**1. Introduction**

Carbon nanotubes (CNTs) have progressively attracted researchers' attention for their lightweight, small size and acceptable flexibility. Moreover, they have both excellent electrical and thermal conductivity, which determines that they have application value and development potential as a high-performance reinforcement material [1]. However, in practical applications, they have failed to reflect the excellent properties of CNTs because they are dispersed randomly and prone to agglomeration [2]. Previous studies on CNTs have concentrated on the preparation [3,4], the optimization of the mechanical properties of CNTs composites [5,6] and the enhancement of the effectiveness of CNTs as capacitor electrode materials [7]. In recent years, studies have shown that high temperature annealing is an effective approach to improve the structure and thermal conductivity of carbon materials [8,9]. Chen et al. [10] found that thermal treatment is capable of repairing the structure of graphene and making graphene sheets accumulate more regularly. Thereby, the thermal conductivity is increased. Mayhew et al. [11] found that the thermal conductivity of carbon nanofibers could be increased by nearly 40 times after annealing at 2800 ◦C for 20 h. However, the effect of high temperature annealing on the thermal conductivity of carbon materials is complicated, for which a mechanism has ye<sup>t</sup> to be figured out.

The traditional method of annealing at present is indirect annealing in the furnace, and the current annealing in this experiment has the superiorities of straightforward and efficient in situ measurement compared with the traditional annealing. Current annealing can be accomplished in a few seconds for the sample annealing treatment. The sample is always in the invariable equipment before annealing until the sample is burned down

**Citation:** Lin, H.; Xu, J.; Shen, F.; Zhang, L.; Xu, S.; Dong, H.; Luo, S. Effects of Current Annealing on Thermal Conductivity of Carbon Nanotubes. *Nanomaterials* **2022**, *12*, 83. https://doi.org/10.3390/ nano12010083

 Academic Editor: Christophe Detavernier

Received: 1 December 2021 Accepted: 24 December 2021 Published: 29 December 2021

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after complete annealing to measure thermal conductivity, which reduces the measurement errors caused by factors such as the pollution of the area under measurement and the different qualities of the sample.

In this work, the focus is on the current annealing effect on CNTB and CNTF. The data is collected by using the TET technique, and the variation of thermal diffusivity with annealing current is analyzed. The evolution of material microstructures is studied based on the variation of their thermal properties.

#### **2. Materials and Methods**

#### *2.1. Experimental Materials*

The CNTB (Suzhou Tanfeng Graphene Technology Co., Ltd., Suzhou, China) was prepared from multi-walled carbon nanotubes (MWCNTs) by floating catalysis to pattern a film with the size of 10 cm × 10 cm (Figure 1a), with an electrical conductivity of (0.8–3) × 10−<sup>5</sup> S/m, a strength of 60–100 MPa and a density of 400 kg/m3. Figure 1b, the SEM image of CNTB, clearly shows that the film is made of innumerable carbon nanotubes arranged desultorily. Moreover, the carbon nanotubes have non-uniform diameters and randomly overlap with others, which makes the surface of the prepared film rough to a certain extent. The tested samples were prepared along the length direction of the square CNTB film (CNTB1) and along the other side of the CNTB film (CNTB2), as shown in Figure 1a.

**Figure 1.** (**a**) The intact carbon nanotube film (CNTB) before the TET experiments. (**b**) The SEM image of the CNTB. The SEM images of CNTF under different magnifications of (**c**) 1500× and (**d**) 20,000<sup>×</sup>. These indicate CNTB and CNTF are made of innumerable carbon nanotube fibers arranged desultorily.

The carbon nanotube fiber (CNTF, Nanjing JCNANO Tech Co., Ltd., Nanjing, China) was also prepared from MWCNTs by using the floating catalyst method, with a density of 675.43 kg/m3, the strength of 310–500 MPa, the modulus of 10 GPa and a tensile rate of 20–30%. From its SEM images (Figure 1c,d), the CNTF sample had a certain degree of twisted texture and roughness, and there is a cross-overlap as well.

