Assumption of an expanded carbon black nanoparticle by interphase and tunneling zones to simulate the electrical conductivity of nanocomposites

In this paper, the key aspects of interphase and tunnels as well as carbon black (CB)/interphase networks are used to advance a simple methodology to determine the conductivity of CB-polymer samples (PCBs). Both interphase and tunneling regions are supposed by expanded CB nanoparticles and their conductivity are predicted by the resistances of interphase and tunneling regions. Then, the conductivity of PCBs containing the expanded CBs is approximated by a simple model with determine factors. The experimental data of various real examples and examination of all parameters are used to verify the methodology. The PCB conductivity grows to 2 S/m by the slimmest tunnels ( λ = 1 nm) with the poorest tunnel resistivity ( p = 50 Ω.m). In addition, a denser interphase with higher conduction yields a higher conductivity, where t = 30 nm and σ i = 400 S/m grow the conduction to 4.5 S/m. However, a nonconductive sample is created at t < 12 nm, revealing the main role of interphase size in the conductivity. Furthermore, the advanced model reveals that less percolation onset, more interfacial tension among polymer and CBs with higher contact diameter enhance the conductivity of PCBs.