Matrix-Imposed Stress-Induced Shifts in the Photoluminescence of

materials.1-6 The PL emission and excitation spectra show characteristic peaks corresponding to optical interband transitions between van Hove sin...
0 downloads 0 Views 302KB Size
Download PDF
NANO LETTERS

Matrix-Imposed Stress-Induced Shifts in the Photoluminescence of Single-Walled Carbon Nanotubes at Low Temperatures

2004 Vol. 4, No. 12 2349-2354

Katharina Arnold,†,‡ Sergei Lebedkin,*,† Oliver Kiowski,†,‡ Frank Hennrich,† and Manfred M. Kappes†,‡ Forschungszentrum Karlsruhe, Institut fu¨r Nanotechnologie, D-76021 Karlsruhe, Germany, and Institut fu¨r Physikalische Chemie, UniVersita¨t Karlsruhe, D-76128 Karlsruhe, Germany Received August 24, 2004; Revised Manuscript Received October 11, 2004

ABSTRACT Photoluminescence spectra of water−surfactant dispersions of semiconducting single-walled carbon nanotubes (SWNTs) show large shifts of interband transition energies upon freezing and cooling the dispersions to 16 K. This is accompanied by an increase of the emission intensities up to ∼10 times in the presence of poly(vinylpyrrolidone). The shifts develop mainly in the temperature interval of ∼100−240 K and are reversible by cycling the temperature. Two groups of nanotubes classified by the value of (n-m) mod 3, where n,m are structure indices, demonstrate opposite shifts, the largest ones from nanotubes with small chiral angles. The experimental data agree well with calculations of Yang et al. [Phys. Rev. B 1999, 60, 13874] for SWNTs under axial compression and indicate that large stresses of up to ∼5 GPa are generated in individual nanotubes by thermal contraction of the ice matrix.

The near-infrared photoluminescence (PL) spectroscopy of semiconducting single-walled carbon nanotubes (SWNTs) has recently been established as a powerful method to gain information about electronic properties of these onedimensional carbon based structures and to characterize different SWNT materials.1-6 The PL emission and excitation spectra show characteristic peaks corresponding to optical interband transitions between van Hove singularities in the valence and conductance zones of semiconducting nanotubes.7 The emission peak corresponds to the transition across the band gap at energy E11, whereas the excitation resonances correspond to E11 and higher interband transitions at energies E22, E33,...Usually, pairs of E11 and E22 emission-excitation resonances are measured since they are the most characteristic and can be reliably assigned to nanotubes with a specific structure, i.e., with a specific diameter and chirality, described by two integer indexes (n,m).2 SWNTs emit light in the nearinfrared spectral range with a quantum yield of ∼10-3 as has been estimated from ensemble measurements of nanotubes dispersed (debundled) in water-surfactant solutions at room temperature.2,8 Despite this moderate efficiency inferred so far for ensembles, PL from single semiconducting SWNTs is readily detectable by using laser microscopy techniques.4,6 Very recently, Klimov et al.9 and Lefebvre et al.10 have extended PL studies of individual nanotubes deposited/grown * Corresponding author. E-mail: [email protected]. † Forschungszentrum Karlsruhe. ‡ Universita ¨ t Karlsruhe. 10.1021/nl048630c CCC: $27.50 Published on Web 10/29/2004

