Optimizing conductive properties of polymer carbon nanofiber composites: Insights from an extended Hui-Shia model

The existing models for the electrical conductivity of polymer composites with carbon nanofiber (CNF) called as PCNFs are incomplete, thereby limiting their optimization. In this study, the Hui-Shia model is simplified and advanced to accurately foresee the PCNF conductivity by incorporating the main features of CNFs, interphase, and tunnels. The volume fraction of the CNF/interphase network is derived based on the onset of percolation and effective CNF content, while the total conductivity of CNF and tunnels is expressed through tunneling properties. The developed model is evaluated using experimental data from various PCNF systems and through parametric analyses. Theoretical and experimental results demonstrate good agreement, validating the developed model. An insulative PCNF is observed at a CNF radius (R) greater than 90 nm and an interphase depth (t) less than 11 nm. Conversely, the maximum conductivity of 1.5 S/m is achieved with the thinnest CNFs (R = 40 nm) and the thickest interphase (t = 40 nm). Furthermore, very small contact diameters (d less than 17 nm) do not result in significant conductivity; however, the maximum conductivity of 0.27 S/m is observed with the widest tunnels (d = 40 nm) and the highest CNF aspect ratio of 1000.