NANO LETTERS
The Effects of O2 Adsorbates on Field Emission Properties of Single-Wall Carbon Nanotubes: A Density Functional Theory Study
2003 Vol. 3, No. 9 1209-1214
Brahim Akdim,† Xiaofeng Duan,‡ and Ruth Pachter*,† Air Force Research Laboratory, Materials & Manufacturing Directorate, AFRL/ML, Aeronautical Systems Center Major Shared Resource Center for High Performance Computing, ASC/HP Wright-Patterson Air Force Base, Ohio 45433 Received June 2, 2003; Revised Manuscript Received June 30, 2003
ABSTRACT We report a theoretical study on the effects of O2 adsorption at tips of single-wall carbon nanotubes for capped and uncapped geometries. Adsorption mechanisms that take place at the tip, also including the effects of an electric field, are described, highlighting configurations that alter emission properties. Changes in the first ionization potentials upon O2 adsorption are consistent with the experimentally observed current suppression, demonstrating the usefulness of first principles calculations in understanding adsorption mechanisms, and the prediction of properties related to field emission.
Carbon nanotubes have opened up new fields in science and technology in the past few years,1 and have been shown to be versatile building blocks for new materials due to their unique electronic,2,3 optical,4,5 and mechanical6,7 properties. Recently, carbon nanotubes have attracted considerable attention for field emission applications, due to their capability of emitting high currents (up to 1 A/cm2) at low field (∼ 5 V/µm).8 Indeed, advances in the production of wellaligned carbon nanotubes, and control over their deposition, have made it possible to use these materials as potential emitters;9 a prototype of a flat panel with color display10 has already been achieved. Notwithstanding the rapid technological progress, there are still unanswered questions in terms of the emission mechanism. Field emission, explained in terms of Fowler-Nordheim’s (FN) theory,11 is assumed to occur through a tunneling process; however, recent experiments12 show a deviation of the current-voltage (I-V) characteristics from the FN model, attributed to the nonmetallic local density of states at the tube tips,13 interactions between tubes,14 or gas adsorption.15 Although the effects of gas adsorption, in particular O2 adsorbates on single-wall carbon nanotubes (SWCNTs), were previously reported, both experimentally,15-17 and theoretically,18-24 the detailed chemistry at the adsorption * Corresponding author: E-mail:
[email protected]. † Air Force Research Laboratory ‡ Aeronautical Systems Center Major Shared Resource Center for High Performance Computing. 10.1021/nl034364b CCC: $25.00 Published on Web 07/30/2003
© 2003 American Chemical Society
sites under an external field, and the resulting field emission properties, have not been adequately explored yet. In this work we study O2 adsorption on SWCNTs, with the aim of gaining an understanding of the adsorption mechanisms at various sites for different tube geometries, and provide an explanation of the O2 adsorption effects on the emission current behavior. Indeed, this comprehensive study provides an outline for our ongoing interest in gaining insight into the effects of adsorbates on field emission characteristics in these materials, such as the enhancement by Cs intercalation or deposition.25,26 All-electron linear combination of atomic orbitals (LCAO) density functional theory (DFT) calculations were carried out using Dmol3 (ref 27) and shown to be appropriate for modeling nanotubes.28 In this study we employed the Perdew-Burke-Ernzerhof (PBE) functional29 within the generalized gradient approximation (GGA) and using a double numerical polarized (DNP) basis set. This method was used to reduce the over-binding effects caused by the local density approximation and because it is known to adequately predict the density of states as compared to experiment.30 A uniform external field directed from the top toward the tube tip was applied to simulate the emission environment. The geometries were optimized in the absence and presence of an electric field. Transition state geometries were first searched by the LST/QST method, and then fully optimized. The optimum geometries were confirmed by harmonic vibrational frequency calculations. The first ioniza-
Figure 2. Reaction path from an O2 physisorption configuration to a chemisorbed configuration in the (p-h) site on a capped SWCNT.
