Scaling Laws and Mesoscopic Modeling of Thermal Conductivity in Carbon Nanotube Materials

The scaling laws describing the thermal conductivity in random networks of straight conducting nanofibers are derived analytically and verified in numerical simulations. The applicability of the scaling laws to more complex structures of interconnected networks of bundles in carbon nanotube (CNT) films and mats is investigated in mesoscopic simulations. The heat transfer in CNT materials is found to be strongly enhanced by self-organization of CNTs into continuous networks of bundles. The thermal conductivity of CNT films varies by orders of magnitude depending on the length of the nanotubes and their structural arrangement in the material.

Figure 1

An example of a 2D system used in calculations of thermal conductivity, $k_{2\mathrm{D}}$, within a model of random contacts between soft-core SCs (a) and the results of the calculations performed for different values of ${\overline{n}}_S=n_S{L}_T^2$ and two values of ${\overline{R}}_T=R_T/L_T$ (b). In (a), the system consists of 1848 SCs, ${\overline{n}}_S=100$, ${\overline{R}}_T=0$, and the SCs are colored by their temperature. In (b), the red and green symbols and solid curves correspond to the values obtained in the numerical calculations for ${\overline{R}}_T$ equal to 0 and 0.03, respectively; the corresponding dashed and dash-dotted lines are the predictions of the analytical scaling law given by Eq. (1). The inset in (b) shows an enlarged view of a part of the plot in a regular scale.

Figure 2

The structure of a continuous network of CNT bundles generated in a mesoscopic dynamic simulation and used in the calculations of the thermal conductivities, $k_{xx}^{\mathrm{network}}$ and $k_{zz}^{\mathrm{network}}$. The heat flux is in the direction of the $x$ axis in (a, c) and in the direction of the $z$ axis in (b, d) as indicated by the black arrows in (c) and (d). The nanotubes are colored by their temperature. The sample consists of 24 681 (10,10) CNTs with length of $1\mu \mathrm{m}$ each. Only a layer with 50 nm thickness is shown in the top view of the film in (a).

Figure 3

Thermal conductivity $k$ as a function of nanotube length $L_T$ for systems composed of (10,10) CNTs with material density of $0.2\mathrm{g}{\mathrm{cm}}^{-3}$. Symbols show the results of the calculations performed for continuous networks of CNT bundles obtained in mesoscopic simulations. The red squares and blue triangles correspond to the calculations of in-plane and out-of-plane conductivities of the anisotropic networks. The solid lines are the root-mean-square power fits to the data points, with the point for $L_T=100\mathrm{nm}$ excluded from the fit for $k_{xx}^{\mathrm{network}}$. The green dashed and black dash-dotted lines show the predictions of the analytical scaling laws given by Eqs. (2, 3), respectively. The value of out-of-plane conductivity $k_{zz}^{\mathrm{film}}=5.7\times {10}^{-4}\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ predicted by Eq. (4) is out of the range shown in the plot. Dimensional values of $k$ are calculated with ${\sigma }_{c0}=5\times {10}^{-11}\mathrm{W}{\mathrm{K}}^{-1}$. Values of $k_{xx}^{\mathrm{film}}$ and $k_{zz}^{\mathrm{film}}$ are calculated with $\Delta z=2R_T+\delta h_0=16.714\AA$.