Percolation threshold and electrical conductivity of a two-phase composite containing randomly oriented ellipsoidal inclusions
Percolation threshold and electrical conductivity of a two-phase composite containing randomly oriented ellipsoidal inclusions
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DOI：
10.1063/1.3671675
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发表时间：
2011-12
影响因子：
3.2
通讯作者：
Yi Pan;G. Weng;S. Meguid;W. Bao;Zheng Hua Zhu;A. Hamouda
中科院分区：
文献类型：
--
作者：
Yi Pan;G. Weng;S. Meguid;W. Bao;Zheng Hua Zhu;A. Hamouda
本文提出了一种明确的、解析的理论来解释含有随机取向椭球体包裹体的双组分体系的渗透阈值、渗透饱和度和有效电导率。椭球体可以呈针状、长条形或扁圆形、球形或圆盘状。这一理论是基于Ponte Castaneda- Willis [P。Ponte Castaneda， J. R. Willis， J. Mech理论物理。固体43,1919(1995)]微观结构与Hashin- Shtrikman [Z。哈辛和S.史崔克曼，J.阿普尔。物理学。33,3125(1962)]上界。确定了两个临界体积浓度c*和c**，分别代表导电网络开始发育的渗流阈值和渗流饱和度。在这个非常短的浓度范围内，复合材料的电导率显示出非常急剧的增加，而在整个范围内，计算出的电导率显示出广泛报道的s形形状。比较wi……
An explicit, analytical theory for the percolation threshold, percolation saturation, and effective conductivity of a two-component system involving randomly oriented ellipsoidal inclusions is proposed. The ellipsoids may take the shape of a needle, prolate or oblate spheroid, sphere, or disk. This theory is based upon consideration of Ponte Castaneda--Willis [P. Ponte Castaneda and J. R. Willis, J. Mech. Phys. Solids 43, 1919 (1995)] microstructure in conjunction with Hashin--Shtrikman [Z. Hashin and S. Shtrikman, J. Appl. Phys. 33, 3125 (1962)] upper bound. Two critical volume concentrations, c* and c**, that represent the respective percolation threshold at which the conductive network begins to develop, and the percolation saturation, are identified. During this very short range of concentration, the electrical conductivity of the composite is found to exhibit a very sharp increase, while over the entire range, the calcutilated conductivity exhibits the widely reported sigmoidal shape. Comparison wi...