- Email: [email protected]
Silicon doping of defect sites in Stone–Wales defective carbon nanotubes: A density functional theory study
Superlattices and Microstructures 60 (2013) 1–9
Contents lists available at SciVerse ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Silicon doping of defect sites in Stone–Wales defective carbon nanotubes: A density functional theory study Maryam Anafcheh, Reza Ghafouri ⇑ Department of Chemistry, Shahr-e-Ray Branch, Islamic Azad University, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 21 December 2012 Received in revised form 1 April 2013 Accepted 12 April 2013 Available online 30 April 2013 Keywords: Stone Wales defect DFT SWCNT DOS
a b s t r a c t Using density-functional theory calculations, we investigate how the stabilities and electronic properties of Stone Wales (SW) defective armchair (4, 4) and (5, 5) nanotubes are modified via Si atom doping at eight selected symmetric positions of SW defect sites with two different orientations, parallel and diagonal. A quasi-tetrahedral bonding configurations of silicon atoms based on sp3 hybridization are formed, which leads to puckered silicon doped rings. Our results indicate that tube diameter affects the doping reactions so that the doping single-walled carbon nanotubes (SWCNTs) with high curvature (small diameter) might be more favorable, based on both energetic and structural considerations. Density of state (DOS) obtained for the systems indicate that the doping of the defect sites causes the redistribution of electronic states of the SW defective SWCNTs. An average charge of 0.5e is also transferred from silicon atoms to first neighboring carbon atoms on the SWCNT, which indicates that charge redistributions after doping process mostly take place to a relatively small number of carbons at the zone of doped atoms. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction The structures of single-walled carbon nanotubes (SWCNTs) could be described as a perfect graphene sheet wrapped up into a cylinder. However, the experimentally available SWCNTs are not perfect. Topological defects such as vacancies, pentagons, heptagons, dopants, and Stone–Wales defects [1–5] ⇑ Corresponding author. Tel.: +98 9356463576. E-mail address: [email protected] (R. Ghafouri). 0749-6036/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.spmi.2013.04.014
2
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
formed inevitably during the growth of carbon nanotubes or introduced during workup (e.g., oxidative cleaning, ultrasonication) [6,7] can significantly change the electronic structure [8–10], chemical reactivity [11–13], mechanical [14] and transport [15,16] properties of the systems. Stone–Wales (SW) defect which is a very important topological one in SWCNTs is comprised of two pairs of pentagons and heptagons (5-7-7-5) formed by rotating one bond of the traditional hexagon by 90° [1]. A number of theoretical investigations revealed that these defective sites are chemically more reactive than the perfect sites in the sidewalls of carbon nanotubes [17–20]. Indeed they could act as nucleation centers for the formation of dislocations in the originally ideal network. Therefore, it is expected that with a local deformation, the nanotube containing SW defects might be more favorable for subsequent reactions. For example, the adsorption of small molecules such as H2 [21], O2 and O3 [12], N2 [22], NH3 [23,24], NO2 [24,25], H2O [26], CO and CO2 [22,27], Ar [28], Ne and Xe [29–31], and some relevant addends like O, SiH2, NH, and CH2 [32] on defective SWCNTs has been reported; it is demonstrated that the adsorption of atoms and molecules on defects is more stable than that on the smooth sidewall, and the chemical and physical properties induced are obviously different. On the other hand, doping of carbon nanotubes by introducing heteroatoms on the sidewall is a significant way to modify their electronic structures and transport properties, making carbon nanotubes more amenable for various potential applications, such as improving the sensitivities of chemical sensors, and opening hollow cavities for gas storage [33] or lithium intercalation [34]. However, the doping of Stone–Wales defects on the surfaces of defective SWCNTs has hardly been investigated before now, to the best of our knowledge, doping of perfect SWCNTs has been the subject of many theoretical and experimental studies. Using first principles calculations, Zeng et al. [35] studied the effect of N doping on the electronic properties of defective zigzag-edged graphene nanoribbons with SW defects. Qin et al. [36] investigated the adsorption of formaldehyde (H2CO) on the Al-doped SW defective graphene, showing that Al-doped SW graphene is more suitable for H2CO gas detection. Therefore, the insight into the effect of defect–dopant combination on the carbon nanotube properties is vital for finding their potential applications. With this initial thought in mind, in the present investigation, we systematically evaluate the doping effect of SW defective armchair SWCNTs with different diameters, (4, 4) and (5, 5), by replacing carbon atoms on the SW defects with silicon ones, exploring possible atomic arrangements and the resulted electronic properties. For all SWCNTs, a rotation about a CAC bond diagonal (D) or parallel (P) to the tube axis gives rise to two different systems which are labeled P-SW and D-SW, respectively, as illustrated in Fig. 1. For each configuration, eight substitution sites (as shown in Fig1) are considered according to the symmetry of the SW defect. Silicon is selected as a dopant because it is the next group IV element in the periodic table after carbon, and although they share several similarities in their
Fig. 1. Two configurations of the Stone–Wales defects on the tube sidewall: (a) parallel (P-SW) and (b) diagonal (D-SW). Five different doping positions at the defective sites of SWCNTs according to the symmetry of the SW defects, C1–C5, and three different positions adjoining the defect sites, C6–C8, are shown.
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
3
electronic structure, their chemistry are very different; unlike C, because of its sp3 hybridization in the bulk, Si, when used in fullerenes or nanotubes, prefers to form dangling bonds rather than single/double bond chains across the pentagon and hexagon rings rings. Thus the structural chemistries of carbon and silicon are different and yet similar. In recent years, there has been renewed interest in Si–C nanocomposites because of their expected potential applications in nanotechnology. For example, it was shown that nanotubes with alternative Si and C atoms were full of point charges [37,38] and hence they would serve as promising materials for hydrogen storage [33].
2. Computational method All density functional theory (DFT) quantum calculations are performed using Gaussian 98 program package [39]. A finite model, including 96 and 120 carbon atoms, is used to represent a defect-free (4, 4) and (5, 5) SWCNTs. The hydrogen atoms are added at the open ends to avoid dangling bonds. Geometries of all systems (perfect SWCNT and SW defective SWCNTs and Si-doped SW defective SWCNTs) are allowed to fully relax during the B3LYP/6-31G optimization process [40]. Real frequencies obtained from frequency calculations confirm that all of them are minimum energy structures. The standard 6-31G basis set is employed due to being affordable and accurate enough for geometry optimization of even large molecules [5,41]. Optimized structures of Si-doped SW defective SWCNTs and their parents have been subjected to calculation of the related properties such as total energies (Etot), relative energies (Erel), reaction energies (Er) and density of state (DOS).