© 2004 American Chemical Society

on a surface to low temperatures down to 4 K. Many new features have been revealed, including, for instance, extremely narrow single-species emission peaks (with line widths less than 1 meV compared to ∼25 meV for ensemble measurements at room temperature), local environmental effects and appearance of new, presumably phonon coupled, PL bands.9,10 Interestingly, however, only a moderate temperature dependence of E11 and E22 energies as well as of the PL intensity has been found. In this work, we investigated temperature effects on the photoluminescence of bulk water-surfactant dispersions of SWNTs upon freezing and cooling to 16 K.11 In contrast to surface-deposited nanotubes,9,10 large and (n,m)-dependent shifts of the PL emission-excitation peaks were observed at temperatures below ∼240 K. The signs and relative magnitudes of the E11 and E22 shifts agree well with calculations of Yang et al. for SWNTs under axial stress applied along the nanotube.12,13 We therefore attribute the PL shifts entirely to the external matrix effect, namely, to axial compressive stress generated in nanotubes by thermal contraction of the ice matrix. This stress is analogous to residual thermal stresses in bulk (bundled) SWNT-polymer composites studied by Lourie and Wagner14 and other researchers15-17 by means of Raman spectroscopy. However, in contrast to those Raman studies, the PL spectroscopy reported here yields unique information about stress influence on the electronic structure of individual (debundled) (n,m) nanotubes. This in turn provides an excellent test for relevant theoretical models. As will be discussed below, our PL data

Figure 1. Photoluminescence maps (emission intensity versus excitation and emission wavelengths) of HiPco (A, B) and PLV (C, D) nanotube dispersions in D2O/1 wt % SDBS/3 wt % PVP at room temperature (A, C) and after freezing and cooling to 16 K (B, D). The emission intensities (right color bars, arb. units) of PLV and HiPco nanotubes are normalized for better comparison and are shown on the same scale for both temperatures. The maps are corrected for the wavelength-dependent excitation intensity (in relative photon flux units), but not for instrumental response of the FTIR spectrometer and detector. The stripe * in D is an artifact due to a ghost line from the near-infrared excitation light source (not observed in C because of much lower scattering from the fluid sample).

suggest that axial compression stresses of individual nanotubes in frozen and cooled dispersions can be as high as ∼5 GPa. Such large matrix-imposed stresses and their influence on the electronic properties of SWNTs are not only of fundamental interest but might also have implications for possible applications of carbon nanotubes. Samples of SWNTs used in this study were produced at Rice University by high-pressure catalytic decomposition of carbon monoxide (HiPco nanotubes18) and in our lab by pulsed laser vaporization of C:Ni:Co targets (PLV nanotubes).19,20 Nanotube diameters ranged from ∼0.7 to ∼1.2 nm and from ∼1.0 to ∼1.4 nm for HiPco and PLV materials, respectively. Raw nanotubes were dispersed by powerful sonication in D2O containing 1 wt % of sodium dodecylbenzene sulfonate (SDBS) surfactant. The resulting suspensions were centrifuged for 2-4 h at 150.000 g in order to separate individual micelle-stabilized nanotubes from the majority of denser bundles and metal catalyst particles. Typical average lengths of such dispersed HiPco and PLV nanotubes were found to be ∼200-300 nm and ∼0.8-1 µm, respectively, according to AFM analysis of spin-coated 2350

substrates. Photoluminescence spectra were measured in a closed-cycle optical cryostat (Leybold) attached to an FTIR spectrometer (Bruker 66/S) equipped with a liquid nitrogen cooled germanium detector and monochromatized light sources based on xenon and tungsten halogen lamps for PL excitation.8 Fluid samples were loaded into the cryostat in a thin “cuvette” comprising two quartz disks sealed with an O-ring. Typical cooling/heating rates were 5-10 K/min. Measurement of a PL map (Figure 1) took ∼0.5-2 h at each temperature. We found that cooling of water-surfactant dispersions of SWNTs down to a freezing temperature is accompanied by a significant decrease of the PL intensities, in particular for nanotubes with higher band gap energies, and by a broadening of the emission peaks. These effects can be attributed to aggregation of individually dispersed nanotubes, resulting initially in the formation of small bundles. It is known that bulk SWNT materials containing large bundles (ropes) of tens to hundreds of nanotubes do not luminesce, presumably because of fast energy transfer and electronic relaxation in metallic nanotubes.1,8 However, small bundles consisting of Nano Lett., Vol. 4, No. 12, 2004

