Rubber elasticity of polymer networks: Theories

Heinrich, Gert; Straube, E.; Helmis, G.

doi:10.1007/bfb0024050

Cited by 250 publications

(273 citation statements)

References 141 publications

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“…While model A has the benefit of simplicity, Ronca and Allegra proposed model B, 16 because it leads (on length scales beyond the tube diameter) to the conservation of intermolecular contacts under strain. Similar conclusions were drawn by Heinrich and Straube 25 and Rubinstein and Panyukov. 43 In the end, this problem will have to be resolved by a derivation of the tube model from more fundamental topological considerations.…”

Section: G Discussionsupporting

confidence: 88%

“…To model confinement due to crosslinking, they used (in our notation) Model A, since this ansatz reproduces the essential properties of phantom models (affine deformation of equilibrium positions and deformation independence of fluctuations). In contrast, Heinrich and Straube 25 , and Rubinstein and Panyukov 43 treated confinement due to entanglements using Model B. Obviously, both effects are present simultaneously in polymer networks.…”

Section: Tube Modelsmentioning

confidence: 99%

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Tube Models for Rubber−Elastic Systems

Mergell

Everaers

2001

Macromolecules

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In the first part of the paper we show that the constraining potentials introduced to mimic entanglement effects in Edward's tube model and Flory's constrained junction model are diagonal in the generalized Rouse modes of the corresponding phantom network. As a consequence, both models can formally be solved exactly for arbitrary connectivity using the recently introduced constrained mode model. In the second part, we solve a double tube model for the confinement of long paths in polymer networks which is partially due to crosslinking and partially due to entanglements. Our model describes a non-trivial crossover between the Warner-Edwards and the Heinrich-Straube tube models. We present results for the macroscopic elastic properties as well as for the microscopic deformations including structure factors.

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Section: G Discussionsupporting

confidence: 88%

Section: Tube Modelsmentioning

confidence: 99%

Tube Models for Rubber−Elastic Systems

Mergell

Everaers

2001

Macromolecules

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“…The real chain is represented by the corresponding PP, which is a series of strands of average molar mass M e connecting the links. The tube model provides a basis for working out analytically the linear and nonlinear viscoelasticty of polymer melts 9,[16][17][18][19][20] and networks 10,15,[21][22][23][24] at a molecular level. Slip link models 19,20,24 also allow for analytical 8,[11][12][13]15,25,26 or stochastic simulation 14,[27][28][29][30][31][32][33][34][35][36][37] treatments with a molecular representation, at the single or many-chain level.…”

Section: Introductionmentioning

confidence: 99%

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

2012

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Abstract:We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, or as certain pairwise uncrossability interactions, as in slip-link models.A pairwise parameter, which varies between these limiting cases, shows that, for the systems studied, the character of the entanglement environment is more pairwise than collective. We employ a novel methodology, which analyzes entanglement constraints into a complete set of pairwise interactions, similar to slip links. Entanglement confinement is assembled by a plethora of links, with a spectrum of confinement strengths, from strong to weak. The strength of interactions is quantified through a link 'persistence', which is the fraction of time for which the links are active. By weighting links according to their strength, we show that confinement is imposed mainly by the strong ones, and that the weak, trapped, uncrossability interactions cannot contribute to the low frequency modulus of an elastomer, or the plateau modulus of a melt. A selfconsistent scheme for mapping topological constraints to specific, strong binary links, according to a given entanglement density, is proposed and validated. Our results demonstrate that slip links can be viewed as the strongest pairwise interactions of a collective entanglement environment. The methodology developed provides a basis for bridging the gap between atomistic simulations and mesoscopic slip link models.

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“…It might be expected that scattering experiments could shed light on these, providing an independent check on the molecular processes which govern melt rheology. The suggested processes include convective constraint release, [20][21][22] tube dilation and distortion, [23][24][25] nonaffine entanglement deformation from local chain force balance, 26 and elastic inhomogeneities. 12,13 In light of this and other scattering studies on deformed melts and solutions 12,13 that also show strong heterogeneities under strain, a better controlled series of experiments is vital.…”

Section: Introductionmentioning

confidence: 99%

Arm Relaxation in Deformed H-Polymers in Elongational Flow by SANS

Heinrich¹,

Pyckhout‐Hintzen²,

Allgaier³

et al. 2002

Macromolecules

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We present a small-angle neutron scattering (SANS) investigation of the relaxation process of branched polymer melts under deformation. The selected model polymer is an H-shaped polyisoprene having deuterium-labeled blocks at the dangling tips of the arms. The melt is step strained in a strain rig especially built for that purpose, where the sample temperature and its deformation conditions are precisely controlled. Uniaxial extensions to values of 2 and 3 are performed at a temperature above the polymer glass transition temperature T g. The sample is then allowed to relax during a given time before being quenched to below its Tg in order to freeze the chains conformation to perform the SANS experiments. Very large anisotropies in S(q) develop on time scales corresponding to the relaxation of the dangling arms. The experimental structure function is then compared to theoretical ones obtained by the random phase approximation applied to the tube model. While theory describes well the scattering for short times, it seems not to be able to describe the increase of intensity in the direction parallel to the strain at higher times, even when highly nonaffine processes such as arm retraction and branch point withdrawal are taken into account.

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Rubber elasticity of polymer networks: Theories

Cited by 250 publications

References 141 publications

Tube Models for Rubber−Elastic Systems

Tube Models for Rubber−Elastic Systems

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

Arm Relaxation in Deformed H-Polymers in Elongational Flow by SANS

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