Analytical-geometrical percolation network model for piezoresistivity of hybrid CNT–CB polymer nanocomposites using Monte Carlo simulations

A 3D Monte Carlo simulation and percolation network model for hybrid nanocomposites reinforced by carbon nanotubes (CNTs) and carbon black (CB) nanoparticles (NPs) is established to investigate the percolation probability and piezoresistivity considering electron tunneling effect. Firstly, a Monte Carlo algorithm is developed to form a representative volume element filled with randomly oriented CNTs and randomly dispersed CB NPs. Later, a percolation like network model is developed to determine the resistivity between each of CNTs and CB NPs, and then the electrical model based on modified location analysis is employed to calculate the corresponding piezoresistive behavior of hybrid CNT–CB polymer nanocomposites under tension. Tunneling resistance variation with the evolution of the conductive network during the inducing strain leads to non-linear and exponential behavior of relative electrical resistance change with strain. Parametric studies are performed to show the effects of CB volume fraction, size and CNT maximum orientation angle on the percolation probability and piezoresistivity of hybrid CNT–CB polymer nanocomposites. Results indicate that the piezoresistive sensitivity is greatly improved in the nanocomposites with the introduction of hybrid CB NPs/short aligned CNTs. Respecting to piezoresistive sensibility, the gauge factor calculated from the change of resistance as a function of applied strain reaches high value for sensitive piezoresistive sensor with lower Poisson’s ratio and larger diameter of CB NPs.