Physics-Based Modeling and Experimental Study of Conductivity and Percolation Threshold in Carbon Black Polymer Nanocomposites

We present a physical model for the effective electrical conductivity and the associated percolation behavior in CB-based polymer nanocomposites exhibiting a 3D conductive network structure. In conductive nanocomposites, the fillers, e.g., carbon black nanoparticles form a three dimensional (3D) network in a polymer matrix. Assuming attached carbon black nanoparticles give rise to nanoparticles with ellipsoidal shapes, the effects on the electrical conductivity of the nanocomposite are investigated by considering the variations of (a) the thickness and conductivity of the interphase region, (b) the conductivities of the filler and the matrix, (c) the size and the aspect ratio of the ellipsoids, (d) the volume fraction, and (e) the electron tunneling distance and the potential barrier height. The presence of an interphase layer is shown to exert a dominant effect on the behavior of the effective electrical conductivity and the associated percolation behavior. To validate the theoretical model, polymer nanocomposites were prepared by incorporating different concentration of CB within polyvinylidene fluoride matrix which shows an approximately 14 orders of magnitude of jump in the conductivity at percolation. The model predicts the value of percolation threshold for CB/PVDF nanocomposite as P c (vol%) = 1 which is in good agreement with the experimental percolation threshold value of P c (vol%) = 1. Also, the present model accurately predicts the reported experimental behavior of the electrical conductivity in a variety of CB-filled nanocomposites employing different polymer matrices, namely polyethylene terephthalate, high density polyethylene, polypropylene, nylon, polyurethane, and natural rubber, over the entire range of the volume fractions. Notably, the model allows accurate computation of the percolation thresholds for conductive nanocomposites at very low volume fractions. Graphical Abstract