Contact diameter in polymer carbon black nanocomposites by interfacial tension, network portion, interphase depth and tunneling distance

Despite the experimental studies of percolation onset and conductivity in polymer nanocomposites of carbon black (CB) called as PCBs, the modeling reports for this system are limited. In this study, we develop two models of PCB conductivity to obtain a simple statement for the tunneling diameter among the nearby CBs ( d ). The tunneling diameter is stated by CB radius, percolation start, interphase size, network share, tunneling size ( λ ), interfacial tension, and the filler ( γ _f ) and polymer ( γ _p ) surface tension. The model's accuracy is stated by investigating the impacts of all terms on the tunneling diameter. γ _f = 45 mN/m and γ _p = 40 mN/m fall d to 0, due to the lowest interfacial tension dispersing the nanoparticles in the system. Conversely, γ _f = 70 mN/m and γ _p = 20 mN/m grow the tunneling diameter to 80 nm. Additionally, CB volume portion ( ϕ _f ) < 0.03 or λ > 6 nm reduce the tunneling diameter to 0, while ϕ _f = 0.1 and λ = 1 nm extend the tunneling diameter to 60 nm. These data display the positive impression of higher interfacial tension, higher amount of CB particles and thinner tunnels on the contact diameter.