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

The universal percolation behavior i.e. σ<inf>eff</inf>(ω, f<inf>con</inf>≈f<inf>c</inf>)∝ω^x and ε<inf>eff</inf>(ω, f<inf>con</inf>≈f<inf>c</inf>)∝ω^-y is satisfied; with x+y=1, where σ<inf>eff</inf> is the effective ac conductivity of the composite, ω is the frequency of applied ac signal and f<inf>c</inf> 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 ε<inf>eff</inf> and σ<inf>eff</inf> in the vicinity of f<inf>c</inf> 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.