Wall-to-wall stress induced in (6,5) semiconducting nanotubes by encapsulation in metallic outer tubes of different diameters: A resonance Raman study of individual C₆₀-derived double-wall carbon nanotubes

Abstract

We measure resonant Raman scattering from 11 individual C₆₀-derived double-wall carbon nanotubes all having inner semiconducting (6,5) tubes and various outer metallic tubes. The Raman spectra show the radial breathing modes (RBM) of the inner and the outer tubes to be simultaneously in resonance with the same laser energy. We observe that an increase in the RBM frequency of the inner tubes is related to an increase in the RBM frequency of the outer tubes. The Raman spectra also contain a sharp G⁻ feature that increases in frequency as the nominal diameter of the outer metallic tubes decreases. Finally, the one-phonon second-order D-band mode shows a two-way frequency splitting that decreases with decreasing nominal wall-to-wall distance. We suggest that the stress which increases with decreasing nominal wall-to-wall distance is responsible for the hardening that is observed in the frequencies of the RBM, D and G⁻ modes of the inner (6,5) semiconducting tubes.

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1. Introduction

Double-wall carbon nanotubes (DWNTs) exhibit optical and vibrational properties that are similar to those of single-wall carbon nanotubes (SWNTs) but their double-wall structure makes them more mechanically and thermally robust.¹ Depending on the metallic (M) or semiconducting (S) nature of their inner and outer tubes, DWNTs can have four possible configurations, S@S, S@M, M@S, M@M, each of which is expected to have particular properties suitable for different electronic device applications.

Possible techniques for fabricating DWNTs include chemical vapor deposition (CVD)^1,2 or the filling of SWNTs with fullerenes that coalesce and form inner tubes of DWNTs upon heat treatment.^3,4 Both types of DWNTs are studied in the present work and are inter-compared. In the case of C₆₀-derived DWNTs (denoted by C₆₀-DWNTs), the coalescence of fullerenes at high temperature (>1200 °C) forms inner tubes with diameters (d_t) close to that of C₆₀.⁴ According to Bandow et al., under prolonged heat treatment the initial diameters of the inner tubes can increase in order to adjust the wall-to-wall (WtW) distances and minimize the energy of the system.⁴ Also, by using high-resolution Raman spectroscopy, Pfeiffer et al.^5–8 and Kuzmany et al.,⁹ observed that the inner tubes of C₆₀-DWNTs can be contained inside outer tubes with different diameters where smaller WtW distances increase the inter-tube interaction and upshift the radial breathing mode (RBM) of the inner tubes. CVD-DWNTs and C₆₀-DWNTs have been shown to have different optical properties that are believed to originate from differences in the WtW distances and the degree of crystallinity of the inner tubes. For instance, on one hand, a quenching of the photoluminescence (PL) signal has been observed in C₆₀-DWNTs and attributed to inter-tube interactions.¹⁰ On the other hand, in CVD-DWNTs, a strong PL emission from the inner semiconducting tubes has been recently reported.¹¹

To the best of our knowledge, most spectroscopic experiments on DWNTs have been performed on bundles or solution-based samples, so that it has been inherently difficult to use Raman spectroscopy to investigate which inner (n,m) tubes are actually contained inside the variety of observed outer (n′,m′) tubes. In order to quantitatively determine which specific inner and outer tubes actually form each DWNT, one must perform experiments on individual DWNTs.¹² Therefore, in the present work individual C₆₀-DWNTs have been dispersed on a substrate and studied independently. Here we report a brief comparison between CVD-DWNT and C₆₀-DWNT bundles and a detailed study of 11 individual isolated C₆₀-DWNTs with inner semiconducting (6,5) tubes and various outer metallic tubes.

