A unified electrical model based on experimental data to describe electrical transport in carbon nanotube-based materials

Understanding the electrical transport in carbon nanotube (CNT) materials is one key to reach very high electrical conductivities. All CNT material resistivity ( $\rho$ (T)) as function of the temperature are fully apprehended by their reduced activation energy $W(T)=-\frac{\text{dln}(\rho )}{\text{dln}(T)}$ curves. Up to now, no model accurately fits W(T) curves, thus preventing from precisely describing the CNT material electrical transport. We present a new electrical transport model that perfectly fits all W(T) curves found in the literature and in our own data. CNT material resistivities are modeled by $\text{ρ}(\text{T})={\text{ρ}}_{\text{o}}\left({\text{T}}^{-\text{α}}+\text{M}\left(1+\text{βT}+\text{γ}{\text{T}}^2\right)\right)$ . Our model has few enough parameters ( $\text{α}$ , M, $\text{β}$ , $\text{γ}$ ) to relate them to the CNT physics. Below 70 K, we experimentally show that CNT material resistivity follows the Luttinger Liquid theory justifying the ${\text{T}}^{-\text{α}}$ term in our model. Above 70 K, the polynomial part becomes dominant and depends on the two different CNT fabrication techniques which lead to two very different yarn structures. For yarns made from floating catalyst chemical vapor deposition CNTs, the polynomial is explained by the percolation of metallic CNT walls. Whereas, the polynomial of yarns spun from CNT arrays is explained by the electrical transport in CNT bundles which are the basic building blocks of this type of yarns.