Response of a single-walled zigzag carbon nanotube to axial tension
Ali Ebrahimi, Marzie Mohammadi
Department of Chemistry, University of Sistan & Balouchestan, P.O. BOX 98135-674 Zahedan.
E-mail: [email protected] (Marzie Mohammadi)
Introduction
Along with more than one decade researches and investigations on carbon nanotubes (CNTs), now it becomes obvious that these materials possess extra ordinary physical properties. Mechanical properties of CNTs are so interesting because they have exceptional Young modules which are greater than any known material [1] and combine high stiffness with resilience and ability to buckle and collapse in a reversible manner[2].
Structures of carbon nanotubes (CNTs) can be specified uniquely with a chiral vector C
= na1 + ma2 defined relative to the two-dimensional graphene sheet [3], where a1 and a2
are the graphene lattice vectors and n and m are integers. They have been classified roughly into three types: armchair, zigzag and chiral structures. Calculations of electronic band structures of singlewalled nanotubes (SWNTs)[4] predict that SWNTs can be either metallic or semiconducting depending on the chiral vector. Armchair-type CNTs should always be metallic, while zigzag- and chiral-type CNTs should alternate between metallic and semiconducting states as a function of the chiral vector. It has also been shown that the band gaps of semiconducting nanotubes decrease with increasing diameter [5].
Tensile behavior of CNTs has been the subject of several studies [6]. It was found out from simulation that CNTs can sustain large strains before any failure (in the range of 20%–30%) [7].
In the present work, the response of a SWZCNT to tension (from energetic and structural properties standpoints) has been studied by a density functional method. Also, the changes in the aromaticity of different six-membered rings of nanotube and the topological analysis of electron density have been considered along tension.
Gaussian98 program package [8] at B3LYP/6-31G level of theory. Nuclear independent chemical shift (NICS)[9] was selected as a criterion to study the aromaticity and antiaromaticity of six-membered rings on some obtained structures along axial tension.
NMR calculations have been performed at B3LYP/6-31G level of theory using GIAO method [10].
Topological properties of electronic charge density have been calculated by the atoms in molecules (AIM) [11] method on the obtained wave functions at B3LYP/6- 31G level using AIM2000 program package [12].
Results and discussion
On the contrary to single walled armchair carbon nanotubes (SWACNTs)[13], the energy and geometrical parameters change smoothly with tension. The sudden changes in energy and geometrical parameters were referenced to sudden changes in the aromaticity of six-membered rings in SWACNTs. Some six-membered rings of (6,0) zigzag CNT are similar by the symmetry. Different rings are specified by A, B and C in Figure 1. Also the calculated NICS values at GIAO- B3LYP/6-31G level at the center of A, B and C vs. strain are shown in Figure 2. As can be seen, the value of NICS at the center of ring A is negative before tension. Thus, this ring is aromatic before the tube elongation. The value of NICS in the center of A becomes more negative by tension.
Therefore the aromaticity of this ring increases by strain and approximately approach a constant value close to failure point.
The NICS vs. strain diagram at the center of ring B is similar to ring A. As can be seen, the value of NICS is negative before tension. Therefore, this ring is aromatic before the tube elongation. The value of NICS at the center of ring B is higher than ring A before tension (approximately four times). Although the aromaticity of this ring increases with tension, but passes through a minimum before failure point. Calculated NICS value at the center of C vs. strain is approximately similar to ring A. Thus, this ring is also aromatic before tension. The NICS value at the center of this ring is higher in the comparison with ring A and is lower in the comparison with ring B. The change is
similar to ring A along tension until failure.
-1
-2 A
B
-3 C
-4
-5 7
-6
-7
0 0.04 0.08 0.12 0.16 0.2
Strain
Figure 1. Different six-membered rings in a limited (6,0) SWZCNT.
Figure 2. NICS (ppm) vs. strain at the center of rings A, B and C.
Topological analysis of electron density has been performed on some structures along tension using AIM analysis. A typical molecular graph, correspond to unstrained nanotube is shown in Figure 3. The values of electron density (ρ) and Laplacian of electron density (∇2ρ) corresponding to critical points of ring A vs. strain are shown in Figure 4.
As can be seen, for ring A, the values of ρ and ∇2ρ are decreased with tension. The changes of ρ and ∇2ρ for rings B and C are also similar to ring A. Thus, there is a relationship between the changes of ρ and ∇2ρ at ring critical points and the changes of NICS values at the center of rings.
A set of ring and cage critical points are observed in molecular graph on the central axis of tube. The changes of ρ and ∇2ρ values corresponding to these critical points are different from RCPs of six-membered rings and pass from a maximum along tension.
1.9 1.6
ρ×100
∇2ρ×10
1.3 1 0.7
NICS(ppm)
References
1. M.M.J. Treacy, T.W. Ebbesen, J.M. Gibson, Nature 381 (1996) 678.
2. M.R. Falvo, G.J. Clary, R.M. Taylor, V. Chi, F.P. Brooks, S. Washburn, R.
Superfine, Nature 389 (1997) 582.
3. R. Saito, M. Fujita, G. Dresselhaus, M.S. Dresselhaus, Mater. Sci. Endin. B 19 (1993) 185.
4. R. Saito, M. Fujita, G. Dresselhaus, M.S. Dresselhaus, Appl. Phys. Lett. 60 (1992) 2204.
5. M.S. Dresselhaus, G. Dresselhaus, R. Saito, Solid State Commun. 84 (1992) 201.
6. T. Belytschko, S.P. Xiao, G.C. Schatz, R.S. Ruoff, Phys. Rev. B 65 (2002) 235430.
7. D. Troya, S.L. Mielke, G.C. Schatz, Chem. Phys. Lett. 382 (2003) 133.
8. M.J. Frisch et al., Gaussian 98, Revision A. 7, Gaussian, Inc., Pittsburgh, PA, 1998.
9. M.K. Cyrafiski, T.M. Krygowski, M. Wisiorowski, N.J.R.v.E. Hommes, P.v.R.
Schleyer, Angew. Chem., Int. Ed. 37 (1998) 177, and the references therein.
10. K. Wolinski, J.F. Hinto, P. Pulay, J. Am. Chem. Soc., 112 (1990) 8251.
11. R.F.W. Bader, Atoms in molecules: A Quantum Theory, Oxford University Press, Oxford, 1990.
12. F.W. Biegler könig, J. Schönbohm, D. Bayles, J.Comput. Chem., 22 (2001) 545.
13. A. Ebrahimi, H. Ehteshami, M. Mohammadi, Comput. Mater. Sci., 2007, DOI:10.1016/J.
