Percolation threshold in ceramic composites with isotropic conducting nanoparticles

The percolation threshold for electrical conductivity of a binary system of electrically insulating and conducting spheres was studied theoretically to yield a roadmap for electrically conductive ceramic composites. Although the crystal grains in such matrix are of irregular shape, the spheres of different sizes are used in the model to keep calculations tractable, where insulating spheres (matrix) are considered to be much larger than conducting ones (filler). This difference influences spatial distribution of conducting spheres. Besides the rough analytical estimation of the percolation threshold, we also use the Metropolis algorithm. The latter must be adapted for the system of conducting spheres which are positioned at the surface of large insulating spheres. We give a suggestion for the modification of this algorithm. Analytical estimation and Metropolis method give qualitatively similar dependence of the percolation threshold on the radii of geometrical objects, but there are significant quantitative differences in the results.