Non-universal scaling behavior of polymer-metal composites across the percolation threshold

The universal percolation behavior i.e. σeff(ω,fcon≈fc)∝ωxσeff(ω,fcon≈fc)∝ωx and εeff(ω,fcon≈fc)∝ω-yεeff(ω,fcon≈fc)∝ω-y is satisfied; with x + y = 1, where σeff is the effective ac conductivity of the composite, ω is the frequency of applied ac signal and fc is percolation threshold. The exponents (x = 0.72 and y = 0.28) obtained under the inter-cluster polarization model for the case of 3D systems are consistent with the experimental values. The critical exponents s, s′ and t which characterize the divergence of εeff and σeff in the vicinity of fc show non-universal values. The non-universality of s, s′ and t is correlated with the extent of spatial connectivity of filler particles, which is reflected from the experimental values of loss tangent.