How Confinement Affects the Dynamics of C60in Carbon Nanopeapods
S. Rols,1,*J. Cambedouzou,2M. Chorro,2H. Schober,1V. Agafonov,3P. Launois,2V. Davydov,4
A.V. Rakhmanina,4H. Kataura,5and J.-L. Sauvajol6
1Institut Laue Langevin, F-38042 Grenoble, France
2Laboratoire de Physique des Solides UMR 8502, Universite ´ Paris-Sud, F-91405 Orsay, France
3Laboratoire d’Electrodynamique des Mate ´riaux Avance ´s, UMR CNRS-CEA 6157, F-37200 Tours, France
4Institute of High Pressure Physics of the RAS, R-142092 Troitsk, Moscow Region, Russian Federation
5Nanotechnology Research Institute, National Institute of Advanced Industrial Science (AIST),
Central 4, Higashi1-1-1, Tsukuba 305-8562, Japan
6Laboratoire des Colloı ¨des, Verres et Nanomate ´riaux (UMR CNRS 5587), Universite ´ Montpellier II,
F-34095 Montpellier Cedex 5, France
(Received 24 December 2007; revised manuscript received 1 June 2008; published 8 August 2008)
The dynamics of confined systems is of major concern for both fundamental physics and applications.
In this Letter, the dynamics of C60fullerene molecules inside single walled carbon nanotubes is studied
using inelastic neutron scattering. We identify the C60vibrations and highlight their sensitivity to
temperature. Moreover, a clear signature of rotational diffusion of the C60is evidenced, which persists
at lower temperature than in 3D bulk C60. It is discussed in terms of confinement and of reduced
dimensionality of the C60chain.
DOI: 10.1103/PhysRevLett.101.065507PACS numbers: 63.22.?m, 63.22.Gh, 64.70.kt
Nanopores, and among them carbon nanotubes , are
ideally suited to host atoms or molecules, forming guest-
host systems whose structure and thermodynamical prop-
erties are most original [2–4]. At a practical level, carbon
nanotube-based guest-host systems have significant poten-
tial for chemical separation and sensing, and for targeted
drug delivery [5,6]. Carbon nanopeapod (NPP) is one of
these systems. It is formed of one-dimensional (1D) C60
fullerene chains confined inside the hollow core of single
walled carbon nanotubes (SWNT) . In its bulk solid
state, C60crystallizes into a face centered cubic structure
at room temperature, and the molecules perform nearly
free rotations about their center of mass [8,9]. Upon cool-
ing, long range orientational order of the C60molecules is
achieved through a first order phase transition towards a
simple cubic phase at T ? 260 K. The ‘‘free’’rotations are
replaced by hindered rotations (librations) [10,11]. In this
phase, the molecules are still jumping between two orien-
tations  down to Tg ’ 85 K, where the orientations are
frozen. The situation is expected to be significantly differ-
ent for the NPP where the C60are confined inside SWNT.
Recent theoretical papers have underlined the importance
of the tube’s diameter on the configuration of the C60chain
[12–14]. In particular, Verberck and Michel [13,14] ca-
lculated that the lowest energy configuration of the C60
inside the nanotube, is the ‘‘pentagonal orientation’’ (the
nanotube’s long axis crossing the center of two opposite
pentagons at the C60’s surface) for nanotubes having a
diameter Dt? 14?A, and the ‘‘standard orientation’’ (the
nanotube’s long axis crossing the center of two opposite
double bonds at the C60’s surface) for 14?A ? Dt?
15:8? A. It is the goal of this Letter to shed light on the
dynamics of the confined C60molecules by combining
inelastic neutron scattering and Raman data measured in
a large temperature range.
A 900 mg peapod sample was prepared using the sub-
limation method  and was characterized by several
techniques [15,16]. The powder contains large bundles
with a narrow diameter distribution centered around
13.6 A˚and a large filling ratio of ?80% . In order to
remove any trace of polymerized C60inside the nanotubes
and of hydrogenated adsorbed molecules, we systemati-
cally baked the sample at 300?C under vacuum prior to the
experiment. A 300 mg raw SWNT sample showing similar
characteristics to the one obtained for the peapod sample
was used as reference. Two sets of experiments were
performed. The first set made use of the IN1BeF filter
analyzer spectrometer at the Institut Laue Langevin (ILL)
to measure the generalized density of states (GDOS) at
high energy transfers. The other set of experiments was
performed using the IN4C spectrometer with neutron inci-
dent wavelengths of 1.1, 1.8, and 2.2 A˚to complete the
measurements in the low and intermediate energy ranges.