3. Results and discussion 3.1. Optimized structural properties and stability We chose the prefect (4, 4) and (5, 5) armchair SWCNTs and the ones with Stone–Wales defects, which is fully optimized at the B3LYP/6-31G level, as the parent molecules for doping. The obtained structural properties of prefect SWCNTs such as the CAC bond lengths in the middle of the tube are predicted to be 1.417 and 1.435 Å, in excellent agreement with previously reported values (1.41 and 1.43 Å) [12]. For (5, 5) SWCNT, the rotation about a CAC bond diagonal (D) or parallel (P) to the tube axis gives rise to two different systems (P-SW and D-SW, respectively). The prediction of bond lengths of the heptagon–heptagon and heptagon–pentagon junctions (i.e., the 7-7 ring fusion and 7-5 ring fusion, respectively) in the SW defective armchair SWCNTs are obtained 1.351–1.354 and 1.452–1.461 Å, respectively, consistent with the values of 1.35 and 1.46 Å reported by Lu et al. [12]. For each configuration, P-SW and D-SW, we select five different doping positions at the defective sites of SWCNTs according to the symmetry of the SW defects, C1–C5, and three different positions adjoining the defect sites, C6–C8. The doping positions C1–C8 for P-SW and D-SW SWCNTs are shown in Fig. 1. Therefore, in our work, the considered configurations for Si-doped SW defective SWCNTs are denoted by P1–P8 (n, n) and D1–D8 (n, n). Total energies (Etot) and relative energies (Erel) of all the Si-doped SW defective SWCNTs are reported in Table 1. As can be seen from Fig. 2, in general, for silicon doped P-SWCNTs, isomer P4 is the most stable followed by P5, P2, P3, P1, P8, P6 and P7. For silicon doped D-SWCNTs, isomers D5 and D1, lying within 0.05 eV of one another, can be considered as essentially isoenergetic, and the relative stabilities are found to be in the order of D1 D5 > D4 > D2 > D3 > D8 > D6 > D7. In fact, a Si atom prefers to form dangling bonds rather than single/double bond chains across the pentagon and hexagon rings, so upon Si doping at the defective SW sites of SWCNTs the quasi-tetrahedral bonding configurations of silicon atoms based on sp3 hybridization are formed. As a result, an evident local radial distortion is observed on the tube wall where silicon atom relaxes outward from the surface, making puckered silicon-doped rings, see Fig. 3. Hence, it seems that puckering of silicon-doped rings due to dislocation of Si atom is responsible for the stability of these isomers. Similar trends were observed by Qin et al. [36] showing that heptagon–heptagon junctions is the most energetically favorable for Al doped site and the Al atom dopant protrudes out of the original plane and results in large distortion in the region around the defect.
4
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
Table 1 Total energy (E in eV), relative energy (Erel in eV), reaction energy (Er in kcal/mol) and charge transfer (C.T) for the Si-doped SW defective SWCNTs.
P1(4, 4) P2(4, 4) P3(4, 4) P4(4, 4) P5(4, 4) P6(4, 4) P7(4, 4) P8(4, 4) P1(5, 5) P2(5, 5) P3(5, 5) P4(5, 5) P5(5, 5) P6(5, 5) P7(5, 5) P8(5, 5)
E
Erel
Er
106638.86 106640.49 106639.69 106640.81 106640.60 106638.51 106638.46 106638.70 110860.59 110862.12 110861.25 110862.42 110862.21 110860.14 110860.10 110860.33
1.96 0.33 1.13 0.00 0.21 2.30 2.35 2.11 1.83 0.30 1.18 0.00 0.22 2.28 2.33 2.09
165.8 128.2 146.7 120.7 125.6 173.8 175.0 169.4 170.1 134.8 131.7 127.9 132.9 180.6 181.6 176.2
C.T
0.558
0.484
D1(4, 4) D2(4, 4) D3(4, 4) D4(4, 4) D5(4, 4) D6(4, 4) D7(4, 4) D8(4, 4) D1(5, 5) D2(5, 5) D3(5, 5) D4(5, 5) D5(5, 5) D6(5, 5) D7(5, 5) D8(5, 5)
E
Erel
Er
C.T
106641.33 106641.09 106640.24 106641.15 106641.36 106639.85 106639.83 106639.98 110862.74 110862.48 110861.69 110862.43 110862.69 110861.53 110861.51 110861.62
0.03 0.27 1.12 0.21 0.00 1.30 1.32 1.17 0.00 0.26 1.05 0.31 0.05 1.21 1.23 1.12
108.8 128.5 148.2 127.3 122.4 157.2 157.8 154.3 132.6 138.6 156.8 139.8 133.9 160.5 161.0 158.4
0.499
0.576
0.527
0.605
Fig. 2. Relative energies for the considered Si-doped SW defective SWNTs.
To obtain profound insight into the doping of silicon atom, we study in detail the structural properties of the most stable systems in which the silicon atom is doped at the C4 and C5 sites of the P-SW and D-SW defects, respectively (see Fig. 3). The results (Table 2) show that the SiAC bond lengths are about 1.819 Å in the 6-6 ring fusion of P4(4, 4) (in good agreement with the corresponding experimental lengths of 1.837 Å for the triangular structure of SiC2 [42]), and about 1.837 and 1.810 Å in the 6-7 ring fusion, a difference of 0.027 Å (because of its different location in the nanotube structure) while the bond angles are 112.6°, 100.7°, and 107.4° (see Table 2) which are close to the ideal sp3 bond-angles (109.5°) and are more favorable in comparison to CASiAC angles in the other isomers. The same is true for D5(4, 4) isomer where the bond angles are 112.1°, 100.5°, and 104.2°. By going to silicon doped SW defective (5, 5) SWCNTs, in which the increased tube diameter leads to a decrease in its curvature, the SiAC bond lengths decrease and reach 1.810, 1.787, and 1.811 Å in the P4(5, 5) and reach 1.790, 1.862, and 1.819 Å in the D5(5, 5), while the bond angles increase, see Table 2. Since one of the primary goals of this work is the structural evolution of Si-doped SW defective SWCNTs, it would be interesting to compare the SiAC bond lengths obtained in these compounds with those of SiC2 clusters. The computed SiAC bond lengths are obtained to be 1.787–1.875 Å, in agreement with the corresponding experimental values of 1.837 Å reported by Michalopoulos et al. [42] for the triangular structure of SiC2.
5
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
Fig. 3. Local distortion of silicon atoms of the most stable isomers of Si-doped SW defective SWNTs.
