Dislocation theory of chirality-controlled nanotube growth

Abstract

The periodic makeup of carbon nanotubes suggests that their formation should obey the principles established for crystals. Nevertheless, this important connection remained elusive for decades and no theoretical regularities in the rates and product type distribution have been found. Here we contend that any nanotube can be viewed as having a screw dislocation along the axis. Consequently, its growth rate is shown to be proportional to the Burgers vector of such dislocation and therefore to the chiral angle of the tube. This is corroborated by the ab initio energy calculations, and agrees surprisingly well with diverse experimental measurements, which shows that the revealed kinetic mechanism and the deduced predictions are remarkably robust across the broad base of factual data.

Fig. 1.

An axial screw dislocation in the CNT. An achiral zigzag (n, 0) tube (A) can be viewed as a perfect crystal, and transformed into a chiral one by cutting, shifting by a Burgers vector b (red arrows in B–D), and resealing a tube-cylinder (B). The chiral (n, 1) in (C) and (n, 2) in (D) tubes contain the axial screw dislocations with a single and double value of b_γ, accordingly; the corresponding kinks at the open tube-end are marked in red. (E) Free energy profile during the growth of a chiral or achiral nanotube.

Fig. 2.

Nucleation of a next atomic row on the growing tube edge (orange), at the catalyst (blue) surface, is shown as sketch-schematics (center) and in atomistic detail (A-F). (A-C) An armchair edge near the metal step on Ni (1, 1, 1), its side view (A), front view (B), and the emerging row segment flanked by the kinks (C). Similarly for a zigzag edge (D-F), its side view (D), front view (E), and the emerging nucleus: the row-segment with the end-kinks (F), which has higher energy than the armchair case in (C). The small left box in the schematics corresponds to the views (A) and (D) in the direction tangential to the tube wall, while the small right box corresponds to the views (C) and (F) in the direction normal to the surface.

Fig. 3.

The distribution of CNT product as a function of chiral angle θ. Experimental data of CoMoCat (25), HiPco (24), arc discharge (28), and ACCVD (27), are extracted from literature. The present model and Eq. 1 predict N ∝ (θ), which yields 11%, 33%, and 56% for the presented intervals (black-gray), to be compared with experimental data (colored).