Study of the critical probability of percolation in a 3D system with pores of random radius for variable grids

Abstract

We numerically study the percolation in 3D porous materials, populated by pores with random sizes at 3D grid of variable sizes. We identify the clusters for each grid as well the infinite cluster that is defined by the critical probability through the neighborhood hybrid structure method. Also we determine the characteristic size of each cluster in the material as well the volume of the infinite cluster that allows optimizing the percolation step at our simulation. In this work several tests were performed by variation the size of the grid. This allows us to determine the optimal size and how it affects the percolation by the simulating grids. Our main results show that in systems with pores having random radius the critical probability increases when size of grid L>40 (that correspond to typical size system about 4000 nm) with respect of the inform pores case.