Simulation of the electrical percolation of carbon nanotube composites in polymethylmethacrylate matrix: two-dimensional and three-dimensional analyses using a tortuosity effect of nanofillers

The present work aims to study the simulation of the electrical percolation of carbon nanotubes (CNTs) in polymethylmethacrylate matrix (PMMA). In order to do this, simulations were employed in two-dimensional and three-dimensional analyses through a program developed by the Monte Carlo method, supported by the excluded volume model in order to analyze the geometric tortuosity in the polymeric matrix. The percolation threshold was analyzed by different aspect ratios, volumetric fractions and conductive load geometries. In the simulations, a decrease in the percolation threshold was observed when the aspect ratio increased and the particles became more tortuous, being these characteristics the parameters to evaluate both two-dimensional and three-dimensional systems. The results show percolation threshold values of 0.625% vol and aspect ratio of 1000 for two-dimensional analyses and, 0.08% vol and aspect ratio of 250 for three-dimensional analyses, being the adequacy to the main models for electrical percolation with tortuosity effect of the nanocarriers proposed by literature.