Advancing conductivity modeling: A unified framework for polymer carbon black nanocomposites

Although numerous experimental data on the conductivity of polymer carbon black (CB) nanocomposites (PCBs) have been reported, the modeling approaches remain incomplete and require further attention. This article proposes a simplified model for predicting the PCB electrical conductivity, incorporating key parameters such as CB radius (R), tunneling distance (λ), contact diameter (d), interphase depth, network percentage, and interfacial tension between CB and polymer. Experimental PCB conductivity data and parametric evaluations are utilized to validate the proposed model. The proposed model predicts that the thinnest and widest tunnels (λ = 2 nm and d = 30 nm) attain a maximum conductivity of 5.5 S/m. However, tunnels bigger than 4 nm cannot enhance the conductivity. Additionally, increasing the concentration of the smallest CBs (R = 10 nm) to 10 vol% boosts PCB conductivity to 4.9 S/m, whereas low concentrations (<5 vol%) of larger CBs (R > 17 nm) have negligible effect. These findings underscore the critical roles of tunneling dimensions together with CB size and concentration in the conductivity of this system.