Observation of Breathing-like Modes in an Individual Multiwalled

pubs.acs.org/NanoLett

Observation of Breathing-like Modes in an Individual Multiwalled Carbon Nanotube Christian Spudat,† Matthias Mu¨ller,‡ Lothar Houben,§ Janina Maultzsch,‡ Karin Goss,† Christian Thomsen,‡ Claus M. Schneider,† and Carola Meyer*,† †

Institut fu¨r Festko¨rperforschung (IFF-9), Forschungszentrum Ju¨lich and JARA Ju¨lich Aachen Research Alliance, D-52425 Ju¨lich, Germany, ‡ Institut fu¨r Festko¨rperphysik, Technische Universita¨t Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany, and § Institut fu¨r Festko¨rperforschung (IFF-8), Forschungszentrum Ju¨lich and Ernst-Ruska Centre (ER-C) for Microscopy and Spectroscopy with Electrons, D-52425 Ju¨lich, Germany ABSTRACT We study collective vibrational breathing modes in the Raman spectrum of a multiwalled carbon nanotube. In correlation with high-resolution transmission electron microscopy, we find that these modes have energies differing by more than 23% from the radial breathing modes of the corresponding single-walled nanotubes. This shift in energy is explained with intershell interactions using a model of coupled harmonic oscillators. The strength of this interaction is related to the coupling strength expected for fewlayer graphene. KEYWORDS Carbon nanotubes, Raman spectroscopy, TEM, radial breathing mode, breathing-like modes

G

raphene and carbon nanotubes (CNTs) have been studied recently as materials for nanoelectromechanical devices. Free-standing graphene sheets have been investigated as resonators1,2 and suspended single-walled carbon nanotubes have been considered as mechanical oscillators.3,4 The functionality of these systems is increasing with the number of graphene layers5 or with the number of shells of a CNT.6,7 The Raman spectrum of these materials changes markedly with the number of layers8,9 and shells,10,11 respectively. This is caused by interlayer and intershell interactions, and Raman spectroscopy is thus a versatile tool to study the nature of this coupling. Its strength has a direct impact on the elastic properties of these materials12-14 and shows up in the movement of the layers and shells against each other. Unfortunately, the corresponding interlayer mode in graphite, the B2g mode, is silent in infrared as well as in Raman spectroscopy.15 In multiwalled carbon nanotubes (MWCNTs), however, the corresponding vibrational motion has its origin in the radial breathing modes (RBMs) of the nanotube walls, which can be observed with Raman spectroscopy. Thus, carbon nanotubes can be seen as a model system for fewlayer graphene. Raman spectroscopy provides only indirect information of the atomic structure of CNTs. A correlation of microscopy and spectroscopy measurements on the same CNT significantly helps to interpret the low-frequency Raman spectrum observed experimentally. For single-walled carbon nanotubes, this correlation has been successfully achieved on the single nanotube level by combining electron diffraction (ED)

patterns obtained in transmission electron microscopy (TEM) either with Rayleigh scattering,16 or with Raman spectroscopy for chirality assignment.17,18 However, the ED patterns are very difficult to interpret if more than two chiralities are involved,19 as is expected for MWCNTs. In this letter, we investigate the coupling between the shells of a single, individual MWCNT. We correlate the information from the low-frequency Raman spectrum with the diameter of the nanotube shells obtained from aberration-corrected high-resolution TEM measurements. In this way, we are able to unambiguously confirm the coupling of the vibrational modes to breathing-like modes (BLMs) as predicted by Popov and Henrard.14 Our results show that the Raman shift of these BLMs deviates from the wellestablished 1/d dependence of the RBMs for SWCNTs. This effect becomes very strong especially for the embedded shells. In this case, the deviation in mode energy can be larger than 23%. We introduce a model to compare the coupling between the nanotube shells to the coupling expected for a few-layer graphene system.12 The investigated MWCNTs are synthesized by chemical vapor deposition (CVD) at a growth temperature of TCVD ) 1030 °C directly onto a Si3N4 TEM grid as described previously.20 After the CVD process, the sample was treated with a high-temperature annealing step at 900 °C at a pressure of p < 1 × 10-7 mbar to remove excess carbon and defects, thus stabilizing the MWCNTs. The resonant Raman measurements were carried out using a micro-Raman setup in backscattering geometry, the samples being excited by a tunable laser with the laser power on the sample below 0.5 mW. High-resolution TEM micrographs were recorded in an FEI Titan 80-300 microscope equipped with a doublehexapole aberration corrector.21 The acceleration voltage