only a few semiconducting nanotubes may still luminesce. Their emission is expected to be broader and on average red-shifted as compared to individual nanotubes due to intertube interactions and energy transfer to smaller band gap nanotubes emitting at longer wavelengths, in accordance with our observations. Aggregation into bundles requires diffusion of nanotubes. This can be reduced either by fast freezing of dispersions by immersion into a liquid nitrogen optical dewar (with measurement temperature limited to 77 K), or, more conviniently, by using viscosity-enhancing additives. For the latter purpose, we have tested several water-soluble polymers, including poly(vinylpyrrolidone) (PVP), poly(vinyl alcohol), and sodium carboxymethylcellulose, as well as polysaccharides, including starch. The best results were obtained with PVP (∼1-5 wt %). Only a moderate degradation of the PL was observed after stirring PVP into a nanotube dispersion and after several subsequent freeze-thaw cycles. The pronounced effect of PVP is very likely due not only to an increase of the dispersion viscosity but also to noncovalent association (wrapping) between this linear polymer and SWNTs in aqueous solutions as studied by O’Connell et al.21 PL spectroscopy provides additional evidence for such an interaction between PVP and nanotubes. The PL peaks of SWNTs dispersed in D2O/SDBS show nearly uniform red shifts of approximately -1% and -0.3% for E11 and E22 energies, respectively, upon addition of 5 wt % PVP at room temperature. The uniform shifts suggest that the interaction is not (n,m) selective. No shifts of PL peaks were found for the other viscosity-increasing additives tested. Figure 1 presents photoluminescence maps of PL intensity as a function of emission and excitation wavelengths for HiPco and PLV nanotubes dispersed in D2O/SDBS/PVP and excited in the E22 energy range at room temperature and at 16 K. Large and nonuniform shifts of the PL peaks, changes of their shapes and enhancements of their intensities are clearly seen in Figure 1. These effects developed mostly in the temperature interval of ∼100-240 K. They were synchronously observed for PL peaks corresponding to different (n,m) nanotubes. All such changes were completely reversible by cycling the temperature several times between 16 and 200 K. We note that similar PL shifts as in Figure 1 were also found for frozen nanotube dispersions prepared with another surfactant (sodium dodecyl sulfate), with the other viscosity-increasing additives (+SDBS), as well as for a D2O/SDBS dispersion quickly cooled by immersion into liquid nitrogen. In the latter cases, however, the emission peaks were broader and weaker, which can be attributed to nanotube aggregation as discussed above. Figure 2 shows a correlation of the PL shifts with the (n,m) structure indices of semiconducting nanotubes assigned from the PL data at room-temperature according to Weisman et al.2 The corresponding E11 and E22 energies and shifts are listed in Table 1. There are apparently two groups of nanotubes classified by the value (n-m) mod 3 ) 1 or 2.22 The first group manifests a decrease of E11 and an increase of E22 upon cooling of frozen dispersions, whereas the second group shows the opposite trends. The relative magnitude of Nano Lett., Vol. 4, No. 12, 2004

Figure 2. Shifts of the photoluminescence emission-excitation resonances of SWNTs dispersed in D2O/1 wt % SDBS/3 wt % PVP observed upon decreasing the temperature (see Figure 1) and their correlation to (n,m) structure indices of nanotubes. Two groups of nanotubes classified by different values of (n-m) mod 3 show opposite shifts of different magnitudes as depicted with blue and red arrows. Table 1. Electronic Energies E11 and E22 Obtained from Photoluminescence Maps of (n,m) Nanotubes Dispersed in D2O/ SDBS/PVP at Room Temperature and Stress-Induced Energy Shifts after Freezing and Cooling the Dispersions to 16 K na

ma

E11, eV c

E22, eV c

8 6 7 10 9 8 7 8 11 9 10 8 9 12 11 12 10 11 9 15 10 13 13 12 11 12 10 11

3 5 5 2 4 4 6 6b 3b 5 5b 7b 7b 4 4 2 6b 6 8b 1 8 5 3 5 7 7 9 9

1.290 1.258 1.200 1.163 1.111 1.103 1.093 1.044 1.022 0.983 0.979 0.969 0.927 0.915 0.892 0.891 0.888 0.877 0.867 0.849 0.833 0.824 0.821 0.820 0.807 0.792 0.787 0.762

