RESONANCE RAMAN SCATTERING OF MULTI-WALLED CARBON NANOTUBES
H. KATAURA*, Y. ACHIBA**, X. ZHAO*** AND Y. ANDO**** Department of Physics, Faculty of Science, Tokyo Metropolitan University, Tokyo 192-0397,
JAPAN, kataura@phys.metro-u.ac.jp** Department of Chemistry, Faculty of Science, Tokyo Metropolitan University, Tokyo
192-0397, JAPAN*** Department of Physics, Meijo University, Nagoya 468-8502, JAPANABSTRACTMulti-walled carbon nanotubes synthesized by the carbon arc in hydrogen gas havevery thin core channels. We have measured resonance Raman scattering of some samples
synthesized in different conditions, and have observed radial breathing mode (RBM) peaks
from 200 to 500 cm-1. Resonance effect of each peak is similar to that of single-walled nanotube.
However, the peak frequencies are about 5 % higher than those of single-walled nanotubes,
which is probably due to the inter-layer interaction. Further, the highest RBM peak splits inthree peaks. The result on the resonance effect and the zone-folding band calculation suggestthat the thinnest core nanotube is (4,3) that have four candidates of second outer nanotubes.
This suggests that the different outer nanotube gives different degree of the interlayerinteraction.
INTRODUCTION
Usually, multi-walled carbon nanotube (MWNT) prepared by carbon arc is thought tobe constructed with concentric tubes. For example, 13C-NMR [1] and the magnetoresistanceresults[2,3] show Aharonov-Bohm effects that are led from the concentric tube structures.
However, the thermal expansion measurement [4] and the doping effects [5] suggest that somekinds of MWNTs have scroll structures. If the radial breathing modes (RBMs), which ischaracteristics of single-walled carbon nanotube (SWNT) [6], were observed in MWNTs, it
might be the experimental evidence of the concentric structure. In many cases, unfortunately,
MWNTs have very large diameters compared with SWNTs even at the core, and no one
succeeded to observe the RBMs, to date. However, Zhao and Ando have succeeded tosynthesize MWNTs with very thin core by electric arc in hydrogen gas. [7] They confirmed thatthe core nanotubes has a diameter less than 1.0 nm by the transmission electron microscope(TEM) observation. Further, the sample indicates many Raman peaks in a low frequency region,
which correspond to the RBMs in SWNTs. [8] If those peaks are RBMs, the resonance effectwill be observed as well as the SWNTs.
In the case of SWNT, electronic states are expressed well by the zone-folding scheme.
Indeed, for the SWNT, results of the optical absorption and the resonance Raman scattering canbe explained by the optical transition between spikes in density of states originating from one
dimensional van Hove singularities. If the similar resonance feature were observed for the low
frequency mode in the case of MWNTs, it will be a sign of the true RBM. Furthermore, thisresonance feature will become a standard for the individual SWNT because MWNT neverconstructs hexagonal bundle structure. Thus, it is very interesting to measure the resonanceRaman scattering of MWNTs synthesized in hydrogen gas.

Fig. 1. TEM photograph of unpurified multi-walled carbon nanotubes fabricated bycarbon arc in 120 Torr hydrogen gas. Inset shows a larger magnification image of therectangle area. It can be seen that the core channel diameter is less than 0.7 nm.
EXPERIMENT
We have prepared several MWNTs samples by carbon arc under different hydrogenpressure from 30 to 120 Torr. In the all conditions, we could get good MWNT samples.
Relative yields were depending on the pressure and the current. Details about the synthesis
method should be explained elsewhere. [7] Briefly, the highest yield of MWNTs was obtained
at 60 Torr. The purity of the sample after the purification by infrared lamp is over 90%. The
diameter distribution of core channel was measured by TEM. Figure 1 shows a typical TEM
photograph of MWNTs. At sight, MWNT looks like a rod, but the high-resolution image
indicates a very small hollow at the core. Most of MWNTs have core diameter around 1.0 nm,
and sometimes we observed it less than 0.7nm.
Spectra Physics Ar+ laser Stabilite 2016, dye laser 375B and Ti: Sapphire laser 3900S
were used as light sources for Resonance Raman measurements. Jobin Yvon U1000 double
monochromator, Hamamatsu Photonics R943-02 photomultiplier tube and photon counting
system were used for the measurement. Raman shift was calibrated by the Raman peak of
crystalline silicon. To avoid local heating effects on the Raman spectrum, laser beam wasfocused linearly on the sample using acylindrical lens. The laser power was set to 50
mW as an optimum value.