* To whom correspondence should be addressed. E-mail: [email protected]. Received for review: 07/1/2010 Published on Web: 10/13/2010 © 2010 American Chemical Society

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FIGURE 1. SEM picture of the Si3N4 TEM grid after CVD growth of the carbon nanotubes. The marker shown in the center of the picture was created using a focused ion beam. The single tube intersecting the hole in position E1 shown in the inset was chosen for TEM and Raman characterization. The SEM images were taken under UHV conditions to prevent deposition of amorphous carbon.

was chosen as 80 kV to reduce damages induced by electron irradiation. Negative spherical aberration (NCSI) conditions22 were applied to achieve optimized phase contrast at a point resolution of 0.18 nm. The shell diameter measurements were refined in a self-consistent way based on the comparison of experimental images with simulated images calculated from an iterated model structure. In this letter, we focus on a location, where only one single MWCNT is spanning across a hole of the grid (Figure 1). This allows for a selective investigation of an individual and suspended MWCNT to be done without any effects caused by tube-tube interactions within a rope and tubesubstrate interactions that could influence the shift of the Raman modes. A marker structure ensures that Raman spectroscopy can be correlated with TEM measurements on the same nanotube (see Figure 1). To understand the atomic structure of the MWCNT under investigation, we first analyze the results obtained from electron microscopy. The high-resolution TEM image (Figure 2a) reveals that this MWCNT is composed of six walls. Figure 2c compares line profiles of the experimental tube image and the simulated tube image based on a model resulting from the iterative refinement of shell diameters. The resulting image after refining the model is shown in Figure 2b. The shell diameters of the tubes are given as those of the refined model and range from d ) 0.78 nm for the innermost tube to d ) 4.34 nm for the outermost tube. Note that the maxima of the image intensity cannot be used to determine the diameters directly. The four outer shells exhibit a constant intershell distance of ∆r ) 0.35 nm, whereas the distance between the second and the third inner tube ∆r23 ) 0.32 nm is somewhat smaller than the distance between graphite layers.23 Considering the background of the precision in the TEM measurements we can, however, hardly distinguish between the refined model and a model using a constant intershell distance of ∆r ) 0.35 © 2010 American Chemical Society

FIGURE 2. (a) HRTEM micrograph of MWCNT. The nanotube shells appear bright above mean value under the chosen imaging conditions. (b) Simulation of the image in (a). (c) Line profile of the image intensity (red) along the arrow in (a) compared to the line profile of the simulation based upon the refined model (blue) and the regularized model (green). The line profiles are offset for clarity. The diameters indicated are obtained from the refined model. All values are given in nanometers.

nm for all shells. The unsystematic measurement uncertainty for the diameter is ∆d ) (0.02 nm for the four outer tubes. For the two inner tubes, this uncertainty is about twice as large since their signal-to-noise ratio is worse. In addition, an off-peeling of the innermost wall caused by irradiation damage most likely leads to an underestimation of its diameter. Therefore, the model with the constant intershell distance, which we call the “regularized model” in the following, is in accordance with the measurement data as well as the refined model (Figure 2c). In the following, we compare the diameters obtained in the TEM measurement to the energy of the resonant Raman modes in the low-frequency spectrum, which depend on the diameter of the tubes. Frequency-dependent Raman measurements of the same MWCNT are shown in Figure 3a. They were performed prior to the TEM imaging to avoid any influence of defects that might be induced by electron irradiation. We observe three modes, which exhibit a strong resonance effect. They have a line width of 3-4 cm-1, which is typical for RBMs of SWCNTs.24 Therefore, we assume that these peaks have their origin in the breathing modes of the tubes, which form the MWCNT. In Figure 3b we compare the resonance energies of the three breathing modes from the Raman measurements and the diameters obtained from the TEM measurements with 4471

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TABLE 1. Comparison of the Measured and Simulated BLM-Frequencies tube no.

dT (nm)

ωRaman [cm-1]

