Theoretical modeling and experimental verification of percolation threshold with MWCNTs' rotation and translation around a growing bubble in conductive polymer composite foams

Foaming is a potential method to prepare high-performance, lightweight, composite materials with enhanced electrical properties. Here, a theoretical model and its experimental verification are presented to assess the evolution of electrical percolation threshold and conductivity as a bubble grows during the foaming of conductive filler/polymer composites. The filler networks were changed by translation and rotation of filler particle during bubble growth that was presented by void fraction increase. The evolution of percolation threshold with filler network was estimated using a Monte Carlo approach. The model results showed that the percolation threshold decreased, and the electrical conductivity increased for void fraction values less than 20%, beyond which the percolation threshold started to increase. Furthermore, a series of polystyrene/multiwalled carbon nanotubes (PS/MWCNTs) composite foams were fabricated at various void fractions matching the parameters in modeling. At an optimum void fraction of approximately 17%, the percolation threshold of the foamed samples was decreased by 20%, from 0.6 vol% down to 0.48 vol%. Further increases in the void fraction increased the percolation threshold. The simulation prediction was in good agreement with the experimental results. The model offers a valuable tool to better understand the electrical behavior and can be used in the design of conductive polymer composite foams with rod-like conductive fillers.