Commentary: Reflections on “Some phenomenological consequences of the Doi-Edwards theory of viscoelasticity,” by William W. Graessley,J. Polym. Sci., Polym. Phys. Ed., 18, 27 (1980)

Graessley, William W.

doi:10.1002/polb.1996.948

Cited by 408 publications

(805 citation statements)

References 5 publications

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“…27). The corresponding molecular weight of the effective gel strands, M c ¼ ð1 À f guest ÞRT=G e ¼ $ 15 Â 10 3 ( = PDMS density, R = gas constant, and T = absolute temperature), was considerably smaller than the prepolymer molecular weight (84 Â 10 3 ) and rather close to the entanglement molecular weight (M e ¼ $ 8:1 Â 10 3 for PDMS 28 ), indicating that Gel-U prepared through the end-linking reaction in bulk contained densely trapped entanglements. 27 This Gel-U sample, supplied in a form of thick disk of the thickness ¼ $ 5 mm, was carefully sliced with a razor into rectangular specimens of the thickness ¼ $ 1 mm, length ¼ $ 20 mm, and width ¼ $ 10 mm, and these specimens were utilized in the elongational test.…”

Section: Experimental Materialsmentioning

confidence: 99%

“…This result unequivocally indicates that the gel strands therein have a broad molecular weight distribution, as fully discussed previously. 25,26 The width of this distribution can be estimated by fitting the G 0 and G 00 data shown in Figure 1 with a Rouse network model: 25,26 Since M w,sol (¼ 45:8 Â 10 3 ) of the sol chains is larger than the entanglement molecular weight for PDMS, M e ¼ 8:1 Â 10 3 , 28 sol of the sol chains is affected by the entanglement with the gel strands as well as the entanglement among the sol chains. From the bulk viscosity data of entangled linear PDMS chains, sol of those sol chains was estimated to be 3 Pa s with the method explained in Appendix A. Utilizing this sol value, we attempted to fit the G 0 and G 00 data of Gel-1/1 with eq 2 to estimate the molecular weight distribution of the strands.…”

Section: Molecular Weight Distribution Of As-prepared Gel-1/1 Strandsmentioning

confidence: 99%

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Nonlinear Mechanical Behavior of Scarcely Crosslinked Poly(dimethyl siloxane) Gel: Effect of Strand Length Polydispersity

Takahashi

Ishimuro

Watanabe

2008

Polym J

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Nonlinear mechanical behavior was examined for a scarcely crosslinked poly(dimethyl siloxane) gel (referred to as Gel-1/1) under constant-rate elongation and large step shear strains. The average molecular weight of the gel strands evaluated from the equilibrium modulus in the linear viscoelastic regime was M c ¼ 190 Â 10 3 , and the strands had a significantly broad molecular weight distribution, M w =M n ¼ $ 600 as estimated by fitting the linear viscoelastic moduli with a Rouse network model. In the elongational test at constant elongational rates _ " " (¼ _ = ; = elongational ratio), the Gel-1/1 sample exhibited _ " "-insensitive strain hardening followed by rupture at max ¼ 4:5. This max was significantly smaller than the max nominally expected for a gel composed of monodisperse strands having M c ¼ 190 Â 10 3 ; max ¼ 53 and max = max ¼ $ 0:08 for those strands. In contrast, a reference experiment made for a Gel-U sample composed of monodisperse strands (M c ¼ 15 Â 10 3 ; including densely trapped entanglements) indicated that max of this gel was close to max ; max ¼ $ 14, max ¼ 16, and max = max ¼ $ 0:9 for Gel-U. These results suggested that the low-M fractions of the strands in the Gel-1/1 sample were highly stretched and broken at much smaller than the max defined for the average M c , thereby governing the nonlinear elongational behavior/rupture of Gel-1/1. Under large step shear strains (> 2), Gel-1/1 exhibited nonlinear decay of the shear stress with time. Analysis of the linear viscoelastic moduli of Gel-1/1 after imposition of large strains indicated that the stress decay under large strains reflected scission of the low-M fractions of the gel strands as well as the motion of scissionformed long strands occurring with time. This behavior was qualitatively similar to the nonlinear elongational behavior, although a delicate difference related to time-dependent cessation/motion of the scission-formed long strands remained between the nonlinearities under the large shear and elongation.KEY WORDS: Scarcely Crosslinked Siloxane Gel / Polydisperse Gel Strands / Large Deformation / Strand Scission / The rubber elasticity has been one of the most important subjects in the field of polymer physics, and the relationship(s) between the mechanical properties and the network structure of rubbers/gels has been studied over several decades. In the early studies, Flory 1 and James and Guth 2 showed that the fluctuation of the crosslinking points reduces the equilibrium modulus compared to the modulus expected for the affine displacements of these points. Langley 3 and Dossin and Graessley 4 demonstrated that the modulus is enhanced by the trapped entanglement (permanent knot) between the network strands, and Murakami et al. 5 suggested a chemo-rheological method for determining the molecular weight between crosslinks. After these pioneering studies, several new aspects have been revealed for natural rubbers (crosslinked cis-polyisoprenes). For example, Toki et al. 6 examined X-ray diffraction from natural rubbers e...

