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

Abstract

The 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. K E Y W O R D Sdielectric response, multi-scale, non-uniform dispersion, porous carbon fiber/mullite composite, X-band How to cite this article: Xia X, Zhao S, Long L, Li Y, Zhou W. Multi-scale modeling for frequency-dependent dielectric responses of non-uniform porous carbon fiber/ mullite composites.

Basic principle, progress, and prospects of coal gangue ceramic proppants

“…The main chemical composition of the mainstream ceramic proppant after sintering is Al 2 O 3 and SiO 2 , and the main phases are corundum (Al 2 O 3 ) and mullite (3Al 2 O 3 ·2SiO 2 ) 23,24 . Corundum and mullite crystals have high strength in nature and can offer satisfactory strength to ceramic proppants 25–27 . Mullite crystals are rod‐shaped and interspersed in corundum crystals to reduce the density and enhance the toughness of ceramic proppants 28 .…”

“…23,24 Corundum and mullite crystals have high strength in nature and can offer satisfactory strength to ceramic proppants. [25][26][27] Mullite crystals are rod-shaped and interspersed in corundum crystals to reduce the density and enhance the toughness of ceramic proppants. 28 The properties of prepared ceramic proppants vary, because the composition of bauxite mined in different regions differs.…”