1.862 2.175 1.914 1.673 1.706 2.098 1.908 1.719 1.554 1.832 1.566 1.694 1.558 1.444 1.717 1.795 1.627 1.440 1.531 1.336 1.424 1.335 1.627 1.550 1.471 1.324 1.390 1.308

∆E11, meV

∆E22, meV

-37 9 -20 -58 -43 29 8 -16 -59 27 -34 10 -13 -39 40 48 30 -27 8 -52 -13 -35 42 41 26 -28 8 -8

23 -23 6 38 28 -36 -15 11 45 -41 25 -9 9 28 -51 -65 -33 22 -6 45 11 35 -60 -45 -25 23 -6 16

θ, degd 15.3 27.0 24.5 8.9 17.5 19.1 27.5 25.3 11.7 20.6 19.1 27.8 25.9 13.9 14.9 7.6 21.8 20.4 28.1 3.2 26.3 15.6 10.2 16.6 22.7 21.4 28.3 26.7

a (n,m) Assignment according to ref 2. b Common nanotubes in dispersions of HiPco and PLV materials. c Determined to an accuracy of (0.1%. d Chiral angles of the nanotubes.

the shift apparently depends on the chirality of nanotubes. The smallest shifts, ∆E, were measured for (n,n-1) nano2351

tubes having a large chiral angle, θ, close to that of “armchair” (n,n) nanotubes (θ ) 30°). These are, for instance, (8,7) and (10,9) nanotubes (see Figure 2 and Table 1). On the other hand, the largest shifts are associated with nanotubes having a small chiral angle close to that of “zigzag” (n,0) nanotubes (θ ) 0°). For instance, (15,1) nanotubes (θ ) 3.2°) show remarkably large shifts of ∆E11 ) +6.2% and ∆E22 ) -3.3%. Note that there are several common (n,m) nanotubes in dispersions of HiPco and PLV materials (Figure 1 and Table 1). In both dispersions these nanotubes demonstrated the same PL shifts. Both the observed (n-m) mod 3 rule for the signs of E11, E22 shifts and the chiral angle dependence found for the magnitudes of E11, E22 shifts are consistent with tight-binding model calculations by Yang et al.12,13 These authors determined electronic structure of SWNTs under axial strain . Their results for a relatively small strain can be summarized as follows: (i) dE11/d is positive for SWNTs satisfying (nm) mod 3 ) 1 and negative for (n-m) mod 3 ) 2 (because of different “shifts” of electronic bands relative to the K-vertices in the Brillouin zone under axial strain deformation); (ii) |dE11/d| increases with decreasing chiral angle; and (iii) dE22/d and dE11/d have opposite signs.12,13 The importance of the (n-m) mod 3 rule and chirality has also been shown in other tight-binding model studies of axially deformed nanotubes.17,23,24 Conclusions i-iii agree perfectly with our experimental data, if axial compression ( < 0) with similar strain for all (n,m) nanotubes is assumed. This agreement alone strongly suggests thermomechanical compressive stress as the reason for the PL energy shifts in frozen SWNT dispersions. Note that the calculations predict different energy shifts for torsional strain in nanotubes.12,13,24 Recently, Wu et al. have investigated the effect of hydrostatic pressure on absorption spectra of dispersed SWNTs in a diamond anvil cell.25 These authors have found (n,m)dependent, but in general negative, shifts of E11 and E22 energies upon increasing the pressure. We conclude that the energy shift pattern is quite sensitive to the type of nanotube strain. In the case of axial strain, the dependence of the emission energy shift ∆E11 on a chiral angle θ is given by13 |∆E11| ) 3t0 || (1 + ν) cos3θ