2. Experimental details

We used a CVD method to synthesize the CVD-DWNT bundles used in this study. The high purity of our CVD-DWNT bundles relative to residual catalyst particles and SWNTs has been confirmed by diamagnetic susceptibility^13,14 and Raman spectroscopy experiments,¹⁵ respectively. The C₆₀-DWNT bundles used herein were fabricated by reacting C₆₀ and SWNTs under vacuum at 600 °C for 24 h. The starting SWNT material was synthesized by the arc-discharge method and purified by Hanwha Corp (Korea). The as-grown peapods were washed with toluene to remove residual C₆₀ and heat treated at 1700 °C in Ar (1 atm) to transform them into C₆₀-DWNT bundles. A high-resolution transmission electron microscopy (HRTEM) image of the resulting C₆₀-DWNT material is shown in Fig. 1(a). A solution containing isolated C₆₀-DWNTs was prepared by dispersing 1 mg of C₆₀-DWNTs in D₂O with 0.5 wt% sodium dodecylbenzene sulfonate (SDBS) and sonicating the dispersion (600 W cm⁻²) for 15–30 min. Subsequently, the solution was ultracentrifuged (320 000 g) for 30 min and 70% of the supernatant solution was collected. Photoluminescence measurements were performed on the resulting C₆₀-DWNT solution with a NIR-PL Shimazu system using a liquid-nitrogen-cooled InGaAs array-type detector. The PL map from the C₆₀-DWNT solution (see Fig. 1(b)) shows the presence of three (n,m) species where the strongest peak corresponds to (6,5) semiconducting tubes.

Fig. 1 (a) HRTEM image of a C₆₀-DWNT produced by heat treating peapods at 1700 °C in Ar (b) Photoluminescence (PL) map of a solution containing isolated C₆₀-DWNTs dispersed in sodium dodecylbenzene sulfonate (SDBS). The strongest PL peak corresponds to semiconducting (6,5) inner tubes.

The solution containing isolated C₆₀-DWNTs was spin-coated on a silicon substrate that is marked with a gold grid and allows for precise recording of the location of an isolated DWNT [see inset of Fig. 2(b)].¹² The distribution of the deposited DWNTs on the silicon substrate is not spatially homogeneous but the nanotube density is low enough to have 0 to 20 nanotubes per 100 μm². The laser spot has a 1 μm diameter and, depending on its location on the substrate, the laser spot illuminated 0 to 5 DWNTs. For bundles, five measurements were performed on different spots and laser power levels were kept below 0.5 mW to avoid excessive heating of the DWNTs. The scattered light was collected through a 100× objective using a backscattering geometry. An Nd:YAG laser was used to generate E_laser = 2.33 eV and a Kr⁺ ion laser generated E_laser = 1.92 eV. A dye laser containing Rhodamine 6Gdye and a Ti:sapphire laser were pumped by the Nd:YAG laser to generate E_laser = 2.05–2.16 eV and E_laser = 1.6 eV, respectively. A thermoelectrically-cooled Si CCD (charge coupled device) detector operating at −75 °C was used to collect Raman spectra.

Fig. 2 (a) Raman spectra for the RBM region for CVD-DWNT and C₆₀-DWNT bundles (E_laser = 2.13 eV). (b) Atomic force microscope (AFM) image of one individual, isolated DWNT. Inset: Silicon substrate with Au markers showing the location of the DWNT. (c) Raman spectra for the RBM Raman region (E_laser = 2.11 eV) for an isolated individual C₆₀-DWNT and (d) AFM height profile of the individual, isolated DWNT shown in (b) with the RBM spectrum shown in (c). The vertical lines connecting (a) and (c) show that the ω_RBM of the prominent tube diameters observed in the C₆₀-DWNT bundles coincide with the ω_RBM of the inner and outer tubes of the isolated C₆₀-DWNTs.

In order to obtain a strong Raman signal from an isolated carbon nanotube, the resonance condition must be met by matching the laser energy to the energy separation between the van Hove singularities of the isolated nanotube.¹⁶ Our laser spot often illuminates nanotubes that are not in resonance with the laser energy. Therefore, in order to find resonant nanotubes with a strong radial breathing mode (RBM) Raman signal, we scanned large substrate areas (900 μm²).