1

0.84a (0.78 ( 0.04)b 1.54a (1.60 ( 0.04)b 2.24a (2.24 ( 0.02)b 2.94a (2.94 ( 0.02)b 3.64a (3.64 ( 0.02)b 4.34a (4.34 ( 0.02)b

270

2 3 4 5 6 a

161 131

ωRBM [cm-1]

ωBLM [cm-1]

266.4a (286.9)b 145.3a (139.8)b 99.9a (99.9)b 76.1

270.9a (289.5)b 162.1a (160.1)b 130.1a (130.1)b 117.4

61.5

94.7

51.6

62.0

Regularized model. b Refined model.

interaction in the MWCNT might play an important role in this case. We conclude that we measure the transitions of the three innermost nanotubes. The Raman shifts ωRaman of the modes observed can be compared with the diameters obtained in the TEM measurements using the relation

ωRBM )

(1)

to convert the tube diameters dT into Raman shifts ωRBM as they would be expected for individual SWCNTs. A and B are sample-dependent constants, which are chosen to be A ) 223.75 cm-1 and B ) 0 for tubes without any additional interactions as suggested by Bandow et al.26 The results for the expected Raman shifts are listed in Table 1. Strong shifts toward higher wave numbers are found in the experiment for the second and especially for the third inner tube, where the mode is shifted by more than 23% with respect to the RBM position expected from the TEM measurement. The qualitative behavior is the same for the refined as well as for the regularized TEM model. In the case of the refined model, the mode of the innermost tube appears to be shifted to lower wave numbers. However, this deviation from the general behavior could be caused by the error in the TEM measurement. Particularly, if the innermost wall were to peel off due to irradiation damage, the estimated diameter would appear too small. The strong shift of the Raman modes belonging to the transitions of the embedded nanotube walls cannot be explained by using different numbers for A and B in eq 1, for which a large variety can be found in the literature.17,27-29 In the following, we are going to show that the stiffening of the Raman modes can be explained by means of a coupling of the phonon modes due to van der Waals (vdW) interactions between the walls of the MWCNT. Therefore, coupled breathing-like modes (BLMs) as predicted by Popov et al.14 are observed rather than individual RBMs.

FIGURE 3. (a) Resonant Raman spectrum of the single MWCNT. (b) Assignment of the transitions for the observed Raman resonances in the Kataura plot (by Popov25) for the laser energies E ) 2.06 eV (blue line) and E ) 1.92 eV (red line) used in (a).

the optical transition energies Eii calculated within the framework of a nonorthogonal tight-binding model.25 This model underestimates the transition energies, which have to be up-shifted by 0.3 eV, if compared to experimental data.25 The interaction of the walls within the MWCNT might influence this shift, but without more data about MWCNTs it is not possible to determine the shift in the transition energy exactly. Assuming an error of (50 meV for the blueshifted transition energies, we can still attribute the observed resonances to the ES22 transition for the first and to the ES33 transition for the second innermost tubes, respectively. The third resonance belongs either to the ES44 or to the EM22 transition. We cannot confirm a stronger blue shift for the ES33 transition as discussed for SWCNTs.18 The tube-tube © 2010 American Chemical Society

A dT + B

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FIGURE 4. (a) BLM frequencies (yellow lines) for increasing coupling frequency Ωc assuming a coupling frequency scaled with the diameter including the surface effect. The dashed white lines indicate the positions of the measured Raman modes with its frequencies, which allow for the assignment of the measured BLM frequencies to the three innermost tubes. (b) Experimental Raman spectra with subtracted background (blue and red) are compared with the calculated positions of the Raman modes (black) at Ωc ) 1.84 THz (black dashed line in (a)).

To investigate the influence of the mode coupling in MWCNTs on the Raman shift, we construct a model based upon previous calculations for DWCNTs,30 assuming the shells of a MWCNT to behave as a one-dimensional chain of coupled harmonic oscillators. When the curvature effect and the interlayer coupling are neglected, each tube within the MWCNT should behave like an individual SWCNT. We assume a constant coupling between the tubes neglecting surface and curvature effects. The equations of motion for N coupled harmonic oscillators are given by

