C NMR Chemical Shifts of Infinite Single-Walled Carbon Nanotubes

Sep 25, 2008 - (4) Marinopoulos, A. G.; Reining, L.; Rubio, A.; Vast, N. Appl. Phys. A: Mater. Sci. Process. 2004, 78, 1157. (5) Weisman, R. B.; Bachi...
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J. Phys. Chem. C 2008, 112, 16417–16421

16417

First-Principles Calculation of 13C NMR Chemical Shifts of Infinite Single-Walled Carbon Nanotubes: New Data for Large-Diameter and Four-Helical Nanotubes Lin Lai,† Jing Lu,*,†,‡ Wei Song,† Ming Ni,† Lu Wang,† Guangfu Luo,† Jing Zhou,† Wai Ning Mei,‡ Zhengxiang Gao,*,† and Dapeng Yu† Mesoscopic Physics Laboratory, Department of Physics, Peking UniVersity, Beijing 100871, P. R. China, and Department of Physics, UniVersity of Nebraska at Omaha, Omaha, Nebraska 68182-0266 ReceiVed: May 30, 2007; ReVised Manuscript ReceiVed: July 24, 2008

By using the density functional theory method, we calculate the 13C NMR isotropic chemical shifts of the semiconducting and semimetallic infinite single-walled carbon nanotubes (SWNTs). We find that the 13C chemical shifts of SWNTs with the diameter smaller than 1.4 Å can be classified into two distinct groups according to their electronic structures: the semiconducting group and the semimetallic group. The chemical shifts of the semiconducting group decrease monotonously with the increasing nanotube diameter, and are 0-12 ppm strikingly larger than those of their semimetallic counterparts in the typical diameter range (1.05 ( 0.2 nm) of SWNTs produced by the common high-pressure CO decomposition method (HiPCO). The chemical shifts of the two groups overlap around the diameter of 1.4 Å. Then the chemical shift of the semimetallic group becomes larger than that of the similar-sized semiconducting group as the diameter is larger than 1.4 Å. The chemical shifts of the four examined helical SWNTs are very close to those of the zigzag SWNTs with similar diameters and electronic structures. Introduction Single-walled carbon nanotubes (SWNTs) have attracted enormous interest because of their considerable potential as building blocks of nanoscale electronics.1 One of the most striking features of SWNTs is that their electronic structures depend on the chirality and diameter.2 SWNTs are (1) metals when n ) m, (2) narrow-gap semimetals when n - m is a multiple of three, and (3) moderate-gap semiconductors otherwise, where (n, m) is the chiral index. A variety of techniques such as scanning tunneling microscopy (STM),3 optical adsorption,4 fluorescence spectroscopy,5 and Raman scattering6 have already been applied to the characterization of SWNT samples. Unfortunately, these techniques even in combination do not provide a full characterization.7 Thus, the development of alternative techniques is desired. 13C nuclear magnetic resonance (NMR) spectroscopy is one possible choice. As a fundamental prerequisite to exploit 13C NMR spectroscopy for characterization of SWNTs, the dependence of 13C NMR spectroscopy on the chirality and diameter has to be made clear. Using a tight-binding approximation (TBA) method and an infinite perfect SWNT model, Latil et al. predicted that the 13C shielding tensor of SWNTs solely depends on the electronic structure, nearly independent of the tube chirality and diameter.8 The semiconducting SWNTs have stronger diamagnetic shielding, and their isotropic shielding tensor is 11 ppm larger than that of metallic SWNTs. Therefore, they concluded that metallic and semiconducting SWNTs could be distinguished from 13C NMR spectroscopy. In sharp contrast, using the Hartree-Fock (HF) method in combination with a truncated tube model, Besley et al. found that the 13C chemical shifts decrease with increasing diameter (The chemical shift is reduced by 7 ppm when the * Corresponding authors. (J.L.) E-mail: [email protected]. (Z.G.) E-mail: [email protected]. † Peking University. ‡ University of Nebraska at Omaha.

