Relation between the critical exponent of elastic percolation networks and the conductivity and geometrical exponents

Abstract

The author discusses the relation between the critical behaviour of elastic percolation networks in which the bond-bending forces are present, and that of percolation conductivity. They propose that if the elastic and geometrical thresholds of the network are equal, the critical exponent f of the elastic moduli, is given by, f=t+2 nu , where t is the conductivity exponent and nu the correlation length exponent. This predicts that f(d=2) approximately=3.96, in complete agreement with the most recent and accurate estimate of f. They also discuss the applicability of the present elastic percolation models to real systems such as gels.