Multi-scale prediction of effective conductivity for carbon nanofiber polymer composites

In this study, a multi-scale method is developed using simple equations and meaningful factors to estimate the effective conductivity of carbon nanofiber (CNF) polymer composites, referred to PCNFs. The interphase around the networked nanofibers is considered in Step I, while the tunneling zone near the CNF/interphase is addressed in Step II. Finally, the effective conductivity of PCNFs, comprising CNFs, interphase, and tunnels, is estimated in Step III. The calculations of the multi-step method are validated by plotting the impacts of all factors and comparing them with experimental data from numerous CNF-filled samples. The minimum ranges of percolating onset ( ϕ p ) and polymer resistivity in the tunnel ( ρ ) maximize the effective conductivity of system, but an insulative sample is observed at ρ > 60 Ω m and ϕ p > 0.015. Additionally, a tunneling distance ( λ ) of 1 nm and a contact diameter ( d ) of 60 nm yield the uppermost effective conductivity of 0.45 S/m, though d < 20 nm results in an insulative PCNF. Consequently, lower percolation onset, smaller polymer tunneling resistivity, narrower tunnels, and larger contact diameters enhance the effective conductivity in PCNFs. Furthermore, the sample with the lowest tunneling resistance demonstrates the highest effective conductivity. This evidence reveals the key role of electron tunneling in PCNFs, validating the multi-scale methodology.