NANO LETTERS
Characterization of Surface Electrostatic Potentials of some (5,5) and (n,1) Carbon and Boron/Nitrogen Model Nanotubes
2003 Vol. 3, No. 1 21-28
Zenaida Peralta-Inga,†,‡ Pat Lane,† Jane S. Murray,† Sylke Boyd,† M. Edward Grice,† Charles J. O’Connor,†,‡ and Peter Politzer*,†,‡ Department of Chemistry and AdVanced Materials Research Institute, UniVersity of New Orleans, New Orleans, Louisiana 70148 Received August 17, 2002; Revised Manuscript Received November 7, 2002
ABSTRACT To help understand and predict nanotube interactions, the electrostatic potentials on both the outer and the inner surfaces of 10 single-walled model systems have been computed at the Hartree−Fock STO-5G//STO-3G level. All structures were optimized computationally. Both carbon and boron/nitrogen tubes were studied, including the open and closed (5,5) and the open (6,1), (7,1), and (8,1), plus fullerene for comparison. Hydrogen atoms were introduced at the ends of the open tubes, to satisfy the unfulfilled valencies. The surface potentials were characterized in terms of both site-specific and global properties: positive and negative extrema and average values, average deviation, positive and negative variances, and electrostatic balance. The all-carbon systems, the closed (5,5) and fullerene, are very weakly positive on most of the outer and all of the inner surfaces, the latter potentials being somewhat stronger. In contrast, the open carbon tubes with charge-donating hydrogens at the ends are slightly negative on the outer lateral surfaces and somewhat less so on the inner, except for the narrowest, the (6,1), which is positive inside. The boron/nitrogen tubes have much stronger and more variable surface potentials than do the carbon; there are characteristic patterns of positive and negative sites on the outer lateral surfaces, while the inner ones are markedly positive. A general feature of all of the systems studied, both carbon and boron/nitrogen, is that stronger potentials are associated with regions of higher curvature.
1. Introduction. Since carbon nanotubes were first reported,1 they have been the focus of numerous theoretical and experimental studies. (For reviews, see Dresselhaus et al.,2 Dai et al.,3 Edelmann,4 Tanaka et al.,5 Ajayan,6 and Odom et al.7) This activity is due to their very interesting and unusual structural, electronic and mechanical properties, which suggest a variety of potential applications: quantum wires,8 high-resolution scanning probes,9 transistors,10 electron field emission sources,11 chemical sensors,12,13 nanotweezers,14 electromechanical actuators,15 etc. An important feature is the large surface-to-mass ratio, which introduces the possibility of a variety of adsorptionrelated applications, e.g., gas storage systems (focusing particularly upon H216-20), pollutant traps,21 separations,22 catalysts, etc. A single-walled nanotube offers the unique advantage over other adsorbents that each atom is available for interaction with foreign species on both the inner and outer surfaces of the tube. Some studies involving H2,16,19 N2 and O2,23 and Xe24,25 have found that these gases adsorb preferentially on the inner surfaces of the nanotubes. It has been shown that the electrical conductivities of nanotubes * Corresponding author. † Department of Chemistry. ‡ Advanced Materials Research Institute. 10.1021/nl020222q CCC: $25.00 Published on Web 12/05/2002
