A predictive model for electrical conductivity of polymer carbon black nanocomposites

Abstract Although many studies have investigated the percolation threshold and conductivity in the polymer carbon black (CB) nanocomposites (PCBs) by experimental data, the modeling in this field is a topic previously overlooked in literature. This paper suggests a simple equation for percolation threshold in PCBs by the surface properties of polymer and CB a well as interphase depth ( t ). Also, the electrical conductivity of PCBs is simulated by CB radius ( R ), tunneling distance ( λ ) and interphase depth. The offered model is validated by experimented findings of numerous samples and parametric examinations. A thicker interphase and a higher interfacial tension positively reduce the percolation onset. The smaller CBs, lower percolation threshold, and smaller tunnels enhance the electrical conductivity of PCBs. The low percolation threshold of 0.01 is obtained by the low R (15 nm) and the thick interphase (35 nm). Also, R = 15 nm and t = 35 nm maximize the PCB conductivity to 6 S/m. These results signify the important roles of CB radius and interphase depth in the percolation threshold and conductivity of PCBs. In addition, network fraction ( f ) of 0.7 and λ = 1 nm produce the uppermost PCB conductivity of 1.6 S/m, but the system is insulated at CB network fraction less than 0.35 or tunneling distance more than 2 nm. Therefore, high network fraction and low tunneling distance are needed to enhance the conductivity of PCBs. Highlights An equation for percolation onset of PCBs is proposed by CB radius and interphase depth. The offered model is validated by experimented data and parametric examinations. A thicker interphase and a higher interfacial tension positively reduce the percolation onset. Smaller CBs, lower percolation onset, and smaller tunnels enhance the PCB conductivity. CB radius and interphase depth significantly manage the conductivity of PCBs.