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Section: Experimental Materialsmentioning

confidence: 99%

Section: Molecular Weight Distribution Of As-prepared Gel-1/1 Strandsmentioning

confidence: 99%

Nonlinear Mechanical Behavior of Scarcely Crosslinked Poly(dimethyl siloxane) Gel: Effect of Strand Length Polydispersity

Takahashi

Ishimuro

Watanabe

2008

Polym J

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“…Since the number of chain entanglements are very limited in the MIM triblocks, the deformation stress is not dissipated by the central block, but directly transferred to the PMMA microdomains. M e for PIOA and for PnBA has been calculated from rheological measurements [27][28][29][30], on the basis of Eq. (3) ( Table 2):…”

Section: Stress-strain Behaviormentioning

confidence: 99%

Synthesis of poly(methyl methacrylate)-b-poly(n-butyl acrylate)-b-poly(methyl methacrylate) triblocks and their potential as thermoplastic elastomers

Tong

Jérôme

2000

Polymer

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A series of well defined poly(methyl methacrylate) (PMMA)-b-poly(n-butyl acrylate) (PnBA)-b-PMMA triblock copolymers (MnBM) has been synthesized by transalcoholysis of PMMA-b-poly(tert-butylacrylate) (PtBA)-b-PMMA precursors (MTM) by n-butanol. Phase separation is observed for all the investigated triblock copolymers, which contain PMMA outer blocks in the 5000-50 000 molecular weight (MW) range and PnBA inner blocks with MW in the 100 000-200 000 range. Although the ultimate tensile properties of these MnBM triblock copolymers are poor compared to traditional diene-based TPEs (SBS and SIS), they are much better than those ones reported for PMMA-b-poly(isooctyl acrylate) (PIOA)-b-PMMA triblocks (MIM). A reasonable explanation for this observation is found in the average molecular weight between chain entanglements (M e ) that has been estimated to be 28 000 for the central PnBA rubbery block, which is consistently much smaller than for PIOA (59 000) and substantially higher than M e for polybutadiene (1700) and polyisoprene (6100). The tensile behavior of MnBM copolymers cannot be fitted by either a simple elastomer model free from chain entanglements (suitable to MIM) or by a "filler" modified rubber model (suitable for diene-based TPEs), supporting the hypothesis that the mechanical properties of the investigated (meth)acrylate thermoplastic elastomers are significantly affected by any change in M e of the central acrylate block. Viscoelastic analysis shows that MnBM triblocks are of higher complex viscosity than the SBS and SIS analogs, leading to a shift in the order-disorder transition temperature to much higher temperature, unless the outer PMMA blocks are of very low molecular weight (5000).

