# A Brief Review on the Recent Experimental Advances in Thermal Rectification at the Nanoscale
## 2 Experimental Study
### Thermal Rectification of Asymmetric Nanotubes  
[PERSON] et al. created a one-dimensional thermal rectifier by loading heavy molecules with non-uniform mass outside the carbon nanotubes (CNT) and boron nitride nanotubes (BNNT) [28]. It was found that a larger heat flow occurs in the direction of lowering the mass density and the maximum rectification ratio reached 7%. A customized microscale thermal measurement device was used to measure the thermal conductivity of the nanotube, driven by a piezoelectrical manipulator operating within a scanning electron microscope (SEM). In this micro-device, two symmetrically fabricated Pt thin film resistors were used as heater and temperature sensors, respectively. The nanotube was suspended between the heater and sensor pads. The thermal measurement was carried out in high-vacuum. The direction of heat flow can be simply changed by exchanging the role of heater and sensor in the experiment. The original multi-walled BNNT was made by improving the fabrication method introduced in Ref. [29], and the high-quality CNT was made by the conventional electric arc method introduced in Ref. [30]. To achieve the thermal rectification effect, the asymmetry of the nanotube was achieved by depositing trimethyl-cyclopentadienyl platinum (C9H16 Pt) at one end of the tube as shown in Figure 3. Since the thermal conductivity of C9H16 Pt was less than 1% of that of the nanotube, its direct contribution to the thermal conductivity could be ignored. The thermal conductivity of the same nanotube was measured in both heat flow directions. The experimental results show that the thermal conductivity is higher when heat flows from the high-mass end to the low-mass end (Figure 4). As for CNT, a 2% thermal rectification coefficient was observed, and for BNNT, a 7.4% thermal rectification coefficient was observed. Figure 2: Thermal rectification coefficient as a function of temperature of different samples. (**A**) First Si/PA nanowire sample. (**B**) Second sample after focused ion beam cutting [25]. In general, the asymmetric geometry can introduce asymmetric phonon scattering boundaries, which can possibly cause asymmetry in the heat transfer. However, following this mechanism, a higher thermal conductivity should be observed when heat flows from the narrow end to the wide end, which is contrary to the phenomenon observed in the experiment. Therefore, the asymmetric boundary is not the cause of the thermal rectification phenomenon. In fact, the \(sp^{2}\) bond in the nanotube is much stronger than the bond between the tube and the condensed C9H16 Pt molecules. The phonons are confined inside the nanotube without propagating between CNT and C9H16 Pt, so the thermal rectification is unaffected by the phonon scattering at asymmetric boundaries. Theoretical studies have shown that stable solitons do exist in the nanotubes. Solitons are the nonperturbative solutions of the non-linear systems, which are localized particle-like entities that can collide with each other without changing shape. For a category of soliton models, the thermal rectification effect is a common phenomenon in the asymmetric structures. For instance, the Korteweg de Veries equation describes the relationship between the reflection magnitude and two different atomic masses. An important result of this equation is that in this mass-asymmetric system, heat is more easily transferred from the high-mass end to the low-mass end, which is consistent with the observed thermal rectification in the experiments. This model can be used to roughly estimate the  
Figure 4: **(A–C)** SEM images of three different BNNTs after C9H16 Pt deposition. **(D)** The temperature change of the sensor as a function of the temperature change of the heater before and after C9H16 Pt deposition. Reprinted with permission from the American Association for the Advancement of Science. Figure 3: Schematic diagram of the thermal rectifier with amorphous C9H16 Pt deposited at one end of the nanotube.