© 2003 American Chemical Society
are significantly affected by the adsorption of gases,12,13,26 introducing the possibility that they could be used as chemical sensors. There is currently considerable interest in the functionalization of carbon nanotubes, one motivation being to increase their very low solubilities in both aqueous and organic solvents.27,28 Both covalent and noncovalent interactions have been reported, including hydrogenation,29 oxidation,30 ozonization31 and other 1,3-dipolar cycloadditions,32 fluorination,33 amidization,34 attachment of polymers,35 immobilization of proteins and other biomolecules,36 etc. The discussion up to this point has dealt only with nanotubes composed entirely of carbon atoms. However the system BxNx is isoelectronic with C2x, and solid boron nitride exists in both graphite-like and diamond-like forms.37-39 It was suggested some time ago that nanotubes with the stoichiometries BxNx, BxCyNx, or even BxCyNz could be produced,40,41 and indeed BxNx4,42-46 and various B/C/N4,47-49 nanotubes have since been synthesized. At least in their initial stages, the interactions of nanotube surfaces, whether covalent or noncovalent, are governed largely by the respective electrostatic potentials. To help develop a predictive capacity for such interactions, we present in this paper detailed characterizations of the electrostatic
Table 1: Computed Surface Quantitiesa,b for Model Nanotubes and for Fullerenec
b
system
(n,m)
radius
AS+
AS-
V h S+
V h S-
Π
σ+2
σ-2
σtot2
ν
VS,max
VS,min
C120 C80H20 C68H14 C62H16 C68H18 B60N60 B40N40H20 B41N41H14 B38N38H16 B42N42H18 C60 (fullerene)
(5,5) (5,5) (6,1) (7,1) (8,1) (5,5) (5,5) (6,1) (7,1) (8,1)
3.44 3.44 2.60 3.00 3.39 3.46 3.46 2.62 3.02 3.42
636 204 201 180 194 474 417 356 356 406 351
80 462 335 347 390 253 261 270 260 282 16
2.6 7.0 6.3 7.0 7.2 18.0 12.3 18.0 17.5 16.7 2.3
-0.5 -3.9 -2.7 -3.0 -3.1 -8.3 -5.7 -8.2 -8.2 -8.2 -0.5
1.8 4.6 4.3 4.5 4.6 14.0 9.4 13.9 13.6 13.1 1.7
4.9 17.2 19.9 17.7 16.5 223.4 72.3 194.5 152.9 126.3 6.5
0.2 2.1 1.2 1.7 1.6 41.7 14.7 24.9 23.1 23.5 0.1
5.0 19.3 21.1 19.4 18.1 265.1 87.0 219.4 176.1 149.8 6.5
0.039 0.097 0.047 0.052 0.052 0.133 0.140 0.101 0.114 0.132 0.015
10.3 14.7 14.8 13.7 13.6 49.0 32.4 49.8 42.4 37.8 10.7
-1.8 -8.0 -7.4 -7.3 -7.3 -25.9 -14.7 -25.4 -23.0 -21.8 -1.0
a Units: the radii are in Å; A + and A - are in Å2; V h S+, V h S-, Π, VS,max, and VS,min are in kcal/mol; σ+2, σ-2, and σtot2 are in (kcal/mole)2; ν is dimensionless. S S HF/STO-5G//HF/STO-3G calculations. c C120 and B60N60 represent closed (5,5) tubes. All others are open at both ends.
potentials on the surfaces of several different carbon and boron/nitrogen model nanotubes. Analogous studies were carried out earlier for some graphene models.50 2. Procedure and Methodology. 2.1 Scope. We examined single-walled carbon and BxNx model nanotubes, open at both ends, of the types (5,5), (6,1), (7,1) and (8,1), as well as the closed (5,5). For comparison, we also included fullerene (C60). For the open tubes, we followed the common practice of introducing hydrogens to satisfy the unfulfilled valencies at the ends.51-55 The compositions of the various systems are given in Table 1. 2.2 Electrostatic Potential. The electrostatic potential V(r) that is created by the nuclei and electrons of a system at any point r in the surrounding space is given rigorously by eq 1,
V(r) )
