Toroidal Single Wall Carbon Nanotubes in Fullerene Crop Circles

We investigate energetics and structure of circular and polygonal single wall carbon nanotubes (SWNTs) using large scale molecular simulations on NAS SP2, motivated by their unusual electronic and magnetic properties. The circular tori are formed by bending tube (n, n) whereas the polygonal tori are constructed by turning the joint of two tubes of (n, n), (n+1, n-1) and (n+2, n-2) with topological pentagon-heptagon defect, in which n=5, 8 and 10. The strain energy of circular tori relative to straight tube decreases by 1/D2 where D is torus diameter. As D increases, these tori change from buckling to an energetically stable state. The stable tori are perfect circular in both toroidal and tubular geometry with strain < 0.03 eV/atom when D > 10, 20 and 40 nm for torus (5,5), (8,8) and (10,10). Polygonal tori, whose strain is proportional to the number of defects and 1/D, are energetically stable even for D < 10 nm. However, their strain is higher than that of perfect circular tori. In addition, the local maxium strain of polygonal tori is much higher than that of perfect circulat tori. It is ~0.03 eV/atom or less for perfect circular torus (5,5), but 0.13 and 0.21 eV/atom for polygonal tori (6,4)/(5,5) and (7,3)/(5,5). Therefore, we conclude that the circular tori with no topological defects are more energetically stable and kinetically accessible than the polygonal tori containing the pentagon-heptagon defects for the laser-grown SWNTs and Fullerene crop circles.