Modeling of conductivity in composites with random resistor networks

Composite polymeric electrolytes (CPE) are well known systems in which an improvement in electrical conductivity of the polymer is achieved by the addition of a non-conductive additive (ceramic powders and immiscible polymers). A new class of conductivity models based on the application of the multi-value random resistor networks to the studies of CPE was developed by the authors. The first stage of the simulation is based on the virtual composite sample generation and its transformation into a form of the three-dimensional resistor network. The sample generation can take into account variable material parameters such as average grain diameter, shell thickness as well as their statistical distribution and different dependencies of local shell conductivity on the distance from the grain surface. The second stage of the algorithm is the use of the modified iteration procedure based on Kirkpatrick approach leading to the direct current resistivity of the virtual sample. The presented results were obtained for the matrix size 100 unit × 100 unit × 100 unit (with assumption 1 unit = 1 μm). The dependency of conductivity on the grain filler concentration was studied for varying grain sizes, changing shell thickness as well as for different statistical distributions of these parameters. The obtained results of simulation are in general agreement with the experimental data.