*3.1. Results*

#### 3.1.1. Positive Effect of Annealing on CNTB1

The annealing process and in-situ TET measurement are first applied to CNTB1 (length: 3620.71 μm; width: 288.42 μm; thickness: 25 μm). The decreasing voltage along with time demonstrate that the MWCNTs dominate the heat conduction in CNTB1 because most carbon materials have a negative temperature coefficient of resistance (TCR) [15]. The varying trend is fitted by Equation (2), and the best-fitted *α* is the effective thermal diffusivity *α*eff of CNTB1. The detailed annealing current *I*a and *α*eff of CNTB1 are summarized in Table 1. With the increase in the annealing current, *α*eff of CNTB1 increases likewise. When less heat is added, *α*eff changes little. As the sample is heated in a vacuum chamber, the thermal reduction would occur in the sample to remove impurity induced in the sample production. With the increase of the current, the degree of reduction is enhanced, and the microstructure is optimized. Thus, the thermal conductivity and *α*eff of CNTB1 rise. The annealing current of burning the sample is 210 mA, and when the annealing current is 200 mA, the thermal diffusivity increases by 33.62%.


**Table 1.** Partial experimental results of CNTB1 during current annealing.

#### 3.1.2. Observation of Thermal Diffusivity Jump on CNTB2 and CNTF

In the process of current annealing experiments for CNTB2 (length: 3657.23 μm; width: 260.23 μm; thickness: 25 μm) and CNTF (length: 3429.35 μm; diameter: 135 μm), an unusual phenomenon appears where the thermal diffusivity of the sample has a "sudden jump". Figure 3a shows the voltage evolution of CNTB2 before annealing. It is obvious that the varying trend is different from that of CNTB1, though both of them are cut from the same carbon nanotube conductive film. The disparate phenomenon of CNTB2 and CNTB1 indicates that they have different physical properties and even structures along their length directions, which lead to the occurrence of different heat conduction mechanisms.

Figure 3b–f shows the *V-t* experimental data and the theoretical fitting curves of CNTB2 under different currents: 140 mA, 160 mA, 165 mA, 170 mA and 300 mA. It presents an interesting evolution of the voltage variations. When the annealing current varies from 0 to 140 mA, the voltage of CNTB2 increases gradually under Joule heating and then reaches the steady-state, which is a typical voltage evolution with a positive TCR. However, when the annealing current is above 150 mA, the TET signal for CNTB2 shows a small decrease at the beginning of Joule heating, and then it rises again until reaching the steady-state. With the increase in the annealing current, the descending part becomes noticeable and begins to dominate the TET signal. When the current passes 170 mA, the signal only has a decreasing trend until reaching the steady-state, and the rising portion completely disappears. The sample initiates to perform the normal signal which the carbon materials originally have when the sample has a negative TCR. The "sudden jump" of thermal diffusivity indicates that with the increase of the annealing current, the TCR of CNTB2 and CNTF turns from positive to negative.

CNTF has a similar behavior as CNTB2. Both samples are annealed with a higher and higher current until the sample is burned down. The thermal diffusivities of CNTB2 and CNTF against the annealing currents are shown in Figure 4a,b, respectively. The detailed annealing condition and determined thermal diffusivity are listed in Table 2. The measured thermal diffusivity is divided into two separate data groups. The lower thermal diffusivity group is denoted as *α*1, and the higher thermal diffusivity group is denoted as *α*2. The corresponding two states before and after switch-on are named State 1 and State 2, respectively. Combining Table 2 and Figure 4, it can be observed that when the annealing currents of CNTB2 and CNTF are 160 mA and 350 mA, the peak thermal diffusivity is 32.01 × 10−<sup>5</sup> m2/s and 19.63 × 10−<sup>5</sup> m2/s. *α*1 is much lower than *α*2. Wang et al. [16] found that high temperature induces C atoms to act in a thermal flutter in a large range at the structural equilibrium position, and this deformation increases the atomic energy in the local region of MWCNTs. When the threshold of the barrier constraint value is reached, the MWCNTs structure will produce irreversible deformation (the minimum distance between C atoms) and even collapse [17]. It can be further determined that the thermal diffusivity peaks in CNTB2 and CNTF occur at the threshold where instability is produced in MWCNTs' structures.

**Figure 3.** (**<sup>a</sup>**–**f**) Comparisons between the theoretical fitting and experimental data of CNTB2 for the voltage under different annealing currents. The red squares are experimental data, and the blue lines are the theoretical fitting. (**a**) Corresponding to the unannealed state and the variation of voltage is monotone increasing, which trend is similar to (**b**) under 140 mA. (**<sup>c</sup>**,**d**) are under 160 mA and 165 mA, respectively. The variations perform as decreasing firstly and then rising to the steady-state. (**<sup>e</sup>**,**f**) 170 mA and 300 mA, respectively, and the variations are monotone decreasing.

**Figure 4.** The curve of thermal diffusivity with an annealing current (*I*a): (**a**) CNTB2; (**b**) CNTF.



3.1.3. Transient Annealing Behavior

The transient voltage variations of CNTB1, CNTB2 and CNTF under different annealing currents are shown in Figure 5. During the process of annealing, the time required by State 1 for CNTB and CNTF decreases. With the increase of the annealing current, State 2 presents complex and diverse changes, and when the annealing current approaches the maximum current that the sample can withstand, the voltage fluctuates greatly. It is clear in Figure 5 that transient voltage variations of CNTB and CNTF appear in a rising trend, suggesting that in the process of annealing, the resistance of the sample increases constantly with the heating temperature rising. This phenomenon is in conflict with the theory that carbon materials have negative TCR in themselves.

