A frequency-dependent theory of electrical conductivity and dielectric permittivity for graphene-polymer nanocomposites

Abstract

Many experiments have shown that electrical conductivity and dielectric permittivity of graphene-polymer nanocomposites are strongly dependent on the loading frequency, but at present no theory seems to be able to address the continuous influence of frequency. In this work we present a new effective-medium theory that is derived from the underlying physical processes including the effects of filler loading, aspect ratio, percolation threshold, interfacial tunneling, Maxwell-Wagner-Sillars polarization, and the extra frequency-affected electron hopping and Debye dielectric relaxation, to determine the loading-frequency dependence of these two fundamental properties. The theory is formulated in the context of complex conductivity under harmonic loading. We highlight this new theory with an application to PVDF/xGnP nanocomposites, and demonstrate that the calculated conductivity and permittivity are in close agreement with the reported experimental data over the frequency range from 102 to 107 Hz. We also show that the electrical conductivity tends to increase with frequency but the dielectric permittivity tends to decrease. We find that, at low frequency, the properties are dominated by filler loading but at high frequency the loading frequency is the dominant factor. The theory also reveals that the percolation phenomenon is clearly defined at low frequency but becomes blurred at high frequency.