(1)

where t0 ≈ 3 eV is the tight-binding overlap integral7 and ν ≈ 0.2 is the Poisson ratio.26,27 The experimental data are satisfactorily described by eq 1, as shown in Figure 3. According to eq 1, the maximum shift of the emission (band gap) energy per 1% strain is ∼110 meV. The observed maximum value ∆E11 ≈ 60 meV corresponds then to a strain of ∼0.5%. A similar value was estimated from a comparison of the PL data with ∆E22 values calculated by Lucas et al.17 for different semiconducting nanotubes using the same approach as that of Yang et al. For the axial Young’s modulus of SWNTs, ENT ≈ 1 TPa,26,27 this strain corresponds to an axial compression of ∼5 GPa. The largest change of E11 with respect to stress, which was observed for nanotubes with small chiral angles, is ∼12 meV/GPa. 2352

Figure 3. Shifts of E11 emission energy as a function of a nanotube chiral angle, θ (see Table 1). The straight line shows the linear behavior predicted by tight-binding model calculations for SWNTs under axial strain (refs 12, 13).

The origin of the high axial stress of individual SWNTs embedded in a frozen dispersion is analogous to residual thermal stresses in cooled carbon fiber-polymer28,29 or SWNT bundles-polymer composites.14-17 In both cases the axial stress is due to a large mismatch of the thermal expansion coefficients of carbon fibers (∼2 × 10-6 K-1)29 or SWNTs (negative axial expansion up to ∼900 K with the coefficient of -(1-10) × 10-6 K-1 at 300 K has been predicted)30,31 and an ice or polymer matrix (∼50 × 10-6 K-1 below a freezing/glass transition point).32,29 Still, the analogy is not straightforward because of the very different characteristic diameters of the fibers concerned: ∼1 nm for individual nanotubes compared to ∼20 nm for SWNT bundles and ∼10 µm for carbon fibers. Stable and reversible PL shifts suggest that (i) there is a firm bond (no creep) between a nanotube and the surrounding ice matrix below ∼240 K and (ii) both a nanotube and the matrix show elastic thermomechanical behavior. Furthermore, the sharpness of PL peaks of stressed nanotubes (Figure 1) indicates that (iii) the matrix is isotropic and (iv) the strain is uniform along nanotubes (negligible effect of nanotube ends) and over ensembles of (n,m) nanotubes. The condition (iii) is probably contributed by high concentrations of PVP in a dispersion, which is known to hinder ice crystallization in favor of amorphous ice structure. The condition (iv) presumes an extended, only moderately bent geometry of nanotubes in a fluid/frozen dispersion, in accordance with neutron spectroscopy results of Zhou et al.33 Pure bending deformation has been calculated to only slightly change the interband transition energies of SWNTs due to compensation of the stretching and compression effects.14,34 However, a strongly bent fragment of a nanotube embedded in a contracting matrix is expected to experience different and nonuniform axial deformation with regard to its straight counterpart. Using a simple continuum mechanics model for a long nanotube firmly embedded in the ice matrix, axial strain  Nano Lett., Vol. 4, No. 12, 2004

Figure 4. Temperature dependence of the relative emission intensity and E11 energy shift for (9,8) and (9,5) nanotubes, respectively. The step-like increase of the emission intensity at ∼265 K corresponds to the freezing of the nanotube dispersion in D2O/ SDBS/PVP and is due to a scatter enhanced photoexcitation of nanotubes in the ice matrix. The solid line shows an approximate temperature dependence of the linear thermal expansion coefficient, R, of polycrystalline ice (H2O, ref 32). Note that R is negative and the energy shift is reversed below ∼50 K.

and stress σA transferred from the matrix to the nanotube are given by14  ≈ (R - RNT) ∆T;

σA ≈ (R - RNT) ∆T ENT

(2)

where R and RNT are temperature-dependent thermal expansion coefficients of the matrix and the nanotube, respectively. ∆T is the temperature gradient, and ENT is an axial Young’s modulus of the nanotube. The contracting matrix also applies a stress component normal to the nanotube axes, σN. This component is equal to the stress in the matrix:15 σN ≈ (R - RNT) ∆T EM ≈ σA (EM/ENT)

