A theory of frequency dependence and sustained high dielectric constant in functionalized graphene-polymer nanocomposites

Functionalized graphene/polymer composites are currently under extensive investigation due to their excellent mechanical and functional properties. Within the framework of electrical properties, many experiments have shown that their electrical conductivity and dielectric permittivity are strongly dependent on the frequency of the applied electric field and the volume concentration of graphene fillers. In this paper we first apply Dyre's hopping function and Debye's relaxation function to build the constitutive equations for the graphene fillers, polymer matrix, and the interface regions. In addition, Cauchy's cumulative probabilistic function is also introduced to account for the drastic increase of electron tunneling and the rapid build-up of Maxwell-WagnerSillars polarization at the interface. These functions are then integrated into an effective-medium framework in the complex domain to establish a complete theory for the frequency dependence of these two effective properties as a function of graphene loading. The developed theory is highlighted by a direct comparison with the experimental data of reduced graphene oxide/polypropylene (rGO/PP) nanocomposites. The results show that both the theory and experiment display a general increase of conductivity but a decrease of permittivity as frequency increases, and that, with the graphene loading of 0.2 vol%, there is a sustained, high level of dielectric constant beyond 1,000 covering the frequency range up to 10(4) Hz. This remarkable feature can be of particular significance to energy storage and conversion.