diameter increases from 4.7 to 7.8 Å) but nearly independent of the electronic structure of SWNTs.7 The former calculation suffers from the unconfirmed reliability of the TBA method in calculating the chemical shifts for SWNT system while the latter suffers from unconfirmed reliability the STO-3G HF method and the convergence difficulty of the finite tube model. Apparently, only a combination of an ab initio method and an infinite perfect SWNT model can clarify this discrepancy. Very recently, two groups have studied the chemical shifts of zigzag (n,0) SWNTs by using a combined procedure of the density functional theory (DFT) method and an infinite perfect SWNT model. Marques et al.9 studied the semiconducting zigzag SWNTs with n ranging from 8 to 20, and they found that the chemical shifts of the semiconducting zigzag SWNTs decrease with the increasing diameter of the nanotubes. Zurek et al.10,11 studied both the semiconducting and semimetallic zigzag SWNTs with n ranging from 7 to 17, and they found that the chemical shifts of both the semimetallic and semiconducting SWNTs decrease with the increasing diameter and the chemical shifts of the semimetallic zigzag SWNTs are 5 ppm significantly smaller than those of similar diameter semiconducting zigzag SWNTs. However, whether this tendency is available in larger size range and whether the chirality affects the chemical shift remain unclear. In this article, we investigate 13C chemical shifts of both semiconducting and semimetallic infinite perfect zigzag (n, 0) SWNTs with n ranging from 7 to 21 and four chiral (i.e., (4,2), (6,2), (6,3), and (8,2)) SWNTs by using the similar combined scheme of Marques9 and Zurek et al.11 Our study reveals that the chemical shifts of the zigzag semimetallic SWNTs are smaller than those of the similar-sized zigzag semiconducting SWNTs at n < 18 but larger than those of the latter at n > 18. The chemical shift of SWNTs appears to be independent of the chirality.

10.1021/jp074180b CCC: $40.75  2008 American Chemical Society Published on Web 09/25/2008

16418 J. Phys. Chem. C, Vol. 112, No. 42, 2008

Lai et al.

TABLE 1: 13C NMR Isotropic Chemical Shift, δiso, Relative to TMS, of Several Small Molecules from Our Calculation and Previous Experiments TMS CH4 C6H6 graphene calculation 179.8 -7.7 136.8 188.1 -7 130.9 expt22

127.4 128

CO

CO2

CF4 CH3F

209.2 141.0 150.0 187.1 129.3 123.6

81.7 71.3

Methods The chemical shift probes the local magnetic field in a sample induced by a uniformly applied external magnetic field and can provide the detailed information of the chemical environment and metal-like properties of the sample. It is experimentally measured by comparing to a standard reference as 5 δ)5 σref 5, where 5 5 σ+K σ is the shielding tensor, contributed by orbital 5 is the Knight shift, which is a Fermi electronic magnetism, and K contact effect of electron spin and inherent to a metal.12 For 13C chemical shifts, the common reference is tetramethylsilane (TMS). In this study, we follow the scheme by Mauri9 using benzene as the reference. The isotropic chemical shift comparing to benzene is, δ(tube) ) σ(C6H6) - σ(tube) + δTMS(C6H6), where δTMS(C6H6) is the experimental value of the isotropic chemical shift for benzene compared to TMS. The isotropic Knight shift (Kiso) for metallic and semimetallic SWNTs is due to the small density of states at the Fermi level, and the calculated Kiso by using the DFT method for metallic and semimetallic SWNTs wider than 0.6 nm is as small as -2 to -1 ppm.13 A uniform external magnetic field B applied to a sample induces an electronic current density J(r). This current produces an induced magnetic field Bin(r),

Bin(r) )

1 c

∫ d3r′j(r′) × |rr--r′|r′3

(1)

