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 \ensuremath{\eta} 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 \ensuremath{\tau} given by \ensuremath{\tau}=\ensuremath{\nu}-${\mathrm{\ensuremath{\beta}}}_{\mathit{p}}$/2, where \ensuremath{\nu} and ${\mathrm{\ensuremath{\beta}}}_{\mathit{p}}$ 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 \ensuremath{\eta} 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 \ensuremath{\tau}'=2\ensuremath{\tau}. Large-scale simulations confirm these scaling laws. The experimentally observed deviations from these scaling laws are also discussed.