Superelastic percolation networks and the viscosity of gels

We define a superelastic percolation network as one composed of Hookean bonds which take on infinite or unit spring constants with probabilities $p$ and $1-p$, respectively. The elastic moduli of such networks diverge with an exponent $\tau$ as the elastic percolation threshold $p_{\mathrm{ce}}$ is approached from below. A homogeneous function representation of elastic moduli of percolation networks in the vicinity of $p_{\mathrm{ce}}$ is proposed. For a two-dimensional triangular network $\tau$ is estimated to be about 1.12 by phenomenological renormalization of Monte Carlo data. We suggest that the viscosity of gels, as $p_{\mathrm{ce}}$ is approached, may possibly diverge with exponent $\tau$ and not with the critical exponent of superconducting networks, as suggested by de Gennes.