The shield tensor 5 σ is defined as the ratio between the induced magnetic field and the external uniform applied magnetic field, T

Bin(r) ) σ(r)B

Figure 1. Dependence of the calculated 13C NMR isotropic shielding tensor (σiso) on the number of k-points along the tube axis direction of (a) the semimetallic (9,0) (squares) and semiconducting (7,0) (circles) zigzag SWNTs, (b) (12,0) SWNT using k-grid with (squares) and without (circles) the Γ point, and (c) (15,0) (squares), (18,0) (circles), and (21,0) (triangles). The k-grids always contain the Γ point unless specified.

(2)

We use the newly developed gauge-including projector augmented-wave (GIPAW) approach14-16 implemented in CASTEP17 package to calculate δiso of SWNTs. This approach allows us to calculate the all-electron related NMR properties from both the norm-conserving18,19 and ultrasoft20 pseudopotential-based scheme. The generalized gradient approximation (GGA) of PW9121 form to the exchange-correlation functional is employed in our calculations. High-resolution NMR experiments are often performed under isotropic averaging conditions such that only isotropic quantities are measured. Therefore, we focus on the isotropic part of the shielding tensor (δiso) of 13C for SWNTs. The macroscopic component σ(G ) 0) of the isotropic nuclear magnetic shielding is taken as -(4π/3)∑iRiiχ as implemented in the CASTEP, where χ is the macroscopic magnetic susceptibility and Rii is 2/3 due to the spherical shape of the macroscopic system. We examine a series of molecules to evaluate our calculation using the first-principles calculation and the GIPAW method, and the result is shown in Table 1. We find that a 390-eV ultrasoft pseudopotential plane-wave cutoff energy can achieve a good convergence within 0.1 ppm. With this cutoff energy, all the molecules are calculated using only the Γ point, and the single-layer graphene is calculated by using the 49 × 49 × 1 k-points mesh. All the structures are fully optimized until the force on each atom is smaller than 0.03 eV/Å before the chemical shielding is calculated. Our results are in agreement with the experiment22 as shown in Table 1. Then, we constructed

a hexagonal supercell with periodic boundary conditions for SWNTs, and the closest distance between the nearest atoms of the nearest tubes is set to be greater than 6 Å, so that the interaction between tubes is negligible. Both the atomic positions and the lattice constant along the tube axis of SWNTs are fully optimized with an ultrasoft pseudopotential plane-wave cutoff energy of 280 eV and a 1 × 1 × 6 Monkhorst-Pack k-points mesh.23 The force convergence criterion is 0.01 eV/Å. The chemical shift for the periodic system of SWNTs is very sensitive to the value of m of the 1 × 1 × m k-points grid in the Brillouin zone. We test the dependence of the 13C δiso of the (7,0) and (9,0) SWNTs on the value of m and plot the results in Figure 1a. The chemical shift of the semiconducting (7,0) SWNT converges faster than that of the semimetallic (9,0) SWNT. The 1 × 1 × 49 k-points mesh can achieve a convergence within 0.2 ppm for both tubes. For the larger semimetallic SWNTs, however, we encountered the same problem that Zurek et al. 10,11 found in a similar DFT calculation about SWNTs. The authors find that the calculated chemical shielding tensor of semimetallic SWNTs oscillates between odd and even k-points and take the average of the odd and even series to estimate the fully converged chemical shielding tensor. As a test, a set of k-points meshes with both odd and even number of k-points is used. One of them contains Γ point and another does not by shifting the origin of the k-points. The result of the dependence of the isotropic chemical shielding tensor on the number of the k-points is plotted in Figure 1b.We find that the isotropic chemical shielding tensor converges to different values with the increasing number of k-points. The calculated isotropic chemical shielding tensor still has a difference of about 9 ppm between the calculation using 79 k-points with and without the Γ point. Therefore, we attribute the convergence

