Critical dynamics of gelation

Broderix, Kurt; Löwe, Henning; Müller, Peter; Zippelius, Annette

doi:10.1103/physreve.63.011510

Cited by 27 publications

(73 citation statements)

References 47 publications

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“…On the other hand, if excluded-volume interactions were absent, the geometric fractal dimension d f would take on p-3 the Gaussian or ideal Rouse value d (G) f ≈ 4. The resulting lower bound for k would then coincide with the exact result in the phantom case that was computed previously [22][23][24].…”

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confidence: 77%

Variational bounds for the shear viscosity of gelling melts

et al. 2007

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We study shear stress relaxation for a gelling melt of randomly crosslinked, interacting monomers. We derive a lower bound for the static shear viscosity η, which implies that it diverges algebraically with a critical exponent k 2ν − β. Here, ν and β are the critical exponents of percolation theory for the correlation length and the gel fraction. In particular, the divergence is stronger than in the Rouse model, proving the relevance of excluded-volume interactions for the dynamic critical behaviour at the gel transition. Precisely at the critical point, our exact results imply a Mark-Houwink relation for the shear viscosity of isolated clusters of fixed size.

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confidence: 77%

Variational bounds for the shear viscosity of gelling melts

et al. 2007

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“…It will be convenient to specify a given crosslink configuration G := {(i e , j e )} M e=1 in terms of its N × N -connectivity matrix Γ, which is defined by the right equality in (1). For part of what follows this setting could be generalised to the crosslinking of N identical molecular units which consist themselves of a given number of monomers that are connected in some fixed manner, such as N identical chains, rings or stars of monomers [37,38]. For the ease of presentation, however, we will not consider such a generalisation here.…”

Section: Dynamical Equationmentioning

confidence: 99%

Dynamics of gelling liquids: a short survey

Löwe

Müller

Zippelius

2005

J. Phys.: Condens. Matter

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The dynamics of randomly crosslinked liquids is addressed via a Rouse-and a Zimm-type model with crosslink statistics taken either from bond percolation or Erdős-Rényi random graphs. While the Rouse-type model isolates the effects of the random connectivity on the dynamics of molecular clusters, the Zimm-type model also accounts for hydrodynamic interactions on a preaveraged level. The incoherent intermediate scattering function is computed in thermal equilibrium, its critical behaviour near the sol-gel transition is analysed and related to the scaling of cluster diffusion constants at the critical point. Second, non-equilibrium dynamics is studied by looking at stress relaxation in a simple shear flow. Anomalous stress relaxation and critical rheological properties are derived. Some of the results contradict long-standing scaling arguments, which are shown to be flawed by inconsistencies.

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“…Spectral properties of Laplacians on bond-percolation (or related) graphs have been studied in the physics literature, see the general accounts [28,9] or the recent examples [4,8,22] for applications to soft matter. The Lifshits tails, whose existence we prove here, were sought after in the numerical simulations [7] for the Neumann Laplacian on two-and three-dimensional bond-percolation graphs.…”

Section: Introductionmentioning

confidence: 99%

Spectral properties of the Laplacian on bond-percolation graphs

2006

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Bond-percolation graphs are random subgraphs of the d-dimensional integer lattice generated by a standard bond-percolation process. The associated graph Laplacians, subject to Dirichlet or Neumann conditions at cluster boundaries, represent bounded, self-adjoint, ergodic random operators with off-diagonal disorder. They possess almost surely the non-random spectrum [0,4d] and a self-averaging integrated density of states. The integrated density of states is shown to exhibit Lifshits tails at both spectral edges in the non-percolating phase. While the characteristic exponent of the Lifshits tail for the Dirichlet (Neumann) Laplacian at the lower (upper) spectral edge equals d/2, and thus depends on the spatial dimension, this is not the case at the upper (lower) spectral edge, where the exponent equals 1/2.Comment: 19 pages; presentation slightly improved, some comments and references added; to appear in Mathematische Zeitschrif

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Critical dynamics of gelation

Cited by 27 publications

References 47 publications

Variational bounds for the shear viscosity of gelling melts

Variational bounds for the shear viscosity of gelling melts

Dynamics of gelling liquids: a short survey

Spectral properties of the Laplacian on bond-percolation graphs

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