A predictive model for electrical conductivity of polymer carbon nanofiber composites considering nanofiber/interphase network and tunneling dimensions

Herein, the dimensions of the interphase and tunneling zones are utilized to develop a model for the conductivity of polymer composites with carbon nanofiber (CNF) named as PCNFs. The effective CNF concentration and percolation onset depend on the interphase depth to estimate the concentration of the CNF/interphase network. Additionally, the length and diameter of tunnels are considered to account for tunneling resistance in the developed model. Accordingly, the current model assumes simple, measurable, and effective factors to estimate the conductivity of PCNF. Parametric analyses and experimental data of conductivity for real examples are used to validate the developed model. A very thin interphase (t = 5 nm) and high percolation onset (phi(p) = 0.03), as well as large tunnels (lambda > 10 nm) and small contact diameters (d < 8 nm), result in an insulative PCNF. However, the thickest interphase (t = 40 nm) and the lowest percolation onset (phi(p) = 0.003) yield the highest conductivity as 0.06 S/m. Additionally, the minimum tunneling distance (lambda = 1 nm) and maximum contact diameter (d = 40 nm) yield the maximum output of 0.045 S/m. Therefore, a deeper interphase, lower onset of percolation, and narrower and wider tunnels are essential to improve the nanocomposite conductivity.