# The Effect of Thermal Contact Number on the Tube–Tube Contact Conductance of Single-Walled Carbon Nanotubes

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{−1}K

^{−1}at room temperature. The thermal conductivity of individual single-walled CNTs (SWCNTs) measured by Pop et al. [3] was close to 3500 Wm

^{−1}K

^{−1}at room temperature. Therefore, CNTs have broad application prospects in the field of thermal management due to their excellent thermal conductivity. They can be used to improve the thermal conductivity of polymer matrices and for the construction of self-supporting CNT network structures. The thermal conductivity of a CNT network can be tuned by changing the orientation, distribution, and connection of individual CNTs.

## 2. Materials and Methods

^{6}time steps (0.5 fs/time step) using the Nosé–Hoover thermostat. Then, to establish a stable temperature difference between the tubes, an NEMD simulation is conducted for another 6 × 10

^{6}steps in the NVE ensemble, in which a constant amount of kinetic energy is added/subtracted to/from the hot/cold slabs at a regular interval (10 time steps). The output of the last 1 × 10

^{6}steps is used to calculate the temperature profile of the tubes.

## 3. Results and Discussion

#### Contact Conductance

_{0}, while that removed from each cold slab in tube 2 and tube 3 per unit time is Q

_{0}. In the calculation, we assumed that the amount of heat conducted from tube 1 to tube 2 or tube 3 per unit time is Q

_{0}. However, it still has to be validated whether the tube–tube contact conductance can be calculated directly by using the average temperature between tube 1 and tube 2 or tube 1 and tube 3. We developed a symmetric calculation model 3 for this purpose consisting of four carbon nanotubes, as shown in Figure 5. The lengths of the CNTs in this setup are 50 unit cells and the positional relationship of each thermal contact is symmetrical. The amounts of heat flow into the hot slabs and out of the cold slabs are both Q

_{0}. The average contact conductance of the thermal contacts calculated by this model is 28.95 pW/K, which is close to that of the double thermal contacts obtained via model 2. That is to say, our calculation method is suitable and effective. These simulation results indicate that the phenomenon reported by Prasher et al. [9], i.e., that the tube–tube contact conductance of the double thermal contacts is 1/10 that of the single thermal contact, was not observed in our simulations.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The calculation model for the thermal contact conductance of two carbon nanotubes with a single thermal contact: (

**a**) aerial view; (

**b**) front view.

**Figure 2.**Typical temperature profile of the two single-walled carbon nanotubes (SWCNTs) in a single thermal contact.

**Figure 3.**The calculation model 1 for the contact conductance of the double thermal contacts: (

**a**) aerial view; (

**b**) front view. (

**c**) Typical temperature profile of the three carbon nanotubes in the double thermal contacts.

**Figure 4.**The calculation model 2 for the contact conductance of the double thermal contacts: (

**a**) aerial view; (

**b**) front view. (

**c**) The variation of the contact conductance of the double thermal contacts with the distance between tubes 2 and 3.

**Figure 6.**Calculation model 4 and model 5 for the contact conductance of the double thermal contacts: (

**a**,

**c**) aerial view; (

**b**,

**d**) front view.

**Figure 7.**Calculation model for the contact conductance of the three thermal contacts: (

**a**) aerial view; (

**b**) front view.

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**MDPI and ACS Style**

Yang, X.; Zhang, X.; Cao, B.
The Effect of Thermal Contact Number on the Tube–Tube Contact Conductance of Single-Walled Carbon Nanotubes. *Nanomaterials* **2019**, *9*, 477.
https://doi.org/10.3390/nano9030477

**AMA Style**

Yang X, Zhang X, Cao B.
The Effect of Thermal Contact Number on the Tube–Tube Contact Conductance of Single-Walled Carbon Nanotubes. *Nanomaterials*. 2019; 9(3):477.
https://doi.org/10.3390/nano9030477

**Chicago/Turabian Style**

Yang, Xueming, Xinyao Zhang, and Bingyang Cao.
2019. "The Effect of Thermal Contact Number on the Tube–Tube Contact Conductance of Single-Walled Carbon Nanotubes" *Nanomaterials* 9, no. 3: 477.
https://doi.org/10.3390/nano9030477