Permanent Set of Cross-Linking Networks:  Comparison of Theory with Molecular Dynamics Simulations

Rottach, Dana; Curro, John G.; Budzien, Joanne; Grest, Gary S.; Svaneborg, Carsten; Everaers, Ralf

doi:10.1021/ma060767x

Cited by 52 publications

(62 citation statements)

References 41 publications

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“…The effect of the chain's interactions with the surrounding material ͑entanglements͒ was first treated by de Gennes, 8 giving rise to the concept of a chain constrained by a tube, and moving by a process of reptation. [17][18][19] Common to all of the models is the belief that the elastic force is a consequence of entropy changes associated with the distribution of network chain end-to-end distances. [17][18][19] Common to all of the models is the belief that the elastic force is a consequence of entropy changes associated with the distribution of network chain end-to-end distances.…”

Section: Introductionmentioning

confidence: 99%

Quantum chemistry and molecular dynamics studies of the entropic elasticity of localized molecular kinks in polyisoprene chains

Hanson

Martin

2010

The Journal of Chemical Physics

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We investigate the thermodynamic consequences of the distribution of rotational conformations of polyisoprene on the elastic response of a network chain. In contrast to the classical theory of rubber elasticity, which associates the elastic force with the distribution of end-to-end distances, we find that the distribution of chain contour lengths provides a simple mechanism for an elastic force. Entropic force constants were determined for small contour length extensions of chains constructed as a series of localized kinks, with each kink containing between one and five cis-1,4-isoprene units. The probability distributions for the kink end-to-end distances were computed by two methods: (1) by constructing a Boltzmann distribution from the lengths corresponding to the minimum energy dihedral rotational conformations, obtained by optimizing isoprene using first principles density functional theory, and (2) by sampling the trajectories of molecular dynamics simulations of an isolated molecule composed of five isoprene units. Analogous to the well-known tube model of elasticity, we make the assumption that, for small strains, the chain is constrained by its surrounding tube, and can only move, by a process of reptation, along the primitive path of the contour. Assuming that the chain entropy is Boltzmann's constant times the logarithm of the contour length distribution, we compute the tensile force constants for chain contour length extension as the change in entropy times the temperature. For a chain length typical of moderately crosslinked rubber networks (78 isoprene units), the force constants range between 0.004 and 0.033 N/m, depending on the kink size. For a cross-linked network, these force constants predict an initial tensile modulus of between 3 and 8 MPa, which is comparable to the experimental value of 1 MPa. This mechanism is also consistent with other thermodynamic phenomenology.

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Section: Introductionmentioning

confidence: 99%

Quantum chemistry and molecular dynamics studies of the entropic elasticity of localized molecular kinks in polyisoprene chains

Hanson

Martin

2010

The Journal of Chemical Physics

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“…Recent efforts have therefore been increasingly devoted to modeling the molecular dynamics of the formation of polymer networks via the cross-linking process. Among them, one can cite the recent work of Rottach [19,20,21] who extended his research to the crosslinking process of network during stretching. Though of obvious interest, this type of model is difficult to directly apply to the case of any particular experimental study.…”

Section: Introductionmentioning

confidence: 99%

Evolution of EPDM networks aged by gamma irradiation – Consequences on the mechanical properties

Planès

Chazeau

Vigier

et al. 2009

Polymer

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words):Different Ethylene Propylene Diene Monomer (EPDM) elastomers with different crosslink densities have been processed in order to evaluate the influence of gamma irradiation on their properties. In the case of a major phenomenon of chain scissions, the consequences are a decrease in the modulus but also a decrease in the strain at break. This decrease in the strain at break is opposite to what is expected for materials with increasing average chain length between crosslinks. To gain more insight into the network architecture, which is presumed to be responsible for this behavior, Charlesby's approach is applied. In tandem, a computational model of the degradation is developed for improved prediction of the evolution of the elastic modulus. Using these calculations, a novel interpretation of the ultimate properties of the elastomer as a function of its architecture is proposed.

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“…These results were published in the journal Macromolecules 17 . Four standard models of rubber elasticity were compared to the simulated permanent set results: phantom 9,10 , affine 8 , constrained junction 18 , and slip tube 19 .…”

Section: Permanent Set From Uniaxial Extension Resultsmentioning

confidence: 75%

Report on ASC project degradation of organic materials.

Thompson¹,

Curro²,

Rottach

et al. 2006

Self Cite

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Using molecular dynamics simulations, a constitutive model for the chemical aging of polymer networks was developed. This model incorporates the effects on the stress from the chemical crosslinks and the physical entanglements. The independent network hypothesis has been modified to account for the stress transfer between networks due to crosslinking and scission in strained states. This model was implemented in the finite element code Adagio and validated through comparison with experiment. Stress relaxation data was used to deduce crosslinking history and the resulting history was used to predict permanent set. The permanent set predictions agree quantitatively with experiment.3

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Permanent Set of Cross-Linking Networks: Comparison of Theory with Molecular Dynamics Simulations

Cited by 52 publications

References 41 publications

Quantum chemistry and molecular dynamics studies of the entropic elasticity of localized molecular kinks in polyisoprene chains

Quantum chemistry and molecular dynamics studies of the entropic elasticity of localized molecular kinks in polyisoprene chains

Evolution of EPDM networks aged by gamma irradiation – Consequences on the mechanical properties

Report on ASC project degradation of organic materials.

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