Order and localization in randomly cross-linked polymer networks

Barsky, Sandra; Plischke, Michael

doi:10.1103/physreve.53.871

Cited by 34 publications

(32 citation statements)

References 14 publications

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“…Similar expression for other types of deformation have been discussed in the literature and are widely used in simulations [49,51,52]. For the phantom and Rouse model Hamiltonians the last, so-called hyper-virial term vanishes.…”

Section: Discussionmentioning

confidence: 64%

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Constrained fluctuation theories of rubber elasticity: General results and an exactly solvable model

Everaers

1998

Eur. Phys. J. B

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Abstract. We present a new model of rubber elasticity where linear forces act to constrain the fluctuations of the eigenmodes of the phantom model. The model allows us to treat the constrained junction and the tube model within the same, transparent formalism, does not require any further approximations, and is particularly suited for the analysis of simulation data for (strained) model polymer networks. As an interesting side result we show that in order for the model to be consistent, the constraints (but not the mean polymer conformations!) have to deform affinely, a severe restriction that might also apply to other models. Complementary, we prove in analogy to the derivation of the virial theorem that introducing constraints into the phantom network Hamiltonian leads to extra terms in addition to the usual Doi-Edwards formulas for the polymer contribution to the stress tensor which vanish only for affinely deforming constraints.

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Section: Discussionmentioning

confidence: 64%

“…Current molecular dynamics simulations of model polymer networks cover the relevant time and length scales and allow to directly determine the restoring forces in strained systems [38,39,[48][49][50]. At the same time, and in contrast to experiments, one has access to the actual chain conformations.…”

Section: Discussionmentioning

confidence: 99%

Constrained fluctuation theories of rubber elasticity: General results and an exactly solvable model

Everaers

1998

Eur. Phys. J. B

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“…1, this picture has been rather well confirmed in molecular dynamics computer simulations of three-dimensional systems of randomly crosslinked, interacting macromolecules, undertaken at Simon Fraser University by Barsky and Plischke [11,12].…”

Section: Replica Statistical Mechanics; Replica Field Theorymentioning

confidence: 71%

Random solids and random solidification: what can be learned by exploring systems obeying permanent random constraints?

Goldbart¹

2000

J. Phys.: Condens. Matter

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Abstract. In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition to a random solid state. In this random solid state, particles are permanently but randomly localized in space, and a rigidity to shear deformations emerges. Owing to the permanence of the random constraints, this phase transition is an equilibrium transition, which confers on it a simplicity (at least relative to the conventional glass transition) in the sense that it is amenable to established techniques of equilibrium statistical mechanics. In this Paper I shall review recent developments in the theory of random solidification for systems obeying permanent random constraints, with the aim of bringing to the fore the similarities and differences between such systems and those exhibiting the conventional glass transition. I shall also report new results, obtained in collaboration with Weiqun Peng, on equilibrium correlations and susceptibilities that signal the approach of the random solidification transition, discussing the physical interpretation and values of these quantities both at the Gaussian level of approximation and, via a renormalization-group approach, beyond.

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“…The purpose of the present section is to examine the conclusions of the Landau theory, especially those concerning universality and scaling, in the light of the extensive molecular dynamics simulations, performed by Barsky and Plischke [13,14]. These simulations address the amorphous solidification transition in the context of randomly cross-linked macromolecular systems, by using an off-lattice model of macromolecules interacting via a Lennard-Jones potential.…”

Section: Comparison With Numerical Simulations: Universality Exhibmentioning

confidence: 99%

“…Perhaps even more strikingly, in extensive numerical simulations of randomly cross-linked macromolecular systems, Barsky and Plischke [13,14] have employed an off-lattice model of macromolecules interacting via a Lennard-Jones potential. Yet again, an essentially identical picture has emerged for the transition to and properties of the amorphous solid state, despite the substantial differences between physical ingredients incorporated in the simulation and in the analytical theory.…”

Section: Introductionmentioning

confidence: 99%

Universality and its origins at the amorphous solidification transition

et al. 1998

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Systems undergoing an equilibrium phase transition from a liquid state to an amorphous solid state exhibit certain universal characteristics. Chief among these are the fraction of particles that are randomly localized and the scaling functions that describe the order parameter and (equivalently) the statistical distribution of localization lengths for these localized particles. The purpose of this Paper is to discuss the origins and consequences of this universality, and in doing so, three themes are explored. First, a replica-Landau-type approach is formulated for the universality class of systems that are composed of extended objects connected by permanent random constraints and undergo amorphous solidification at a critical density of constraints. This formulation generalizes the cases of randomly cross-linked and end-linked macromolecular systems, discussed previously. The universal replica free energy is constructed, in terms of the replica order parameter appropriate to amorphous solidification, the value of the order parameter is obtained in the liquid and amorphous solid states, and the chief universal characteristics are determined. Second, the theory is reformulated in terms of the distribution of local static density fluctuations rather than the replica order parameter. It is shown that a suitable free energy can be constructed, depending on the distribution of static density fluctuations, and that this formulation yields precisely the same conclusions as the replica approach. Third, the universal predictions of the theory are compared with the results of extensive numerical simulations of randomly cross-linked macromolecular systems, due to Barsky and Plischke, and excellent agreement is found. 82.70.Gg, 64.60.Ak

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Order and localization in randomly cross-linked polymer networks

Cited by 34 publications

References 14 publications

Constrained fluctuation theories of rubber elasticity: General results and an exactly solvable model

Constrained fluctuation theories of rubber elasticity: General results and an exactly solvable model

Random solids and random solidification: what can be learned by exploring systems obeying permanent random constraints?

Universality and its origins at the amorphous solidification transition

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