Enhanced conductivity in ionic conductor-insulator composites: numerical models in two and three dimensions

We describe a two-dimensional (2D) and a three-dimensional (3D) percolation model for ionic conductor-insulator composites such as copper(I) bromide-titanium dioxide (CuBr-TiO2) or lithium iodide-alumina (LiI-Al2O3). These composites present an enhanced conductivity closely related to the insulator concentration. This effect is explained by the formation of highly conducting space charge regions near the phase boundaries which are represented by good conductor bonds. Our numerical model takes into account grain size and correlation effects. The dimension has a leading role for the conduction properties. In the 2D case, the good conductor bonds do not percolate, whatever the insulator concentration, and the maximum conductivity of the composite samples is of the same order as that of the ionic conductor grains. The behavior of the system is very different in the 3D case where, for a large domain of composition, the good conductors percolate through the regions between the conductor grains. For the CuBr-TiO2 composites the conductivity versus composition curve is bell-shaped. Conversely, in the LiI-Al2O3 system, a linear relation between the conductivity and the insulator volume fraction is obtained in the experiments. Our model gives a plausible interpretation of the conductivity in both systems.