The measurements were performed at 10 K on both instru-
ments and for peapods and nanotube samples. Additional
measurements were performed in the temperature range
[10; 300 K] on the IN4C spectrometer. The Raman data
were collected at 50 K using a 488 nm incident laser
radiation. The results obtained from the measurements
are discussed in the light of calculations of the GDOS
that we performed assuming a force field model detailed
in . All calculations were performed at 0 K in the
‘‘crystal phase’’ assuming a perfect orientational order of
the C60along the entire length of the tube. The calculations
presented here are those in the ‘‘pentagonal orientation’’ of
the inserted molecules, but several other orientations of the
PRL 101, 065507 (2008)
8 AUGUST 2008
© 2008 The American Physical Society
C60were tested. The calculated GDOSare broadened using
a Gaussian linewidth of 2 meV (full width at half maxi-
mum—FWHM) to account for the spectrometer resolu-
Figure 1 shows the GDOS and the Raman spectrum of
the peapod sample. They are compared to the GDOS of the
SWNT sample. The Raman spectrum shows the dominant
features originating from the tubes’resonant modes as well
as additional peaks, the positions of which are in reason-
able agreement with the Raman active modes for molecu-
lar C60. This indicates a weak influence of the confinement
on these modes, in agreement with previous Raman studies
already published . The nanotube GDOS has char-
acteristic features that are rendered almost perfectly by
the calculations that Ye et al.  performed on a
(10,10) armchair nanotube using density functional theory
(DFT). The peapods GDOS significantly differs from that
of the SWNT.The C60additional features modify the shape
of the large band between 150 and 200 meV. Additional
features are observed at 94, 121, and 148 meV. The low-
frequency part of the spectrum (see also Fig. 2) shows a
sequence of features at 33, 44, 50, and 53 meV that are in
good correspondence with the Hg, Guand T2u, Huand Hg
C60modes, respectively (see Fig. 2 and ). These latter
features are very sensitive to the temperature : they pro-
gressively broaden to finally disappear into a sloping back-
ground upon warming up to 300 K (for clarity purposes,
only the evolution of the Hgmode at 33 meV is presented
on Fig. 2). Moreover, there is no clear signature of any
libration mode of the confined C60in the low-frequency
part ofthe GDOS,bycontrast towhatisobservedforC60in
its ordered phase and to what is predicted by the calcula-
Figure 3 represents the results of the low-frequency
study of the NPP dynamics. Several representations are
used on the same figure. First, the scattering function
S?Q;!? measured at 280 K is represented as a 2D graph
using an appropriate color scheme (bottom right image). A
signal appearing in the so-called quasielastic region, and
having a strong Q dependence is clearly evidenced. The
particularity of this signal stands in the two lobes centered
on 3.4 and 5:5?A?1. Each of the spectra located at a fixed Q
value can be fitted by the superposition of an elastic
component (the delta function or the spectrometer func-
tion) and of a Lorentzian line shape modeling the quasi-
elastic signal. The energy integrated intensity of the
Lorentzian line is displayed in Fig. 3(c) (squares), where
it is compared to the theoretical dependence calculated for
a coherent quasielastic signal originating from ‘‘free’’
(isotropic) rotations of the C60molecules [8,10,11], and
from uniaxial 1D rotations of molecules in the pentagonal
or standard orientations. The Q dependence of the experi-
mental intensity seems in good agreement with all these
models, the low quality of our data at high Q making a
discrimination between them difficult. However, Michel
and Verberck  predict that C60pentagonal orientations
in 13.6 A˚peapods are separated by barriers that can be as
small as 30 K (this is the energy difference between the
standard and pentagon orientation). Therefore, ‘‘pseudo’’
isotropic rotations—implying more or less complex reor-
ientations of the molecules around different axes—appear
morelikely.Moreover,onewouldexpect oscillations ofthe
FIG. 1 (color online).
peapod sample (top spectrum) and of the SWNT sample (middle
spectrum) measured at 10 K using the IN1BeF spectrometer
compared with the Raman spectrum of the peapod sample (full
line spectrum). The Raman active Agand Hgmodes are marked
with a star and a cross symbol, respectively. Note that the Raman
spectrum is plotted on a logarithmic scale for the y axis.