Table 2 Optimized bond lengths (Å) and bond angles (degree) for for the silicon doped defective SWCNTs. Si–C1 Si–C2 Si–C3 C1–Si–C2 C1–Si–C3 C2–Si–C3 P1(4, 4) P2(4, 4) P3(4, 4) P4(4, 4) P5(4, 4) P6(4, 4) P7(4, 4) P8(4, 4) D1(4, 4) D2(4, 4) D4(4, 4) D5(4, 4) D6(4, 4) D7(4, 4) D8(4, 4)
1.890 1.862 1.928 1.837 1.838 1.862 1.885 1.902 1.846 1.908 1.866 1.875 1.888 1.879 1.881
1.890 1.916 1.842 1.810 1.853 1.848 1.852 1.844 1.934 1.886 1.907 1.792 1.899 1.878 1.854
1.739 1.943 1.851 1.819 1.872 1.878 1.865 1.861 1.827 1.903 1.864 1.835 1.893 1.891 1.913
89.5 82.5 85.6 112.6 111.9 101.8 93.0 90.0 89.8 85.5 100.9 112.1 94.3 93.5 101.7
103.82 92.2 92.6 100.7 99.5 92.1 100.9 90.8 103.4 89.8 99.5 100.5 102.8 100.9 94.9
103.81 92.0 96.8 107.4 99.3 90.2 92.1 100.8 96.4 11.0 96.3 104.2 94.5 94.3 92.8
Si–C1 Si–C2 Si–C3 C1–Si–C2 C1–Si–C3 C2–Si–C3 P1(5, 5) P2(5, 5) P3(5, 5) P4(5, 5) P5(5, 5) P6(5, 5) P7(5, 5) P8(5, 5) D1(5, 5) D2(5, 5) D4(5, 5) D5(5, 5) D6(5, 5) D7(5, 5) D8(5, 5)
1.840 1.856 1.829 1.810 1.826 1.880 1.868 1.873 1.851 1.832 1.788 1.819 1.919 1.873 1.867
1.840 1.912 1.798 1.787 1.844 1.858 1.862 1.911 1.906 1.933 1.747 1.862 1.881 1.874 1.882
1.711 1.925 1.806 1.811 1.861 1.854 1.894 1.851 1.774 1.847 1.812 1.790 1.898 1.892 1.923
95.7 82.8 116.5 116.5 111.6 102.6 100.0 100.1 92.4 84.8 122.1 110.1 104.8 94.7 96.0
109.6 93.3 102.9 103.7 100.6 93.5 91.2 88.9 106.2 97.8 109.3 106.0 95.5 102.1 103.1
109.6 94.9 112.3 108.9 100.3 91.8 91.2 90.9 101.9 107.7 106.9 106.0 95.4 94.8 93.9
Based on the obtained results (Fig. 2), D1 is isoenergy with the most stable configuration D5 while P1 models have the largest relative energies of P1–P5 models. It can be due to the different orientation of C@C bond on the 7-7 ring fusion of SW defects. A close examination of the geometrical parameters of P-SW and D-SW nanotubes indicates that the CC bond in the 7-7 ring fusion of P-SW (1.343 Å, compared to 1.35 Å for H2C@CH2) is shorter than the corresponding CC bond of D-SW (1.563 Å), perhaps because of the different location of SW defect on the sidewalls of the defective SWCNTs. Therefore, it seems that C1 sites of P-SW defective SWCNTs are not favorable for silicon doping. This outcome can
6
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
be due to the fact that the different orientations of SW defects on the sidewalls of the defective SWCNTs induce different curvatures to carbon sites relative to each other. The reaction energies of the considered models are also computed at the B3LYP/6-31G level of theory as follows:
Er ¼ ESi—SWCNT þ EC ESWCNT ESi where Er stands for reaction energy; ESi–SWCNT denotes the total energy of the silicon doped SWCNTs; ESWCNT represents the total energy of the Stone–Wales defective SWCNTs; and EC and ESi correspond to the energies of the carbon and silicon atoms. It can be seen that the reaction energies of silicon doped SWCNTs are all positive values (Table 1), which implies that the doping reactions are endothermic. As can be seen in Table 1, the reaction energies obtained for the most stable isomers, i.e. P4, D1 and D5, are 120.7, 108.8 and 122.4 kcal/mol in (4, 4), and 127.9, 132.6 and 133.9 kcal/mol in (5, 5) at the B3LYP/631G level of theory. Generally, the calculated reaction energies for the Si doping of SW defective sites in our SWCNTs are found to be much smaller than those obtained in Zeng et al. study [35] for the N doping of SW defective sites at different substitutional sites of zigzag-edged graphene nanoribbon (223.4–246.7 kcal/mol), in which they show N atom prefers to occupy a site directly on the rotated bonds in a SW defect. Among all the isomers, the reaction energies of the most stable isomers have the smallest values, meaning that these C sites of SW defect in the armchair SWCNTs is more reactive than other carbon sites. On the other hand, the reaction energies for the Si-doped defective (5, 5) SWCNTs have larger values than those for (4, 4) SWCNTs. It is expected that with decreasing curvature in the Si-doped defective SWCNTs the CASiAC angles are increased, and substantially far away from the ideal sp3 bond angles (109.5°). Hence, they are not favorable to form quasi-tetrahedral bonding configurations. The result is in line with the relative energies discussed above. Hence, our DFT results indicate that tube diameter affects the doping reactions such that the doping of SWCNTs with high curvature (small diameter) might be more favorable because of both energetic and structural considerations, which is in agreement with the results obtained by Bian et al. [43] for the Si doping of carbon nanotubes. They found that the formation energies increase with an increase in the tube diameter, indicating that the embedding of Si into narrower CNTs is more energetically favorable. Moreover Huda and Ray [44] examined the evolution of the cage and bowl type structures of C20nSin clusters with n < 10. They found that a bowl shaped structure of C20 would prefer sp2 bonding, unsuitable for Si substitution, while the higher curvature for the cage structure would yield a higher ratio of sp3 to sp2 bonding. Therefore, it is expected that nanostructures with high curvature would be a favorable environment for the substitution of Si atoms in comparison to bowl or planar structures. Despite some suggestions that, on the basis of the adsorption of atoms and molecules, the first neighboring of the SW defective sites is chemically more reactive sites than defective sites [12], our calculations propose that Si atoms adjacent to the SW defects is less likely to be observed. This outcome can be due to the fact that the substitution of Si for these sites perturbs the conjugation of hexagonal network on the sidewall of a tube. 3.2. Electronic structure One purpose of the doping of carbon nanotubes is to significantly modify their electrical conductivity, especially for chemical sensors and nanobioelectronic devices. Therefore, we study the effect of substitutionally doping on electronic properties of the considered models. Fig. 4 illustrates a comparison between densities of states of: (a) perfect SWCNTs, (b) SW defective SWCNTs and (c) silicon doped SW defective SWCNTs. As can be seen from Fig. 4, SW defects noticeably influence the electronic properties of the semiconductor SWCNTs by introducing defect states into the band gap region. In comparison to the DOS of the SW defective SWCNTs, we can affirm that the doping on the defect sites causes the redistribution of electronic states of SWCNTs, especially in the zone of doped atoms. DOS for the silicon doped P-SW SWCNTs (P4 models, for example) shows a distinct change near the valence level (or LUMO) compared to that of undoped ones; a local energy level appears after the doping of Si atom and the LUMO shifts to lower energies while Eg shows no significant change. The same is true for the DOS of the silicon-doped D-SW SWCNTs (D1 and D5 models, for example), also indicating
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
7
Fig. 4. Calculated density of states for (a) perfect SWCNTs, (b) SW defective SWCNTs and (c) the most stable Si-doped SW defective SWCNTs.
the LUMO shifts to lower energies after the doping of Si atom which would results in an Eg reduction from 0.888 eV in the undoped D-SW defective SWCNTs to 0.825 and 0.817 eV in the D1(4, 4) and D5(4, 4) models, respectively (see Fig. 4). Charge distribution analysis (Table 1) provides interesting insights into the local charge distribution of the nanotubes. Table 1 indicates that an average charge of 0.5e is also transferred from silicon atoms to the first neighboring carbon atoms on the SWCNTs. This indicates that charge redistributions
8
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
after doping process mostly take place to a relatively small number of carbons at the zone of doped atoms. Typically, the charge transfers (from the Si to C atoms) in the different systems descend in the following sequence: D5(4, 4) > D5(5, 5) > P4(4, 4) > P4(5, 5) > D1(4, 4) > D1(5, 5). It is important to note that when carbon atoms are replaced with silicon ones at the edge of Stone–Wales defect, i.e. C5 and C4 sites (see Fig. 1) charge transfer has the larger value in compared to that of silicon atoms that located at the C1 sites. Meanwhile, the charge transfers for the Si-doped defective (4, 4) SWCNTs have larger values than those for (5, 5) SWCNTs. Based on Froudakis’s findings on hydrogen absorption in nanotubes, point charges upon the material’s surface increase the binding energy of hydrogen whereby they can improve the storage capacity [33]. For example, silicon carbide nanotubes with alternative Si and C atoms were predicted to serve as good candidates for hydrogen storage because they were shown to be full of point charges [37,38]. In fact, high point charges are predicted to establish an overall charge transfer on the surface of nanotubes, and then the resulted charge-induced dipole interaction gives additional stabilization to the H2 molecule [45]. On this basis, it seems silicon-doped SW defective SWCNTs deserve more consideration in the field of hydrogen storage and chemical sensors for the adsorption of small molecules.
