Finite-Size Scaling Features of Electric Conductivity Percolation in Nanocomposites

Using conductive nanocomposites for bipolar plates in fuel cells can improve their performance. Percolation is the mechanism for nanocomposite conductivity. When the volume fraction of fillers in a composite material reaches a critical value, percolation starts to happen. If the composite material has an infinitesize, the probability of conductivity jumps from zero to 100% at the critical volume fraction. However, for finite-size composites, the probability would rise in a Gaussian-error-like smooth curve function. This research uses Monte Carlo simulations to study the percolation probability of finite-size nanocomposites cubes. The analyses show that there are two critical volume fractions. As the cube size approaches infinity, the two critical volume rates converge and should be equal to the theoretical value. Using the normal-cumulated-distribution function model, a power-law equation is obtained to estimate the critical volume fraction from the corresponding nanocomposite cube size. However, the Monte-Carlo simulations in this research have been based on a uniform distribution of nanotubes in the composite cube. In practical implementation, the CVF obtained from this research can be treated as the lower bound of possible real values.