# A Thermal Transport Study of Branched Carbon Nanotubes with Cross and T-Junctions
## 5 Conclusions  
In this study, NEMD simulations were conducted to investigate the thermal transport behavior inside branched CNTs with cross and T-junction. Junctions were prepared through the thermal welding of (6, 6) CNTs by removing atoms such that Euler formula-based topological requirements were satisfied. All of the connecting branches had the same length and chirality. The effects of branch length, topological defects at junctions, and temperature on the thermal flow were studied. The simulation results indicated that the heat current preferentially flowed into the side branch rather than the straight one for the cross-junction structures; however, the heat inside the T-junction behaved differently. This directional heat transfer was obvious especially in short branches and low temperatures. Moreover, the atomic configuration at junctions with different topological defects only had a marginal influence on the heat transfer. As the branch length increased, the heat tended to flow equally into each branch. The directional heat transfer cannot be explained using diffusive-based thermal circuit theory even when the anisotropic thermal conductance at the junction was considered. Finally, the collective atomic velocity cross-correlation spectra between branches were used to examine phonon transport mechanisms for the branched CNTs. Furthermore, we found that the phonon correlation function, which describes the similarity of atomic vibration between branches, could only provide information regarding the phonon scattering behavior during thermal transport. Moreover, this function could not be directly related to the amount of transferred heat because the heat current can be transported by both diffusive and ballistic phonons, and the heat carried by diffusive phonons cannot be reflected in the atomic velocity cross-correlation spectra. This finding provides deep insight into the thermal transport mechanisms of branched CNTs, which can be useful when employed in thermal management applications.  
Conceptualization, W-J.C. and I-L.C.; methodology, W-J.C.; software, W-J.C.; validation, W-J.C.; formal analysis, W-J.C. and I-L.C.; investigation, W-J.C.; resources, I-L.C.; data curation, W-J.C. and I-L.C.; writing--original draft preparation, W-J.C. and I-L.C.; writing--review and editing, W-J.C. and I-L.C.; visualization, W-J.C.; supervision, I-L.C.; project ad  
Figure 12: Collective power spectra of the velocity cross-correlation of (**a**) longitudinal and (**b**) transverse vibrations of branch 1 with those of branches 2 and 3 for T-junction 1.  
ministration, I.-L.C.; funding acquisition, I.-L.C. Both authors have read and agreed to the published version of the manuscript.  
This research and the APC were funded by the Taiwan Ministry of Science and Technology, MOST 106-2923-E-006-004-MY3 and MOST 105-2628-E-006-003-MY3.  
Not applicable.  
This research was financially supported by the Taiwan Ministry of Science and Technology under the grants MOST 106-2923-E-006-004-MY3 and MOST 105-2628-E-006-003-MY3. The authors want to thank [PERSON] for preparing the cross-junction model. We also thank the National Center for High-performance Computing (NCHC) for providing the computational and storage resources.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.