4. Conclusion We have DFT calculations to investigate how the electronic properties and stabilities of armchair (4, 4) and (5, 5) SWCNTs with Stone Wales (SW) defects are modified via Si atom doping at different positions of SW defect sites. Considering two different orientations of SW defect, parallel and diagonal, we substitute Si atoms for C ones at eight selected symmetric positions of the defect sites. The optimized structures show a quasi-tetrahedral bonding configuration around Si atoms on the tube wall. Hence, it seems that dislocation of Si atom or puckering of silicon-doped rings is responsible for stability of these isomers. Our results indicate that tube diameter affects the doping reactions such that the doping of SWCNTs with high curvature (small diameter) might be more favorable, on the basis of both energetically and structural considerations. Doping of SW defects noticeably influence the electronic properties of SWCNTs such that the doping on the defect sites causes the redistribution of electronic states of SWCNTs, especially in the zone of doped atoms. The charge distribution indicates that an average charge of 0.5e is also transferred from silicon atoms to first neighboring carbon atoms on the SWCNT. This signifies that charge redistributions after doping process mostly take place to a relatively small number of carbons at the zone of doped atoms. We stress here that the focus is not to find precise structural and electronic properties for a given composition; instead, the primary purpose is to show that defect–dopant combination in SWCNTs deserve further experimental and theoretical studies to have clear understanding of defect–dopant-vacancy combination in SWCNTs or possibility of having more SW defects and dopants in SWNCTs. References [1] A.J. Stone, D.J. Wales, Chem. Phys. Lett. 128 (1986) 501–503. [2] M. Bockrath, W. Liang, D. Bozovic, J.H. Hafner, C.M. Lieber, M. Tinkham, H. Park, Science 291 (2001) 283–285. [3] T. Maltezopoulos, A. Kubetzka, M. Morgenstern, R. Wiesendanger, S.G. Lemay, C. Dekker, Appl. Phys. Lett. 83 (2003) 1011– 1013. [4] A. Hashimoto, K. Suenaga, A. Gloter, K. Urita, S. Iijima, Nature 430 (2004) 870–873. [5] D. Wang, C. Zhao, G. Xin, D. Hou, J. Mol. Struct.: THEOCHEM 962 (2010) 62–67. [6] J.-C. Charlier, Acc. Chem. Res. 35 (2002) 1063–1069. [7] P.C.P. Watts, W.-K. Hsu, H.W. Kroto, D.R.M. Walton, Nano Lett. 3 (2003) 549–553. [8] T.C. Dinadayalane, J. Leszczynski, Chem. Phys. Lett. 434 (2007) 86–91. [9] C. Wang, G. Zhou, H. Liu, J. Wu, Y. Qiu, B.-L. Gu, W. Duan, J. Phys. Chem. B 110 (2006) 10266–10271. [10] S.H. Yang, W.H. Shin, J.W. Lee, S.Y. Kim, S.I. Woo, J.K. Kang, J. Phys. Chem. B 110 (2006) 13941–13946. [11] H.F. Bettinger, J. Phys. Chem. B 109 (2005) 6922–6924. [12] X. Lu, Z. Chen, P.V.R. Schleyer, J. Am. Chem. Soc. 127 (2005) 20–21. [13] J. Andzelm, N. Govind, A. Maiti, Chem. Phys. Lett. 421 (2006) 58–62. [14] S.L. Mielke, T. Belytschko, G.C. Schatz, Annu. Rev. Phys. Chem. 58 (2007) 185–209. [15] T. Zhou, J. Wu, W. Duan, B.L. Gu, Phys. Rev. B 75 (2007) 205410. [16] H.J. Choi, J. Ihm, S.G. Louie, M.L. Cohen, Phys. Rev. Lett. 84 (2000) 2917–2920. [17] L.G. Zhou, S.Q. Shi, Carbon 41 (2003) 579–625.
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
9
[18] N. Chakrapani, Y.M. Zhang, S.K. Nayak, J.A. Moore, D.L. Carroll, Y.Y. Choi, P.M. Ajayan, J. Phys. Chem. B 107 (2003) 9308– 9311. [19] M. Grujicic, G. Cao, A.M. Rao, T.M. Tritt, S. Nayak, Appl. Surf. Sci. 214 (2003) 289–303. [20] S. Picozzi, S. Santucci, L. Lozzi, L. Valentini, B. Delley, J. Chem. Phys. 120 (2004) 7147–7152. [21] J.W. Lee, H.S. Kim, J.Y. Lee, J.K. Kang, Appl. Phys. Lett. 88 (2006) 143126. [22] M. Arab, F. Picaud, M. Devel, C. Ramseyer, C. Girardet, Phys. Rev. B 69 (2004) 165401. [23] X. Feng, S. Irle, H. Witek, K. Morokuma, R. Vidic, E. Borguet, J. Am. Chem. Soc. 127 (2005) 10533–10538. [24] J. Lu, S. Nagase, Y. Maeda, T. Wakahara, T. Nakahodo, T. Akasaka, D. Yu, Z. Gao, R. Han, H. Ye, Chem. Phys. Lett. 405 (2005) 90–92. [25] K. Seo, K.A. Park, C. Kim, S. Han, B. Kim, Y.H. Lee, J. Am. Chem. Soc. 127 (2005) 15724–15729. [26] A. Maiti, J. Andzelm, N. Tanpipat, P. von Allmen, Phys. Rev. Lett. 87 (2001) 155502. [27] L. Chen, J.K. Johnson, Phys. Rev. Lett. 94 (2005) 125701. [28] S. Rols, M.R. Johnson, P. Zeppenfeld, M. Bienfait, O.E. Vilches, J. Schneble, Phys. Rev. B 71 (2005) 155411. [29] S. Talapatra, V. Krungleviciute, A.D. Migone, Phys. Rev. Lett. 89 (2002) 246106. [30] A. Kleinhammes, S. Mao, X. Yang, X. Tang, H. Shimoda, J. Lu, O. Zhou, Y. Wu, Phys. Rev. B 68 (2003) 075418. [31] V.V. Simonyan, J.K. Johnson, A. Kuznetsova, J.T. Yates Jr, J. Chem. Phys. 114 (2001) 4180–4185. [32] W. An, X. Wu, J.L. Yang, X.C. Zeng, J. Phys. Chem. C 111 (2007) 14105–14112. [33] G. Mpourmpakis, G.E. Froudakis, G.P. Lithoxoos, J. Samios, Nano Lett. 6 (2006) 1581–1583. [34] V. Meunier, J. Kephart, C. Roland, J. Bernholc, Phys. Rev. Lett. 88 (2002) 075506. [35] H. Zeng, J. Zhao, J.W. Wei, H.F. Hu, Eur. Phys. J. B 79 (2011) 335–340. [36] X. Qin, Q. Meng, W. Zhao, Science 605 (2011) 930–933. [37] A. Mavrandonakis, G.E. Froudakis, M. Schnell, M. Muhlhauser, Nano Lett. 3 (2003) 1481–1484. [38] M. Menon, E. Richter, A. Mavrandonakis, G. Froudakis, A.N. Andriotis, Phys. Rev. B 69 (2004) 115322. [39] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery Jr., R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, Gaussian, 98, Gaussian Inc., Pittsburgh, PA, 1998. [40] P.C. Hariharan, J.A. Pople, Mol. Phys. 27 (1974) 209–214. [41] Y. Zhang, A. Wu, X. Xu, Y. Yan, J. Phys. Chem. A 111 (2007) 9431–9437. [42] D.L. Michalopoulos, M.E. Geusic, P.R.R. Langridge, R.E. Smalley, J. Phys. Chem. 80 (1984) 3556–3560. [43] R. Bian, J. Zhao, H. Fu, J. Mol. Model. 19 (2013) 1667–1675. [44] M.N. Hudaa, A.K. Ray, Chem. Phys. Lett. 457 (2008) 124–129. [45] M.R. Momeni, F.A. Shakib, Chem. Phys. Lett. 492 (2010) 137–141.