Generalized density of states of the
FIG. 2 (color online).
peapod sample measured on the IN4C spectrometer at 10 K
(a), 150 K (b), 300 K (c), and the one calculated using the model
developed in the text (d). The GDOS of a pure C60sample
measured at 10 K (e) is also shown for comparison. Inset: the
GDOS calculated for a NPP model (squares and triangles) and
for a SWNT model (labeled ‘‘SWNT,’’ full line). The GDOS
were folded with a Gaussian function (2 meV FWHM) to
account for the instrument resolution. The curve with triangles
symbols has its part originating from the C60vibrations further
folded with a Lorentzian having a FWHM of 6 meV to mimick
the effect of the C60rotations (see text).
Generalized density of states of the
PRL 101, 065507 (2008)
8 AUGUST 2008
molecules around axes perpendicular to the tubes in the
case of 1D rotations. These would show up as librations
bands in the inelastic region, in contrast to what is
The relaxation nature of the signal can further be
checked by correcting the scattering function for the ther-
mal occupation. The corrected function is directly related
to the imaginary part of the susceptibility ?00?Q;!?
through the fluctuation-dissipation theorem: S?Q;!? ?
??1 ? exp??@!
use the convenient representation !?1?00?Q;!? and will
often call this function susceptibility . This represen-
tation is used in Figs. 3(a) and 3(b) for two different Q
vectors: at Q ? 1:8?A?1, the susceptibility measured at
50 K, 100 K, and 200 K are observed to superimpose,
which is characteristic of a phononlike temperature depen-
dence. At Q ? 5:4? A?1, however, a clear jump is observed
between the susceptibility measured at 200 K and those
measured at 100 K and 50 K, the two last superimposing.
The difference in the temperature dependence of the sus-
ceptibility at different Q can be explained bythe fact that at
low Q, the structure factor of the C60rotation is very weak
so that the signal measured is mainly originating from low-
frequency excitations. These can be low lying radial de-
formation modes of carbon nanotubes and out-of-plane
k?T???1?00?Q;!?. In the following, we will
acoustic phononsfrom thegraphitic impurities  present
in the sample. In particular, the latter contribution is maxi-
mum in this Q range as the (0 0 2) diffraction peak of
graphite is observed at 1:85?A?1. This is not the case at
higher Q values where the quasifree rotations of the C60
molecules dominate the signal (see the two clear peaks in
the structure factor located at 3.4 and 5:5?A?1) implying a
nonbosonic T dependence in this Q range. At this point, it
is necessary to emphasize that our data suggest that the C60
are performing fast diffusional reorientations at a tempera-
ture of 200 K, a temperature which is 60 K lower than the
260 K order-disorder transition temperature for cubic C60.
A clear change in the C60dynamics occurs while lowering
the temperature from 200 K down to 100 K. The boson-
dependence of the intensity of the signal at T ? 100 K
suggests that the C60rotation has lost its relaxation nature.
This change in the dynamics can be made responsible for
the drastic temperature dependence of the C60vibrations.
Under the assumption of a complete decoupling between
the intramolecular modes of the C60and their rigid-body
rotations, the scattering function of the C60intramolecular
modes is the convolution of that of the rotations (i.e., a
Lorentzian line shape) with a delta function (i.e., the
spectrometer resolution function) centered at the frequency
of the modes. To appreciate quantitatively this effect, the
part of the numerical GDOS associated with the C60vi-
brations was folded with a Lorentzian having a 6 meV
FWHM.Thevalue of 6 meVis thewidth of the quasielastic
broadening measured using the 1.1 A˚incident wavelength
at 300 K. This value is consistent with the value of the
quasielastic width at large Q values  measured for C60
in its disordered phase at the same temperature. The results
of the calculation are presented in the inset of Fig. 2, where
it is evident that the fast rotations make the sharp features
from the fullerenes unobservable by merging them into the
background originating essentially from the nanotube
The main result from this study certainly stands in the
surprisingly high orientational mobility of the C60mole-
cules -down to relatively low temperatures- when confined
inside a nanotube. We already mentioned that these mole-
cules undergo ‘‘free’’ rotations down to a transition tem-
perature Ttwhich is much lower than its unconfined 3D
equivalent of 260 K (100 K ? Tt? 200 K). Moreover,
this transition is not followed by the appearance of intense
and sharp inelastic features originating from librational
modes like for 3D cubic C60and characteristics of an
orientational ordering. This implies that the transition is
different in nature in each case. A possible scenario able to
interpret the experimental data has to account for the
specificity of the C60when confined in a 13.6 A˚diameter
nanotube with a strong filling factor. Michel and Verberck
[13,14] predict very small barrier for C60reorientations
inside 14 A˚diameter tubes. Therefore, while the nanotube
field restricts the center of mass position of the fullerenes
FIG. 3 (color online).
