Critical properties of viscoelasticity of gels and elastic percolation networks

Abstract

Two superelastic percolation models are proposed to explain the observed behavior of the viscosity η of gels near the gel point. The elastic moduli G of one model diverge at the percolation threshold ${\mathit{p}}_{\mathit{c}}$ with a critical exponent τ given by τ=ν-${\mathrm{\beta }}_{\mathit{p}}$/2, where ν and ${\mathrm{\beta }}_{\mathit{p}}$ are the critical exponents of percolation correlation length and the strength of the infinite cluster, respectively. We propose that this system can model the behavior of η in the Zimm limit. In the second model, which we propose to be appropriate for the Rouse limit, G diverge at ${\mathit{p}}_{\mathit{c}}$ with an exponent τ’=2τ. Large-scale simulations confirm these scaling laws. The experimentally observed deviations from these scaling laws are also discussed.