Critical behaviour of the Rouse model for gelling polymers

Abstract

It is shown that the traditionally accepted "Rouse values" for the critical exponents at the gelation transition do not arise from the Rouse model for gelling polymers. The true critical behaviour of the Rouse model for gelling polymers is obtained from spectral properties of the connectivity matrix of the fractal clusters that are formed by the molecules. The required spectral properties are related to the return probability of a "blind ant"-random walk on the critical percolating cluster. The resulting scaling relations express the critical exponents of the shear-stress-relaxation function, and hence those of the shear viscosity and of the first normal stress coefficient, in terms of the spectral dimension $d_s$ of the critical percolating cluster and the exponents $\sigma$ and $\tau$ of the cluster-size distribution.

9 pages, slightly extended version, to appear in J. Phys. A

References in corpus (8)

• Stress Relaxation of Near-Critical Gels
• Viscoelasticity near the gel-point: a molecular dynamics study
• Critical Dynamics of Gelation
• Viscosity critical behaviour at the gel point in a 3d lattice model
• Shear viscosity of a crosslinked polymer melt
• Dynamical signatures of the vulcanization transition
• Anomalous stress relaxation in random macromolecular networks
• Normal stresses at the gelation transition

Cited by in corpus (4)

• Spectral properties of the Laplacian on bond-percolation graphs
• Dynamics of gelling liquids: a short survey
• Rheology of gelling polymers in the Zimm model
• Asymptotic versus mesoscopic spectral dimensions in networks and inhomogeneous structures