This does not include the surface effect, which describes the increasing number of interacting atoms for increasing diameters. According to eq 3, the coupling frequency ωc depends not only on the coupling constant kc, but also on the difference of the masses between two adjacent layers mn+1 - mn. The mass of individual layers in our onedimensional model is given by the number of carbon atoms on the layer surface. This is proportional to the diameter of each layer, while the mass difference for two adjacent layers decreases for larger diameters. Thus, the interlayer coupling is expected to increase for larger diameters, which can be described by a scaled coupling frequency

x¨ ) -ωnxn - ωc(n)(xn - xn+1) - ωc(n)(xn - xn-1) (2)

ωc(n) ) with n ) 1, ..., N, the tube frequency of the nth tube is ωn, the coupling frequency is ωc, and the boundary conditions x0 ) xN+1 ) 0. In our case, we observe N ) 6 resulting in six coupled equations of motion, which are integrated in time and Fourier transformed afterward to obtain the resulting frequencies for each harmonic oscillator. The mass of each oscillator mn and its spring constant kn are expressed by their eigenfrequencies

ωn )




kn mn

dn+1 - dn Ωc dn+1

(4)

between the nth and (n + 1)th layer with their diameters dn and dn+1 tending to ωc(∞) ) Ωc ) 3.81 THz as the B2g mode in graphite31 for infinite diameters (and number of layers). The result of the Raman shift for all BLMs depending on the coupling strength is shown in Figure 4a using the diameters of the regularized model to obtain the RBM positions for Ωc ) 0. All BLM shifts increase with increasing coupling frequency Ωc. This effect is most prominent for the intermediate phonon modes, while the highest and lowest BLM shifts are less affected. This is in agreement with calculations for MWCNTs,14 where the smallest BLM shift resembles the in-phase mode, while the strongest BLM shift is the counter-phase mode. The intermediate modes are of mixed character. In Figure 4b, the experimentally obtained spectra are compared with the position of the Raman modes obtained

(3)

which are nothing but the Raman shifts ωRBM determined from the diameters measured in TEM by eq 1. © 2010 American Chemical Society




1-

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discussions. This work is financially supported by the DFG Forschergruppe FOR 912.

from the simulation. The best agreement between simulated and measured Raman shifts is found at a coupling frequency of Ωc ) 1.84 THz. The values obtained for the Raman shifts ωBLM of the BLMs reflect the experimental data very well (see Table 1), which shows that the stiffening of the modes can indeed be explained by a coupling between the walls. The shifts ωBLM obtained using the diameters of the refined model (see Table 1) do not differ much for the two embedded walls as well as the value obtained for the coupling strength Ωc ) 1.93 THz. We can unambiguously attribute the Raman mode at ωRaman ) 270 cm-1 to the counter-phase BLM, while the modes at ωRaman ) 161 cm-1 and at ωRaman ) 131 cm-1 are the first two BLMs of mixed modes. Three more modes are expected to be observed at ωBLM ) 117 cm-1, at ωBLM ) 95 cm-1, and at ωBLM ) 62 cm-1 following the model. These modes do not show up in our measurements, because they are masked by the edge of the Rayleigh peak. To summarize, we have studied the phonon coupling in an individual MWCNT with six walls combining high-resolution TEM microscopy and frequency-dependent Raman spectroscopy on the same nanotube. The diameters of the tubes within the MWCNT were determined from the TEM measurements. Furthermore, we observed three Raman modes at different laser energies in the low-frequency regime of the Raman spectrum. Correlating the transition energies with the diameter obtained from the TEM measurement, these modes can be assigned to originate from the breathing modes of the three innermost tubes. With respect to the breathing modes of SWCNTs, a strong shift toward higher wave numbers is found (up to >23%) for the breathing modes of the embedded tubes. A model of coupled harmonic oscillators was used to simulate the spectrum of the MWCNT. It confirms that the stiffening is due to phononcoupling and that breathing-like modes14 are observed instead of individual RBMs. We conclude that the interlayer coupling in MWCNTs cannot be neglected as in DWCNTs, where the effect has been shown to be small.32 The coupling strength we obtain from the model to be Ωc ) 1.84 THz is smaller than expected. Calculations for few-layer graphene12 predict values which are smaller than for graphite but Ωc > 3 THz. To understand this deviation and also possible influences of the curvature, a model would be needed that includes the van der Waals interaction explicitly.

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Acknowledgment. The authors thank J. Mennig for FIB processing and W. Harneit as well as H. Telg for fruitful

© 2010 American Chemical Society

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