# A Review of Double-Walled and Triple-Walled Carbon Nanotube Synthesis and Applications
## 1 Introduction and Motivation
### Double- and Triple-Walled Carbon Nanotubes
[32] studied several different DWNTs systems, and they found that in incommensurate M@S DWNTs the electronic density of states of the semiconducting tubes were weakly perturbed by its coupling to the inner metallic tubes, which presented a constant density of electronic states in the region of interest (\(\pm 1\) eV). In commensurate M@S DWNTs, where the IL interactions are more effective, the VHS of the semiconducting tubes shift to higher energies, and an increase in the density of states in the bandgap is observed. For commensurate S@M DWNTs, the coupling between the inner semiconducting tube and the outer metallic tube modifies more strongly the semiconducting tube, which has its bandgap reduced due to the fact that its valence band blueshifts by 30 meV. The outer metallic tube remains basically unchanged [32]. [PERSON] and [PERSON] studied a commensurate M@M DWNT (more specifically, a \((5,5)\)@\((10,10)\)) and demonstrated that such a DWNT system behaves as its isolated counterparts. The reason is that the IL coupling slightly changes the electronic and vibrational properties of both the inner and the outer tube, but these changes balance out on average [60]. In their calculations, they also predicted superconductivity behavior for the M@M DWNT. It is important to note that superconductivity had been observed in  
Figure 4: (**a,b**) The electron diffraction pattern of a \((11,11)\)@\((22,9)\) DWNT and the absorption spectrum of the same DWNT, respectively. The dashed lines in (**b**) show the expected emission for the constituting SWNTs, and when compared to the experimental data, it is evident that the DWNT emissions are all redshifted. Reproduced with permission from [55], Copyright Nature Publishing Group, 2014. (**c**) Theoretical calculations showing the energy bands for a \((27,3)\)@\((36,3)\) DWNT that presents Moir\({}^{\ell}\) patterns. The left panel shows the energy bands for each constituent SWNT without the influence of interlayer (IL) interactions. The middle panel shows the changes in the energy bands when the IL interactions are present. The right panel shows the DWNT density of states (DOS). The dotted red (blue) lines are DOS for inner (outer) nanotubes and the solid black line is the DOS for the coupled DWNT. Reproduced with permission from [54], Copyright American Physical Society, 2015. MWNTs (with the number of walls greater than three) [61; 62], but only recently was it observed in DWNTs [28; 63; 64]. [PERSON] _et al_. [65] performed calculations on S@S DWNTs, demonstrating the possibility for energy transfer mechanisms involving the two semiconducting tubes constituting the DWNT systems, and confirmed that the phenomenon of energy transfer strongly depends on the commensurability of the DWNTs, as well. The mechanical properties of DWNTs and TWNTs are also addressed in the literature. [PERSON] _et al_. [66] studied the mechanical properties of DWNTs under hydrostatic pressures using Raman spectroscopy. They found that the outer tubes protect the inner tubes from the effects of pressure. In fact, they found that the tangential stress depends on the diameter for the outer tubes, but it stays constant for the inner tubes. The results found by [PERSON] _et al_. [66] are in agreement with the calculations performed by [PERSON] _et al_. [67], which show that the outer tube indeed takes most of the hydrostatic pressure. Their calculation suggested that the IL interactions become negligible with increasing the pressure load, and this shields the inner tube in a DWNT system. [PERSON] _et al_. [68] reported enhanced ductile behaviors in DWNTs and TWNTs submitted to axial tensions at temperatures above 2000 \({}^{\circ}\)C. They explain the super-elongation observed in the tubular structure as being essentially related to creep deformations of the CNTs structures at high temperatures. [PERSON]'s group confirms the same mechanical shielding of the inner tubes when multi-walled structures are submitted to strain/stress [69; 70; 71]. Recently, [PERSON] _et al_.