Energetics and structures of fullerene crop circles

The energetics and structures of carbon tori are studied using molecular simulation. They include circular and polygonal tori, formed by bending (n, n) tubes and by joining (n, n) and (n+1, n−1) or (n+2, n−2) tubes with pentagon–heptagon defects, respectively, in which n=5, 8 and 10. The strain energy of a circular and polygonal torus decreases by D−2 and D−1, respectively, where D is the torus diameter. Comparisons in average and local maximum strain suggest that defect-free circular tori are more energetically stable and kinetically accessible than defective polygonal tori. This confirms the hypothesis that circular tori are the predominant constituents of the observed fullerene crop circles in laser-grown single-wall carbon nanotubes.