(3)

where EM is a Young’s modulus of the matrix. In the case of SWNTs (ENT ≈ 1 TPa)26,27 embedded in the ice matrix (EM e 10 GPa),32 the normal stress component is therefore negligible compared to the axial one. In this simple model we neglect an intermediate layer of surfactant/PVP molecules around nanotubes. This layer likely plays an important role for the “binding” of nanotubes to the ice matrix. On the other hand, its composition seems to be not so important for the overall matrix contraction effect: as pointed out above, similar energy shifts were observed with different surfactants, without addition of PVP and by different cooling regimes. According to eq 2, since R > RNT from a freezing point down to ∼60 K,30-32 the temperature dependence of nanotube strain and, consequently, of PL shifts is mainly determined by the thermal expansion coefficient of the ice matrix, R. This is illustrated in Figure 4 by a comparison between a representative temperature dependence of the E11 energy shift for (9,5) nanotubes and the thermal expansion curve for polycrystalline H2O ice.32 We assume that this curve approximately describes the thermal expansion of the actual Nano Lett., Vol. 4, No. 12, 2004

D2O/SDBS/PVP ice matrix as well. Upon decreasing the temperature, significant energy shifts start to develop at ∼240 K (corresponding probably to complete freezing of an interface layer around the nanotubes) and then follow the thermal contraction of the ice matrix (Figure 4). Additional striking evidence for the coupling of the matrix thermal contraction/expansion to nanotube strain is a reversal of the energy shifts below ∼50 K where the thermal expansion coefficient of ice is known to be negative.32 The reversal of the shifts indicates also that the negative thermal expansion of ice in this temperature region (R ≈ -5 ×10-6 K-1 at 25 K)32 surmounts the negative thermal expansion of SWNTs, in accordance with calculations of Kwon et al.31 The total linear contraction of the ice matrix upon cooling from 250 to 16 K is about 0.5%, which is in accordance with the nanotube strain estimated from eq 1. Figure 4 also shows another intriguing observation, namely, a significant increase of the emission intensity for specific nanotubes in frozen D2O/SDBS/PVP dispersions upon decreasing the temperature to 16 K. The increase of emission intensity was found to be (n,m)-dependent and most pronounced for (n,n-1) nanotubes, i.e., for nanotubes with small energy shifts. For instance, the maximum PL signal of (9,8) nanotubes increased ∼10 times from 260 K (just below the freezing point at ∼265 K) to 16 K, and ∼2 times from 100 to 16 K (Figure 4). Note that this curve does not correlate closely with the temperature dependence of the energy shifts (shown in Figure 4 for (9,5) nanotubes). On the other hand, the PL intensity of (10,2) nanotubes increased only ∼2.5 times from 260 to 100 K and practically leveled off below 100 K (not shown). The reasons for such (n,m)dependent increase of emission intensity of different (n,m) nanotubes in frozen dispersions and a possible contribution of the axial strain and interactions of nanotubes with PVP molecules are not clear at the moment. Important additional information might be provided by time-resolved PL measurements at low temperatures. The PL decay for dispersed SWNTs at room-temperature proceeds on the time scale of ∼30 ps and presumably does not show a significant (n,m)dependence.35,36 With our apparatus, using low power N2laser pulses for excitation and a near-infrared Hamamatsu photomultiplier for detection, we estimated that the PL decay at 16 K is still much faster than ∼1 ns. Another interesting feature in the photoluminescence of SWNT dispersions at low temperatures is the asymmetric shape of the emission peaks which generally show a steep high-energy edge and a long low-energy tail. This is especially pronounced for HiPco nanotubes, not so much for PLV nanotubes (Figure 1B,D). Emission peaks having similar shapes have been observed by Klimov et al. for surface-deposited HiPco nanotubes below ∼50 K and have been tentatively ascribed to exciton interactions with accidental dopants, such as oxygen molecules, adsorbed in low concentrations on nanotubes.9 Surfactant and PVP molecules associated with nanotubes in dispersions as well as structural defects in nanotubes (+ends) might also play the role of such dopants. Because of the similar dispersion procedure, one can speculate that the reason PLV nanotubes demonstrate 2353

