Continuous Random Alloy Networks: Glass Transition and Elasticity

Theissen, O.; Zippelius, Annette; Goldbart, Paul M.

doi:10.1142/s0217979297001015

Cited by 8 publications

(16 citation statements)

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“…Rotational symmetry is broken for any single realization of disorder but is statistically restored. (This type of order has also been predicted for other systems [15,16]). The order parameter involves an average over all chains, which is equivalent to an average over all directions.…”

supporting

confidence: 77%

“…Stationarity of the free energy with respect to Q, ξ, and η yields a continuous gelation transition at µ 2 c = 1 characterized by a nonzero gel fraction Q ∼ 2(µ 2 − 1), independent of l. These results are universal for the gelation transition in the saddle point approximation and have been confirmed for various models (e.g. [13,14,15]). The localization length and the degree of orientational order depend on the stiffness of the WLC.…”

supporting

confidence: 60%

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Anisotropic Random Networks of Semiflexible Polymers

Benetatos

Zippelius

2007

Phys. Rev. Lett.

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Motivated by the organization of crosslinked cytoskeletal biopolymers, we present a semimicroscopic replica field theory for the formation of anisotropic random networks of semiflexible polymers. The networks are formed by introducing random permanent crosslinks which fix the orientations of the corresponding polymer segments to align with one another. Upon increasing the crosslink density, we obtain a continuous gelation transition from a fluid phase to a gel where a finite fraction of the system gets localized at random positions. For sufficiently stiff polymers, this positional localization is accompanied by a continuous isotropic-to-nematic (IN) transition occuring at the same crosslink density. As the polymer stiffness decreases, the IN transition becomes first order, shifts to a higher crosslink density, and is preceeded by an orientational glass (statistically isotropic amorphous solid) where the average polymer orientations freeze in random directions.

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supporting

confidence: 77%

supporting

confidence: 60%

Anisotropic Random Networks of Semiflexible Polymers

Benetatos

Zippelius

2007

Phys. Rev. Lett.

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“…The control parameters are the cross-link density measured by µ 2 , the polymer flexibility measured by L/L p , and the crosslinking angle θ. Irrespective of the cross-linking angle, independent of the stiffness of the filaments and of the softness of the cross-links there is a continuous gelation transition accompanied by random local orientational ordering (SIAS phase) at the critical cross-link density µ 2 c = 1. This glassy ordering has been encountered previously for randomly linked molecules with many legs (p-Beine) [20,22]. The free energy of the SIAS is above the free energy of the sol, which however is unstable beyond µ 2 = 1 and hence, is not available in this region of the phase diagram.…”

Section: Phase Diagramsupporting

confidence: 58%

Orientational order and glassy states in networks of semiflexible polymers

2011

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Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, we study orientationally ordered phases in two-dimensional networks of randomly cross-linked semiflexible polymers. We consider permanent cross-links which prescribe a finite angle and treat them as quenched disorder in a semi-microscopic replica field theory. Starting from a fluid of un-cross-linked polymers and small polymer clusters (sol) and increasing the cross-link density, a continuous gelation transition occurs. In the resulting gel, the semiflexible chains either display long range orientational order or are frozen in random directions depending on the value of the crossing angle, the crosslink concentration, and the stiffness of the polymers. A crossing angle θ ∼ 2π/M leads to long range M -fold orientational order, e.g., "hexatic" or "tetratic" for θ = 60 • or 90 • , respectively. The transition to the orientationally ordered state is discontinuous and the critical cross-link density, which is higher than that of the gelation transition, depends on the bending stiffness of the polymers and the crosslink angle: the higher the stiffness and the lower M , the lower the critical number of cross-links. In between the sol and the long range ordered state, we always expect a gel which is a statistically isotropic amorphous solid (SIAS) with random positional and random orientational localization of the participating polymers.

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“…4.4 we have calculated the free energy cost of elastic deformations of a molecular network. 38 What emerges from this calculation is that the network acquires a nonzero shear rigidity, precisely at the critical bond density, where an infinite network and, hence, a nonzero gel fraction first appear. Furthermore, we find that the shear modulus rises continuously from zero with a critical exponent t = 4, as indicated schematically in Fig.…”

Section: Related Avenuesmentioning

confidence: 94%

“…Under this transformation flj--> fir, with 3 .u(q 2 )fi(k°,...,k" + q 1 ,...,k' 3 + q 2 , ,k n ) 2V 2 -^ E Ek Q -u(q 1 )k a .u(q 2 )fi(k 0 ,...,k a + qi + q 2 ,...,k"), (38) qi,q2a=l…”

Section: Elastic Propertiesmentioning

confidence: 99%

Vulcanised Matter: A Model Glass?

Zippelius¹,

Goldbart²

1997

Series on Directions in Condensed Matter Physics

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The aim of this article is to provide a general picture of the subject of vulcanised matter and the vulcanisation transition, viewed from the vantage point of equilibrium statistical mechanics. By the term vulcanised matter we mean matter, such as macromolecular and molecular liquids, the configurations of which are subject to a large number of permanent random constraints (crosslinked rubber providing the classic example). By the term vulcanisation transition we mean the contin uous equilibrium phase transition, driven by the density of constraints, from a liquid state to a novel solid state: the equilibrium amorphous solid state. We describe the characteristic ingredient of this state-its random static density fluctuations-and discuss the various diagnostic tools con structed to identify and quantify this ingredient, the gel fraction and the distribution of localisation lengths, along with elasticity and critical fluctuations. Moving from the general to the specific, we apply the techniques of replica statistical field theory to a semi-microscopic model of vulcan ised macromolecular matter, due to Deam and Edwards, in which crosslinks are represented by quenched random constraints. We examine an exact mean-field solution of this model, compare its predictions with results from extensive molecular dynamics computer simulations due to Plischke and Barsky, and discuss the extent to which our general expectations for the properties of the amorphous solid state are borne out. In an effort to enquire into the universality of our results, we examine alternative physical systems that exhibit amorphous solidification, such as endlinked macromolecular systems. We also explore related avenues, including covalently-bonded atomic and molecular network-formers, and discuss the extent to which vulcanised systems represent model vitreous systems.

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Continuous Random Alloy Networks: Glass Transition and Elasticity

Cited by 8 publications

References 0 publications

Anisotropic Random Networks of Semiflexible Polymers

Anisotropic Random Networks of Semiflexible Polymers

Orientational order and glassy states in networks of semiflexible polymers

Vulcanised Matter: A Model Glass?

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