On the damping function of shear relaxation modulus for entangled polymers

As well known, the relaxation modulus of polymer liquids at long times can be written in the separable form as 1,2) G(t, γ) = G(t )h( γ)( 1) where G(t,γ ) is the relaxation modulus at time t and strain γ, and G(t ) is the linear relaxation modulus, h( γ) being the damping function. For highly entangled linear polymers with narrow molecular weight distributions, the damping function in shear usually show a stronger strain dependence than the Doi-Edwards (DE) theory 1) predicts. The origin of the strong damping is considered to be due to the deformation-induced phase separation.3) Originally, this was proposed for the shear deformation but must be applicable to the uniaxial elongation, because the possibility of phase separation depends only on the (pseudo-) strain energy function, which can generally be described by the strain invariants, for the polymer melts.We have reported the damping behavior of highly entangled high density polyethylene (HDPE) in shear and in uniaxial elongation. 4,5) These show that damping function in uniaxial elongation does not show such strong damping even if the damping function in shear shows a strong damping. 4,5)For highly entangled polyisobutylene (PIB) melts, the similar behavior has been observed. 6) In addition, the effect of slipping at the interface between the metal plate of rheometer and the sample surface on the damping behavior has been examined for the PIB sample.6) The PIB sample stuck on the metal plates by using an adhesive ("with-adhesive" sample)shows a stress development as elastomers do in the course of step-like strain application process for stress relaxation. 6) On the other hand, the PIB sample without adhesive ("withoutadhesive" sample) moves on the same path as "with-adhesive" in the small strain region but then shows branching in the large strain region. 6) This bifurcation is considered to be a critical point of slipping for the PIB sample.6)The PIB sample employed above was just one grade, so that we cannot clarify whether or not the critical stress becomes a material constant (if the metal species of the fixture is specified). In this study, the damping and stress growth behavior of two PIB samples (PIB-1 and PIB-3), which are different from the sample used in the previous study (we designate here the previous PIB sample as PIB-2), are examined in shear. By combining obtained data with those for PIB-2 how the molecular weight of PIB affects the critical stress for slipping is examined.PIB-1 and PIB-3 were purchased from Sigma-Aldrich Co., USA. The number-average and weight-average molecular weights (M n and M w , respectively), and the ratio M w /M n for the PIB samples are listed in Table I, together with those for PIB-2. Since the molecular weight between entanglements (M e ) for PIB is reported to be 8900, 7) we calculated the number of entanglements per chain for the three PIB samples by M n /M e . These values are also listed in Table I. According to the Osaki's criterion, 2) PIB-2 and PIB-3 are categorized in to the highly entangled systems because...

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“…As well known, the relaxation modulus of polymer liquids at long times can be written in the separable form as 1,2) …”

Section: Notementioning

confidence: 99%

Damping and Slipping Behavior of Highly Entangled Polyisobutylene

Yoshikawa

Teng

Kabeya

et al. 2016

J. Soc. Rheol., Jpn

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“…1,7,8) Looking at G(t, g ) for highly entangled linear polymers with narrow MWD obtained in shear, 9,10) we notice that the shape is quite different from that for the moderately entangled systems: The strong damping emerges for the highly entangled systems, as reviewed by Osaki.…”

Section: Introductionmentioning

confidence: 82%

“…[1][2][3][4][5][6][7][8] The experimental results, which are mostly obtained in the deformation mode of shear, have shown that at long times the relaxation modulus G(t, g) at time t and strain g can be written in a factorable form as [1][2][3][4][5][6][7][8] (1) …”

Section: Introductionmentioning

confidence: 99%

“…At least, the damping function for flexible linear polymers becomes universal 1,8) regardless of polymer species, molecular weight or polymer concentration, if the molecular weight distribution (MWD) is narrow and the number of entanglements per chain (n e ), which is defined 8) by n e = M / M e , is smaller than 50, with M and M e being the molecular weight and the molecular weight between entanglements, respectively. According to Osaki 8) we call here the linear polymers with n e < 50 "moderately entangled systems", and those with n e ≥ 50 "highly entangled systems".…”

Section: Introductionmentioning

confidence: 99%

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Damping Behavior of Highly Entangled High Density Polyethylene after Uniaxial Step Strains

Kabeya

Yoshikawa

Horinaka

et al. 2015

J. Soc. Rheol., Jpn

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“…Equation (1) holds for polymer liquids at long times [4][5][6] . The quantities, G(t, ) and G(t) are determined by the stress relaxation experiments.…”

mentioning

confidence: 99%

Slipping in Stress Relaxation in Shear Estimated by Damping and Stress- Strain Behavior of Polyisobutylene

Yoshikawa

Teng

Horinaka

et al. 2017

J. Soc. Mat. Sci., Japan

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In this article the slipping of less entangled polyisobutylene (PIB) melts and solutions in shear is investigated by the damping as well as the stress growth behavior. The obtained data are also compared with those of the moderately and highly entangled PIB systems. The concentrated solutions do not show the slipping at the sample-fixture interface probably because the stress level on the stress-strain curves is very low even at large preset strains. The less entangled melts do not show strong damping, although they show a stress peak whose value amounts to the critical stress of the moderately and highly entangled PIB samples. It is suggested that little slipping occurs for the melts of the less entangled PIB due to the existence of the fast stress relaxation processes.

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On the damping function of shear relaxation modulus for entangled polymers

Cited by 229 publications

References 37 publications

Damping and Slipping Behavior of Highly Entangled Polyisobutylene

Damping and Slipping Behavior of Highly Entangled Polyisobutylene

Damping Behavior of Highly Entangled High Density Polyethylene after Uniaxial Step Strains

Slipping in Stress Relaxation in Shear Estimated by Damping and Stress- Strain Behavior of Polyisobutylene

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