more symmetric emission peaks is that they have a lower effective defect density than HiPco material. This issue, like the (n,m)-dependent increase of PL intensities, requires further investigation. In conclusion, we have found that frozen aqueous dispersions of (debundled) SWNTs can be considered as nanoscaled “composites”, in which individual nanotubes are firmly bound to the ice matrix. Because of a mismatch of the thermal expansion coefficients, the nanotubes undergo large axial strain deformation of ∼0.5% corresponding to a stress of ∼5 GPa upon freezing and cooling the dispersions from room temperature to 16 K. The strain results in large shifts of E11 and E22 electronic energies which are readily observed in the photoluminescence spectra of semiconducting SWNTs. The signs and relative magnitudes of the energy shifts depend on the structure and chirality of nanotubes and agree well with tight-binding model calculations of Yang et al. for SWNTs under axial stress.12,13 This agreement shows that the simple tight-binding model can successfully predict changes in the electronic structure of elastically deformed nanotubes. The matrix-imposed stress-induced PL shifts can be employed to determine thermal expansion of individual (n,m) nanotubes and to verify the theoretical predictions of the unusual negative thermal expansion of SWNTs.31 This would require, however, better accuracy of the energy shift measurements and/or another matrix with a lower thermal expansion than in the present study. Acknowledgment. This work was supported by the Deutsche Forschungsgemeinschaft and by the BMBF. The authors are grateful to Prof. R. E. Smalley for a sample of HiPco nanotubes. References (1) O’Connell, M. J.; Bachilo, S. M.; Huffman, C. B.; Moore, V. C.; Strano, M. S.; Haroz, E. H.; Rialon, K. L.; Boul, P. J.; Noon, W. H.; Kittrell, C.; Ma, J.; Hauge, R. H.; Weisman, R. B.; Smalley, R. E. Science 2002, 297, 593. (2) Bachilo, S. M.; Strano, M. S.; Kittrell, C.; Hauge, R. H.; Smalley, R. E.; Weisman, R. B. Science 2002, 298, 2361. (3) Lefebvre, J.; Homma, Y.; Finnie, P. Phys. ReV. Lett. 2003, 90, 217401. (4) Hartschuh, A.; Pedrosa, H. N.; Novotny, L.; Krauss, T. D. Science 2003, 301, 1354. (5) Lebedkin, S.; Hennrich, F.; Skipa, T.; Kappes, M. M. J. Phys. Chem. B 2003, 107, 1945.

