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 τ as the elastic percolation threshold pce is approached from below. A homogeneous function representation of elastic moduli of percolation networks in the vicinity of pce is proposed. For a two-dimensional triangular network τ is estimated to be about 1.12 by phenomenological renormalization of Monte Carlo data. We suggest that the viscosity of gels, as pce is approached, may possibly diverge with exponent τ and not with the critical exponent of superconducting networks, as suggested by de Gennes.