Figure 1. O2 adsorption on a capped tube. (top) O2 adsorption at the hexagon-hexagon (h-h) site represented by config.-(a), leading to config.-(b) through an etched transition state. (bottom) O2 adsorption at the hexagon-pentagon (p-h) site as shown by config.(c), leading to the etched config.-(d). The transition states were confirmed by vibrational frequency calculations, obtaining one imaginary frequency in each case: 274 (cm-1) and 396 (cm-1) for the transition states leading to config.-(b), and config.-(d), respectively.
tion potential (IP)31 was obtained by evaluating the energy difference between a neutral molecule and its corresponding +1 charged cation. The adsorption energy (Ead) was defined as Ead ) E(SWCNT + O2) - E(SWCNT) - E(O2); a positive or a negative change in Ead refers to an endothermic or exothermic reaction, respectively. To compare our results with previous theoretical work, we studied C(5,5) capped and uncapped SWCNT tips; a three-unit cell C(5,5) tube, terminated with a half C60 molecule on one end and saturated with hydrogen atoms at the other end, was used to model a capped SWCNT (Figure 1); O2 physisorption on a capped tube is shown in Figure 2. To model an open-ended SWCNT (uncapped), we used a three-unit cell C(5,5) tube model saturated with hydrogen atoms on one end (Figures 3 and 4). As the emission in these 1210
systems involves the topmost layers, only the adsorption at the tip was taken into account. Under an applied electric field, the stems of the tubes were fixed to simulate an attached nanotube to a substrate. Reaction Mechanisms of O2 Adsorption. Reaction paths of O2 interacting at the (h-h) and (p-h) sites of a capped tube, for config.-(a) and config.-(c), respectively, are summarized in Figure 1. The initial adsorption process at the (h-h) site forms weak single O-O and O-C bonds, changing the C-C double bond to a single bond. In the absence of an electric field, the reaction is endothermic with an adsorption energy of 0.11 eV (Table 1), suggesting that the reaction is not favorable; however, if the conditions for chemisorption exist, the O2 molecule can react further to etch the tube. When etching, structures with a partial double CdO bond are formed after the dissociation of the O-O bond, lowering the energy by about 1.5 eV with respect to the initial structure. However, a large energy barrier of 3.4 eV needs to be overcome for the etching to occur; this result is larger than the estimated value by Moon et al.22 (1.02 eV), using a self-consistent tight-binding method. In comparing the energetics and structural parameters for the adsorption at the (p-h) and (h-h) sites, we note that the O2 adsorption at the (p-h) site has a higher energy (0.85 eV) (Table 1). The etching process takes place by overcoming an energy barrier of about 3.2 eV (Figure 1), slightly lower than that at the (h-h) site, but larger than a previously reported value of 0.9 eV.22 The formation of the O-C bonds in the etched configurations stabilizes the structure by lowering the energy by ca. 2 eV, through an exothermic reaction. We also studied the reaction path of a physisorbed O2 configuration toward a chemisorption on the (p-h) site, as shown in Figure 2. An energy barrier of 0.77 eV was calculated, which is lower than the energy barrier needed to Nano Lett., Vol. 3, No. 9, 2003
Table 1. Structural Parameters and Adsorption Energies on (a) Capped and (b) Uncapped SWCNT Tips (distances in Å; EAd in eV) (a) Capped Tube (h-h) adsorption site (h-h)-config.-(a)
(p-h) adsorption site
(h-h)-config.-(b)
(p-h)-config.-(c)
(p-h)-config.-(d)
EF, eV/Å
Ead
dO-O
dO-C
dC-C
Ead
dO-O
dO-C
dC-C
Ead
dO-O
dO-C
dC-C
Ead
dO-O
dO-C
dC-C
0.0 1.0 2.0
0.11 -0.60 -5.83
1.51 1.54 2.86
1.46 1.49 1.40
1.57 1.58 1.90
-1.41 -2.74 -6.09
2.64 2.60 2.72
1.21 1.24 1.32
2.79 2.76 2.78
0.85 -0.81
1.52 1.53
1.46 1.56
1.56 1.58
-1.17 -3.39 -6.96
2.79 2.69 2.82
1.22 1.25 1.30
2.78 2.76 2.75
(b) Uncapped Tube config.-(f)
config.-(g)
config.-(h)
EF, eV/Å
Ead
dO-O
dO-C
dC-C
Ead
dO-O
dO-C
dC-C
Ead
dO-O
d(O-C)1
d(O-C)2
dC-C
0.0 1.0
-2.81 -7.42
1.52 2.80
1.40 1.26
1.38 1.51
-5.94 -7.42
2.80 2.80
1.23 1.26
1.54 1.51
-6.46 -7.97
2.94 2.98
1.41 1.44
1.25 1.27
1.45 1.43
Figure 3. O2 adsorption on an uncapped tube. (top) Intermediate states, shown by config.-(f) and config.-(g). (bottom) Partial reaction path of O2 adsorbed on an uncapped tube represented by config.-(g); an increase of O-O distance leads to config.-(h), where one of the oxygens is bonded with two carbons. The transition state was also confirmed in this case, with a 196 cm-1 imaginary frequency.