488 nmIntensity (arb. units)

RESULTSH

230 T orr

One-phonon Raman spectra of fourkinds of samples are shown in Fig.2. All
60 T orrsamples show typical Raman spectra of
MWNTs. This is reasonable, because thestructural differences between our samples
90 T orrand the other MWNTs are only a few layers at
the center of MWNTs. On the other hand, we
120 T orr
observed very strong new peak at 1850 cm-1.
0
500
1000
1500
2 000
The peak intensity strongly depends on the
R am an shift (cm )preparation condition. MWNTs at the lower
hydrogen pressure show the larger peak Fig. 2. Raman spectra of four kinds ofintensity. There is no one-phonon density of MWNTs samples fabricated in different
states at 1850cm-1, so that the unknown peak hydrogen pressure.
should be assigned as a two-phonon mode. Of
course, in the reaction chamber, soot contains
many kinds of C-H compounds as impurities. One might think the peak is originating from theimpurities. However, MWNTs were grown on the cathode, and were kept in very hightemperature during the deposition. Thus, the most of C-H compounds were expected to bevaporized. Further, this peak show very sharp and strong resonance effect, just like a SWNT,
from visible to infrared region. This suggests that the peak is concerning with the nanotube-likeelectronic states. The peak frequency 1850cm-1 is just the sum of the D-band frequency 1350
cm-1 and the observed highest RBM frequency 490 cm-1. Tentative assignment of this peak isthe combination of the RBM and the D-band.
Figure 3 shows the low frequency Raman spectra of the purified MWNTs measured
using various lasers. Peaks between 150 and 200 cm-1 are due to the air. Peaks above 200cm-1
show very sharp resonance, which strongly suggests that these structures are originating fromthe RBM of nanotubes. Indeed, resonance feature of the peaks between 200 and 350 cm-1 isquite similar to that of SWNTs synthesized by laser ablation using RhPd catalyst. [9,10] Further,
we found that peaks are located 4 or 5 % higher frequencies than the case of SWNTs. For
example, the RBM peak at 280 cm-1 shows maximum intensity at 2.41 eV. This is the same
behavior as the peak at 268 cm-1 in SWNTs. In the same way, the peaks at 239, 270 and 304
cm-1 correspond to the peaks at 227, 260 and 285 cm-1 in SWNTs, respectively. These up-shifts
are probably due to the interlayer interactions. Recently, some reports about bundle effects on
the RBM frequency of SWNTs were published. [11] In the theoretical calculation, RBM
frequency of SWNT in the infinite bundle becomes 10% higher than the isolated SWNT.
Unfortunately, there is no report about the interlayer interactions on the vibrational properties ofthe MWNTs. However, the similar effects should be expected in the case of MWNT.
For a region over 350 cm-1, large bands at 388 and 490 cm-1 are observed with sharp
resonance around 2.4 and 1.7 eV, respectively. The highest RBM peak observed in SWNTs is at
328 cm-1. Thus, we don’t have any references in this frequency region. If these are RBMs,
however, candidates are strongly restricted. From the simple relationship between diameter and
RBM frequency, [6] the candidates for the peak at 490 cm-1 are (5,1), (6,0), (4,3) and (5,2)
having RBM frequencies at 509.6, 472.8, 466.4 and 454.3 cm-1, respectively. If we take into
-1

Excitation
(eV)

air

2.73
2.66
2.62
2.60

Intensity (a rb. un its)

2.54
2.50
2.47
2.41
2.16
2.01
1.96
1.91
1.78
1.75
1.72
1.67
1.64
1.62

150

200

250

300

350

400

450

500

550

-1

R am an shift (cm )Fig. 3. Low frequency Raman spectra of purified MWNTs. Excitations are indicated in
the figure. The complicated peak structures below 200 cm-1 are due to the air.
account the 5% up-shift due to the interlayer interactions, the candidates are narrowed down to(6,0), (4,3) and (5,2). Their diameters are 0.470, 0.477 and 0.489 nm that are consistent with the
TEM observations. It is very interesting that (6,0) nanotube has the same structure of D6h C36.
[12] However, we have to consider the electronic states of the nanotube to see the resonanceeffect. By the zone-folding band calculation [13], assuming the transfer integral γ = 2.75 eV, it
is found that (6,0) and (5,2) are metallic nanotubes and have the first energy gaps at 4.0 eV.
Since the resonance energy of the peak is 1.7 eV, we assigned the peak at 490 cm-1 to (4,3)
which is the semiconductor having the first gap at 1.6 eV. In the same way, the candidates for
the Raman band at 388 cm-1 are (7,1) and (5,4). The nanotube (7,1) is metallic and has the first
gap at 3.4 eV, while (5,4) is the semiconductor and has the first and second energy gaps at 1.28
and 2.52 eV, respectively. Thus, this peak should be assigned to (5,4) because of the resonanceat 2.4 eV.
Now we consider the interlayer interactions. The band at 490 cm-1 is splitting into
three peaks indicating the same resonance feature. These peaks cannot be explained by different

