Random resistor network application to modelling of d.c. ionic conductivity in composite polymeric electrolytes

A new class of conductivity models based on the application of the random resistor network approach is developed to study composite polymeric electrolytes. The simulation is based on virtual composite sample generation and its transformation into the form of a three-dimensional resistor network. Average grain diameter and its statistical distribution, shell thickness and different dependencies of local shell conductivity on the distance from the grain surface can act as variables. The use of the modified iteration procedure based on the Kirkpatrick approach leads to direct current resistivity value. The results were obtained for the matrix size 100 × 100 × 100 units (with assumption 1 unit = 1 μm). The dependency of conductivity on the grain filler concentration was studied for varying grain sizes, changing shell thickness and for different statistical distributions of these parameters. The obtained results of simulation are in general agreement with the experimental data.