etch the tube, suggesting that the transition from physisorption to chemisorption could occur if the thermodynamic conditions exist to trigger it. In the absence of an electric field, we found physisorption to be exothermic, with no structural changes, and a small adsorption energy of -0.12 eV at a distance of 3.3 Å from the tip. Interestingly, the Nano Lett., Vol. 3, No. 9, 2003
Figure 4. Effects of saturating uncapped SWCNT tips by O2 adsorption are shown for (top) O2 adsorption on the C(5,5) armchair tube (config.-(i) and config.-(j)) and (bottom) O2 adsorption on the C(10,0) zigzag tube; config.-(k) shows an O2 adsorption and config.-(l) represents a saturated tip.
adsorption energy is comparable to H2 physisorption (-0.1 eV).32 Although the adsorption energy compares well with that reported by Peng et al.33 for O2 physisorbed on the sidewall of a (10,0) nanotube (-0.1 eV), the adsorption distance was smaller (2.7 Å). Jhi and co-workers,18 obtained a larger value at 2.7 Å (-0.25 eV), applying DFT to model sidewall adsorption. Note that our results are consistent with recent MP2 calculations on the interaction of O2 with a (9,0) carbon nanotube.34 Indeed, it is important to emphasize that to discern long-range dispersion effects accurately using DFT, theoretical studies have to be carried out systematically 1211
Table 2. Ionization Potentials (eV) for (a) Capped and (b) Uncapped SWCNTs (a) Capped Tube O2@(h-h) site
O2@(p-h) site
EF, eV/Å
pristine C(5,5)
config.-(e)
config.-(a)
config.-(b)
config.-(c)
config.-(d)
0.0 1.0
6.16 6.21
6.21 6.92
6.24 6.25
6.28 11.56
6.28 6.60
6.30 6.78
EF eV/Å
pristine C(5,5)
config.-(f)
config.-(g)
config.-(h)
config.-(i)
config.-(j)
0.0 1.0
6.16 6.65
6.20 7.00
6.34 7.00
6.34 7.33
6.17 7.57
6.87 7.57
(b) Uncapped (5,5) Tube
(c) Uncapped (10,0) Tube EF eV/Å
pristine C(10,0)
config.-(k)
config.-(l)
0.0 1.0
4.06 5.98
4.69 6.10
5.80
with an appropriate exchange-correlation functional, recently carefully assessed for a variety of weakly bound test problems.35 Moreover, improvements have been suggested to take into account dynamical correlations, including semiempirical36 and hybrid methods35 or improved correlation functionals,37 while most recently time-dependent DFT calculations for evaluating the frequency-dependent polarizabilities, employing the PB0AC (asymptotically corrected) exchange-correlation functional, were shown to be reliable for a series of dimers, which will enable more accurate calculations in the future.38 The O2 chemisorption reaction is more favorable in the open-ended tip as compared to the closed tip. This is demonstrated by the negative adsorption energies for uncapped tip configurations, previously also studied by Zhu et al.,19 using a self-consistent tight-binding method in the absence of an electric field. Figure 3 shows an O2 molecule reacting with the open-ended tip (config.-(f)) as well as the adsorption of O2 on top of the arm site of the tip (config.(g)), forming two O-C bonds with bond lengths of 1.23 Å and an O-O distance of 2.8 Å (Table 1). We studied part of the reaction path to config.-(h), which is the most stable state in this case. A slight increase of the O-O bond length drives the structure to config.-(h), overcoming a small energy barrier of 0.23 eV and gaining about 0.5 eV through an exothermic reaction. In addition, we investigated the effects of O2 adsorption for fully saturated tips (config.-(i) and config.-(j) for C(5,5), and config.-(k) and config.-(l) for C(10,0) (Figure 4)). Config.-(i) is a metastable state with an adsorption energy of -2.73 (eV/O2) and IP of 6.17 eV (Table 2). These values are comparable to those of config.-(f), suggesting that the saturation at the tip in this case has a small effect on field emission properties. On the other hand, the IP in config.-(j) increased by 9% and the tip opening stretched out by about 4% compared to the pristine nanotube, due to the formation of a CdO double bond and repulsion of neighboring oxygens. In the case of C(10,0), namely config.-(k), the IP was found to be lower under zero electric field as compared to the C(5,5) uncapped tip. 1212
Figure 5. Average partial atomic charges (Mulliken population analysis) on the oxygen of capped and uncapped configurations with and without an applied electric field.
