Structures of the helical carbon nanotubes

Abstract

The structures of helical carbon nanotubes have been studied by selected area electron diffraction (SAED) methods in parallel with high resolution transmission electron microscopy. The diffraction patterns confirm the existence of a variety of structures in the nanotubes. The tube may have a cross section that is either circular or polygonal with extended flat regions. Tubes of circular cross section may contain from 1 to 9 or more different helix angles depending upon the number of graphitic sheets in the tube, as indicated by the number of hexagonal sets of hk0 spots, mutually rotated, appearing in the SAED patterns. The helix angle changes after every three to five graphitic sheets. For most tubes the helix angles increase by regular increments, probably due to the residual memory effect of the successive sheet groups on the underlying helical structure. An analysis of the way in which the hexagonal configuration of carbon atoms in successive sheets may fit together suggests that neighboring sheets may maintain the same helix angle by changing the pitch of the helix, and that the helix angles within symmetrical tubes are limited to a well defined set of possible values in agreement with experimental observations. For tubes of polygonal cross section, hkℓ spots are seen to lie on characteristic ellipses in the SAED patterns, and a grouping of fringes in the HRTEM images is seen to correspond with the groups of graphitic sheets having a constant helix angle.