Infinite Single-Walled Carbon Nanotubes

J. Phys. Chem. C, Vol. 112, No. 42, 2008 16419

TABLE 2: The Diameter (d), Band Gap (Eg), and 13C NMR Isotropic Chemical Shift (δiso) of SWNTs as a Function of Chiralitya (n, m)

d (nm)

Eg (eV)

δiso (ppm)

(7,0) (8,0) (9,0) (10,0) (11,0) (12,0) (13,0) (14,0) (15,0) (16,0) (17,0) (18,0) (21,0) (4,2) (6,2) (8,2) (6,3)

0.553 0.631 0.707 0.782 0.865 0.938 1.019 1.092 1.171 1.251 1.326 1.409 1.641 0.414 0.565 0.718 0.621

0.25 0.63 0.09 0.75 0.92 0.04 0.56 0.72 0.18 0.48 0.59 0.07 0.01 0.28 0.63 0.07 0.12

140.3 134.3 122.7 130.5 126.9 117.7 125.4 123.5 118.5 123.1 121.8 120.9 123.8 156.6 144.0 120.6 120.6

a The isotropic Knight shift is taken as Kiso ) -1.5 ppm for all the examined semimetallic SWNTs according to previous work.4 No simple relationship between the band gaps and chemical shifts is found. The values of the semimetallic SWNTs are averaged over the maximal neighboring odd and even k points.

problem to the inclusion of the Γ point in the k-points mesh during the calculation. In this study, we employ the scheme used by Zurek et al.11 to estimate the fully converged chemical shift because we cannot afford the cost for the converged computations. We carefully test the convergence of the isotropic chemical shift as shown in Figure 1a-c and use as many k-points as possible in the computation. It should be noticed that our reported results on small-gap semimetallic SWNTs may have an uncertainty of several ppm. As a result, we choose m ) 49 for the semiconducting SWNTs and m ) 71 for the semimetallic SWNTs in the calculation. The value of the chemical shift for semimetallic SWNTs is taken as the average of the shift with m ) 71 and m ) 72. Results and Discussion We present the calculated 13C isotropic chemical shifts δiso of the zigzag SWNTs in Table 2 and plot their dependence on the tube diameter in Figure 2. The shielding tensor of the reference benzene is calculated within the same level of theory. The checked semimetallic SWNTs have a diameter range of 0.7-1.6 nm, and we take Kiso ) -1.5 ppm for them according to the previous work.13 The δiso of SWNTs can be clearly classified into two main groups according to the electronic structure: the semiconducting group and the semimetal group. The δiso of the semiconducting zigzag group shows a monotonic decrease with increasing tube diameter and can be further classified into two minor groups with l ) 1 and l ) 2, respectively, where l ) mod(n - m, 3). This is in agreement with the two recent DFT+GIPAW calculations for the infinite semiconducting zigzag SWNTs.9,11 The chemical shifts δiso of each semiconducting zigzag group can be fitted to δiso ) A/dX + B, where d is the tube diameter, and A, B, and X are the fitting parameters. We obtain

δiso ) 9.7/d1.5 + 116.2, if l ) 1

(3)

6.9/d1.9 + 117.7, if l ) 2 In the limit of infinite diameter, the δiso of a semiconducting zigzag SWNT converges to 116.2 and 117.7 ppm, for l ) 1

