*3.2. Discussions*

#### 3.2.1. Mechanism of Phonon Scattering

Heat conduction is normally dominated by phonons of carbon materials [18], whose heat transport is critical to the heat transport of materials. It is speculated that during the current annealing process of CNTB1, the size of graphite microcrystals increases, some of the impurity atoms are moved, and the order of the graphite microcrystalline structure is improved. These transformations reduce the probability of phonons colliding with other phonons, grain boundaries, impurities and edge boundaries in the process of heat transport, thus reducing the amount of phonon scattering and the scattering intensity. The integrity of phonon heat transport improves, and the phonon mean free path increases. Therefore, the thermal conductivity of CNTB1 increases.

The phonon scattering of CNTB2 and CNTF is determined by Umklapp scattering, normal scattering, impurity scattering, phonon-boundary scattering, phonon-defect scattering and thermal contact resistance. Normal scattering generally occurs at low temperatures, and Umklapp scattering is more likely to occur at higher temperatures. Combined with the previous analysis of the "sudden jump", in State 1, because of the interaction between adjacent pure carbon nanotube (P-CNT) and impurities-embedded carbon nanotube (I-CNT), the thermal diffusivity of material is restrained. Thermal expansion mismatch occurs between P-CNT and I-CNT due to thermal stress, which results in different degrees of stretching or contraction of carbon nanotubes. However, P-CNT is not separated from the surrounding I-CNT, and the restraint of boundary scattering on phonon heat transport is amplified to some extent, resulting in the thermal diffusivity decrease.

In the switch-on state, with the enhancement of annealing, the temperature increases gradually, and the elastic vibration of the lattice increases. Furthermore, more highfrequency phonons are excited, and the number of phonon groups increases, which promotes the heat transport of phonons. The thermal diffusivity of the material is ultimately

improved. Because I-CNT is purified and the structure of CNT is optimized continuously, the effect of impurity and boundary scattering on heat conduction is weakened. Therefore, the thermal diffusivity peaks of CNTB2 and CNTF appear at this state.

In State 2, P-CNT and I-CNT are completely separated, and Umklapp scattering is more prevalent. Umklapp scattering is dominant in the phonon scattering mechanism [19], and the process of Umklapp scattering generally causes thermal resistance, which also affects the phonon mean free path. As the annealing temperature increases, the influence of thermal stress goes up. MWCNTs are continuously stretched or compressed, and the structure deforms to different degrees, which is irreversible due to excessive thermal stress [16]. The scattering produced by structural changes is classified as structure scattering. Because of the high thermal stress, the structure of MWCNTs collapses, and the structure scattering is enhanced, which impairs the original larger thermal conductivity of carbon nanotubes. In this state, MWCNT impurities are further removed, and the density of the defect is reduced, which results in the impurity scattering and defect scattering effects being weakened. The high temperature excites more high-frequency phonons to promote heat transport, but it also excites more scattering between phonons, which enhances Umklapp scattering and increases the thermal resistance. Combining with the above factors, the thermal diffusivity of CNTB2 and CNTF decreases.

#### 3.2.2. Effects on Thermal Conductivity

MWCNT torsional sliding induced by high temperature is one of the reasons for the decrease of thermal conductivity. Wang et al. [20] showed that the external load causes the global buckling of carbon nanotubes and even the large torsion. Charlier et al. [21] found that Buckyball molecules rotate freely when it reaches the transition temperature (258 K), which can easily slide into or out of each other, and such movements are unhindered at room temperature. With the increase of annealing, the graphitization degree increases, the structure becomes ordered, and the density of the defect decreases. Chen [22] showed that structure defects limit rotation and sliding between MWCNTs layers. Therefore, the reduction of defect density promotes the rotational migration of CNT to some extent. With the increase of the annealing current, the effect of annealing on the structure gradually increases. When the current increases to a certain degree, the annealing will produce large thermal stress. The stress is equivalent to applying an external load on the material; the CNT rotates under the torque generated by the high temperature, resulting in the deviation of the MWCNTs distribution direction. The axial direction of the MWCNTs cylinder forms a certain angle with the length direction, and even the phenomenon that the MWCNTs is perpendicular to the axial direction appears. The more orderly structure also indicates that more CNT may rotate together along a certain angle and form an ordered arrangemen<sup>t</sup> with the axial direction [23]. Therefore, the thermal conductivity of CNTB2 and CNTF decreases.

