An X-band theory of electromagnetic interference shielding for graphene-polymer nanocomposites

Several experiments have revealed that the electromagnetic interference (EMI) shielding effectiveness (SE) of graphene-polymer nanocomposites in the X-band range is dependent on the AC frequency and graphene loading, but at present, no related theory seems to exist. In this paper, we develop an effective-medium theory that also considers the interface effects, percolation threshold, electron tunneling, Maxwell-Wagner-Sillars polarizations, Dyre's frequency-assisted electron hopping, and Debye's dielectric relaxation, to calculate the electrical conductivity, dielectric permittivity, and magnetic permeability of the nanocomposites. We then implement these properties into Maxwell's equations for a plane wave to address this issue. To provide the EMI SE over the X-band, the effective-medium theory is written in the complex setting, with the complex electrical conductivity and real magnetic permeability as the homogenization variables. We highlight the developed theory with applications to reduced graphene oxide/polystyrene nanocomposites, and show that the predicted EMI SEs are in close agreement with the measured data in the 8.2-12.4 GHz range at the graphene loadings of 0.87, 1.95, and 3.47 vol. %. We also show that the effective conductivity increases markedly in the high frequency range, while the dielectric permittivity decreases to a very low value. The EMI SE is found to increase with the conductivity and permeability, but weakly decrease with the permittivity. To provide the sources of shielding, the separate contributions from multiple-reflection loss, absorption loss, and reflection loss, to the overall EMI SE of the nanocomposite are also illustrated. Published by AIP Publishing.