∑A |R
ZA A
- r|
-
V hS )
(1)
1
m+n
m
VS-(ri) ∑ m i )1
[∑ n
1
i )1
VS+ (ri) +
(3) m
Π)
1
m+n
m+n
i )1
∑ |VS(ri) - Vh S|
V h S+ ) 22
1
n
VS+ (ri) ∑ n i )1
(2)
(4)
(5)
(d) the positive, negative and total variances of VS(r), 1
n
∑[VS+ (ri) - Vh S+ ]2 +
n i )1
1
m
∑[VS-(ri) - Vh S- ]2
m i )1 in which ZA is the charge on nucleus A, located at RA, and F(r) is the electronic density. The sign of V(r) in any region depends on whether the positive contribution of the nuclei or the negative contribution of the electrons is dominant there. The electrostatic potential has been used extensively as a guide to reactive behavior.56-61 It is particularly effective in relation to noncovalent interactions and the early stages of processes that involve bond formation and/or charge transfer. For these applications, we compute V(r) on the molecular surface, or in the present work, the nanotube surface; we take this to be the 0.001 electrons/bohr3 contour of the electronic density F(r), as proposed by Bader et al.62 We characterize the features and overall pattern of the surface potential, VS(r), by means of certain statistical quantities: (a) the most positive and most negative values, VS,max and VS,min; (b) the positive, negative and overall average potentials on the surface,
]
VS-(ri) ∑ i )1
(c) the average deviation of VS(r), Π,
2 ) σ+2 + σ-2 ) σtot
F(r′) dr′
∫ |r′ - r|
V h S- )
(6)
and (e) an electrostatic balance parameter, ν,
ν)
σ+2 σ-2 2 2 [σtot ]
(7)
VS,max and VS,min indicate sites that are favorable for the initial approaches of nucleophiles and electrophiles, and can also be correlated with hydrogen-bond-donating and -accepting tendencies.63 The quantities defined in eqs 2-7 are global in nature. Π is interpreted as a measure of the local polarity, or internal charge separation, that exists even in systems with no dipole moment,64 e.g., para-dinitrobenzene, 2 reflect the range and variability of while σ+2 , σ-2 , and σtot VS(r), emphasizing the contributions of the extrema due to the terms being squared. ν is a measure of the degree of balance between the positive and negative surface potentials; its upper limit is 0.250 when σ+2 ) σ-2 . We have shown that a variety of liquid, solid, and solution macroscopic properties can be expressed analytically, with good accuracy, in terms of subsets of the global and siteNano Lett., Vol. 3, No. 1, 2003
Table 2: Computed Surface Quantitiesa,b for Some Representative Moleculescand for Graphene Modeld molecule
V h S+
V h S-
Π
σ+2
σ-2
2 σtot
ν
VS,max
VS,min
butylbenzene benzene 1-hexanol p-dichlorobenzene ammonia piperazine methylamine methanol acetamide 2,4,6-trinitrotoluene graphene model (C62H20)
3.7 4.6 5.0 6.2 9.2 9.3 9.3 10.3 12.7 20.6 6.4
-4.5 -4.9 -9.2 -7.0 -12.8 -17.4 -20.2 -18.4 -20.6 -14.7 -4.6
3.9 4.8 5.8 6.2 10.7 11.1 12.1 12.6 14.9 17.2 4.9
4.9 7.3 9.9 18.0 27.6 26.3 34.6 48.9 68.0 104.3 13.2
13.0 8.5 132.5 10.2 73.7 207.2 263.0 181.9 150.8 53.2 2.5
17.9 15.8 142.4 28.1 101.3 233.5 297.6 230.8 218.8 157.5 15.7
0.199 0.249 0.065 0.231 0.198 0.100 0.103 0.167 0.214 0.224 0.135
8.5 9.5 12.6 15.2 18.1 22.9 21.4 29.9 32.0 37.5 15.9
-12.4 -10.2 -36.7 -11.1 -29.0 -47.8 -53.2 -41.6 -40.6 -28.8 -7.9
2 a Units: A + and A - are in Å2; V h S+, V h S-, Π, VS,max, and VS,min are in kcal/mol; σ+2 , σ-2 , and σtot are in (kcal/mol)2; ν is dimensionless. b HF/STO-5G//HF/ S S STO-3G calculations. c Reference 76. d Reference 50.