3. Results and discussion

3.1 Bundle DWNTs

Before starting the discussion on individual C₆₀-DWNTs, we briefly comment on the RBM spectra of our C₆₀-DWNT and CVD-DWNT bundle samples. As shown in Fig. 2(a), and in agreement with a previous report,⁸C₆₀-DWNTs have a narrower d_t distribution than CVD-DWNTs. This observation was expected because, in the case of C₆₀-DWNTs, the d_t distribution of the starting SWNT material limits the possible choice of d_t for the inner tubes when the fullerenes coalesce through heat treatment. In the case of CVD-DWNTs, this d_t limitation is not present and, when using E_laser = 2.13 eV, we find resonance with semiconducting tubes for 8 different diameters and metallic tubes with d_t = 1.41 and 0.97 nm [see Fig. 2(a)]. As is expected, the RBM frequencies of the inner and outer tubes of the individual C₆₀-DWNTs that we study in the following section, coincide with the RBM frequencies of the most prominent tube diameters observed in the C₆₀-DWNT bundles [See vertical lines connecting the shaded Lorentzians in Fig. 2(a) to the RBM pair in Fig. 2(c)].

3.2 Isolated, individual C₆₀-DWNTs

Herein we describe the procedures that allowed us to detect isolated C₆₀-DWNTs and we then discuss the dependence of the ω_RBM, ω_G⁻ and ω_D frequencies on DWNT nominal inner tube diameter and WtW distance.

After studying the large area Raman maps of the Si substrate, on a few occasions (ca. <5%), it was possible to find locations on the Si substrate that showed two RBM modes, simultaneously in resonance with the same E_laser. These pairs of RBMs come from two nanotubes, one with a small diameter (∼0.7 nm) and another one with a large (∼1.3 nm) diameter. The observation of these RBM pairs [see Fig. 2(c)] suggested that we had found a resonance with the inner and outer tubes of the same DWNT. However, although the probability is low, a rope of 2–3 DWNTs could also generate a pair of RBMs if the inner and outer tubes of two different DWNTs happen to be in resonance with the same E_laser. Therefore, in order to confirm that the two observed RBMs were indeed coming from the same DWNT, we verified that only one DWNT was being illuminated by the laser spot. This verification consisted of three steps whose results are shown, for the same DWNT, in Fig. 2:

(1) We used AFM (atomic force microscopy) to check that the DWNT was completely isolated and far away from the other tubes on the substrate [see Fig. 2(b)]. The inset in Fig. 2(b) shows the Au grid used to mark and record the location of each individual DWNT.

(2) We checked that the height of the DWNT as measured by AFM corresponds to the diameter of the outer tube of the DWNT as deduced from its low-frequency RBM. Fig. 2(d) shows the AFM height profile of our DWNT. The difference between the measured Raman and AFM outer tube diameter estimates is ∼0.1 nm.

(3) Finally we scan the same spot in the sample with multiple laser lines in order to eliminate the presence of additional nanotubes that might not have been in resonance with the initial laser energy. Fig. 2(c) shows the RBM region of the Raman spectrum coming from one isolated DWNT taken with E_laser = 2.11 eV. The same spot on the substrate was also scanned with nine different laser energies (2.33, 2.16, 2.14, 2.12, 2.10, 2.07, 2.05, 1.92 and 1.60 eV) and no additional RBMs coming from other nanotubes were detected.

Performing AFM and acquiring Raman spectra with many E_laser on isolated DWNTs is feasible¹² but also experimentally challenging. While attempting to increase the throughput of the above mentioned technique, we discovered that it is also possible to use less AFM time and only one laser line and still be almost certain that we are in resonance with the inner and outer tubes of the same DWNT. We now describe a new procedure that allowed us to detect 11 isolated C₆₀-DWNTs.