Contents lists available at SciVerse ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
Silicon doping of defect sites in Stone–Wales defective carbon nanotubes: A density functional theory study Maryam Anafcheh, Reza Ghafouri ⇑ Department of Chemistry, Shahr-e-Ray Branch, Islamic Azad University, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 21 December 2012 Received in revised form 1 April 2013 Accepted 12 April 2013 Available online 30 April 2013 Keywords: Stone Wales defect DFT SWCNT DOS
a b s t r a c t Using density-functional theory calculations, we investigate how the stabilities and electronic properties of Stone Wales (SW) defective armchair (4, 4) and (5, 5) nanotubes are modified via Si atom doping at eight selected symmetric positions of SW defect sites with two different orientations, parallel and diagonal. A quasi-tetrahedral bonding configurations of silicon atoms based on sp3 hybridization are formed, which leads to puckered silicon doped rings. Our results indicate that tube diameter affects the doping reactions so that the doping single-walled carbon nanotubes (SWCNTs) with high curvature (small diameter) might be more favorable, based on both energetic and structural considerations. Density of state (DOS) obtained for the systems indicate that the doping of the defect sites causes the redistribution of electronic states of the SW defective SWCNTs. An average charge of 0.5e is also transferred from silicon atoms to first neighboring carbon atoms on the SWCNT, which indicates that charge redistributions after doping process mostly take place to a relatively small number of carbons at the zone of doped atoms. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction The structures of single-walled carbon nanotubes (SWCNTs) could be described as a perfect graphene sheet wrapped up into a cylinder. However, the experimentally available SWCNTs are not perfect. Topological defects such as vacancies, pentagons, heptagons, dopants, and Stone–Wales defects [1–5] ⇑ Corresponding author. Tel.: +98 9356463576. E-mail address: [email protected] (R. Ghafouri). 0749-6036/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.spmi.2013.04.014
2
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
formed inevitably during the growth of carbon nanotubes or introduced during workup (e.g., oxidative cleaning, ultrasonication) [6,7] can significantly change the electronic structure [8–10], chemical reactivity [11–13], mechanical [14] and transport [15,16] properties of the systems. Stone–Wales (SW) defect which is a very important topological one in SWCNTs is comprised of two pairs of pentagons and heptagons (5-7-7-5) formed by rotating one bond of the traditional hexagon by 90° [1]. A number of theoretical investigations revealed that these defective sites are chemically more reactive than the perfect sites in the sidewalls of carbon nanotubes [17–20]. Indeed they could act as nucleation centers for the formation of dislocations in the originally ideal network. Therefore, it is expected that with a local deformation, the nanotube containing SW defects might be more favorable for subsequent reactions. For example, the adsorption of small molecules such as H2 [21], O2 and O3 [12], N2 [22], NH3 [23,24], NO2 [24,25], H2O [26], CO and CO2 [22,27], Ar [28], Ne and Xe [29–31], and some relevant addends like O, SiH2, NH, and CH2 [32] on defective SWCNTs has been reported; it is demonstrated that the adsorption of atoms and molecules on defects is more stable than that on the smooth sidewall, and the chemical and physical properties induced are obviously different. On the other hand, doping of carbon nanotubes by introducing heteroatoms on the sidewall is a significant way to modify their electronic structures and transport properties, making carbon nanotubes more amenable for various potential applications, such as improving the sensitivities of chemical sensors, and opening hollow cavities for gas storage [33] or lithium intercalation [34]. However, the doping of Stone–Wales defects on the surfaces of defective SWCNTs has hardly been investigated before now, to the best of our knowledge, doping of perfect SWCNTs has been the subject of many theoretical and experimental studies. Using first principles calculations, Zeng et al. [35] studied the effect of N doping on the electronic properties of defective zigzag-edged graphene nanoribbons with SW defects. Qin et al. [36] investigated the adsorption of formaldehyde (H2CO) on the Al-doped SW defective graphene, showing that Al-doped SW graphene is more suitable for H2CO gas detection. Therefore, the insight into the effect of defect–dopant combination on the carbon nanotube properties is vital for finding their potential applications. With this initial thought in mind, in the present investigation, we systematically evaluate the doping effect of SW defective armchair SWCNTs with different diameters, (4, 4) and (5, 5), by replacing carbon atoms on the SW defects with silicon ones, exploring possible atomic arrangements and the resulted electronic properties. For all SWCNTs, a rotation about a CAC bond diagonal (D) or parallel (P) to the tube axis gives rise to two different systems which are labeled P-SW and D-SW, respectively, as illustrated in Fig. 1. For each configuration, eight substitution sites (as shown in Fig1) are considered according to the symmetry of the SW defect. Silicon is selected as a dopant because it is the next group IV element in the periodic table after carbon, and although they share several similarities in their
Fig. 1. Two configurations of the Stone–Wales defects on the tube sidewall: (a) parallel (P-SW) and (b) diagonal (D-SW). Five different doping positions at the defective sites of SWCNTs according to the symmetry of the SW defects, C1–C5, and three different positions adjoining the defect sites, C6–C8, are shown.
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
3
electronic structure, their chemistry are very different; unlike C, because of its sp3 hybridization in the bulk, Si, when used in fullerenes or nanotubes, prefers to form dangling bonds rather than single/double bond chains across the pentagon and hexagon rings rings. Thus the structural chemistries of carbon and silicon are different and yet similar. In recent years, there has been renewed interest in Si–C nanocomposites because of their expected potential applications in nanotechnology. For example, it was shown that nanotubes with alternative Si and C atoms were full of point charges [37,38] and hence they would serve as promising materials for hydrogen storage [33].
2. Computational method All density functional theory (DFT) quantum calculations are performed using Gaussian 98 program package [39]. A finite model, including 96 and 120 carbon atoms, is used to represent a defect-free (4, 4) and (5, 5) SWCNTs. The hydrogen atoms are added at the open ends to avoid dangling bonds. Geometries of all systems (perfect SWCNT and SW defective SWCNTs and Si-doped SW defective SWCNTs) are allowed to fully relax during the B3LYP/6-31G optimization process [40]. Real frequencies obtained from frequency calculations confirm that all of them are minimum energy structures. The standard 6-31G basis set is employed due to being affordable and accurate enough for geometry optimization of even large molecules [5,41]. Optimized structures of Si-doped SW defective SWCNTs and their parents have been subjected to calculation of the related properties such as total energies (Etot), relative energies (Erel), reaction energies (Er) and density of state (DOS).
