Percolation threshold and electrical conductivity of a two-phase composite containing randomly oriented ellipsoidal inclusions

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 Casta n eda - Willis P. Ponte Casta n eda 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 with measurement on a multi-walled carbon nanotube/alumina composite indicates that the theory could capture the major features of the experimentally observed trends sufficiently well.