First we used one laser line (2.08 or 2.10 eV) to find as many spectra as possible containing two simultaneous RBMs (see Fig. 3) that matched the expected inner and outer tube diameters of the individual DWNTs present in our sample (see Fig. 4). By plotting the low-frequency RBM (large diameter outer tubes) vs. high-frequency RBM (small diameter inner tubes) for each spectrum, we found that the frequencies of most of the simultaneously detected RBM pairs (80%) were correlated [see Fig. 5(a)]. We know a priori that if the two simultaneously resonant RBMs do not correspond to the same DWNTs we should observe random low-frequency RBM vs. high-frequency RBM relationships. Therefore, the trend followed by the simultaneous RBM pairs plotted in Fig. 5(a) suggests that each RBM pair is indeed coming from the inner and outer tubes of a single isolated DWNT. Thus, if the observed pair of RBMs fits the trend in Fig. 5(a), then the pair is identified as most likely coming from the same isolated DWNT and the pair is then retained; otherwise the spectra are discarded in this analysis.

Fig. 3 Kataura plot of the resonant transition energies vs. RBM frequencies for SWNTs based on the extended tight binding model.¹⁷ The location on the plot of the measured DWNT RBMs are marked with triangles. The laser energies (2.08 and 2.10 eV) chosen to excite DWNTs with inner semiconducting and outer metallic tubes are marked with horizontal lines. The vertical lines denote the ranges of ω_RBM measured for the inner and outer tubes.

Fig. 4 (a) RBM-band and (b) D and G-band regions of the Raman spectra corresponding to five different DWNTs whose inner and outer walls are simultaneously in resonance with the same laser line E_laser = 2.10 eV. Vertical lines in (a) denote outer M tubes and inner S (6,5) tubes and the dark vertical line denotes a Si Raman feature. The vertical lines in (b) denote D- and G-band features (see text).

Fig. 5 All the inner tubes for the 11 C₆₀-DWNTs in this figure are (6,5) tubes. (a) Correlation between the ω_RBM of the inner and outer tubes of the same C₆₀-DWNT. (b) Correlation between the WtW distance of each DWNT with ω_RBM for its inner tube. An increase in the ω_RBM of the inner tubes is accompanied by a decrease in the nominal WtW distance. (c) Plot of ω_G⁻vs. ω_RBM for the inner tube of each DWNT. An upshift in ω_G⁻ results from a decrease in the nominal WtW distance and the resulting increased inter-tube interaction. (d) The ω_D1 for each component of the D-band vs. ω_RBM for the inner tube for each of the 11 DWNTs. The splitting of the D-band into ω_D1 and ω_D2 decreases as ω_RBM of the inner tube increases with decreasing nominal WtW distance. Note that ω_D2 remains almost constant while ω_D1 increases.

The Kataura plot in Fig. 3 shows that, when using E_laser = 2.08 and 2.10 eV, we excited the E^S₂₂ transitions of (6,5) inner semiconducting tubes and the E^M₁₁ transitions of outer metallic tubes mainly from family 2n + m = 33. The Kataura plot was calculated within the ETB (extended tight binding) framework,¹⁷ including many-body corrections, fitted to the RRS (resonance Raman scattering) data from sodium dodecyl sulfate-wrapped HiPCO (high-pressure CO conversion) SWNTs.¹⁸ We find that such a Kataura plot (Fig. 3) which is based on prior studies on SWNTs,¹⁷ is accurate enough for the qualitative identification of the (n,m) assignment for small diameter tubes within DWNTs. Although the relationship between ω_RBM and d_t for the inner tubes and outer tubes of DWNTs is not expected to be the same as it would be for isolated SWNTs, we approximate the nanotube diameters for both the inner and outer tubes of DWNTs in this work by using the SWNT-based RBM relation ω_RBM = 218.3/d_t + 15.9,¹⁴ because there are no experimental or theoretical ω_RBMvs. d_t relationships presently available for the inner and outer tubes that constitute the four different kinds of DWNT configurations (S@S, S@M, M@S, M@M) as mentioned above. Also, nanotube–substrate van der Waals interactions are known to induce radial deformations that can upshift the ω_RBM of large-diameter SWNTs.¹⁹ However, in this work we assume that nanotube–substrate interactions have a negligible effect on the ω_RBM of each of the two layers of our DWNTs because (a) the d_t of the outer tubes is relatively small (1.3 nm) and therefore has a small contact area with the substrate, (b) the deformation of the outer tube is reduced by the presence of the inner tube, and (c) because, to a first order approximation, the inner tube is shielded and not affected by the substrate.