S?Q;!? measured for the NPP sample at 280 K. Intensity is
given by the classical thermal color scale. The intense elastic line
centered at 0 meV is saturating the image (dark horizontal line).
(a) and (b) Temperature dependence of the NPP susceptibility
!?1?00?Q;!? (triangles ? 200 K; circles ? 100 K; squares ?
50 K) measured at two wave vector transfers (a) Q ? 1:8?A?1;
(b) Q ? 5:4?A?1). The susceptibility of ‘‘bulk’’ C60is also
drawn in (b) (bottom spectrum line, T ? 200 K) showing the
librations peaks at ? ? 2:5 meV. (c) Integrated intensity of the
quasielastic signal measured at 280 K (squares) and calculated
for a free rotation model of the C60(full line) and for 1D rotation
models in the pentagonal orientation (long dashes) and the
standard orientation (dots).
Bottom right: the scattering function
PRL 101, 065507 (2008)
8 AUGUST 2008
on a 1D chain along the nanotube axis, the molecular Download full-text
orientation of these molecules will be monitored by neigh-
boring C60-C60interactions. This system can be described
by a 1D-Ising type of model with nearest neighbor inter-
actions between the C60and with a static random field
originating from the multitude of energetically very similar
orientations of the C60with regards to the host. In that
picture, there is no proper ordering of the C60at finite
temperature, and the molecules can statistically adopt a
large number of orientations. Atlowtemperature, however,
the weak but nonzero potential barrier that a C60has to
overcome to change from one orientation to another be-
comes non-negligible, and the molecules are pinned in
various orientations in a time scale of the instrument
resolution (i.e., in a ps time scale). Additional ingredients
could be introduced in the model to give a more accurate
description of the reduction of orientational mobility like
the role of defects at the tube surface or the nonuniform
filling of the tubes.
We have calculated that the librations of the C60appear
as well-defined features in the GDOSof a perfect crystal of
peapods. However, its frequency is very sensitive to the
orientation of the C60, ranging from ?0 up to 3.5 meV. A
distribution of orientations results in a distribution of li-
bration frequencies which would appear as a broad
‘‘quasielastic-like’’ signal. Its intensity would follow a Q
dependence very similar to the one expected for free
rotations (as it is the case for cubic C60). Moreover,
any coupling with the low-frequency nanotube modes will
further broaden the response of the librations. The absence
of well-defined features associated to librations in the low-
frequency region of the GDOS, even at the lowest tem-
perature we considered (5 K), is somehow not surprising as
far as a ‘‘static’’ orientational disorder of the C60is con-
sidered. It is important to note that below 100 K, our data
are unable to give more precise information about slower
relaxations in this system. In particular, any reorientation
of the C60in a time scale larger than the picoseconds is out
of reach. Additional experimental investigations, and, in
particular, relaxation thermal measurements similar to
those performed to study the glass transition in crystalline
C60, would be of great interest in order to shed light on
the thermodynamic state of the confined fullerenes at low
In conclusion, we have used inelastic neutron scattering
to probe the dynamics of NPP in a large energy and Q
range. At a temperature of 10 K, the intramolecular modes
of C60are clearly observed forthe firsttime and are in good
agreement with what is expected from our calculations. At
high temperature, a Q-dependent quasielastic signal is
observed and attributed to rotations of the confined C60.
The temperature dependence of this signal shows a strong
reduction of the orientational mobility of the C60at a
temperature 100 K ? Tt? 200 K, but the absence of
well-defined libronic excitations at low temperature sug-
gests a strong orientational disorder even at the lowest
temperature reached (5 K). These results raise new ques-
tions both for experimentalists and theoreticians.
The authors acknowledge Dr. R. Almairac, Dr. L.
Alvarez, and Dr. C. Goze-Bac for fruitful scientific dis-
cussions. This work benefited from the expert assistance of
Dr. H. Mutka, Dr. J. Stride, and Dr. A. Ivanov during the
Note added in proof.—Recently, the authors became
aware of a NMR study on the C60relaxations inside
SWNT . We recommend reading this article as a
complement to our work.
Montpellier II, F-34095 Montpellier Cedex 5, France.
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