2354

(6) Lefebvre, J.; Fraser, J. M.; Finnie, P.; Homma, Y. Phys. ReV. B 2004, 69, 075403. (7) Saito, R.; Dresselhaus, G.; Dresselhaus, M. S. Physical Properties of Carbon Nanotubes; Imperial College Press: London, 1998. (8) Lebedkin, S.; Arnold, K.; Hennrich, F.; Krupke, R.; Renker, B.; Kappes, M. M. New J. Phys. 2003, 5, 140. (9) Htoon, H.; O’Connell, M. J.; Cox, P. J.; Doorn, S. K.; Klimov, V. I. Phys. ReV. Lett. 2004, 93, 027401. (10) Lefebvre, J.; Finnie, P.; Homma, Y. ArxiV.org/pdf/cond-mat/0403715, 2004. (11) some results of this work were presented at the IWEPNM 2004. (12) Yang, L.; Anantram, M. P.; Han, J.; Lu, J. P. Phys. ReV. B 1999, 60, 13874. (13) Yang, L.; Han, J. Phys. ReV. Lett. 2000, 85, 154. (14) Lourie, O.; Wagner, H. D. J. Mater. Res. 1998, 13, 2418. (15) Wood, J. R.; Frogley, M. D.; Meurs, E. R.; Prins, A. D.; Peijs, T.; Dunstan, D. J.; Wagner, H. D. J. Phys. Chem. B 1999, 103, 10388. (16) Hadjiev, V. G.; Iliev, M. N.; Arepalli, S.; Nikolaev, P.; Files, B. S. Appl. Phys. Lett. 2001, 78, 3193. (17) Lucas, M.; Young, R. J. Phys. ReV. B 2004, 69, 085405. (18) Guo, T.; Nikolaev, P.; Thess, A.; Colbert, D. T.; Smalley, R. E. Chem. Phys. Lett. 1995, 243, 49. (19) Bronikowski, M. J.; Willis, P. A.; Colbert, D. T.; Smith, K. A.; Smalley, R. E. J. Vac. Sci. Technol. A 2001, 19, 1800. (20) Lebedkin, S.; Schweiss, P.; Renker, B.; Malik, S.; Hennrich, F.; Neumaier, M.; Stoermer, C.; Kappes, M. M. Carbon 2002, 40, 417. (21) O’Connell, M. J.; Boul, P.; Ericson, L. M.; Huffman, C.; Wang, Y.; Haroz, E.; Kuper, C.; Tour, J.; Ausman, K. D.; Smalley, R. E. Chem. Phys. Lett. 2001, 342, 265. (22) p ) (n-m) mod 3 is defined here as n - m ) 3q + p, where q is an integer and p ) 0, 1, 2. Statistically, two-thirds of nanotubes (p ) 1, 2) are semiconducting, one-third (p ) 0) is metallic and nonluminescent. (23) Heyd, R.; Charlier, A.; McRae, E. Phys. ReV. B 1997, 55, 6820. (24) Ding, J. W.; Yan, X. H.; Liu, C. P.; Tang, N. S. Chin. Phys. Lett. 2004, 21, 704. (25) Wu, J.; Walukiewicz, W.; Shan, W.; Bourret-Courchesne, E.; Ager, J. W., III; Yu, K. M.; Haller, E. E.; Kissell, K.; Bachilo, S.; Weisman, R. B.; Smalley, R. E. Phys. ReV. Lett. 2004, 93, 017404. (26) Reich, S.; Thomsen, C.; Ordejo´n, P. Phys. ReV. B 2002, 65, 153407. (27) Jin, Y.; Yuan, F. G. Comput. Sci. Technol. 2003, 63, 1507. (28) Wood, J. R.; Wagner, H. D.; Marom, G. Proc. Royal Soc. Ser. A 1996, 452, 235. (29) Filiou, C.; Galiotis, C. Comput. Sci. Technol. 1999, 59, 2149. (30) Schelling, P. K.; Keblinsky, P. Phys. ReV. B 2003, 68, 035425. (31) Kwon, Y.-K.; Berber, S.; Tomanek, D. Phys. ReV. Lett. 2004, 92, 015901. (32) Fletcher, N. H. The Chemical Physics of Ice; University Press: Cambridge, 1970. (33) Zhou, W.; Islam, M. F.; Wang, H.; Ho, D. L.; Yodh, A. G.; Winey, K. I.; Fischer, J. E. Chem. Phys. Lett. 2004, 384, 185. (34) Kane, C. L.; Mele, E. J. Phys. ReV. Lett. 1997, 78, 1932. (35) Hagen, A.; Moos, G.; Talalaev, V.; Tomm, J. W.; Hertel, T. Appl. Phys. A 2004, 78, 1137. (36) Ma, Y. Z.; Stenger, J.; Zimmermann, J.; Bachilo, S. M.; Smalley, R. E.; Weisman, R. B.; Fleming, G. R. J. Chem. Phys. 2004, 120, 3368.

NL048630C

Nano Lett., Vol. 4, No. 12, 2004