Frequency-dependent scaling behavior of polyvinylidene fluoride/metal composites

The frequency-dependent percolation and scaling behavior of a variety of polymer/metal composites(PMC),based on polyvinylidene fluoride(PVDF)matrix and various types of fillers such as;metal/alloy particles of different sizes,prepared through cold/hot pressing process conditions have undergone investigation.The universal percolation behavior in the vicinity of percolation threshold((fc),i.e.,σ_(e_(ff))(ω,f_(con)≈f_(c))α/ω^(x)andε_(eff)(ω,f_(con)≈f_(c))α/ω^(-y)is well satisfied,which suggests fc to be independent of frequency,where
eff and"eff are the effective ac conductivity and effective dielectric constants of the composite andωis the frequency of applied ac signal.The obtained experimental values of the exponents are consistent with the inter-cluster polarization model(x=0:72 and y=0:28),satisfying x+y=1.The widely used percolative equations are well fitted with the experimental results of all PMC at all values of the frequency.The value of fc is found to be independent of frequency of the applied signal,suggesting the studied PMC are real percolating systems.The critical exponents(s and s0)which characterize the divergence of"ε_(ff)and
ε_(ff)in the vicinity of f_(c)are found to decrease with the increase of frequency.The rate of decrease of‘s’and‘s′’with increase of frequency is attributed to the method of preparation,size of the fillers,adhesiveness of polymer/filler and the rate of decrease of e_(ff) with frequency(due to the absence of different extents of contributions of various types of conventional polarizations).