Unraveling of electrical conductivity for nanocomposites containing carbon black: a new insight into tunneling resistance

Herein, a useful model is developed for electrical conductivity of polymer nanocomposites integrating carbon black (CB) named as PCBs. The developed Kovacs model provides a clearer understanding of how key parameters such as interphase thickness (t), tunnel size (λ), network fraction and tunneling resistance (R_t) affect the conductivity of PCBs. Empirical results of many samples corroborate the precision and logical consistency of the refined model. The electrical conductivity of PCBs exhibits an inverse relationship with the radius of CB nanoparticles (R), percolation threshold, tunneling resistance and tunneling distance, underscoring the need to minimize these parameters to enhance the conductivity. Conversely, increasing some factors such as CB volume portion (φ_f), interphase thickness, and network fraction positively impacts the conductivity of PCBs. The highest amount of the smallest CB nanoparticles can provide the highest conductivity in PCBs. R = 5 nm and φ_f = 0.08 improve the PCB conductivity to 5 S/m. Nevertheless, R = 30 nm and φ_f = 0.01 cause an insulative sample. Also, the densest interphase (t = 20 nm) and the narrowest tunnels (λ = 1 nm) produce the superlative conductivity of 1.9 S/m at φ_f = 0.05, while t < 3 nm cannot enhance the PCB conductivity.