# A Thermal Transport Study of Branched Carbon Nanotubes with Cross and T-Junctions
## 4 Discussion  
Through NEMD simulation of branched CNTs, directional heat transfer on the branches could be observed. The directional heat transfer behavior in branched CNTs can be attributed to two possible causes: asymmetric polygonal rings in the junction regions and ballistic phonon transport [31]. First, it was reported that phonons exhibit different interactions with asymmetric polygon rings, which resulted in directional flow due to the specific location of the polygon rings [29]. This effect became weaker as the branch length increased because the thermal resistance was influenced more by the branches than the junctions. Therefore, heat currents tended to flow equally into each branch at long branch lengths. However, similar heat current results were obtained regardless of the atomic configuration at the junction (Figure 5 (cross-junctions) and Figure 7 (T-junctions)). Even if the configuration of the polygon rings changed (e.g., from two heptagons in parallel to two heptagons in series) by shifting the hot region to the bottom side, the heat still tended to flow sideways rather than straight, as displayed in Figure 6a. Thus, the results indicated that the directional heat transfer in branched CNTs was not dominated by local asymmetric polygonal rings. Second, heat may exhibit ballistic transport rather than diffusive scattering inside branched CNTs, especially for short branches. When a branch was longer than the phonon mean free path, ballistic to diffusive crossover of heat flow occurred and the heat was transported predominantly through diffusive scattering; thus, an equal heat current occurred in each branch. As ballistic phonon transport was more pronounced at low temperatures [1; 21; 34; 35], the temperature effect was studied to further investigate the thermal flow mechanism inside branched CNTs with cross and T-junctions. The hot and cold regions were controlled at 50 \(\pm\) 30 K to observe how the heat currents between branches changed. As illustrated in Figure 8a,b, the heat current ratios for branch 2 exhibited relatively high deviation from the conventional predictions for both junctions, which indicates the thermal transport mechanisms in these branches were less diffusive and more ballistic at lower temperatures. Moreover, the NEMD simulation was conducted on the branched CNT with a defect-containing T-junction (Figure 2) to examine the different directional thermal flow behaviors between cross and T-junctions. Compared with the T-junction, the defect-containing T-junction, which was the intermediate construction stage of a cross-junction, had an additional opening in its bottom region. As displayed in Figure 9, the size dependence of the heat current ratio in branch 2 of the defect-containing T-junction was similar to that on the size of a cross-junction and completely different from that on the size of the T-junction. It is likely that phonons would scatter by the additional opening at the bottom of defect-containing T-junction. Thus, the presence of an additional opening at the bottom caused the heat current to tend to flow sideways into branch 2 rather than straight into branch 3, which was unlike the phenomenon observed for the T-junction. Figure 8: Effect of the temperature on heat flow in branched CNTs with (**a**) cross-junction 1 and (**b**) T-junction 1. Moreover, to analyze the thermal transport mechanism inside the branched CNTs with different junctions, the collective atomic velocity cross-correlation spectra between branches were examined to determine whether the phonons still maintained their original vibrational characteristics after passing the junction structure.