Predicting of tunneling conductivity for polymer-carbon black nanocomposites by interphase percolation

Earlier studies primarily focused on the experimental aspects of percolation onset and conductivity in polymer/carbon black (CB) nanocomposites, but the modeling approach was largely underexplored. In this study, a new equation is developed to determine the CB percolation threshold, taking into account the superficial properties of CB and polymer, as well as crucial terms such as CB radius (R) and interphase thickness (t). Also, a model is advised to simulate the conductivity of CB-filled examples by accounting for R, contact circle diameter, the number of contacts, and "t". Validation by laboratory data confirms the reliability of the proposed model. The results indicate that a smaller "R" and a higher volume portion of CB significantly enhance the conductivity, achieving 7.7 S/m at minimum R = 5 nm and the highest CB volume fraction of 0.036. A direct correlation is also found between the number of CB contacts (m) and composite conductivity, where the highest network volume portion of 0.88 and supreme m = 37 produce the supreme conductivity of 2.45 S/m.