3. Results and discussion 3.1. Optimized structural properties and stability We chose the prefect (4, 4) and (5, 5) armchair SWCNTs and the ones with Stone–Wales defects, which is fully optimized at the B3LYP/6-31G level, as the parent molecules for doping. The obtained structural properties of prefect SWCNTs such as the CAC bond lengths in the middle of the tube are predicted to be 1.417 and 1.435 Å, in excellent agreement with previously reported values (1.41 and 1.43 Å) [12]. For (5, 5) SWCNT, the rotation about a CAC bond diagonal (D) or parallel (P) to the tube axis gives rise to two different systems (P-SW and D-SW, respectively). The prediction of bond lengths of the heptagon–heptagon and heptagon–pentagon junctions (i.e., the 7-7 ring fusion and 7-5 ring fusion, respectively) in the SW defective armchair SWCNTs are obtained 1.351–1.354 and 1.452–1.461 Å, respectively, consistent with the values of 1.35 and 1.46 Å reported by Lu et al. [12]. For each configuration, P-SW and D-SW, we select five different doping positions at the defective sites of SWCNTs according to the symmetry of the SW defects, C1–C5, and three different positions adjoining the defect sites, C6–C8. The doping positions C1–C8 for P-SW and D-SW SWCNTs are shown in Fig. 1. Therefore, in our work, the considered configurations for Si-doped SW defective SWCNTs are denoted by P1–P8 (n, n) and D1–D8 (n, n). Total energies (Etot) and relative energies (Erel) of all the Si-doped SW defective SWCNTs are reported in Table 1. As can be seen from Fig. 2, in general, for silicon doped P-SWCNTs, isomer P4 is the most stable followed by P5, P2, P3, P1, P8, P6 and P7. For silicon doped D-SWCNTs, isomers D5 and D1, lying within 0.05 eV of one another, can be considered as essentially isoenergetic, and the relative stabilities are found to be in the order of D1 D5 > D4 > D2 > D3 > D8 > D6 > D7. In fact, a Si atom prefers to form dangling bonds rather than single/double bond chains across the pentagon and hexagon rings, so upon Si doping at the defective SW sites of SWCNTs the quasi-tetrahedral bonding configurations of silicon atoms based on sp3 hybridization are formed. As a result, an evident local radial distortion is observed on the tube wall where silicon atom relaxes outward from the surface, making puckered silicon-doped rings, see Fig. 3. Hence, it seems that puckering of silicon-doped rings due to dislocation of Si atom is responsible for the stability of these isomers. Similar trends were observed by Qin et al. [36] showing that heptagon–heptagon junctions is the most energetically favorable for Al doped site and the Al atom dopant protrudes out of the original plane and results in large distortion in the region around the defect.
4
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
Table 1 Total energy (E in eV), relative energy (Erel in eV), reaction energy (Er in kcal/mol) and charge transfer (C.T) for the Si-doped SW defective SWCNTs.
P1(4, 4) P2(4, 4) P3(4, 4) P4(4, 4) P5(4, 4) P6(4, 4) P7(4, 4) P8(4, 4) P1(5, 5) P2(5, 5) P3(5, 5) P4(5, 5) P5(5, 5) P6(5, 5) P7(5, 5) P8(5, 5)
E
Erel
Er
106638.86 106640.49 106639.69 106640.81 106640.60 106638.51 106638.46 106638.70 110860.59 110862.12 110861.25 110862.42 110862.21 110860.14 110860.10 110860.33
1.96 0.33 1.13 0.00 0.21 2.30 2.35 2.11 1.83 0.30 1.18 0.00 0.22 2.28 2.33 2.09
165.8 128.2 146.7 120.7 125.6 173.8 175.0 169.4 170.1 134.8 131.7 127.9 132.9 180.6 181.6 176.2
C.T
0.558
0.484
D1(4, 4) D2(4, 4) D3(4, 4) D4(4, 4) D5(4, 4) D6(4, 4) D7(4, 4) D8(4, 4) D1(5, 5) D2(5, 5) D3(5, 5) D4(5, 5) D5(5, 5) D6(5, 5) D7(5, 5) D8(5, 5)
E
Erel
Er
C.T
106641.33 106641.09 106640.24 106641.15 106641.36 106639.85 106639.83 106639.98 110862.74 110862.48 110861.69 110862.43 110862.69 110861.53 110861.51 110861.62
0.03 0.27 1.12 0.21 0.00 1.30 1.32 1.17 0.00 0.26 1.05 0.31 0.05 1.21 1.23 1.12
108.8 128.5 148.2 127.3 122.4 157.2 157.8 154.3 132.6 138.6 156.8 139.8 133.9 160.5 161.0 158.4
0.499
0.576
0.527
0.605
Fig. 2. Relative energies for the considered Si-doped SW defective SWNTs.
To obtain profound insight into the doping of silicon atom, we study in detail the structural properties of the most stable systems in which the silicon atom is doped at the C4 and C5 sites of the P-SW and D-SW defects, respectively (see Fig. 3). The results (Table 2) show that the SiAC bond lengths are about 1.819 Å in the 6-6 ring fusion of P4(4, 4) (in good agreement with the corresponding experimental lengths of 1.837 Å for the triangular structure of SiC2 [42]), and about 1.837 and 1.810 Å in the 6-7 ring fusion, a difference of 0.027 Å (because of its different location in the nanotube structure) while the bond angles are 112.6°, 100.7°, and 107.4° (see Table 2) which are close to the ideal sp3 bond-angles (109.5°) and are more favorable in comparison to CASiAC angles in the other isomers. The same is true for D5(4, 4) isomer where the bond angles are 112.1°, 100.5°, and 104.2°. By going to silicon doped SW defective (5, 5) SWCNTs, in which the increased tube diameter leads to a decrease in its curvature, the SiAC bond lengths decrease and reach 1.810, 1.787, and 1.811 Å in the P4(5, 5) and reach 1.790, 1.862, and 1.819 Å in the D5(5, 5), while the bond angles increase, see Table 2. Since one of the primary goals of this work is the structural evolution of Si-doped SW defective SWCNTs, it would be interesting to compare the SiAC bond lengths obtained in these compounds with those of SiC2 clusters. The computed SiAC bond lengths are obtained to be 1.787–1.875 Å, in agreement with the corresponding experimental values of 1.837 Å reported by Michalopoulos et al. [42] for the triangular structure of SiC2.
5
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
Fig. 3. Local distortion of silicon atoms of the most stable isomers of Si-doped SW defective SWNTs.
Table 2 Optimized bond lengths (Å) and bond angles (degree) for for the silicon doped defective SWCNTs. Si–C1 Si–C2 Si–C3 C1–Si–C2 C1–Si–C3 C2–Si–C3 P1(4, 4) P2(4, 4) P3(4, 4) P4(4, 4) P5(4, 4) P6(4, 4) P7(4, 4) P8(4, 4) D1(4, 4) D2(4, 4) D4(4, 4) D5(4, 4) D6(4, 4) D7(4, 4) D8(4, 4)
1.890 1.862 1.928 1.837 1.838 1.862 1.885 1.902 1.846 1.908 1.866 1.875 1.888 1.879 1.881
1.890 1.916 1.842 1.810 1.853 1.848 1.852 1.844 1.934 1.886 1.907 1.792 1.899 1.878 1.854
1.739 1.943 1.851 1.819 1.872 1.878 1.865 1.861 1.827 1.903 1.864 1.835 1.893 1.891 1.913
89.5 82.5 85.6 112.6 111.9 101.8 93.0 90.0 89.8 85.5 100.9 112.1 94.3 93.5 101.7
103.82 92.2 92.6 100.7 99.5 92.1 100.9 90.8 103.4 89.8 99.5 100.5 102.8 100.9 94.9
103.81 92.0 96.8 107.4 99.3 90.2 92.1 100.8 96.4 11.0 96.3 104.2 94.5 94.3 92.8
Si–C1 Si–C2 Si–C3 C1–Si–C2 C1–Si–C3 C2–Si–C3 P1(5, 5) P2(5, 5) P3(5, 5) P4(5, 5) P5(5, 5) P6(5, 5) P7(5, 5) P8(5, 5) D1(5, 5) D2(5, 5) D4(5, 5) D5(5, 5) D6(5, 5) D7(5, 5) D8(5, 5)
1.840 1.856 1.829 1.810 1.826 1.880 1.868 1.873 1.851 1.832 1.788 1.819 1.919 1.873 1.867
1.840 1.912 1.798 1.787 1.844 1.858 1.862 1.911 1.906 1.933 1.747 1.862 1.881 1.874 1.882
1.711 1.925 1.806 1.811 1.861 1.854 1.894 1.851 1.774 1.847 1.812 1.790 1.898 1.892 1.923
95.7 82.8 116.5 116.5 111.6 102.6 100.0 100.1 92.4 84.8 122.1 110.1 104.8 94.7 96.0
109.6 93.3 102.9 103.7 100.6 93.5 91.2 88.9 106.2 97.8 109.3 106.0 95.5 102.1 103.1
109.6 94.9 112.3 108.9 100.3 91.8 91.2 90.9 101.9 107.7 106.9 106.0 95.4 94.8 93.9
