Critical Dynamics of Gelation

Abstract

Shear relaxation and dynamic density fluctuations are studied within a Rouse model, generalized to include the effects of permanent random crosslinks. We derive an exact correspondence between the static shear viscosity and the resistance of a random resistor network. This relation allows us to compute the static shear viscosity exactly for uncorrelated crosslinks. For more general percolation models, which are amenable to a scaling description, it yields the scaling relation $k=\varphi -\beta$ for the critical exponent of the shear viscosity. Here $\beta$ is the thermal exponent for the gel fraction and $\varphi$ is the crossover exponent of the resistor network. The results on the shear viscosity are also used in deriving upper and lower bounds on the incoherent scattering function in the long-time limit, thereby corroborating previous results.

34 pages, 2 figures (revtex, amssymb); revised version (minor changes)

References in corpus (9)

• How do the properties of a glass depend on the cooling rate? A computer simulation study of a Lennard-Jones system
• Randomly Crosslinked Macromolecular Systems: Vulcanisation Transition to and Properties of the Amorphous Solid State
• A single defect approximation for localized states on random lattices
• Analytic computation of the Instantaneous Normal Modes spectrum in low density liquids
• Statistical mechanics of macromolecular networks without replicas
• Critical Exponents for Diluted Resistor Networks
• Shear viscosity of a crosslinked polymer melt
• Renormalization-Group Approach to the Vulcanization Transition
• Dynamical signatures of the vulcanization transition

Cited by in corpus (15)

• Gel to glass transition in simulation of a valence-limited colloidal system
• Nonequilibrium continuous phase transition in colloidal gelation with short-range attraction
• Stress Relaxation of Near-Critical Gels
• Spectral properties of the Laplacian on bond-percolation graphs
• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• The rigidity transition in polymer melts with van der Waals interactions
• Dynamical Scaling Behavior of Percolation Clusters in Scale-free Networks
• Critical behaviour of the Rouse model for gelling polymers
• Anomalous stress relaxation in random macromolecular networks
• A model for gelation with explicit solvent effects: Structure and dynamics
• Normal stresses at the gelation transition
• Dynamics of gelling liquids: a short survey
• Diffusion of gelation clusters in the Zimm model
• Correlated rigidity percolation and colloidal gels
• Variational bounds for the shear viscosity of gelling melts