Analysis of the effective permittivity in percolative composites using finite element calculations

Using ab initio   finite-element calculations we study the dielectric properties of the continuum (off-lattice)-percolation system consisting of two-dimensional equilibrium distributions of randomly distributed circular and partially penetrable disks (or parallel, infinitely long, identical, partially penetrable circular cylinders) throughout a host matrix. We analyze the critical behavior governing the behavior of the real, ɛ′ɛ′, and imaginary, ɛ″ɛ″, parts of the effective permittivity of these two-phase random heterostructures near the percolation threshold ϕ2cϕ2c. We perform a quantitative test of the McLachlan (TEPPE) equation by comparing its prediction of the effective permittivity to the simulation results obtained on systems with overlapping disks.