and 2, respectively. The value is close to our calculated chemical shift of a graphene sheet of 121.5 ppm relative to benzene. The fitting curve of δiso for the l ) 1 group is about 1 ppm slightly larger than that of the l ) 2 group at the same size in the checked diameter range. In sharp contrast, the isotropic chemical shifts of the semimetallic zigzag SWNTs (l ) 0) initially decrease with increasing diameter and minimize around d ) 0.9 nm. Then they increase with the increasing diameter. The δiso of the (9,0), (15,0), (18,0), and (21,0) tubes is 5.0, 0.8, 3.2, and 6.1 ppm larger than that of the (12,0) SWNT, respectively. We cannot compute the chemical shift of metallic armchair SWNTs limited by the present GIPAW method. But the properties of metallic SWNTs appear quite similar to those of semimetallic SWNTs in many cases. For example, both metallic and semimetallic SWNTs have extremely large polarizability24,25 along the tube axis and similar isotropic Knight shift.12 People often do not make a distinction between the two species. We conjecture that δiso of metallic SWNTs can be ascribed to the semimetallic group. As reported by Zurek et al. previously,11 the semimetallic SWNTs generally have a stronger isotropic diamagnetic shielding and thus have a smaller isotropic chemical shift δiso than the semiconducting SWNTs for small-diameter SWNTs with d e 1.17 nm. The isotropic chemical shift of the (18,0) and (21,0) SWNT is not smaller than that of the semiconducting SWNTs with the diameter ranging from 1.41 to 1.64 nm in our study. It is still unclear about the chemical shift of SWNTs with the diameter larger than 1.64 nm for the computational reason. The δiso of the semimetallic SWNT is about 8 ppm smaller than that of the similar-sized semiconducting SWNT around d ) 0.7 nm. The chemical shift of the (21,0) SWNT is about 3 ppm larger than the similar diameter semiconducting SWNT. Our calculated difference in chemical shifts between the semiconducting and semimetallic SWNTs in the diameter range of 0.7-1.2 nm is somewhat different from that of Zurek et al.11 It may be due to differences of the exchange-correlation functional, the cutoff energy, the size of the supercell, and the relaxation of the structures used in the calculations. The calculated difference in δiso between the (9,0) (d ) 0.703 nm) and (10,0) (d ) 0.789 nm) SWNTs is 8 ppm; in contrast, the HF method in combination with the cluster model7 predicted that the difference in δiso between the (9,0) and (10,0) SWNTs is only 0.2 ppm.

Figure 2. The calculated 13C NMR isotropic chemical shift (δiso) of the zigzag (n ) 7-21) and four chiral (4,2), (6,2), (6,3), and (8,2) SWNTs as a function of the tube diameter (d). The solid black lines are the fits to l ) 1 and 2 zigzag SWNTs, respectively. The calculated δiso of an isolated graphene sheet is labeled as a black dashed line. The values of the semimetallic SWNTs are averaged over the maximal neighboring odd and even k points.

