Estimation of electrical conductivity for polymer composites with carbon black nanoparticles by interphase depth, tunneling characteristics and network percentage

Despite many experimented works on the conductivity of carbon black (CB)-polymer nanocomposites (PCBs), the modeling methodology in this field is imperfect requiring more development. The current article suggests a simple and accurate equation for the electrical conductivity of PCBs by CB radius, interphase depth, tunneling characteristics (λ), percolation onset, network percentage and interfacial tension. At the first step, the impact of model's parameters on the PCB conductivity is designed and justified. Then, the offered model is validated by the real data of numerous samples with dissimilar polymer media and CB nanoparticles. Bigger tunnels with the smaller widest weaken the conductivity, however the peak conductivity of 11.5 S/m is attained at tunneling distance (λ) of 2 nm and contact diameter (d) of 45 nm, while λ > 5 nm or d < 20 nm produce an insulating sample. Also, higher polymer surface energy (γ_p) and poorer CB surface tension (γ_f) reduce the conductivity and an insulated sample is detected at γ_p > 30 mN/m and γ_f < 45 mN/m. Nevertheless, the supreme conductivity of 1.6 S/m is gained by the lowest γ_p = 20 mN/m and the top γ_f = 60 mN/m. Hence, both tunneling dimensions and surface tensions of components manipulate the conductivity of PCBs.