ESTIMATION OF THE CRITICAL CONCENTRATION IN AN ANISOTROPIC PERCOLATION NETWORK

A formulation based on statistical arguments is presented for estimating the critical volume fraction of cylinders necessary for the formation of a three-dimensional percolation network. Parameters included in the analysis are the geometry of the cylinder and the state of orientation of the cylinders. The principal cylinder geometric parameter is shown to be the cylinder aspect ratio. The cylinder orientation distribution is described in terms of two orientation parameters; one describes the orientation state with respect to an "axial" orientation and the other with respect to a "planar" orientation. The analysis shows that the critical volume fraction for the formation of the percolation network will vary from less than 1% to more than 20%.