# A Thermal Transport Study of Branched Carbon Nanotubes with Cross and T-Junctions
## 1 Introduction  
Since the discovery of carbon nanotubes (CNTs) in 1991, considerable research has been conducted on their mechanical, optical, and electronic properties. CNTs have been proposed as the most promising building blocks for nanoelectronic devices and thermal management applications due to their high thermal conductivity and mechanical stability [1, 2]. However, the quasi-one-dimensional thermal transport of CNTs has restricted their applications. Therefore, branched CNTs [3, 4] have been proposed as alternatives to CNTs. Due to their strong sp2 covalent bonds, branched CNTs exhibit lower thermal resistance than those structures with van der Waals interactions (e.g., CNT bundles [5, 6], intermolecular junctions [7, 8, 9], and CNT networks [10, 11]). In addition, high-quality and high-purity branched CNTs have been synthesized using various approaches [12, 13, 14, 15, 16, 17, 18]. Moreover, branched CNTs demonstrate potential in rectifying electrical currents [12, 13, 14] and heat [3, 19]. Therefore, the thermal transport behavior inside branched CNTs should be investigated to identify their possible applications. Molecular dynamic (MD) simulation is an appropriate tool for characterizing the collective and individual behavior of atomics or molecules at the nanoscale level. Compared with other atomistic methods, such as the use of Boltzmann transport equations, lattice dynamics, and non-equilibrium Green's function, MD simulation can more accurately capture the dynamics of lattice vibration, including harmonic and anharmonicinteractions [20]. MD simulations have been widely adopted to investigate the thermal transport mechanisms of pristine CNTs. A frequently researched aspect of pristine CNTs is their length-dependent thermal conductivity, which involves ballistic or diffusive phonon transport behavior at varying lengths [21; 22; 23]. However, similar examinations on the phonon transport mechanism or thermal energy transfer inside branched CNTs have rarely been conducted. Branched CNTs possess topological defects and the possibility of multi-directional thermal transfer in junction regions, whereas pristine CNTs do not. Some studies have examined the influences of the aforementioned phenomena on the thermal transport behavior [3; 4; 24; 25; 26]. The topological defects at the junction area of branched CNTs must satisfy [PERSON]'s polyhedral formula [27; 28]. Topological defects often cause considerable phonon scattering and thus an increase in thermal resistance, which subsequently influences heat transfer [24; 26]. Moreover, the connections of different carbon structures, such as CNTs and graphene, must facilitate multi-directional thermal transfer; however, dimensional mismatch occurs at the junction, which causes an increase in resistance, a decrease in transmission, and changes in the incident phonon mode [24; 29; 30]. Some researchers have investigated thermal ratification behaviors for branched CNTs by conducting experiments [19], heat pulse simulations [3], and wave packet simulations [4]. [PERSON] et al. [31] investigated the thermal transfer inside a branched CNT with T-junctions and observed that the heat preferred to flow straight rather than sideways, especially for short branch lengths. They also noticed that symmetric temperature setups exhibited lower transmission than asymmetric temperature setups because the phonons were forced to change their propagation directions in the symmetric temperature setups. The aforementioned phenomenon has been attributed to the occurrence of ballistic phonon transport and topological defects (i.e., heptagons and octagons). However, the underlying dominant mechanisms of the directional heat transfer inside branched CTNs have yet to be determined. In the present study, the heat flow inside branched CNTs with cross and T-junctions was investigated using non-equilibrium molecular dynamics (NEMD) simulations. The junctions in the CNTs were constructed through thermal welding.