Based on the obtained results (Fig. 2), D1 is isoenergy with the most stable configuration D5 while P1 models have the largest relative energies of P1–P5 models. It can be due to the different orientation of C@C bond on the 7-7 ring fusion of SW defects. A close examination of the geometrical parameters of P-SW and D-SW nanotubes indicates that the CC bond in the 7-7 ring fusion of P-SW (1.343 Å, compared to 1.35 Å for H2C@CH2) is shorter than the corresponding CC bond of D-SW (1.563 Å), perhaps because of the different location of SW defect on the sidewalls of the defective SWCNTs. Therefore, it seems that C1 sites of P-SW defective SWCNTs are not favorable for silicon doping. This outcome can
6
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
be due to the fact that the different orientations of SW defects on the sidewalls of the defective SWCNTs induce different curvatures to carbon sites relative to each other. The reaction energies of the considered models are also computed at the B3LYP/6-31G level of theory as follows:
Er ¼ ESi—SWCNT þ EC ESWCNT ESi where Er stands for reaction energy; ESi–SWCNT denotes the total energy of the silicon doped SWCNTs; ESWCNT represents the total energy of the Stone–Wales defective SWCNTs; and EC and ESi correspond to the energies of the carbon and silicon atoms. It can be seen that the reaction energies of silicon doped SWCNTs are all positive values (Table 1), which implies that the doping reactions are endothermic. As can be seen in Table 1, the reaction energies obtained for the most stable isomers, i.e. P4, D1 and D5, are 120.7, 108.8 and 122.4 kcal/mol in (4, 4), and 127.9, 132.6 and 133.9 kcal/mol in (5, 5) at the B3LYP/631G level of theory. Generally, the calculated reaction energies for the Si doping of SW defective sites in our SWCNTs are found to be much smaller than those obtained in Zeng et al. study [35] for the N doping of SW defective sites at different substitutional sites of zigzag-edged graphene nanoribbon (223.4–246.7 kcal/mol), in which they show N atom prefers to occupy a site directly on the rotated bonds in a SW defect. Among all the isomers, the reaction energies of the most stable isomers have the smallest values, meaning that these C sites of SW defect in the armchair SWCNTs is more reactive than other carbon sites. On the other hand, the reaction energies for the Si-doped defective (5, 5) SWCNTs have larger values than those for (4, 4) SWCNTs. It is expected that with decreasing curvature in the Si-doped defective SWCNTs the CASiAC angles are increased, and substantially far away from the ideal sp3 bond angles (109.5°). Hence, they are not favorable to form quasi-tetrahedral bonding configurations. The result is in line with the relative energies discussed above. Hence, our DFT results indicate that tube diameter affects the doping reactions such that the doping of SWCNTs with high curvature (small diameter) might be more favorable because of both energetic and structural considerations, which is in agreement with the results obtained by Bian et al. [43] for the Si doping of carbon nanotubes. They found that the formation energies increase with an increase in the tube diameter, indicating that the embedding of Si into narrower CNTs is more energetically favorable. Moreover Huda and Ray [44] examined the evolution of the cage and bowl type structures of C20nSin clusters with n < 10. They found that a bowl shaped structure of C20 would prefer sp2 bonding, unsuitable for Si substitution, while the higher curvature for the cage structure would yield a higher ratio of sp3 to sp2 bonding. Therefore, it is expected that nanostructures with high curvature would be a favorable environment for the substitution of Si atoms in comparison to bowl or planar structures. Despite some suggestions that, on the basis of the adsorption of atoms and molecules, the first neighboring of the SW defective sites is chemically more reactive sites than defective sites [12], our calculations propose that Si atoms adjacent to the SW defects is less likely to be observed. This outcome can be due to the fact that the substitution of Si for these sites perturbs the conjugation of hexagonal network on the sidewall of a tube. 3.2. Electronic structure One purpose of the doping of carbon nanotubes is to significantly modify their electrical conductivity, especially for chemical sensors and nanobioelectronic devices. Therefore, we study the effect of substitutionally doping on electronic properties of the considered models. Fig. 4 illustrates a comparison between densities of states of: (a) perfect SWCNTs, (b) SW defective SWCNTs and (c) silicon doped SW defective SWCNTs. As can be seen from Fig. 4, SW defects noticeably influence the electronic properties of the semiconductor SWCNTs by introducing defect states into the band gap region. In comparison to the DOS of the SW defective SWCNTs, we can affirm that the doping on the defect sites causes the redistribution of electronic states of SWCNTs, especially in the zone of doped atoms. DOS for the silicon doped P-SW SWCNTs (P4 models, for example) shows a distinct change near the valence level (or LUMO) compared to that of undoped ones; a local energy level appears after the doping of Si atom and the LUMO shifts to lower energies while Eg shows no significant change. The same is true for the DOS of the silicon-doped D-SW SWCNTs (D1 and D5 models, for example), also indicating
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
7
Fig. 4. Calculated density of states for (a) perfect SWCNTs, (b) SW defective SWCNTs and (c) the most stable Si-doped SW defective SWCNTs.
the LUMO shifts to lower energies after the doping of Si atom which would results in an Eg reduction from 0.888 eV in the undoped D-SW defective SWCNTs to 0.825 and 0.817 eV in the D1(4, 4) and D5(4, 4) models, respectively (see Fig. 4). Charge distribution analysis (Table 1) provides interesting insights into the local charge distribution of the nanotubes. Table 1 indicates that an average charge of 0.5e is also transferred from silicon atoms to the first neighboring carbon atoms on the SWCNTs. This indicates that charge redistributions
8
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
after doping process mostly take place to a relatively small number of carbons at the zone of doped atoms. Typically, the charge transfers (from the Si to C atoms) in the different systems descend in the following sequence: D5(4, 4) > D5(5, 5) > P4(4, 4) > P4(5, 5) > D1(4, 4) > D1(5, 5). It is important to note that when carbon atoms are replaced with silicon ones at the edge of Stone–Wales defect, i.e. C5 and C4 sites (see Fig. 1) charge transfer has the larger value in compared to that of silicon atoms that located at the C1 sites. Meanwhile, the charge transfers for the Si-doped defective (4, 4) SWCNTs have larger values than those for (5, 5) SWCNTs. Based on Froudakis’s findings on hydrogen absorption in nanotubes, point charges upon the material’s surface increase the binding energy of hydrogen whereby they can improve the storage capacity [33]. For example, silicon carbide nanotubes with alternative Si and C atoms were predicted to serve as good candidates for hydrogen storage because they were shown to be full of point charges [37,38]. In fact, high point charges are predicted to establish an overall charge transfer on the surface of nanotubes, and then the resulted charge-induced dipole interaction gives additional stabilization to the H2 molecule [45]. On this basis, it seems silicon-doped SW defective SWCNTs deserve more consideration in the field of hydrogen storage and chemical sensors for the adsorption of small molecules.
