Equation for the effective permittivity of particle-filled composites for material design applications

A new simple equation for the effective permittivity of particle-filled composites is presented. The equation does not involve any free parameters in addition to the volume fraction of inclusions, the semi-axes of ellipsoidal inclusions and the permittivities of materials. Alternatively, instead of semi-axes, the percolation threshold can be used as a parameter. It is derived in a similar manner as the Maxwell Garnett mixing equation, but by including an enhanced background permittivity effect when the volume filling ratio of inclusions increase. The result is a mixing equation which has the Maxwell Garnett mixing equation as a low volume filling ratio limit, but which approaches the Bruggeman mixing equation as the volume fraction of inclusions increases. The mixing equation is compared with classical mixing formulae, and to numerical simulations and measurements from the literature.