Predictive modeling of conductivity for carbon black nanocomposites: influence of filler features, interfacial effects and network portion

The conductivity of carbon black samples depends on more than one or two obvious variables; it arises from a complex interaction of structural and surface factors acting in concert. Considering these interdependencies in a model is essential for designing materials that achieve reliable performance. In this study, we developed a theoretical framework that integrates the filler geometry, interphase thickness, tunneling resistance, tunneling distance, tunneling diameter, percolation threshold, and intrinsic conductivity of the filler. Rather than considering these parameters in isolation, the model allows them to interact, and its predictions are validated using experimental datasets. When the carbon black radius drops to 10 nm and the networked fraction of nanoparticles is 1, the conductivity of the composite increases to 1 S/m. As the particle radius increases or the fraction of networks decreases, the conductivity of the system decreases sharply and, in some cases, returns to the insulating state. The results further show that the composite conductivity is strongly governed by the polymer tunneling resistivity (p) and the interphase conductivity (σint). The lowest σint (< 200 S/m) produces an insulated system, while the composite conductivity maximizes to 3 S/m at p = 10 Ω.m and σint = 8000 S/m. Accordingly, more interphase conduction and less polymer tunnel resistivity are desirable to improve the conductivity of samples.