#### *2.2. Transient Electro-Thermal Technique*

The thermal conductivities of carbon nanotube materials were measured by using TET. Figure 2 shows the schematic diagram of the TET experimental system. The samples were suspended on a sample holder with two separate electrodes. A small amount of silver paste was applied to stabilize both ends of the samples on the electrodes to reduce the contact resistance between the samples and electrodes. Then the sample holder was placed into a vacuum chamber to exclude heat convection. As the air pressure in the vacuum chamber during the measurement was maintained at 1 × 10−<sup>3</sup> mbar, the heat convection effect on the measured thermal diffusivity was negligible. A step current supplied by a current source (KEITHLEY 2611A, Keithley Instruments Inc., Cleveland, OH, USA) was fed to the samples to generate Joule heating in the samples. The thermal diffusivity of the samples was obtained by analyzing the temperature rise curve with a physical model discussed below.

**Figure 2.** The schematic diagram of the TET experiment. TET is composed of a vacuum chamber, current source and oscilloscope. In the vacuum chamber, the air pressure is less than 1 × 10−<sup>3</sup> mbar during the measurement. The sample is placed on the electrodes, and a silver paste is applied to the ends for reducing contact resistance.

As the CNTB and CNTF samples have a large aspect ratio, a one-dimensional heat transfer model was used for analysis [12]. The average temperature change of the sample directly affects the variation of the voltage over the sample as [13]:

$$V\_{\text{Sample}} = IR\_0 + I\eta \frac{4q\_0L^2}{k\tau^2} \sum\_{m=1}^{\infty} \frac{1 - \exp[\left(-\left(2m-1\right)^2 \pi^2 a\_{\text{eff}}t\right)/L^2]}{\left(2m-1\right)^4} \tag{1}$$

where *η* is the temperature coefficient of resistance, *q*0 is the electrical heating power per unit of volume, *k* is the thermal conductivity, *α*eff is the effective thermal diffusivity of the sample.

Defining a normalized average temperature rise as *T*∗ = (*<sup>T</sup>*t − *<sup>T</sup>*0)/(*<sup>T</sup>*<sup>t</sup>→∞ − *<sup>T</sup>*0), it can be expressed as [13,14]:

$$T^\* = \frac{48}{\pi^4} \prod\_{m=1}^{\infty} \frac{1 - \left(-1\right)^m}{m^2} \frac{1 - \exp\left[-m^2 \pi^2 a\_{\rm eff} t / L^2\right]}{m^2} \tag{2}$$

When a step current is applied to a sample, its resistance varies with the temperature, which leads to a change of voltage. Therefore, the experimental value of the normalized temperature rise *<sup>T</sup>*<sup>∗</sup>exp can be calculated by the change of voltage as: *<sup>T</sup>*<sup>∗</sup>exp = *V*∗ = (*<sup>V</sup>*sample − *<sup>V</sup>*0)/(*<sup>V</sup>*∞ − *<sup>V</sup>*0), where *V*0 and *V*∞ are the initial and steady-state voltages across the sample, respectively. The *V-t* curve of the sample was recorded by an oscilloscope (DSO-X3052A, Agilent Technologies Inc, Santa Clara, CA, USA); combined with Equation (1), the thermal diffusivity (*α*) of the sample was obtained, which was used to fit the normalized temperature curve. The *α* value with the best fitting was determined as *α*eff, and associates with the density (*ρ*) and specific heat capacity (*cp*) of the sample, its effective thermal conductivity (*k*eff) can be obtained as calculated by: *k*eff = *ρcp<sup>α</sup>*eff.

#### *2.3. Experimental Procedure*

The current annealing was applied to the sample in the same experimental setup as TET in this study. After the sample was laid in a vacuum chamber, the *α*eff of the sample at room temperature was first measured using a step current with low intensity in order to raise the temperature as small as possible. Then a Direct Current (DC) with high intensity was applied to the same sample to generate large heat in the sample and complete the thermal annealing. The thermal annealing lasted for more than 120 s to ensure thermal equilibrium for one run. The second *α*eff was measured after the sample finished the first annealing run. The annealing run and in-situ TET measurement were then performed alternatively by switching the form of the current between the large DC current (for annealing) and small step current (for TET measurement). The DC current increases a little at a time until the sample is burned down. This method can fully realize the effective monitoring of the structural variation in the annealing process. The error of transferring samples between the different annealing and measurement devices is successfully avoided. This is the whole current annealing procedure, in which the effects of current annealing on thermal conductivity are investigated.

#### **3. Results and Discussions**