As shown in Figure 6a, the normalized resistance (*R*\*) of both samples has an upward trend with the rise of annealing power (*P*). After several times of annealing, the samples are burnt due to high-temperature heating eventually, and the final breakpoints of samples are shown in Figure 6b–d. CNTB1 is fractured at about 3/4 of the sample length, and CNTB2 and CNTF are both fractured at about 1/2 of their length, which indicates that during the annealing process, the temperature distribution along the length of the sample

is non-uniform. The temperature at the breakpoint is the highest, and thus the fracture occurs first.

**Figure 5.** The transient voltage variations with time during annealing: (**a**) CNTB1; (**b**) CNTB2; (**c**) CNTF. The arrows indicate State 1 and State 2. During the current annealing, the time required for each sample in State 1 is reduced.

#### 3.1.4. Temperature Distribution and Thermal Conductivity Change of CNTB

The temperature at different positions along the length of the sample is calculated by using a numerical method, and the results are shown in Figure 7a. The temperature distribution is non-uniform along the length of CNTB1 and CNTB2. The temperature at the middle point is the highest, and those further away from the middle point are lower in temperature. Moreover, the highest temperature of CNTB1 is lower than that of CNTB2, indicating that the thermal conductivity of CNTB1 is smaller than that of CNTB2, which is consistent with the experimental results that the thermal diffusivity of CNTB1 is smaller than that of CNTB2. In addition, the breakpoint of CNTB1 is further away from the middle point, and the inhomogeneity of temperature distribution will also cause the simulation temperature of CNTB1 to be at a low level.

**Figure 6.** (**a**) Curves of sample-normalized resistance with annealing power. The *R*\* of samples has different degrees of increase with the increase of *P*. Diagram of burning down after annealing: (**b**) CNTB1; (**c**) CNTB2; (**d**) CNTF. The locations of breakpoints are shown in the figures.

Figure 7b indicates that the Joule heating generated by the current provides the high temperature environment required by the annealing process for CNTB. With the increase of heating energy, the average temperature of samples continues to rise, which makes the annealing process proceed in an orderly manner. The rising rate of the average temperature shows a trend of gradual decrease, which reveals that in the process of annealing, the graphitization levels increase. Nevertheless, the process of graphitization is slowing down, and the degree of graphitization is decreasing, indicating that the graphitizing level is close to the maximum degree of the sample.

Figure 7c shows the variation curves of the thermal conductivity of the middle point (*k*m) with the annealing temperature of the middle point (*T*mid) of CNTB1 and CNTB2, respectively. *k*m of CNTB2 also appears to make a "sudden jump", as mentioned above. *k*m,1 and *k*m,2 correspond to the low thermal conductivity before switch-on and the high thermal conductivity after switch-on of CNTB2. As shown in this figure, with the increase of *T*mid, the *k*m of CNTB1 increases, while the *k*m of CNTB2 decreases, which reveals that a single annealing treatment does not always have a positive effect on the thermal conductivity of carbon materials, and the analysis from the overall samples also shows this. *α*eff and the average temperature (*T*ave) reflect the average properties of the material. As shown in Figure 7d, with the increase of *T*ave, *α*eff of CNTB1 increases, the low *<sup>α</sup>*eff,1 and the high *<sup>α</sup>*eff,2 of CNTB2 decreases.

**Figure 7.** (**a**) Temperature distribution along the length of CNTB. The x-coordinate zero is the midpoint of the sample. (**b**) The average temperature of CNTB under different heating conditions. (**c**) Thermal conductivity of the midpoint varies with the annealing temperature of the midpoint. *k*m,1 and *k*m,2 correspond to the low thermal conductivity before switch-on and the high thermal conductivity after switch-on of CNTB2. (**d**) The thermal diffusivity varies with the average annealing temperature. *<sup>α</sup>*eff,1 and *<sup>α</sup>*eff,2 also correspond to the states before and after switch-on of CNTB2.

#### 3.1.5. Temperature Distribution and Thermal Conductivity Change of CNTF

Unlike the "sudden jump" of CNTB2, CNTF does not have low-level thermal conductivity before switch-on. Therefore, the focus of CNTF is only the part with the high thermal conductivity after switch-on. As shown in Figure 8a, the temperature distribution along the length of CNTF is also non-uniform, and the temperature at the middle point is the highest.

Figure 8b shows the variation of the high *k*m with *T*mid after the switch-on of CNTF, indicating that *k*m decreases continuously with the increase of *T*mid. Figure 8c is the curve of *T*ave under different heating conditions, and Figure 8d is the variation of *α*eff against *T*ave, which shows that the current annealing in this experiment has a certain degree of "negative" effect on the thermal conductivity of CNTF.

**Figure 8.** (**a**) Temperature distribution along the length of CNTF. The x-coordinate zero is the midpoint of the sample. (**b**) Thermal conductivity of the midpoint varies with the annealing temperature of the midpoint. (**c**) The average temperature of CNTF under different heating conditions after switch-on. (**d**) The thermal diffusivity varies with the average annealing temperature.