The effects of an electric field on the adsorption energies and structural parameters of the capped and uncapped SWCNTs are listed in Table 1, and the corresponding Mulliken populations are summarized in Figure 5. In the initial adsorption process, characterized by config.-(a) and config.-(c) for the capped tubes, the values of the adsorption energies decrease smoothly as a function of field strength, as shown in Figure 6. This suggests that an applied voltage lowers the adsorption energy, thus setting the conditions for a chemisorption process to take place, which, in turn, leads to etching. A 2 eV/Å increase in the field alters significantly the structural parameters, resulting in a lower energy barrier for an etching process to occur. Indeed, a 2 eV/Å applied field has desorbed the oxygen from the tip in config.-(c), whereas in the final adsorption process (config.-(b) and config.-(d)), it is difficult to achieve desorption without disintegrating the nanotube tip. Note that Kim et al.39 have previously calculated O2 adsorption for an uncapped SWCNT, also with an applied field; however, an analysis for C(10,0) was primarily emphasized. In our study, the C(5,5) open-ended tip was examined, and although the adsorption energies for configs.(f), -(g), and -(h) are systematically upshifted by about 1.4 eV as compared to previous self-consistent tight-binding calculations,19 the relative values between intermediate Nano Lett., Vol. 3, No. 9, 2003
Figure 6. Adsorption energy as a function of field strength for a capped tip.
configurations are comparable. Furthermore, we found that under a 1 eV/Å field, config.-(f) converges to config.-(g) by forming a double bond (structural results in Table 1). Stronger adsorption under a 1 eV/Å field is shown, as has been observed for capped tubes. In config.-(g) and config.(h) we note small structural changes, suggesting no desorption at 1 eV/Å field strength; however, longer O-C bonds were observed at a higher field (2 eV/Å). Overall, our results show that O2 chemisorption is endothermic on a capped tip, with the (h-h) adsorption site being energetically more favorable than the (p-h) site. If the thermodynamic conditions exist for chemisorption to occur, an energy barrier larger than 3 eV is required to etch the tube. The application of an electric field sets the conditions for the chemisorption to take place. In open-ended tips, the examined interactions were exothermic with lower adsorption energies. This suggests that the observed current suppression,15 when a carbon nanotube sample was exposed to O2, can be rationalized as being due to the presence of a high percentage of open-ended tips or tubes with structural defects. Effects of O2 Adsorption on the Ionization Potentials. The work function40 is approximated by the first IP,41 as previously used by Maiti et al.32 (Table 2 summarizes the results for capped and open-ended configurations). Under a zero electric field, a small increase of about 2% in the IP was noted for capped tubes, suggesting that O2 adsorption does, indeed, play a role in the current suppression observed experimentally.15 An applied field exacerbates this current suppression, as shown by the notable increase of the IP, ranging from 2% to 6% for config.-(c), and 8% for config.(d). While in config.-(a) a small change of the IP has been observed with an applied field, config.-(b) shows a much higher IP, with an increase of about 46%, which could be explained by the specific geometry at the adsorption site. As expected, charge transfer occurs upon adsorption from the carbon to oxygen (cf. Figure 5). We also note that an applied field appears to increase the negative partial atomic charge on the oxygen atom. Upon O2 adsorption in the absence of an electric field in uncapped tubes, no significant effect on the IP is observed in config.-(f) with respect to pristine C(5,5); however, an Nano Lett., Vol. 3, No. 9, 2003
