Theory of screw dislocation and chiral angle controlled carbon nanotube growth

Feng Ding1, Boris I. Yakobson2

1) Institute of Textile and Clothing, Hong Kong Polytechnic University, Kowloon, Hong Kong 2) ME&MS and Chemistry Department, Rice University, Houston, TX 77005

E-mail: tcfding@inet.polyu.edu.hk

Challenge to produce nanotubes of a prescribed chiral-type (n,m) has motivated more than decade-long research of growth mechanisms, both theoretical and experimental. In the course of theoretical study, numerous molecular dynamic (MD)/Monte Carlo (MC) simulations[1-4], structure optimizations, and static calculations have been done. Yet none of these simulations could yield a SWNT of well defined (n,m) (Fig. 1), and no calculations seemed to reveal the origin of CNT chiral-angle bias that has been observed in the number of different experiments.

We have considered the CNT growth from entirely new viewpoint: as a dislocation facilitated crystal growth, that mimics the Burton-Cabrera-Frank (BCF) theory, well established for 3D-crystals. Achiral SWNTs (zigzag SWNTs) are taken as basis-perfect cylindrical crystal and a SWNT of any chiral angle was viewed as a perfect crystal (or an achiral SWNT) with a screw dislocation (Fig. 2).1 Due to the screw dislocation core location in the vacuum-hollow and the single atomic layer cylindrical structure of the SWNT, there is no penalty energy for the formation of screw dislocation, which allows multiple dislocations to pile together (or the existence of SWNT of any chiral angle). Starting from the screw dislocation model, detailed analysis together with ab initio calculations lead to a conclusion that SWNT growth rate is proportional to the tube chiral angle. This appears in surprising agreement with experimental data widely observed (Fig. 3).

Fig. 1. A simulated SWNT always owns multi-folds of defects and thus it’s impossible to assign a pair of chiral indexes (n,m).

Fig. 2. A chiral SWNT can be viewed as a “defective” achiral SWNT with a screw dislcoation. a, a “perfect” achiral SWNT. b&c, two “defective” achiral SWNTs with one or two-folds screw dislocations.

Fig. 3. SWNT populations as a function of chiral angle from different experiments are in good agreement with the theoretical prediction.

REFERENCES [1] F. Ding, P. Larsson, J. A. Larsson, R. Ahuja, H. Duan, A.

Rosén, K. Bolton, K., “The Importance of Strong Carbon-Metal Adhesion for Catalytic Nucleation of Single-Walled Carbon Nanotubes”, Nano. Lett. 8, 463-368 (2008)

[2] F. Ding, A. Rosén, and K. Bolton, “Molecular dynamics study of the catalyst particle size dependence on carbon nanotube growth”, J. Chem. Phys. 121, 2775 (2004)

[3] F. Ding, A. Rosén, and K. Bolton, “Nucleation and growth of single-walled carbon nanotubes: A molecular dynamics study”, J. Phys. Chem. B 108, 17369-17377 (2004)

[4] F. Ding, A. R. Harutyunyan, B. I. Yakobson, “Dislocation theory of chirality controlled carbon nanotube growth”, PNAS 106, 2506-2509 (2009)

a b c

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