specific features of VS(r). Among these properties are heats of phase transitions, solubilities and solvation free energies, boiling points and critical constants, partition coefficients, surface tensions, viscosities, diffusion coefficients, liquid and solid densities, lattice energies, and impact sensitivities. This work has been reviewed elsewhere.61,65-67 2.3. Computational Procedure. The Gaussian 98 code68 was utilized to carry out a Hartree-Fock (HF) STO-3G geometry optimization of each model nanotube and fullerene. The HF/STO-5G electrostatic potentials were then computed on the surfaces corresponding to F(r) ) 0.001 electrons/ bohr3, the VS,max and VS,min were determined, and the global quantities defined by eqs 2-7 were evaluated. The very large numbers of atoms involved in these calculations necessitated the use of minimum basis sets; however, our (and others’) experience has been that these are quite satisfactory for our present purposes.59,61,64,69 3. Results and Discussion. 3.1. General. For each system studied, Table 1 lists the positive and negative surface areas, AS+ and AS-, and the properties of the surface electrostatic potential that were discussed in section 2.2. To provide perspective, Table 2 gives these quantities for a group of representative molecules, as well as for the largest model graphene that we studied earlier,50 C62H20. (Hydrogens were attached along the peripheries of the carbon sheet.) Figures 1-9 show the computed electrostatic potentials on both the outer and the inner surfaces of eight of the model nanotubes and fullerene. The interior views are obtained by “slicing” away a portion of the tube. 3.2. Structures. In graphite, all of the C-C bonds are equivalent, with a length of 1.420 Å.70 In fullerene, however, they are of two types, the 6,6 and the 6,5, depending upon whether they fuse two six-membered rings or six- and fivemembered ones. Our optimized HF/STO-3G bond lengths are 1.376 and 1.463 Å, respectively, in satisfactory agreement with experimental determinations, 1.386 to 1.401 Å for the 6,6 bonds and 1.434 to 1.458 Å for the 6,5.71-73 In nanotubes, the possible orientations of the bonds relative to the tube axis result in two nonequivalent types of bonds in the (n,n) and (n,0) and three in the (n,m).74,75 Thus our carbon model nanotubes show a range of C-C distances, primarily between 1.41 and 1.45 Å; in the BxNx systems; on Nano Lett., Vol. 3, No. 1, 2003
Figure 1. Calculated electrostatic potential on the molecular surface of closed (5,5) C120; (a) is an outside view, while (b) shows the interior. Color ranges, in kcal/mol: red, greater than 8; yellow, between 8 and 0; green, between 0 and -5; blue, between -5 and -7.5.
the other hand, the bond lengths are more uniform, mostly 1.44 and 1.45. The radii of the nanotubes in Table 1 were obtained from their circumferences.2,4,40 For this purpose, the average C-C distance was taken to be 1.44 Å,2 and 1.45 Å was used for the B-N.40 3.3. Carbon Nanotubes. Two all-carbon systems were investigated: the closed (5,5) nanotube, C120, and fullerene, C60. Table 1 and Figures 1 and 2 show that their surface electrostatic potentials are very similar - and quite bland. The values of Π, our measure of internal charge separation, and the total variance σ2tot, are among the lowest that we have encountered in analyzing more than 300 organic and inorganic molecules; only alkane hydrocarbons are comparable.77 Essentially the entire surfaces, both inner and outer, are positive (AS+ . AS- ) but only weakly so: V h S+ ) 2.6 and 2.3 kcal/mol. The inner surfaces are more positive than the outer, reflecting the fact that the former points are in 23
Figure 3. Calculated electrostatic potential on the molecular surface of open (6,1)C68 H14; (a) is an outside view, while (b) shows the interior. Color ranges, in kcal/mol: red, greater than 8; yellow, between 8 and 0; green, between 0 and -5; blue, between -5 and -7.5. Figure 2. Calculated electrostatic potential on the molecular surface of fullerene, C60; (a) is an outside view, while (b) shows the interior. Color ranges, in kcal/mol: red, greater than 8; yellow, between 8 and 0; green, between 0 and -5; blue, between -5 and -7.5.
