Shear viscosity of a crosslinked polymer melt

Abstract

We investigate the static shear viscosity on the sol side of the vulcanization transition within a minimal mesoscopic model for the Rouse-dynamics of a randomly crosslinked melt of phantom polymers. We derive an exact relation between the viscosity and the resistances measured in a corresponding random resistor network. This enables us to calculate the viscosity exactly for an ensemble of crosslinks without correlations. The viscosity diverges logarithmically as the critical point is approached. For a more realistic ensemble of crosslinks amenable to the scaling description of percolation, we prove the scaling relation $k=\varphi -\beta$ between the critical exponent $k$ of the viscosity, the thermal exponent $\beta$ associated with the gel fraction and the crossover exponent $\varphi$ of a random resistor network.

8 pages, uses Europhysics Letters style; Revisions: results extended

References in corpus (3)

• Conductivity Exponent and Backbone Dimension in 2-d Percolation
• Statistical mechanics of macromolecular networks without replicas
• Critical Exponents for Diluted Resistor Networks

Cited by in corpus (13)

• Stress Relaxation of Near-Critical Gels
• Viscoelasticity near the gel-point: a molecular dynamics study
• Critical Dynamics of Gelation
• 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
• Phase diagram of selectively cross-linked block copolymers shows chemically microstructured gel
• A model for gelation with explicit solvent effects: Structure and dynamics
• Normal stresses at the gelation transition
• Dynamics of gelling liquids: a short survey
• Rheology of gelling polymers in the Zimm model
• Variational bounds for the shear viscosity of gelling melts