Stress Relaxation of Near-Critical Gels

Abstract

The time-dependent stress relaxation for a Rouse model of a crosslinked polymer melt is completely determined by the spectrum of eigenvalues of the connectivity matrix. The latter has been computed analytically for a mean-field distribution of crosslinks. It shows a Lifshitz tail for small eigenvalues and all concentrations below the percolation threshold, giving rise to a stretched exponential decay of the stress relaxation function in the sol phase. At the critical point the density of states is finite for small eigenvalues, resulting in a logarithmic divergence of the viscosity and an algebraic decay of the stress relaxation function. Numerical diagonalization of the connectivity matrix supports the analytical findings and has furthermore been applied to cluster statistics corresponding to random bond percolation in two and three dimensions.

29 pages, 15 figures

References in corpus (4)

• Conductivity Exponent and Backbone Dimension in 2-d Percolation
• A single defect approximation for localized states on random lattices
• Critical Dynamics of Gelation
• Shear viscosity of a crosslinked polymer melt

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