increase of 2% is shown for the intermediate config.-(g) and final config.-(h). The corresponding HOMO energies are consistent with the IPs trend (-4.81, -4.82, -4.96, and -4.93 eV, for a pristine tube and configs.-(f), -(g), and -(h), respectively). However, under a 1 eV/Å applied field, the IPs increase to about 5% in configs.-(f) and -(g), and 9% in config.-(h), respectively. Once again, this implies that the current suppression is exacerbated by an applied field, accompanied by an increase in the charge transfer from carbon to oxygen. We note that the IPs of the pristine capped and uncapped tubes, under zero electric field, are comparable. However, under a 1 eV/Å field strength, the IP of the uncapped tip is 6% higher than that of a capped tube. As for the O2 adsorbed tips, different values were obtained depending on the adsorption sites. The effect of O2 adsorption on the field emission properties is in general more pronounced in the C(10,0) than in the C(5,5) tip, with an increase in the IP of 13% and 30% in config.-(k) and config.-(l), respectively, as compared to the pristine C(10,0) tube. The increase in the IPs for saturated tips is in agreement with experimental results,15 where a decrease in the output current as a function of the O2 exposure time was observed. In conclusion, a comprehensive examination of the adsorption mechanisms on capped and uncapped SWCNT tip geometries provided insight into the chemistry upon exposure of SWCNTs to O2. We have shown that the chemisorption at a capped tip is endothermic, whereas the physisorption is exothermic. The desorption mechanism was examined under an applied field, revealing that once O2 dissociates and attaches to the tip, it becomes difficult for the desorption to take place. Indeed, the inclusion of an electric field provided a more realistic emission environment, showing that the field exacerbates current suppression upon O2 adsorption by lowering the adsorption energy at the capped tip, thus setting the conditions for an etching process to occur. Our adsorption energies and first IPs clearly illustrate the sites involved in current suppression, and the increase in IP for saturated openended tubes is in agreement with experimental results. Finally, this study offers a framework for our ongoing interest in gaining insight into the effects of Cs adsorbates on field emission characteristics of SWCNTs.42 Acknowledgment. We thank the ASC/MSRC for their excellent support in carrying out the calculations. References (1) Baugham, R. H.; Zakhidov, A. A.; de Heer, W. A. Science 2002, 297, 787. (2) Mintmire, J. W.; Dunlap, B. I.; White, C. T. Phys. ReV. Lett. 1992, 68, 631. (3) Hamada, N.; Sawada, S.-I.; Oshiyama, A. Phys. ReV. Lett. 1992, 68, 1579. (4) Charlier, J.-C.; Limbin, Ph. Phys. ReV. B 1998, 57, 15037. (5) Corio, P.; Shapro, M. Phys. ReV. Lett. 2001, 86, 131. (6) Demczyk, B. G.; Wang, Y. M.; Cumings, J.; Hetman, M.; Han, M.; Zettl, A.; Ritchie, R. O. Mater. Scien. Eng. A 2002, 334, 173. (7) Yakobson, B. I.; Avouris, Ph. In Carbon Nanotubes: Synthesis, Structure, Properties, and Applications; Dresselhaus, M. S., Dresselhaus, G., Avouris, Ph., Eds.; Springer-Verlag: Berlin 2000, p 391. (8) Bonard, J.-M.; Croci, M.; Klinke, C.; Kurt, R.; Noury, O.; Weiss, N. Carbon 2002, 40, 1715-1728. (9) Deheer, W. A.; Chatelain, A.; Ugarte, D. Science 1995, 270, 5239. 1213