Based on the SWNT-based RBM relation mentioned above, we find that the ω_RBM values for the 11 DWNT specimens experimentally measured in this work yield nominal inner (outer) tube diameters in the 0.69–0.73 nm (1.28–1.35 nm) range. The nominal WtW distances for these 11 C₆₀-DWNTs are calculated by subtracting the nominal d_t of the inner tubes from the nominal d_t of the outer tubes obtained by the above procedure, yielding nominal WtW distances in the 0.58–0.65 nm range. In Fig. 5(a) we plot the measured ω_RBM of each inner tube vs. the ω_RBM of its corresponding outer tube for the 11 measured tubes. All the inner tubes in this work are assigned to (6,5) nanotubes and we observe that their measured ω_RBM values upshift with increasing measured outer tube ω_RBM values [Fig. 5(a)]. Similarly, the measured ω_RBM of the inner tubes upshifts with decreasing nominal WtW distance as shown in Fig. 5(b) and in qualitative agreement with the results in refs. 5–9.

Because of the strong carbon–carbon bond and the small d_t of the (6,5) tubes, we do not expect the actual diameter of the inner tubes to decrease to the values given by the SWNT-based ω_RBMvs. 1/d_t relation given above. Instead, the observed hardening of the measured ω_RBM as the nominal WtW distance decreases corresponds to a minimal change in actual inner tube d_t and provides an indirect measure of the stress that is felt by the inner tube. All of the 11 inner tubes shown herein are Type II semiconducting (6,5) tubes but the outer tubes that surround them vary somewhat in diameter and can be identified with a few different (n,m) values from one another, but certainly far less than 11 different values.

3.2.1 Dependence of ω_G⁻ on inner tube ω_RBM and wall-to-wall distance. The tangential G-band modes in carbon nanotubes can be TO (transverse optic) and LO (longitudinal optic). The frequencies of the LO and TO modes vary with the degree of confinement, curvature and chiral angle of each particular (n,m) nanotube, and the intensities of the TO and LO modes are sensitive to the angle formed between the nanotube axis and the polarization of the incoming light.²⁰ For semiconducting nanotubes, the LO mode (G⁺-band) is a bond-stretching mode with little diameter dependence and the TO mode is a bond-bending mode whose frequency decreases with decreasing nanotube diameter (G⁻-band).²¹ Also, the G⁻-band feature of isolated semiconducting tubes (S-SWNTs) generally has a smaller FWHM linewidth than that of metallic tubes.²²

Since the inner tubes of our DWNTs are semiconducting, their spectra show sharp G⁻ features that are easy to fit unambiguously with a Lorentzian lineshape. If we correlate ω_G⁻, the frequency of the G⁻-band, to the low frequency RBM (corresponding to the inner tube) in our spectra for DWNTs, we observe an increase in ω_G⁻ as ω_RBM for the inner nanotube increases [see Fig. 5(c)]. This behavior is opposite to the well-documented diameter dependence of the G⁻ (LO) mode in S-SWNTs.¹⁶

We explain this observation in the following way. We know from Fig. 5(b) that DWNTs whose inner tube show an upshifted ω_RBM tend to have smaller nominal WtW distances. A smaller nominal WtW distance implies a higher degree of inter-tube interaction and a higher mutually induced stress felt by both the inner and outer tubes of an individual DWNT. Therefore, we expect the observed hardening of the G⁻ frequency with increasing inner tube ω_RBM [see Fig. 5(c)] to be caused by the increased stress that the outer and inner tubes exert on each other in the case of DWNTs as the WtW distances decrease. Experimentally, although not shown explicitly in this work, the intensity of the G⁻-band is not observed to show any significant dependence on the nominal WtW distance.

