Calculation of the effective conductivity and diffusivity in composite solid electrolytes

In this paper, two geometric models for describing the effective ionic conductivity in a composite solid electrolyte are analysed. The models make use of insulating particles, which are coated with a highly ionically conducting phase, and are embedded in an ionically conducting matrix. Using a straightforward Maxwell type analysis we derive expressions for the effective ionic conductivity and diffusivity in the composite. We also employ Monte Carlo random walk methods to calculate the effective conductivity/diffusivity. It is shown that at low volume fractions of insulating phase the Maxwell approach provides much better agreement with the Monte Carlo data than previous analytical descriptions of the effective conductivity/diffusivity.