Polymers in quenched random environment: Weak replica symmetry breaking

Haronska, P.; Vilgis, Thomas A.

doi:10.1063/1.467623

Cited by 21 publications

(19 citation statements)

References 12 publications

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“…, which agrees with various calculations of the different type [1,19]. This result for Gaussian chains states simply that the size of the chain is entirely determined by the disorder.…”

Section: B Annealed and Quenched Disordersupporting

confidence: 91%

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Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking

Migliorini

Rostiashvili

Vilgis

2003

The European Physical Journal B - Condensed Matter

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The Langevin dynamics of a self -interacting chain embedded in a quenched random medium is investigated by making use of the generating functional method and one -loop (Hartree) approximation. We have shown how this intrinsic disorder causes different dynamical regimes. Namely, within the Rouse characteristic time interval the anomalous diffusion shows up. The corresponding subdiffusional dynamical exponents have been explicitly calculated and thoroughly discussed. For the larger time interval the disorder drives the center of mass of the chain to a trap or frozen state provided that the Harris parameter, (∆/b d )N 2−νd ≥ 1, where ∆ is a disorder strength, b is a Kuhnian segment length, N is a chain length and ν is the Flory exponent. We have derived the general equation for the non -ergodicity function f (p) which characterizes the amplitude of frozen Rouse modes with an index p = 2πj/N . The numerical solution of this equation has been implemented and shown that the different Rouse modes freeze up at the same critical disorder strength ∆c ∼ N −γ where the exponent γ ≈ 0.25 and does not depend from the solvent quality.

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“…, which agrees with various calculations of the different type [1,19]. This result for Gaussian chains states simply that the size of the chain is entirely determined by the disorder.…”

Section: B Annealed and Quenched Disordersupporting

confidence: 91%

“…A large number of theoretical studies emphasizing the statical [10,11,12,13,14,15,16,17,18,19] and dynamical [12,20,21,22,23,24,25,26] aspects of the problem. When discussing the static properties one should discriminate between the annealed and quenched averaging.…”

Section: Introductionmentioning

confidence: 99%

Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking

Migliorini

Rostiashvili

Vilgis

2003

The European Physical Journal B - Condensed Matter

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“…There has been much interest in recent years in the properties of polymer chains in a quenched random environment [1][2][3][4][5]. This problem is directly related to that of a quantum particle in a random medium [6,7] and to that of a flux line in a type II superconductor in the presence of random columnar defects [8,9] as will be made clear below.…”

Section: Introductionmentioning

confidence: 99%

Replica field theory for a polymer in random media

Goldschmidt

2000

Phys. Rev. E

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In this paper we revisit the problem of a (non-self-avoiding) polymer chain in a random medium which was previously investigated by Edwards and Muthukumar (EM) [J. Chem. Phys. 89, 2435 (1988)]. As noticed by Cates and Ball (CB) [J. Phys. (France) 49, 2009 (1988)] there is a discrepancy between the predictions of the replica calculation of EM and the expectation that in an infinite medium the quenched and annealed results should coincide (for a chain that is free to move) and a long polymer should always collapse. CB argued that only in a finite volume one might see a "localization transition" (or crossover) from a stretched to a collapsed chain in three spatial dimensions. Here we carry out the replica calculation in the presence of an additional confining harmonic potential that mimics the effect of a finite volume. Using a variational scheme with five variational parameters we derive analytically for d<4 the result R approximately (g|ln &mgr;|)(-1/(4-d)) approximately (g ln V)(-1/(4-d)), where R is the radius of gyration, g is the strength of the disorder, &mgr; is the spring constant associated with the confining potential, and V is the associated effective volume of the system. Thus the EM result is recovered with their constant replaced by ln V as argued by CB. We see that in the strict infinite volume limit the polymer always collapses, but for finite volume a transition from a stretched to a collapsed form might be observed as a function of the strength of the disorder. For d<2 and for large V>V' approximately exp(g(2/(2-d))L((4-d)/(2-d))) the annealed results are recovered and R approximately (Lg)(1/(d-2)), where L is the length of the polymer. Hence the polymer also collapses in the large L limit. The one-step replica symmetry breaking solution is crucial for obtaining the above results.

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“…Here we use a ''pair field'' to decouple the quartic interaction. 14,15 To see this, we start by introducing the generating functional .…”

Section: The Field Theorymentioning

confidence: 99%

Melts of polymeric fractals and D-dimensional manifolds: Saturation vs screening

Haronska

Vilgis

1995

The Journal of Chemical Physics

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This paper discusses the behavior of melts of polymeric fractals in their dense state. It is shown that melts of polymeric fractals of spectral dimension D behave differently when D exceeds a critical value, i.e., D S ϭ2d/(2ϩd). Here d is the dimension of space. For larger connectivities the fractals are saturated, whereas fractals with smaller connectivity behave similarly to melts of linear polymer chains. In the latter case the polymers interpenetrate each other to a great extent, screen their excluded volume, and retain their ideal shape. This conclusion is drawn by studying screening processes in melts of polymeric manifolds of arbitrary connectivity. It is shown that for systems above the critical spectral dimension a screening length exists, i.e., in other words, a concentration, for which the screening condition can never be satisfied. It is shown that this fact corresponds to saturation. Below the critical connectivity dimension the classical excluded volume screeningcomparable to the case in linear polymer chains-takes place. The condition on the spectral dimension is equivalent to a condition in terms of the Gaussian fractal dimension d f ϭ2D/(2ϪD), i.e., the melt saturates when the embedding space dimension is less or equal than the Gaussian fractal dimension, i.e., dрd f .

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Polymers in quenched random environment: Weak replica symmetry breaking

Cited by 21 publications

References 12 publications

Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking

Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking

Replica field theory for a polymer in random media

Melts of polymeric fractals and D-dimensional manifolds: Saturation vs screening

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