(10) Choi, W. B.; Chung, D. S.; Kang, J. H.; Kim, H. Y.; Jin, Y. W.; Han, I. T.; Lee, Y. H.; Jung, J. E.; Lee, N. S.; Park, G. S.; Kim, J. M. Appl. Phys. Lett. 1999, 75, 3129-3131. (11) Fowler, R. H.; Nordheim, L. Proc. R. Soc. London, Ser. A 1928, 119, 173. (12) Collazo, R.; Schlesser, R.; Sitar, Z. Diamond Related Mater. 2002, 11, 769-773. (13) Saito, Y.; Hamaguchi, K.; Nishino, T.; Hata, K.; Tohji, K.; Kasuya, A.; Nishina, Y. Jpn. J. Appl. Phys., Part 2 1997, 36, L1340. (14) Bonard, J.-M.; Salvetat, J.-P.; Stockli, T.; De Heer, W. A.; Forro, L.; Chatelain, A. Appl. Phys. Lett. 1998, 73, 918. (15) Lim, S. C.; Choi, Y. C.; Jeong, H. J.; Shin, Y. M.; An, K. H.; Bae, D. J.; Lee, Y. H.; Lee, N. S.; Kim, J. M. AdV. Mater. 2001, 13, 1563. (16) Kung, S.-C.; Hwang, K. C.; Lin, N. Appl. Phys. Lett. 2002, 80, 4819. (17) Ulbricht, H.; Moos, G.; Hertel, T. Phys. ReV. B 2002, 66, 075404. (18) Jhi, S.-H.; Louie, S. G.; Cohen, M. L. Phys. ReV. Lett. 2000, 85, 1710. (19) Zhu, X. Y.; Lee, S. M.; Lee, Y. H.; Frauenheim, Th. Phys. ReV. Lett. 2000, 85, 2757. (20) Park, N.; Han, S.; Ihm, J. Phys. ReV. B 2001, 64, 125401. (21) Sorescu, D. C.; Jordan, K. D.; Avouris, Ph. J. Phys. Chem. B 2001, 105, 11227. (22) Moon, C.-Y.; Kim, Y.-S.; Lee, E.-C.; Jin, Y.-G.; Chang, K. J. Phys. ReV. B 2002, 65, 155401. (23) Steckel, J. A.; Jordan, K. D.; Avouris, Ph. J. Phys. Chem. A 2002, 106, 2572. (24) Grujicic, M.; Cao, G.; Gresten, B. Appl. Surf. Science 2003, 206, 167. (25) Wadhawan, A.; Stallcup, R. E.; Perez, J. M. Appl. Phys. Lett. 2001, 78, 108. (26) Suzuki, S.; Bower, C.; Watanabe, Y.; Zhou, O. J. Electron Spectrosc. 2001, 114, 225. (27) Delley, B. J. Chem. Phys. 2000, 113, 7756; implemented by Accelyrs, Inc. (28) Akdim, B.; Duan, X.; Adams, W. W.; Pachter, R. Phys. ReV. B 2003, 67, 245404.
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(29) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (30) Avramov, P. V.; Kudin, K. N.; Scuseria, G. E. Chem. Phys. Lett. 2003, 370, 597. (31) A comparison of adiabatic and vertical IPs for selected configurations (config.-(c) and config.-(h)) shows small structural changes in the uncapped tube, leading to a decrease of ca. 4% in the IP in the adiabatic case; however, for the capped tube no changes were observed in the structure and IP. In this work we assume that no structural changes occur during the emission process, thus considering vertical ionizations using the unrestricted spin polarization scheme for open shell species. (32) Maiti, A.; Andzelm, J.; Tanpipat, N.; Allen, P. V. Phys. ReV. Lett. 2001, 87, 155502. (33) Peng, S.; Cho, K. Nanotechnology 2002, 11, 57. (34) Ricca, A.; Drocco, J. A. Chem. Phys. Lett. 2002, 362, 217. (35) Wu, X.; Vargas, M. C.; Nayak, S.; Lotrich, V. C.; Scoles, G. J. Chem. Phys. 2001, 115, 8748. (36) Allen, M. J.; Tozer, D. J. J. Chem. Phys. 2002, 177, 11113. (37) Elstner, M.; Frauenheim, Th.; Kaxiras, E.; Seifert, G.; Suhai, S. Phys. Status Solidi B 2000, 217, 357. (38) Heselmann, A.; Jansen, G. Chem. Phys. Lett. 2003, 367, 778. (39) Kim, C.; Choi, Y. S.; Lee, S. M.; Park, J. T.; Kim, B.; Lee Y. H. J. Am. Chem. Soc. 2002, 124, 9906. (40) Sun, J. P.; Zhang, Z. X.; Hou, S. M.; Zhang, G. M.; Gu, Z. N.; Zhao, X. Y.; Liu, W. M.; Xue, Z. Appl. Phys. A 2002, 75, 479. (41) Our calculations show that the IP is not dependent on the tube length, as compared to the HOMO-LUMO gap, adopted in the work of Kim C.; Kim B. Phys. ReV. B 2002, 65, 165418. In particular, calculations of two capped C(5,5) nanotubes with different tube lengths, namely, 40 and 50 carbon atoms in addition to the cap, showed an increase of about 5% in the IP with the tube length, while the HOMO-LUMO gap increased by 76%. (42) Akdim, B.; Duan, X.; Pachter, R., manuscript in preparation.
NL034364B
Nano Lett., Vol. 3, No. 9, 2003