closer proximity to more carbon nuclei than are the latter. Thus the inner maxima are greater than 10 kcal/mol while the outer are no more than about 4 kcal/mol. It should be noted in Figure 1 that the few negative spots, which are on the outer surface, as well as the most positive ones, on the inner, are all associated with the regions of highest curvature, the fullerene-like caps at the ends of the tube. The picture is quite different for the open carbon nanotubes with hydrogens at the ends (for which the computed statistical quantities in Table 1 are similar to those of the graphene model, C62H20, in Table 2). The major portion of each total surface is now negative: AS- > AS+. The outer surfaces are entirely negative except for the ends, where the hydrogens are located; the VS,min are in the neighborhood of -8 kcal/ mol. These negative outer surfaces are due to the electronic charge withdrawn from the hydrogens, which in turn are the most positive portions of these nanotubes, with Vmax approaching 15 kcal/mol, only 3 kcal/mol less than for the hydrogens in ammonia (Table 2). The potentials on the inner surfaces reflect two opposing factors: the negative charge gained from the hydrogens vs the closer proximity to more positive carbon nuclei. In the narrowest of these tubes, the (6,1) C68H14, the latter effect dominates and its inner surface is virtually completely positive (Figure 3). As the tube radius increases from (6,1) to (7,1) to (8,1) to (5,5), however, the proximity factor becomes less significant and more of the inner surface becomes negative (Figure 4), until it is completely so in (5,5) C80H20 (Figure 5). The greater variation 24
in the surface potentials of these nanotubes can be seen in 2 the magnitudes of Π and σtot , which are now distinctly larger than for the all-carbon systems. However, they are still much less than for most of the molecules in Table 2; the surface potentials of these nanotubes are still, overall, quite weak. (Compare their V h S- to those in Table 2, keeping in mind that 60% to 70% of these nanotube surfaces are now negative.) 3.4. BxNx Nanotubes. The data in Table 1 show immediately that the BxNx nanotube surface potentials differ very markedly from those of the carbon systems. The former are much stronger and more variable, quite comparable to typical substituted molecules such as those in Table 2. A characteristic feature of the outer lateral surfaces of all of the BxNx tubes examined is a pattern of positive and negative potentials associated with the boron and the nitrogen atoms, respectively. This can be seen in Figures 6-9. The closed (5,5) B60N60 tube is shown in Figure 6. The overall surface is predominantly positive, AS+ > AS-, as is also true for the open BxNx tubes (unlike their carbon counterparts). On the outer lateral surfaces of (5,5) B60N60, the positive regions above the borons are stronger than the negative ones of the nitrogens; the former have local maxima of 22 to 23 kcal/mol, while the local minima of the latter are only -7 to -9 kcal/mol. At the capped ends of the tube, however, where the curvature is the greatest, the negative potentials do reach -26 kcal/mol. The inner surface of the (5,5) B60N60 tube is very positive (Figure 6b), the potential ranging between 42 and 49 kcal/mol. (Note that these potentials are stronger than the VS,max of the hydrogenbonding hydroxyl group in methanol, Table 2.) The variNano Lett., Vol. 3, No. 1, 2003
Figure 4. Calculated electrostatic potential on the molecular surface of open (8,1) C68 H18; (a) is an outside view, while (b) shows the interior. Color ranges, in kcal/mol: red, greater than 8; yellow, between 8 and 0; green, between 0 and -5; blue, between -5 and -7.5.
ability of the positive potential, as indicated by σ+2 , is the greatest of any of the systems in Table 1. When the (5,5) tube is opened and hydrogens are attached at the ends, giving B40N40H20, the picture remains qualitatively the same (Figure 7) but the variability of the surface 2 decrease considerably potential diminishes; Π and σtot (Table 1). The negative regions above the nitrogens are stronger than before, -13 to -15 kcal/mol, and the positive ones of the borons are slightly weaker, 18 to 20 kcal/mol. The inner surface is still positive, but not as strongly so, reaching 32 kcal/mol. It is interesting that the presence of the hydrogens at the ends of the tubes is not more clearly manifested in the potential. This is presumably because they are attached alternately to charge-donating borons and charge-withdrawing nitrogens, and thus make negative and positive contributions to the potential, respectively, which largely balance each other. The open (6,1), (7,1), and (8,1) BxNx nanotubes continue the pattern, on their outer lateral surfaces, of positive and negative regions associated with the borons and nitrogens, respectively (Figures 8 and 9). The former are in the 18 to 23 kcal/mol range for (6,1) B41N41H14, but diminish somewhat to 15 to 18 kcal/mol in going to (8,1) B42N42H18; the negative potentials are in the neighborhood of -15 kcal/ mol. The inner surfaces of these tubes are strongly positive, but there is the usual tendency to weaken as the radius Nano Lett., Vol. 3, No. 1, 2003
Figure 5. Calculated electrostatic potential on the molecular surface of open (5,5) C80 H20; (a) is an outside view, while (b) shows the interior. Color ranges, in kcal/mol: red, greater than 8; yellow, between 8 and 0; green, between 0 and -5; blue, between -5 and -7.5; purple, more negative than -7.5.
