Influence of filler waviness and aspect ratio on the percolation threshold of carbon nanomaterials reinforced polymer nanocomposites

Adding a small amount of conductive high aspect one-dimensional nanomaterials such as carbon nanotubes and carbon nanofibers to the initially non-conductive polymeric matrix can induce an insulator to conductor transition which has both scientific merit and application importance. The critical fiber concentration necessary for this transition is called the percolation threshold, which is determined by the filler shape and size. This study investigates the filler waviness effect on the critical behavior of composite conductivity, since the high aspect ratio fillers in actual composites are often bent and entangled instead of being straight. Individual filler was modeled by a linked three straight-segment components with three-dimensional (3D) bending characteristics. In addition, 3D Monte Carlo method has been used to simulate the random distribution of the fillers. Statistical analyses of the fiber networks reveal waviness influence on the percolation threshold in terms of the average contacts per fiber with other fibers. The critical number of average contacts per fiber (B c) for percolation strongly depends on the waviness and deviates substantially from identity for straight fillers. The study demonstrates that the semi-analytic excluded volume theory cannot be used to predict the percolation threshold until the correct B c value is determined.