Anomalous stress relaxation in random macromolecular networks

Abstract

Within the framework of a simple Rouse-type model we present exact analytical results for dynamical critical behaviour on the sol side of the gelation transition. The stress-relaxation function is shown to exhibit a stretched-exponential long-time decay. The divergence of the static shear viscosity is governed by the critical exponent $k=ϕ-β$, where $ϕ$ is the (first) crossover exponent of random resistor networks, and $β$ is the critical exponent for the gel fraction. We also derive new results on the behaviour of normal stress coefficients.