Figure 6. Calculated electrostatic potential on the molecular surface of closed (5,5) B60N60; (a) is an outside view, while (b) shows the interior. Color ranges, in kcal/mol: red, greater than 20; yellow, between 20 and 0; green, between 0 and -10; blue, between -10 and -20; purple, more negative than -20.
increases: the inside maximum decreases from 50 kcal/mol for the (6,1) to 38 kcal/mol for the (8,1). These three systems - the (6,1), (7,1), and (8,1) - differ from the other open BxNx tube, (5,5) B40N40H20, in that the 25
Figure 8. Calculated electrostatic potential on the molecular surface of open (6,1) B41N41H14; (a) is an outside view, while (b) shows the interior. Color ranges, in kcal/mol: red, greater than 20; yellow, between 20 and 0; green, between 0 and -10; blue, between -10 and -20; purple, more negative than -20.
Figure 7. Calculated electrostatic potential on the molecular surface of open (5,5) B40N40H20; (a) is an outside view, while (b) shows the interior. Color ranges, in kcal/mol: red, greater than 20; yellow, between 20 and 0; green, between 0 and -10; blue, between -10 and -20.
hydrogens at one end are all attached to borons while at the other end they are all on nitrogens. Thus, instead of the balancing effect observed for (5,5) B40N40H20, mentioned above and seen in Figure 7, these tubes clearly show local B+H- polarity at one end and N-H+ at the other (Figures 8 and 9). This is reflected in increased values of Π (Table 1). The N-H+ polarity is particularly pronounced, the nitrogen potentials being about -24 kcal/mol and the hydrogens, 36 kcal/mol. 4. Summary. A general feature of the systems that we have studied is that the magnitudes of both the positive and negative surface potentials associated with the basic carbon or boron/nitrogen framework (ignoring hydrogen effects) tend to be larger where the curvature is greater; this can refer to the end cap in a given closed tube or to the lateral surfaces in comparing tubes with different indices. This observation is consistent with a number of reports that link local strain and reactivity to degree of curvature.31,52,78,79 A related point is that the potentials on the inner surfaces are regularly more positive than on the outer. This is particularly striking in the case of the BxNx tubes. Their outer lateral surfaces all show patterns of distinctly positive and negative regions (the former being somewhat stronger); in contrast, the inner surface potentials are entirely positive, and with higher magnitudes. In both the carbon and the 26
Figure 9. Calculated electrostatic potential on the molecular surface of open (8,1) B42N42H18; (a) is an outside view, while (b) shows the interior. Color ranges, in kcal/mol: red, greater than 20; yellow, between 20 and 0; green, between 0 and -10; blue, between -10 and -20; purple, more negative than -20.
