Elasticity and Chain Dimensions in Gaussian Networks

Graessley, William W.

doi:10.1021/ma60048a031

Cited by 87 publications

(59 citation statements)

References 2 publications

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“…In fact, this difference from the Doi-Edwards model raised some concern among the authors. However, we argue here that their result is more in line with theory [30][31][32][33][34] than that of the single-chain models above.…”

Section: Pcn Simulationsupporting

confidence: 86%

“…The single-chain model should predict the same magnitude for the elastic modulus as multi-chain models and therefore estimate the same entanglement density when comparing with rheological data. Cross-linked network calculations have already established the importance of node fluctuations for this agreement [30][31][32][33][34]. In the present paper, we verify only qualitatively whether the effect of ESFs on the plateau modulus in single-chain mean-field models is consistent with that observed in multi-chain models.…”

Section: Introductionsupporting

confidence: 75%

“…The same result can be derived straightforwardly from the Green-Kubo relation, hence the check mark in the last column. Assuming that entanglements are binary interactions, which are analogous to tetrafunctional cross-links, consistency with multi-chain network models [30][31][32][33][34] then suggests that α + β = − 1 2 , so that the front factor becomes 1 2 . A second relation between α and β may be obtained from consistency with the stress-optic rule.…”

Section: Modelmentioning

confidence: 99%

“…We are primarily concerned with these issues here. Determining how fluctuations affect the predicted plateau modulus has plagued entanglement theories from early on [30][31][32][33][34]. The Doi-Edwards model contains very few fluctuations, yet the question of a factor of 4/5 in the plateau modulus persisted for many years, presumably related to monomer density fluctuations along a fixed, constant-length primitive path [7,35].…”

Section: Introductionmentioning

confidence: 99%

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Fluctuating Entanglements in Single-Chain Mean-Field Models

2013

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Abstract:We consider four criteria of acceptability for single-chain mean-field entangled polymer models: consistency with a multi-chain level of description, consistency with nonequilibrium thermodynamics, consistency with the stress-optic rule, and self-consistency between Green-Kubo predictions and linear viscoelastic predictions for infinitesimally driven systems. Each of these topics has been considered independently elsewhere. However, we are aware of no molecular entanglement model that satisfies all four criteria simultaneously. Here we show that an idea from Ronca and Allegra, generalized to arbitrary flows, can be implemented in a slip-link model to create a model that does satisfy all four criteria. Aside from the direct benefits of agreement, the result modifies the relation between the initial relaxation modulus G(0) and the entanglement molecular weight M e . If this implementation is correct, current estimates for M e would require modification that brings their values more in line with estimates based on topological analysis of molecular dynamics simulations.

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Section: Pcn Simulationsupporting

confidence: 86%

Section: Introductionsupporting

confidence: 75%

Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fluctuating Entanglements in Single-Chain Mean-Field Models

2013

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“…[4][5][6][7][8][9][10][11][12][13][14][15][16] The studies by these authors led to the evaluation of various physical properties, such as molecular dimensions of the chains, their scattering characteristics, and the elastomeric properties of the networks in various deformations. In one important example, 9 Pearson calculated mean-square fluctuations of points along the network chains and correlated these results with topological characteristics of the networks.…”

Section: Introductionmentioning

confidence: 99%

Chain dimensions and fluctuations in elastomeric networks in which the junctions alternate regularly in their functionality

Skliros¹,

Mark²,

Kloczkowski³

2009

The Journal of Chemical Physics

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A matrix method is used to determine fluctuations of junctions and points along the polymer chains making up a phantom Gaussian network that has the topology of an infinite, symmetrically grown tree. The functionalities of the junctions alternates between 1 and 2 , such that one end of each network chain has functionality 1 , while the opposite end has functionality 2 . Quantities calculated include fluctuations of 1 -functional and 2 -functional junctions, and fluctuations of points along network chains, as well as correlations of these fluctuations. This was done for points and junctions along any path in the network, where these points and junctions were separated by no junctions or several junctions, Fluctuations have also been calculated for the distances between points and junctions. The present results represent significant generalizations of earlier work in this area ͓Kloczkowski et al., Macromolecules 22, 1423 ͑1989͔͒. These generalizations and extensions should be very useful in a number of contexts, such as interpreting small-angle neutron scattering results on labeled paths in polymer networks, or fluctuations of loops in the Gaussian network model of proteins.

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Elasticity, Rubber‐like

Queslel

Mark

2001

Encyclopedia of Polymer Science and Technology

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Long, flexible polymer chains with high mobility and weak interchain interactions may be covalently linked together to form network structures. These materials exhibit a unique behavior called rubber‐like elasticity, which is high and reversible deformability (up to 10 times the original dimension). The origin of elasticity at thermodynamic equilibrium is the decrease in entropy of the chains between cross‐linking points resulting from the extension. Elastomers therefore follow thermodynamic laws similar to those for gases. There is a minor intramolecular energetic component in the retractive force which can be extracted from thermoelasticity experiments and is related to conformational energy changes of the chains. Most of the theoretical and experimental works in the field of rubber‐like elasticity have been devoted to the characterization of network structures. Molecular models based on statistical mechanics have been applied to the analysis of equilibrium properties such as stress–strain measurements in uniaxial extension and swelling by a solvent. The real behavior of rubbers is between the predictions of the simple affine and phantom models and is well represented by molecular models which include entanglement constraints. These models associated with topological descriptions of networks are powerful tools to describe network structures.

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Elasticity and Chain Dimensions in Gaussian Networks

Cited by 87 publications

References 2 publications

Fluctuating Entanglements in Single-Chain Mean-Field Models

Fluctuating Entanglements in Single-Chain Mean-Field Models

Chain dimensions and fluctuations in elastomeric networks in which the junctions alternate regularly in their functionality

Elasticity, Rubber‐like

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