16420 J. Phys. Chem. C, Vol. 112, No. 42, 2008 In order to check the dependence of δiso on the chirality, we also calculate the isotropic chemical shifts of four chiral (4,2), (6,2), (6,3), and (8,2) SWNTs. As shown in Figure 2, the chemical shift of the semiconducting (4,2) and (6,2) tubes lies in the two fitting curves of the two semiconducting zigzag groups whereas that of the semimetallic (8,2) SWNT nearly coincides with that of the semimetallic zigzag (9,0) SWNT. The δiso of the semimetallic (6,3) SWNT with d ) 0.62 nm is about 12 ppm smaller than that of the similar-sized semiconducting (8,0) SWNTs with d ) 0.63 nm. Therefore, the chemical shift appears independent of the chirality but only dependent on the diameter and electronic structure. It is apparent that whether the electronic property of SWNTs can be resolved from the 13C isotropic chemical shift spectrum depends on the diameter distribution of the sample. The diameter distribution of SWNTs depends on the preparation method, carbon source, and catalyst. The common preparation methods include arc discharge, laser ablation, and chemical vapor deposition (CVD). In CVD method, one frequently used carbon source is CO (HiPCO), which can lead to thin tubes with a high quality. The peak position of the diameter of SWNTs produced by arc discharge and laser ablation lies typically in the range of 1-2 nm.26 The typical diameter distribution of SWNTs produced by the HiPCO method is 1.05 ( 0.2 nm.26,27 The chemical shifts of the semiconducting group are 122-129 ppm, centered around 126 ppm, in the diameter range of 1.05 ( 0.2 nm. These values are 0-12 ppm larger than those of their semimetallic counterparts (117-122 ppm), centered around 120 ppm. In principle, the high-resolution NMR measurement is capable to resolve semimetallic/metallic and semiconducting character of HiPCO SWNTs or SWNTs with a similar diameter distribution when the sample is in gas phase or solution phase where the interaction between SWNTs on 13C NMR spectrum is negligible. The major obstacle to measurement of 13C NMR spectrum for SWNTs is the remaining ferromagnetic and paramagnetic impurities, which lead to a very large broadening of the NMR signal. Despite this difficult, several groups have reported 13C NMR measurement of SWNTs. The measured δiso ranges from 116, 124, to 126 ppm.28-30 By removing the ferromagnetic impurities, the 13C NMR signal in solution phase was resolved in two overlapping components at 128 and 144 ppm.31 As pointed out previously, the peak positions of the semiconducting and metallic species are about 126 and 120 ppm, respectively, for SWNTs with d ) 1.05 ( 0.2 nm. If that sample has similar diameter distribution with HiPCO SWNTs, the theoretical peakto-peak separation of 6 ppm between the metallic and semiconducting SWNTs is quite smaller than the experimental value of 16 ppm.31 SWNTs are typically grown as mixtures of metallic and semiconducting tubes, which hurdles their widespread application. Recently, several methods have been developed to separate semiconducting and metallic SWNTs.32-34 The enrichment of metallic or semiconducting species was characterized by optical adsorption, Raman scattering, or electrical resistivity measurement. We point out that the metal-insulator ratio of the final separation product can be alternatively probed from the relative intensity of the high-resolution 13C NMR split signal if the sample has a diameter distribution of 1.05 ( 0.2 nm. Conclusions In summary, combining the first principles method and an infinite SWNT model, we reveal that the 13C NMR isotropic chemical shifts of SWNTs depend on both the electronic