boron/nitrogen systems, the inner surfaces become more positive as the tube radius decreases. The computed electrostatic potentials on carbon nanotube surfaces are very weak; their low solubilities27,28 are not surprising. The all-carbon (5,5) C120 is slightly positive on the outer surface and somewhat more so on the inner. (Similar results are obtained for fullerene, C60.) This may Nano Lett., Vol. 3, No. 1, 2003
account for the reports that carbon nanotubes adsorb gases preferentially on their inner surfaces.16,19,23-25 However, the introduction of even a relatively small number of hydrogens at the ends, to produce (5,5) C80H20, suffices to make both the outer and inner potentials slightly negative. (In the case of the narrower (6,1) C68H14, the inside remains positive even in the presence of the hydrogens.) Hydrogens at the carbon tube ends evidently act as charge donors. It can be anticipated that electron-withdrawing functional groups may make the lateral surface potentials significantly more positive. This will be investigated in future work. The BxNx nanotubes are clearly of interest because of their strong and variable surface potentials, characterized by significantly positive and negative sites. Our results suggest that by appropriately varying the structure and composition, tubes can be designed with potential patterns tailored to specific objectives, e.g., trapping particular polar gas molecules. Acknowledgment. We appreciate the support provided by the Advanced Materials Research Institute through NSF Grant No. DAAD19-01-1-0546. References (1) Iijima, S. Nature 1991, 354, 56. (2) Saito, R.; Dresselhaus, G.; Dresselhaus, M. S. Physical Properties of Carbon Nanotubes; Imperial College Press: London, 1998. (3) Dai, H.; Kong, J.; Zhou, C.; Franklin, N.; Tombler, T.; Cassell, A.; Fan, S.; Chapline, M. J. Phys. Chem. B 1999, 103, 11246. (4) Harris, P. J. F. Carbon Nanotubes and Related Structures; Cambridge University Press: Cambridge, UK, 1999. (5) The Science and Technology of Carbon Nanotubes; Tanaka, K.; Yamabe, T.; Fukui, K., Eds.; Elsevier: Amsterdam, 1999. (6) Ajayan, P. M. Chem. ReV. 1999, 99, 1787. (7) Odom, T. W.; Huang, J.-L.; Kim, P.; Lieber, C. M. J. Phys. Chem. B 2000, 104, 2794. (8) Tans, S. J.; Devoret, M. H.; Dai, H.; Thess, A.; Smalley, R. E.; Geerlings, L. J.; Dekker, C. Nature 1997, 386, 474. (9) Wong, S. S.; Harper, J. D.; Lansbury, P. T., Jr.; Lieber, C. M. J. Am. Chem. Soc. 1998, 120, 603. (10) Tans, S. J.; Verschueren, A. R. M.; Dekker, C. Nature 1998, 393, 49. (11) Fan, S.; Chapline, M.; Franklin, N.; Tombler, T.; Cassell, A.; Dai, H. Science 1999, 283, 512. (12) Kong, J.; Franklin, N. R.; Zhou, C.; Chapline, M. G.; Peng, S.; Cho, K.; Dai, H.; Science 2000, 287, 622. (13) Collins, P. G.; Bradley, K.; Ishigami, M.; Zettl, A. Science 2000, 287, 1801. (14) Kim, P.; Lieber, C. M. Science 1999, 286, 2148. (15) Baughman, R. H.; Cul, C.; Zakhidov, A. A.; Iqbal, Z.; Barisci, J. N.; Spinks, G. M.; Wallace, G. G.; Mazzoldi, A.; DeRossi, D.; Rinzler, A. G.; Jaschinski, O.; Roth, S.; Kertesz, M. Science 1999, 284, 1340. (16) Dillon, A. C.; Jones, K. M.; Bekkedahl, T. A.; Kiang, C. H.; Bethune, D. S.; Heben, M. J. Nature 1997, 386, 377. (17) Ye, Y.; Ahn, C. C.; Witham, C.; Fultz, B.; Liu, J.; Rinzler, A. G.; Colbert, D.; Smith, K. A.; Smalley, R. E. Appl. Phys. Lett. 1999, 74, 2307. (18) Lee, S. M.; An, K. H.; Lee, Y. H.; Seifert, G.; Frauenheim, T. J. Am. Chem. Soc. 2001, 123, 5059. (19) Cheng, H.; Pez, G. P.; Cooper, A. C. J. Am Chem. Soc. 2001, 123, 5845. (20) Hou, P.; Yang, Q.; Bai, S.; Xu, S.; Liu, M.; Cheng, H. J. Phys. Chem. B 2002, 106, 963. (21) Long, R. Q.; Yang, R. T. J. Am. Chem. Soc. 2001, 123, 2058. (22) Mao, Z.; Sinnott, S. B. J. Phys. Chem. B 2001, 105, 6916. (23) Fujiwara, A.; Ishii, K.; Suematsu, H.; Kataura, H.; Maniwa, Y.; Suzuki, S.; Achiba, Y. Chem. Phys. Lett. 2001, 336, 205. (24) Kuznetsova, A.; Yates, J. T., Jr.; Liu, J.; Smalley, R. E. J. Chem. Phys. 2000, 112, 9590. Nano Lett., Vol. 3, No. 1, 2003
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