thus, the ζ reduction, speculatively discussed for entangled melts so far, was experimentally confirmed, for the first time, for unentangled melts. Quantitatively, the hardening at intermediate Wi was stronger and the softening at higher Wi was weaker for PtBS53 than for PS27 despite the similarity of their nK values, which suggested that the magnitude of ζ reduction depends on the chemical structure of the chains. For estimation of this magnitude, the FENE-PM model (a FENE bead–springmodel with a pre-averaged FENE spring strength) was modified for the ζ reduction in an empirical way with an assumption that ζ at a given time is fully determined by the chain stretch and orientation and, thus, by the tensile stress σE at that time.This modified model was able to mimic the steady state ηE data excellently, and the ζ reduction utilized in the modification was weaker for PtBS53 than for PS27 to confirm the dependenc eof the magnitude of ζ reduction on the chemical structure of the chain. Nevertheless, the same modified model failed to mimic the transient stress growth and relaxation data on start-up and cessation of fast flow (at Wi ≥ 4) despite its success for the steady state ηE data in the entire range of Wi. Specifically, changes of ζ in the unentangled melts with time during the relaxation for large Wi were delayed compared to the model calculation. This result suggests, as one possibility, that ζ in those melts is determined not only by the chain stretch and orientation (i.e., by σE) at respective times but also by the transient changes of the stretch and orientation (by σ̇E), with those changes vanishing in the steady state thereby allowing the model to mimic the ηE data. The origin of this change of ζ with the transient changes of the stretch and orientation is discussed in relation to the local motion of the chain necessary for adjusting its friction to the changes of the stretch/orientation environment.

AB - Nonlinear rheological behavior under uniaxial elongation was examined for unentangled melts of polystyrene (PS27; molecular weight M = 27k) and poly(p-tert-butylstyrene) (PtBS53; M = 53k) having nearly the same number of Kuhn segments per chain (nK = 30 and 35for PS27 and PtBS53, respectively). For both materials, the steady state elongational viscosity, ηE, exhibited strain-rate-hardening and then strain-rate-softening on an increase of the Weissenberg number Wi ≥ 0.3 (Wi = ε̇τ1eq, with τ1eq and ε̇ being the longest relaxation time in the linear viscoelastic regime and the Hencky strain rate, respectively). For the unentangled melts, the hardening and softening were free from any entanglement nonlinearity, so that the hardening was unequivocally related to the finite extensible nonlinear elasticity (FENE) of the chain, and the softening, to the suppression of the FENE effect due to reduction of the segment friction ζ occurring for the highly stretched and oriented chain. Thus, the ζ reduction, speculatively discussed for entangled melts so far, was experimentally confirmed, for the first time, for unentangled melts. Quantitatively, the hardening at intermediate Wi was stronger and the softening at higher Wi was weaker for PtBS53 than for PS27 despite the similarity of their nK values, which suggested that the magnitude of ζ reduction depends on the chemical structure of the chains. For estimation of this magnitude, the FENE-PM model (a FENE bead–springmodel with a pre-averaged FENE spring strength) was modified for the ζ reduction in an empirical way with an assumption that ζ at a given time is fully determined by the chain stretch and orientation and, thus, by the tensile stress σE at that time.This modified model was able to mimic the steady state ηE data excellently, and the ζ reduction utilized in the modification was weaker for PtBS53 than for PS27 to confirm the dependenc eof the magnitude of ζ reduction on the chemical structure of the chain. Nevertheless, the same modified model failed to mimic the transient stress growth and relaxation data on start-up and cessation of fast flow (at Wi ≥ 4) despite its success for the steady state ηE data in the entire range of Wi. Specifically, changes of ζ in the unentangled melts with time during the relaxation for large Wi were delayed compared to the model calculation. This result suggests, as one possibility, that ζ in those melts is determined not only by the chain stretch and orientation (i.e., by σE) at respective times but also by the transient changes of the stretch and orientation (by σ̇E), with those changes vanishing in the steady state thereby allowing the model to mimic the ηE data. The origin of this change of ζ with the transient changes of the stretch and orientation is discussed in relation to the local motion of the chain necessary for adjusting its friction to the changes of the stretch/orientation environment.

U2 - 10.1021/acs.macromol.8b01954

DO - 10.1021/acs.macromol.8b01954

M3 - Journal article

VL - 51

SP - 9710

EP - 9729

JO - Macromolecules

JF - Macromolecules

SN - 0024-9297

IS - 23

ER -