Research on the Influence of Matrix Shape on Percolation Threshold Values for Current Flow Conducted Using the Monte Carlo Simulation Method

Abstract

In this study, in order to determine the effect of matrices’ shape on the percolation threshold values, computer simulations were performed using the Monte Carlo method for a 200 × 200 square-shaped matrix and rectangular matrices containing the same number of nodes as the square matrix. Based on the simulations, the average values of the percolation thresholds and standard deviations for the current flow along and across the matrices were determined. It was determined that for a square-shaped matrix, the average values of the percolation thresholds in both directions of the current flow were the same. Extending the rectangular matrix while reducing its height causes the average value of the percolation threshold in the direction of the current flow along the matrix to increase from 0.592740 to 0.759847, while in the transverse direction, it decreases from 0.592664 to 0.403614. The values of the classical asymmetry coefficients of the probability distributions of the percolation thresholds for both directions of the current flow were determined. Histograms of the probability distributions of the percolation threshold values for a square-shaped matrix and rectangular matrices were made and compared with the normal distributions. It was found that the occurrence of two percolation thresholds in rectangular layers should be considered when analyzing the electrical conductivity measurements of nanocomposite thin films.

Keywords

• percolation
• conductivity
• nanocomposite
• matrix
• simulation