On the other hand, high annealing temperature may result in greater thermal resistance between MWCNTs, which affects the thermal transport of materials. Gong [24] proved that 1800 °C is the appropriate annealing temperature to remove the impurities of MWCNTs. When the annealing temperature rises to 2100 ◦C, agglomeration occurs in MWCNTs, and aggregates are generated on the surface of the sample. This indicates that with the increase of annealing, the structure of MWCNTs deforms, becomes rough and even agglomerates, so the thermal resistance is increased, and the heat transport is inhibited. Feng et al. [25] showed that high temperature stimulates more phonon scattering, resulting in increased thermal resistance and reduced thermal conductivity. Kim et al. [26] reported that lattice defects of carbon tubes at high temperatures would motivate the Umklapp scattering, causing an increase in thermal resistance. Liu et al. [27] showed that in the graphitization process of carbon fiber, although the crystal size of material increases, the probability of the occurrence of maximum defects and large holes also increased. Therefore, it is speculated that during the annealing process, with the increasing of annealing temperature, the presence of thermal stress leads MWCNT to agglomerate. In the process of graphitization, larger vacancy and hole defects appear in the material, which causes greater

thermal resistance, and hinders and inhibits the effective heat transport of phonons. At the beginning of annealing, the TCR of CNTB2 is positive, which means thermal resistance plays an important role in heat transfer. This also explains that the thermal conductivity decreases with the increase of annealing current.

#### 3.2.3. Effects of Annealing on Structure

The Raman characterization of CNTB after burning off is shown in Figure 9. The positions of the measuring point are numbered as 1 to 9, which are closer and closer to the breakpoint from bottom to top. It can be seen that the effect of annealing is ununiformed along the length during the current annealing process, which appears as the effect of annealing is continuously enhanced from both ends to the breakpoint of the sample. Three prominent peaks are at around 1315 cm<sup>−</sup>1, 1586 cm<sup>−</sup><sup>1</sup> and 2610 cm<sup>−</sup>1, which correspond with D peak, G peak and 2G peak, respectively. Figure 10 shows the ratio of peak intensities *I*D/*I*G of different points of CNTB. From the endpoint to the breakpoint, the decreased *I*D/*I*G ratio means a lower defect. With the enhancement of annealing, the sample becomes orderly, the disorder of internal structure decreases and the defect density also decreases.Moreover, the closer to the breakpoint, the shape of the G peak and 2D peak in Raman become steeper with a narrower line width and stronger intensity, which also indicates the larger crystalline size and structure of the sample is improved gradually.

**Figure 9.** The Raman spectrum with measuring point positions 1–9 of the burned CNTB sample. Point 1 is the furthest from the breakpoint, and 9 is the closest.

**Figure 10.** The *I*D/*I*G of CNTB varies with the position of measuring points 1–9.

## **4. Conclusions**

This work shows the current annealing effect on the thermal conductivity of CNTB and CNTF. In the annealing process, the thermal diffusivity of CNTB1 increases gradually, and the highest thermal conductivity is 1.34 times the original thermal conductivity. Although both CNTB1 and CNTB2 are cut from the same carbon nanotube conductive film, the thermal diffusivity of CNTB2 has a "sudden jump", and the TCR of CNTB2 changes from positive to negative. 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. The results show that the high-level thermal diffusivity of CNTB2 is 2.28–2.46 times higher than the low one.

The high-level thermal diffusivity of CNTF is 1.65–3.85 times higher than the low one. The main reasons for the decrease of the thermal conductivity of CNTB2 and CNTF are as follows: enhanced Umklapp scattering; torsional sliding occurs in MWCNTs induced by high temperature; high thermal resistance between MWCNTs.

**Author Contributions:** H.L., J.X., F.S., L.Z., S.X., H.D. and S.L. wrote the main manuscript text. H.L. designed experiments. J.X., F.S., L.Z. carried out experiments. S.X. and H.D. analyzed experimental results. S.L. assisted with analyze the Raman result. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Key Research and Development Program (2019YFE0119900), Natural Science Foundation of Shandong Province (ZR2020ME183 and ZR2019MEE015) and China Postdoctoral Science Foundation (2017M612225).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** Huan Lin and Shen Xu are grateful to the China Scholarship Council. Shen Xu is grateful to the research supported by the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning.

**Conflicts of Interest:** The authors declare no conflict of interest.
