Multi‐scale modeling for frequency‐dependent dielectric responses of non‐uniform porous carbon fiber/mullite composites

Abstract

AbstractThe frequency‐dependent dielectric responses of non‐uniformly dispersed porous carbon fiber/mullite composites fabricated by gel‐casting are intensively investigated in the X‐band range. Experimental data have shown the frequency dependence of dielectric permittivity and electrical conductivity of the overall composite. The dielectric responses of non‐uniformly dispersed porous carbon fiber/mullite composites in X‐band are quantitatively modeled through a multi‐scale homogenization method based on the effective‐medium approximation. The non‐uniform dispersion of carbon fibers and micro‐pores in the mullite ceramic has been included via a corresponding multi‐scale geometric setting. The effective dielectric permittivity and electrical conductivity of the composite both enhance with the fiber volume concentration. It is demonstrated that the decreasing dielectric permittivity and increasing electrical conductivity with respect to the AC frequency can be attributed to frequency‐dependent dielectric relaxation and electron hopping effects at the interface. Furthermore, improving the uniform dispersion of carbon fibers in the mullite is essential to achieve the enhanced dielectric response of porous carbon fiber/mullite composites. The present paper can provide the directions to design the porous carbon fiber/mullite composites for micro‐electronic devices in the high‐temperature environment.