4. Conclusion We have DFT calculations to investigate how the electronic properties and stabilities of armchair (4, 4) and (5, 5) SWCNTs with Stone Wales (SW) defects are modified via Si atom doping at different positions of SW defect sites. Considering two different orientations of SW defect, parallel and diagonal, we substitute Si atoms for C ones at eight selected symmetric positions of the defect sites. The optimized structures show a quasi-tetrahedral bonding configuration around Si atoms on the tube wall. Hence, it seems that dislocation of Si atom or puckering of silicon-doped rings is responsible for stability of these isomers. Our results indicate that tube diameter affects the doping reactions such that the doping of SWCNTs with high curvature (small diameter) might be more favorable, on the basis of both energetically and structural considerations. Doping of SW defects noticeably influence the electronic properties of SWCNTs such that the doping on the defect sites causes the redistribution of electronic states of SWCNTs, especially in the zone of doped atoms. The charge distribution indicates that an average charge of 0.5e is also transferred from silicon atoms to first neighboring carbon atoms on the SWCNT. This signifies that charge redistributions after doping process mostly take place to a relatively small number of carbons at the zone of doped atoms. We stress here that the focus is not to find precise structural and electronic properties for a given composition; instead, the primary purpose is to show that defect–dopant combination in SWCNTs deserve further experimental and theoretical studies to have clear understanding of defect–dopant-vacancy combination in SWCNTs or possibility of having more SW defects and dopants in SWNCTs. References [1] A.J. Stone, D.J. Wales, Chem. Phys. Lett. 128 (1986) 501–503. [2] M. Bockrath, W. Liang, D. Bozovic, J.H. Hafner, C.M. Lieber, M. Tinkham, H. Park, Science 291 (2001) 283–285. [3] T. Maltezopoulos, A. Kubetzka, M. Morgenstern, R. Wiesendanger, S.G. Lemay, C. Dekker, Appl. Phys. Lett. 83 (2003) 1011– 1013. [4] A. Hashimoto, K. Suenaga, A. Gloter, K. Urita, S. Iijima, Nature 430 (2004) 870–873. [5] D. Wang, C. Zhao, G. Xin, D. Hou, J. Mol. Struct.: THEOCHEM 962 (2010) 62–67. [6] J.-C. Charlier, Acc. Chem. Res. 35 (2002) 1063–1069. [7] P.C.P. Watts, W.-K. Hsu, H.W. Kroto, D.R.M. Walton, Nano Lett. 3 (2003) 549–553. [8] T.C. Dinadayalane, J. Leszczynski, Chem. Phys. Lett. 434 (2007) 86–91. [9] C. Wang, G. Zhou, H. Liu, J. Wu, Y. Qiu, B.-L. Gu, W. Duan, J. Phys. Chem. B 110 (2006) 10266–10271. [10] S.H. Yang, W.H. Shin, J.W. Lee, S.Y. Kim, S.I. Woo, J.K. Kang, J. Phys. Chem. B 110 (2006) 13941–13946. [11] H.F. Bettinger, J. Phys. Chem. B 109 (2005) 6922–6924. [12] X. Lu, Z. Chen, P.V.R. Schleyer, J. Am. Chem. Soc. 127 (2005) 20–21. [13] J. Andzelm, N. Govind, A. Maiti, Chem. Phys. Lett. 421 (2006) 58–62. [14] S.L. Mielke, T. Belytschko, G.C. Schatz, Annu. Rev. Phys. Chem. 58 (2007) 185–209. [15] T. Zhou, J. Wu, W. Duan, B.L. Gu, Phys. Rev. B 75 (2007) 205410. [16] H.J. Choi, J. Ihm, S.G. Louie, M.L. Cohen, Phys. Rev. Lett. 84 (2000) 2917–2920. [17] L.G. Zhou, S.Q. Shi, Carbon 41 (2003) 579–625.
M. Anafcheh, R. Ghafouri / Superlattices and Microstructures 60 (2013) 1–9
9
[18] N. Chakrapani, Y.M. Zhang, S.K. Nayak, J.A. Moore, D.L. Carroll, Y.Y. Choi, P.M. Ajayan, J. Phys. Chem. B 107 (2003) 9308– 9311. [19] M. Grujicic, G. Cao, A.M. Rao, T.M. Tritt, S. Nayak, Appl. Surf. Sci. 214 (2003) 289–303. [20] S. Picozzi, S. Santucci, L. Lozzi, L. Valentini, B. Delley, J. Chem. Phys. 120 (2004) 7147–7152. [21] J.W. Lee, H.S. Kim, J.Y. Lee, J.K. Kang, Appl. Phys. Lett. 88 (2006) 143126. [22] M. Arab, F. Picaud, M. Devel, C. Ramseyer, C. Girardet, Phys. Rev. B 69 (2004) 165401. [23] X. Feng, S. Irle, H. Witek, K. Morokuma, R. Vidic, E. Borguet, J. Am. Chem. Soc. 127 (2005) 10533–10538. [24] J. Lu, S. Nagase, Y. Maeda, T. Wakahara, T. Nakahodo, T. Akasaka, D. Yu, Z. Gao, R. Han, H. Ye, Chem. Phys. Lett. 405 (2005) 90–92. [25] K. Seo, K.A. Park, C. Kim, S. Han, B. Kim, Y.H. Lee, J. Am. Chem. Soc. 127 (2005) 15724–15729. [26] A. Maiti, J. Andzelm, N. Tanpipat, P. von Allmen, Phys. Rev. Lett. 87 (2001) 155502. [27] L. Chen, J.K. Johnson, Phys. Rev. Lett. 94 (2005) 125701. [28] S. Rols, M.R. Johnson, P. Zeppenfeld, M. Bienfait, O.E. Vilches, J. Schneble, Phys. Rev. B 71 (2005) 155411. [29] S. Talapatra, V. Krungleviciute, A.D. Migone, Phys. Rev. Lett. 89 (2002) 246106. [30] A. Kleinhammes, S. Mao, X. Yang, X. Tang, H. Shimoda, J. Lu, O. Zhou, Y. Wu, Phys. Rev. B 68 (2003) 075418. [31] V.V. Simonyan, J.K. Johnson, A. Kuznetsova, J.T. Yates Jr, J. Chem. Phys. 114 (2001) 4180–4185. [32] W. An, X. Wu, J.L. Yang, X.C. Zeng, J. Phys. Chem. C 111 (2007) 14105–14112. [33] G. Mpourmpakis, G.E. Froudakis, G.P. Lithoxoos, J. Samios, Nano Lett. 6 (2006) 1581–1583. [34] V. Meunier, J. Kephart, C. Roland, J. Bernholc, Phys. Rev. Lett. 88 (2002) 075506. [35] H. Zeng, J. Zhao, J.W. Wei, H.F. Hu, Eur. Phys. J. B 79 (2011) 335–340. [36] X. Qin, Q. Meng, W. Zhao, Science 605 (2011) 930–933. [37] A. Mavrandonakis, G.E. Froudakis, M. Schnell, M. Muhlhauser, Nano Lett. 3 (2003) 1481–1484. [38] M. Menon, E. Richter, A. Mavrandonakis, G. Froudakis, A.N. Andriotis, Phys. Rev. B 69 (2004) 115322. [39] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery Jr., R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, Gaussian, 98, Gaussian Inc., Pittsburgh, PA, 1998. [40] P.C. Hariharan, J.A. Pople, Mol. Phys. 27 (1974) 209–214. [41] Y. Zhang, A. Wu, X. Xu, Y. Yan, J. Phys. Chem. A 111 (2007) 9431–9437. [42] D.L. Michalopoulos, M.E. Geusic, P.R.R. Langridge, R.E. Smalley, J. Phys. Chem. 80 (1984) 3556–3560. [43] R. Bian, J. Zhao, H. Fu, J. Mol. Model. 19 (2013) 1667–1675. [44] M.N. Hudaa, A.K. Ray, Chem. Phys. Lett. 457 (2008) 124–129. [45] M.R. Momeni, F.A. Shakib, Chem. Phys. Lett. 492 (2010) 137–141.