Finally, we expect the G⁺ region of our DWNTs to contain a contribution from the LO mode of its S inner tube and the TO mode of its M outer tube. Unfortunately, the ω_G⁺ of the inner tubes and the ω_G⁺ of the outer tubes from our DWNTs overlap so that we can not distinguish the separate contributions made by each of the tubes to the G⁺ feature and we were not able to study possible correlations between ω_G⁺ and the ω_RBM of the inner nanotube.

3.2.2 Dependence of ω_D on the inner tube ω_RBM and the wall-to-wall distance. The D-band is a one-phonon second-order band that appears when the translational symmetry of a nanotube is broken. In the case of SWNTs, the D-band can be fit with one Lorentzian and, like the G⁻-mode, the D-band softens with decreasing nanotube diameter.¹⁶ The lineshape of the observed D-band from our DWNTs [see Fig. 4(b)] can be fit with one low (ω_D1) and one high (ω_D2) frequency Lorentzian which can be correlated with the inner (lower frequency) and outer (higher frequency) tubes of each DWNT. A factor that contributes to the splitting of the D-band in this collection of DWNTs is the diameter dependence of ω_D which makes the splitting more evident for larger nominal WtW distances between inner and outer tubes [see leftmost part of Fig. 5(b) and (d)]. As shown in Fig. 5(d), we observe that when the ω_RBM of the inner tube increases, ω_D1 then also upshifts, probably due to a decreased WtW distance that results in an increasingly stressed inner tube. Finally, although not shown explicitly in this work, the intensity of the D-band components (D1 and D2) do not show a clear correlation with the ω_RBM of the inner tube.

4. Conclusions

In this work we obtained the Raman spectra of 11 isolated C₆₀-DWNTs all with inner semiconducting (6,5) tubes but with different outer metallic tubes by searching for RBM pairs that were simultaneously in resonance with the same E_laser and that matched the expected inner and outer tube diameters of individual DWNTs. In this collection of isolated C₆₀-DWNTs we observed that the ω_RBM of the inner (6,5) semiconducting tube hardens as the diameter of the outer metallic tube decreases. We also measured an increase in ω_G⁻ with decreasing wall-to-wall distances and attributed the upshift of ω_G⁻ to the stress felt by the inner tubes of the DWNTs due to increasing inter-tube interaction and mutual stress. Finally, we noted that the D-band mode splits into two components where the lower frequency component ω_D1 is related to the inner tube and hardens with decreasing nominal WtW distances. The upper frequency D-band component ω_D2 related to the outer tube is independent of the nominal WtW distance. In the future we expect to use the same technique to find specimens with the remaining three DWNT configurations and compare their optical properties as the inter-tube distances are varied.

Acknowledgments

The authors gratefully acknowledge financial support from CONACYT Mexico: 56787 (Laboratory for Nanoscience and Nanotechnology Research-LINAN), 45772 (M.T.), 58899-Inter American Collaboration (M.T.), the MIT-CONACYT program (M.S.D., M.T.), 2004-01-013/SALUD-CONACYT(M.T.). We also thank CONACYT graduate student grants, Vilore Foods Co. and SEP Mexico for financial support (F.V.P). The authors M.E., Y.A.K and H.M. acknowledge support from the CLUSTER project (second stage) and a grant for Specially Promoted Research (No. 19002007) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. The authors F.V.P., and M.S.D. gratefully acknowledge support from NSF/DMR 07–04197. The authors are grateful to D. Nezich for providing marked Si substrates and to A. Reina, M. Hofmann, E. Barros, A. G. Souza and L. G. Cancado for helpful discussions.

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