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“…9,10 Therefore, we believe a consistent and convincing physical mechanism for the anomalous frequency dependence of the initial decay of the disentanglement process remains to be identified theoretically, and it must be different from the mechanism leading to non-reptation-like scaling of the longest relaxation time or viscosity. In PMC theory, this mechanism is the tracer shape fluctuations, as has been shown in section 3.A of paper I, and will further be discussed in section 3.E where the dielectric measurements of Adachi and co-workers 9 are analyzed; see also refs 25-27. Whereas various different non-self-consistent phenomenological formulations of the constraint release mechanism [12][13][14]25 have been considered as extensions of the reptation/tube approach, the constraint porosity effects of the PMC description, captured in e.g., eqs I. 68 and I.69, have no analog in the phenomenological models for polymer melts and solutions.…”

Section: Introductionmentioning

confidence: 99%

“…11 The consideration of the dynamics of the surrounding matrix is an aspect of PMC theory it shares with the constraint release models of Graessley 12 and Klein. 13,14 Whereas, in these two approaches, the diffusion coefficients of the reptative and constraint release dynamics are phenomenologically added, in the PMC approach the effects of both decay channels on the entanglement friction functions depend on length scale and are derived from one set of approximations for the microscopic intermolecular forces, as shown in eqs I.11-I.27 of paper I.…”

Section: Introductionmentioning

confidence: 99%

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 2. Comparison with Experiment

Fuchs

Schweizer

1997

Macromolecules

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The predictions of polymer mode coupling theory for the finite size corrections to the transport coefficients of entangled polymeric systems are tested in comparison with various experimental data. It is found that quantitative descriptions of the viscosities, η, dielectric relaxation time, τ , and diffusion coefficients, D, of polymer melts can be achieved with two microscopic structural fit parameters whose values are in the range expected from independent theoretical or experimental information. An explanation for the (apparent) power law behaviors of η, τ , and D in (chemically distinct) melts for intermediate molecular weights as arising from finite size corrections, mainly the self-consistent constraint release mechanism, is given. The variation of tracer dielectric relaxation times from Rouse to reptationlike behavior upon changes of the matrix molecular weight is analyzed. Self-diffusion and tracer diffusion constants of entangled polymer solutions can be explained as well, if one further parameter of the theory is adjusted. The anomalous scaling of the tracer diffusion coefficients in semidilute and concentrated polystyrene solutions, D ∼ N -2.5 , is predicted to arise due to the spatial correlations of the entanglement constraints, termed "constraint porosity". Extensions of the theory to polymer tracer diffusion through poly(vinyl methyl ether) and polyacrylamide gels provide an explanation of the observation of anomalously high molecular weight scaling exponents in a range where the size of the tracer, Rg, already considerably exceeds the gel pore size, g. IntroductionThe microscopic polymer mode coupling (PMC) theory connects the dynamics of entangled polymeric systems to the underlying equilibrium liquid structure. This description therefore naturally includes corrections arising from the finite molecular weights of tracer or matrix polymers. In the preceding paper, 1 referred to as paper I, the PMC predictions with finite size corrections have been worked out for the transport properties of entangled solutions and melts and for polymer tracer motion in gels. In the present paper these results are compared with data from many experiments. As the PMC approach has been detailed in the preceding paper, 1 it shall be summarized only shortly in this section and then compared to alternative approaches. The resulting formulas of paper I will be referenced by the equation numbers of that paper with a prefix I.The PMC approach of paper I treats the Rouseentangled crossover problem in a simple interpolative manner. The PMC contributions capturing the entanglement corrections are combined with the Rouse, unentangled quantities, see eqs I.52 and I.68 for D, eqs I.55 and I.67 for η, and eqs I.58 and I.70 for τ . Appreciable deviations from the asymptotes for high molecular weights are therefore not explained by corrections of the Rouse dynamics to the asymptotic, entangled motion. In stark contrast to the contour length fluctuation model of Doi, 2,3 the repton model of Rubinstein, 4 and the Rouse-fluc...

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Commentary: Reflections on “Some phenomenological consequences of the Doi-Edwards theory of viscoelasticity,” by William W. Graessley,J. Polym. Sci., Polym. Phys. Ed., 18, 27 (1980)

Cited by 408 publications

References 5 publications

Nonlinear Mechanical Behavior of Scarcely Crosslinked Poly(dimethyl siloxane) Gel: Effect of Strand Length Polydispersity

Nonlinear Mechanical Behavior of Scarcely Crosslinked Poly(dimethyl siloxane) Gel: Effect of Strand Length Polydispersity

Synthesis of poly(methyl methacrylate)-b-poly(n-butyl acrylate)-b-poly(methyl methacrylate) triblocks and their potential as thermoplastic elastomers

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 2. Comparison with Experiment

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