# A Review of Geometry, Construction and Modelling for Carbon Nanotori
## 5 Physical Roles, Properties and Applications
### Some Potential Applications  
Due to the strong attractive energy, carbon nanotori might be used as traps for both charged and uncharged atoms, and the key factors controlling the trap performance are the major and minor radii  
Figure 15: Relation between induced magnetic moment and temperature for various carbon nanotori in a perpendicular magnetic field of 0.1 T (solid) and 0.2 T (dashed) obtained from [64]. Reprinted figure with permission from [PERSON] and [PERSON] and [PERSON] and [PERSON], Colossal paramagnetic moments in metallic carbon nanotori, 88, 217206 (2002). Copyright (2019) by the American Physical Society.  
of the nanotori. The simulation results show that the optimal major radius that provides the strongest attraction is linearly proportional to the minor radius [69]. Further, the minimum energy of the carbon nanotori and the ions can be expressed in terms of the van der Waals parameters for the specific atomic types [40]. Figure 16 illustrates the energy profiles for numerous atoms and ions along the central axis of a nanotorus.  
Carbon nanotori can also serve as the host to encapsulate carbon atomic chains. The interaction energy between the carbon nanotori and the carbon chain suggest that the chain prefers to remain inside the interior cavity of the nanotori, and the major and minor radii play a critical role in the encapsulation. Especially, the minor radius should be greater than 0.317 nm, while the nanotori with major radii greater than 1.5 nm and minor radii around 0.369 nm provide the optimal configurations for carbon chain encapsulation [70].  
In addition, carbon nanotori can encapsulate chains of metallic atoms, such as iron (Fe), copper (Cu) and gold (Au). By introducing the metallic chains into the nanotori with a scanning tunnelling microscope, the composite nanotori show some novel magnetic features. The carbon nanotori encapsulating Fe, Cu and Au chains provide positive, neutral and negative magnetic moments, respectively, and all three metal chains are linearly stable at zero temperature [71].  
Further, carbon nanotori may be viewed as components of nano-scaled gigahertz oscillators. By placing a carbon nanotube situated inside the central cavity of the nanotori, the interaction with the nanotube produces a pulse-like force acting at either end of the nanotube, so that the carbon nanotori are sucked by the van der Waals interaction onto the exterior of the carbon nanotube and will oscillate back and forth along the nanotube with frequency of the oscillatory motion in the megahertz range [45].  
Other interesting applications of carbon nanotori arise from their charge free interior cavities, which have been proposed as regions to encapsulate nanostructures. If the major and minor radii are sufficiently large, their interaction energy induces an oscillatory motion of the encapsulated nanoparticle within the closed loop of the carbon nanotori. Such motions can generate gigahertz frequencies, such that the minor radius is inversely proportional to the frequency of the oscillation [46; 72].  
Figure 16: Energy profiles for various atoms and ions interacting with nanotorus.