Elastically Effective Strand Density in Polymer Networks

Langley, Neal R.

doi:10.1021/ma60004a015

Cited by 243 publications

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“…MPa for linear PDMS 43,44 ). From eq 1 the trapping factor can be thought of as the fraction of entanglements that are trapped by the network (i.e., not relieved in the swelling process).…”

Section: Network Ideality: Swellingmentioning

confidence: 99%

Linking Network Microstructure to Macroscopic Properties of Siloxane Elastomers Using Combined Nuclear Magnetic Resonance and Mesoscale Computational Modeling

et al. 2011

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It is well established that many fundamental properties of polymer materials are directly governed by chain dynamics, and both experimental and computational efforts to probe this motional spectrum have been manifold. Recently, multiple quantum (MQ) nuclear magnetic resonance (NMR) has afforded the capability to extract meaningful quantities from such measurements, namely, an effective molecular weight distribution between various topological constraints (cross-links, entanglements, etc.). We describe herein the results of recent work on model end-linked poly(dimethylsiloxane) networks where mesoscale computational studies were used to calculate elastic moduli using the NMR-derived molecular weight distributions as their sole input. These results are then compared to dynamic mechanical analysis measurements to assess the degree to which this new methodology can predict the mechanical properties of these simple elastomers. The results of this initial study suggest a high confidence in prediction and portend a nondestructive methodology capable of monitoring subtle changes in network structural motifs associated with material performance and age.

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“…MPa for linear PDMS 43,44 ). From eq 1 the trapping factor can be thought of as the fraction of entanglements that are trapped by the network (i.e., not relieved in the swelling process).…”

Section: Network Ideality: Swellingmentioning

confidence: 99%

Linking Network Microstructure to Macroscopic Properties of Siloxane Elastomers Using Combined Nuclear Magnetic Resonance and Mesoscale Computational Modeling

et al. 2011

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“…For example, Flory 16) and James and Guth 17) indicated that the fluctuation of the crosslinking points reduces the equilibrium modulus. Later, Langley 18) and Dossin and Graessley 19) demonstrated that the modulus is enhanced by the trapped entanglement (permanent knot) between the network strands, and Murakami et al 20) proposed a chemo-rheological method for determining the molecular weight between crosslinks. Recently, Urayama et al 14) made an extensive test of molecular models for rubber elasticity and demonstrated that a version of the slip-link model (Edwards-Vilgis model 21) ) describes most successfully the experimental data in a wide range of strain for various modes of deformation (e.g., uniaxial and biaxial elongation).…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic Behavior of Scarcely Crosslinked Poly(dimethyl siloxane) Gel

Takahashi

Ishimuro

Watanabe

2006

J. Soc. Rheol., Jpn

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Linear viscoelastic behavior was investigated for a poly(dimethyl siloxane) (PDMS) gel formed through a bulk double-liquid crosslinking reaction of two types of vinyl-terminated PDMS prepolymers of the molecular weights M pre ≅ 35×10 rapidly decreased to its equilibrium plateau at the modulus G e = 2800 Pa. On a further decrease of ω well in the plateau regime of G', G" decreased in proportion to ω 0.3 . Thus, the gel exhibited the fast and slow relaxation processes characterized with these types of power-law behavior of G". The molecular weight between the crosslinks evaluated from the G e data (as well as the equilibrium swelling ratio in toluene), M c ≅ 340×103 , was about ten times larger than M pre . The crosslinking reaction was made in the bulk state but still gave such a scarce gel network (with M c ≅ 10 M pre ) possibly because a large amount of sol chains and dangling chains had diluted the trapped entanglements during the reaction. From the analysis of the G' and G" data on the basis of the above M c value and the intrinsic Rouse relaxation time, the fast relaxation process was assigned as the Rouse-like constraint release (CR) process of individual gel strands. The polydispersity of the strands was found to be essential for the power-law behavior (G"∝ω n with n ≅ 0.6) to be observed in the plateau regime of G'. The slow relaxation process was related to fluctuation of the crosslinking points, which is equivalent to cooperative Rouse-CR motion of many gel strands connected at these points.

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“…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).…”

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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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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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Elastically Effective Strand Density in Polymer Networks

Cited by 243 publications

References 0 publications

Linking Network Microstructure to Macroscopic Properties of Siloxane Elastomers Using Combined Nuclear Magnetic Resonance and Mesoscale Computational Modeling

Linking Network Microstructure to Macroscopic Properties of Siloxane Elastomers Using Combined Nuclear Magnetic Resonance and Mesoscale Computational Modeling

Viscoelastic Behavior of Scarcely Crosslinked Poly(dimethyl siloxane) Gel

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

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