Lai et al. structure and the diameter but appear independent of the chirality. The chemical shifts of the zigzag semimetallic SWNTs are smaller than those of the similar-sized zigzag semiconducting SWNTs at n < 18 but larger than those of the latter at n > 18 and coincide at n ) 18. In view of the difference of 0-12 ppm in the isotropic chemical shift between semimetallic/metallic and semiconducting species in the diameter range of 1.05 ( 0.2 nm, high-resolution 13C NMR technique is a promising experimental tool for distinguishing the electronic property of HiPCO SWNTs or other SWNTs in this size range. Acknowledgment. This work was supported by the NSFC (Grant Nos. 10774003, 10474123, 10434010, 90606023, and 20731160012), the National 973 Project (Nos. 2002CB613505 and 2007CB936200, MOST of China), 211, 985, and Creative Team Projects of MOE of China, and Nebraska Research Initiative (No. 4132050400). Our calculations were partially carried out in the HP Cluster of the Calculation Center of Science and Engineering of Peking University. References and Notes (1) Baughman, R. H.; Zakhidov, A. A.; de Heer, W. A. Science 2002, 297, 787. (2) Hamada, N.; Sawada, S.-i.; Oshiyama, A. Phys. ReV. Lett. 1991, 68, 1579. (3) Wildoer, J. W. G.; Venema, L. C.; Rinzler, A. G.; Smalley, R. E.; Dekker, C. Nature 1998, 391, 59. (4) Marinopoulos, A. G.; Reining, L.; Rubio, A.; Vast, N. Appl. Phys. A: Mater. Sci. Process. 2004, 78, 1157. (5) Weisman, R. B.; Bachilo, S. M.; Tsyboulski, D. Appl. Phys. A: Mater. Sci. Process. 2004, 78, 1111. (6) Dresselhaus, M. S.; Dresselhaus, G.; Saito, R.; Jorio, A. Phys. Rep. 2005, 409, 47. (7) Besley, N. A.; Titman, J. J.; Wright, M. D. J. Am. Chem. Soc. 2005, 127, 17948. (8) Latil, S.; Henrard, L.; Bac, C. G.; Bernier, P.; Rubio, A. Phys. ReV. Lett. 2001, 86, 3160. (9) Marques, M. A. L.; D’Avezac, M.; Mauri, F. Phys. ReV. B 2006, 73, 125433. (10) Zurek, E.; Autschbach, J. J. Am. Chem. Soc. 2004, 126, 13079. (11) Zurek, E.; Pickard, C. J.; Walczak, B.; Autschbach, J. J. Phys. Chem. A 2006, 110, 11995. (12) Knight, W. D. Phys. ReV. 1949, 76, 1259. (13) Yazyev, O. V.; Helm, L. Phys. ReV. B 2005, 72, 245416. (14) Mauri, F.; Pfrommer, B. G.; Louie, S. G. Phys. ReV. Lett. 1996, 77, 5300. (15) Mauri, F.; Pfrommer, B. G.; Louie, S. G. Phys. ReV. B 1999, 60, 2941. (16) Pickard, C. J.; Mauri, F. Phys. ReV. B 2001, 63, 245101. (17) Milman, V.; Winkler, B.; White, J. A.; Pickard, C. J.; Payne, M. C.; Akhmatskaya, E. V.; Nobes, R. H. Int. J. Quantum Chem. 2000, 77, 895. (18) Lin, J. S.; Qteish, A.; Payne, M. C.; Heine, V. Phys. ReV. B 1993, 47, 4174. (19) Rappe, A. M.; Rabe, K. M.; Kaxiras, E.; Joannopoulos, J. D. Phys. ReV. B 1990, 41, 1227. (20) Vanderbilt, D. Phys. ReV. B 1990, 41, R7892. (21) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671. (22) Jameson, A. K.; Jameson, C. J. Chem. Phys. Lett. 1987, 134, 461. (23) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (24) Benedict, L. X.; Louie, S. G.; Cohen, M. L. Phys. ReV. B 1995, 52, 8541. (25) Kozinsky, B.; Marzari, N. Phys. ReV. Lett. 2006, 96, 166801. (26) Dresselhaus, M. S.; Eklund, P. C. AdV. Phys. 2000, 49, 705. (27) Samsonidze, G. G.; Chou, S. G.; Santos, A. P.; Brar, V. W.; Dresselhaus, G.; Dresselhaus, M. S.; Selbst, A.; Swan, A. K.; Unlu, M. S.; Goldberg, B. B.; Chattopadhyay, D.; Kim, S. N.; Papadimitrakopoulos, F. Appl. Phys. Lett. 2004, 85, 1006. (28) Goze-Bac, C.; Latil, S.; Lauginie, P.; Jourdain, V.; Conard, J.; Duclaux, L.; Rubio, A.; Bernier, P. Carbon 2002, 40, 1825. (29) Hayashi, S.; Hoshi, F.; Ishikura, T.; Ohshima, S. Carbon 2003, 41, 3047. (30) Tang, X. P.; Kleinhammes, A.; Shimoda, H.; Fleming, L.; Bennoune, K. Y.; Sinha, S.; Bower, C.; Zhou, O.; Wu, Y. Science 2000, 288, 492.

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J. Phys. Chem. C, Vol. 112, No. 42, 2008 16421 J.; Zhang, X. W.; Gao, Z. X.; Yu, Y. P.; Nagase, S.; Kazaoui, S.; Minami, N.; Shimizu, T.; Tokumoto, H.; Saito, R. J. Am. Chem. Soc. 2005, 127, 10287. (34) Arnold, M. S.; Green, A. A.; Hulvat, J. F.; Stupp, S. I.; Hersam, M. C. Nat. Nanotechnol. 2006, 1, 60.

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