nanotubes, since there are no other candidates. The nanotube (5,1) is only the candidate having
the nearest diameter and the nearest energy gap. However, the calculated energy gap of (5,1) is
1.7 eV, which is 0.1 eV wider than (4,3). If one of the peaks is originating from (5,1), theresonance feature should be different from the other peaks. Further, the RBM frequency of (5,1)
becomes 534 cm-1, taking into account the 5 % up-shift. Thus, it is proper to think that thesethree peaks are originating from the same nanotube. The possible reason of the splitting is theinterlayer interaction. When the first layer is (4,3), (10,7) is the best selection as the second
layer since the interlayer distance is 0.342 nm which is a typical value for MWNTs. [14] The
other nearest candidates of the second layers are (13,3), (9,8) and (11,6) having inter-layer
distances 0.339, 0.339 and 0.347 nm, respectively. The interlayer distance (13,3) and (9,8) haveabout 1% smaller than the typical inter-layer distance and (11,6) is 1.5% larger. A magnitude of
the interlayer interaction should depend on the interlayer distance, and consequently, the RBM
frequency of the first layer may depend on the chiral index of the second layer. Indeed, theobserved frequency separation between split peaks is about 2%, which is consistent with thedifference in interlayer distances. The splitting into three RBM peaks probably indicates that
there are at least three kinds of second layers. In other words, the splitting means that thesecond layer nanotube has closed tube structure as well as the core nanotube. This strongly
suggests that the MWNT fabricated by the electric arc in hydrogen gas has a concentric
structure.
For the thinnest nanotube (4,3), the RBM frequency of the second layer is 191 cm-1.
This should be the highest RBM frequency of the second layer nanotube. Since the low
frequency region is affected by the signals from the air, we measured Raman spectra keeping
the sample in argon gas. However, we could not observe any peak below 200 cm-1. This result
suggests that only the core nanotube has the considerable Raman intensity. The core layer has
only the outer nanotube as a neighbor while the other nanotubes, except for the outermost layer,
have both the inner and the outer nanotubes. The interlayer interaction probably broadens the
one-dimensional band structure, in like manner to the bundle effect in SWNTs. [15] The bandbroadening decreases joint density of states at the energy gap. Then, the resonance Raman
intensity of the second layer may become very weak. On the other hand, the RBM frequency ofthe outermost layer is too low to measure because of its large diameter. Thus, we can observe
the RBMs only of the core nanotubes.
CONCLUSION
Resonance Raman spectra of MWNTs were measured and RBM peaks originatingfrom very thin core nanotubes were observed. The assigned thinnest nanotube (4,3) has very
close diameter to (6,0) or D6h C36. [12] The splitting of RBM peaks indicates that both the first
and the second thinnest layers have closed tube structures. This result strongly suggests that the
MWNTs fabricated by carbon arc in hydrogen gas have the concentric structures. On the other
hand, the fact of the existence of the thin nanotubes is very important to think about the growthmechanisms, because these thin nanotubes cannot be closed by the hemispherical cap satisfying
the isolated pentagon rule (IPR). When we think about the nucleation of core nanotubes, wehave to consider the possibility of the non-IPR carbon cage structures. Now, we have muchinterested in the cap structures of these thin nanotubes. Further, the new strong Raman band at1850 cm-1 is very interesting, since the frequency is basically in the silent region of the
one-phonon density of states in the two-dimensional carbon network structure. It makes us
imagine new carbon network structures.

ACKNOWLEDGMENTS
Authors are grateful to Mr. Misaki for taking HRTEM photographs of MWNTs. This
work was supported in part by Japan Society for Promotion of Science Research for the Future
Program and supported in part by the Grant-in-Aid for Scientific Research on the Priority Area
"Fullerenes and Nanotubes" by the Ministry of Education, Science, and Culture of Japan.
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