Ordered phases of fullerene molecules formed inside carbon nanotubes

A simulated annealing method was used to study the minimum energy configurations of ${\mathrm{C}}_{60}$ molecules inside carbon nanotubes. Simulations for over 50 nanotubes with radii from 6.27 Å to 13.57 Å showed that ten different phases exist in this size range. Both chiral and achiral phases were found. The achiral phases consist of layers of stacked polygons rotated by an angle of $360/\left(2k\right)\mathrm{}$ relative to each other, where k is an integer. The chiral phases consist of multistranded helices. Tubes of larger radii, each of the $\mathrm{}(n,n)\mathrm{}$ type, were also studied; these also exhibited helical and polygonal-layered phases. For tubes larger than (24,24), ${\mathrm{C}}_{60}$ molecules can be at the tube center as well as at the wall. The effects of multiwalled versus single-walled tubes were shown to be small. The phase structure is very sensitive to the tube radius and is different from that for the packing of hard spheres.