Radial thermal expansion of pure and Xe-saturated bundles of single-walled carbon nanotubes at low temperatures
The radial thermal expansion coefficient ar of pure and Xe-saturated bundles of single-walled carbon nanotubes (CNT) has been measured in the interval 2.2-120 K. The coefficient is positive above T = 5.5 K and negative at lower temperatures. The experiment was made using a low-temperature capacitanc...
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nasplib_isofts_kiev_ua-123456789-1172182025-06-03T16:26:44Z Radial thermal expansion of pure and Xe-saturated bundles of single-walled carbon nanotubes at low temperatures Dolbin, A.V. Esel'son, V.B. Gavrilko, V.G. Manzhelii, V.G. Popov, S.N. Vinnikov, N.A. Danilenko, N.I. Sundqvist, B. Наноструктуры при низких температурах The radial thermal expansion coefficient ar of pure and Xe-saturated bundles of single-walled carbon nanotubes (CNT) has been measured in the interval 2.2-120 K. The coefficient is positive above T = 5.5 K and negative at lower temperatures. The experiment was made using a low-temperature capacitance dilatometer with a sensitivity of 2·10⁻⁹ cm and the sample was prepared by compacting a CNT powder such that the pressure applied oriented the nanotube axes perpendicular to the axis of the cylindrical sample. The data show that individual nanotubes have a negative thermal expansion while the solid compacted material has a positive expansion coefficient due to expansion of the intertube volume in the bundles. Doping the nanotubes with Xe caused a sharp increase in the magnitude of ar in the whole range of temperatures used, and a peak in the dependence ar(T) in the interval 50-65 K. A subsequent decrease in the Xe concentration lowered the peak considerably but had little effect on the thermal expansion coefficient of the sample outside the region of the peak. The features revealed have been explained qualitatively. We wish to thank Prof. V.M. Loktev for valuable discussion. The authors are indebted to the Science and Technology Center of Ukraine (STCU) for the financial support of this study (project No. 4266). 2009 Article Radial thermal expansion of pure and Xe-saturated bundles of single-walled carbon nanotubes at low temperatures / A.V. Dolbin, V.B. Esel'son, V.G. Gavrilko, V.G. Manzhelii, S.N. Popov, and N.A.Vinnikov, N.I. Danilenko, B. Sundqvist // Физика низких температур. — 2009. — Т. 35, № 6. — С. 613-621. — Бібліогр.: 50 назв. — англ. 0132-6414 PACS: 74.70.Wz https://nasplib.isofts.kiev.ua/handle/123456789/117218 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Наноструктуры при низких температурах Наноструктуры при низких температурах |
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Наноструктуры при низких температурах Наноструктуры при низких температурах Dolbin, A.V. Esel'son, V.B. Gavrilko, V.G. Manzhelii, V.G. Popov, S.N. Vinnikov, N.A. Danilenko, N.I. Sundqvist, B. Radial thermal expansion of pure and Xe-saturated bundles of single-walled carbon nanotubes at low temperatures Физика низких температур |
| description |
The radial thermal expansion coefficient ar of pure and Xe-saturated bundles of single-walled carbon nanotubes (CNT) has been measured in the interval 2.2-120 K. The coefficient is positive above T = 5.5 K and negative at lower temperatures. The experiment was made using a low-temperature capacitance dilatometer with a sensitivity of 2·10⁻⁹ cm and the sample was prepared by compacting a CNT powder such that the pressure applied oriented the nanotube axes perpendicular to the axis of the cylindrical sample. The data show that individual nanotubes have a negative thermal expansion while the solid compacted material has a positive expansion coefficient due to expansion of the intertube volume in the bundles. Doping the nanotubes with Xe caused a sharp increase in the magnitude of ar in the whole range of temperatures used, and a peak in the dependence ar(T) in the interval 50-65 K. A subsequent decrease in the Xe concentration lowered the peak considerably but had little effect on the thermal expansion coefficient of the sample outside the region of the peak. The features revealed have been explained qualitatively. |
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Article |
| author |
Dolbin, A.V. Esel'son, V.B. Gavrilko, V.G. Manzhelii, V.G. Popov, S.N. Vinnikov, N.A. Danilenko, N.I. Sundqvist, B. |
| author_facet |
Dolbin, A.V. Esel'son, V.B. Gavrilko, V.G. Manzhelii, V.G. Popov, S.N. Vinnikov, N.A. Danilenko, N.I. Sundqvist, B. |
| author_sort |
Dolbin, A.V. |
| title |
Radial thermal expansion of pure and Xe-saturated bundles of single-walled carbon nanotubes at low temperatures |
| title_short |
Radial thermal expansion of pure and Xe-saturated bundles of single-walled carbon nanotubes at low temperatures |
| title_full |
Radial thermal expansion of pure and Xe-saturated bundles of single-walled carbon nanotubes at low temperatures |
| title_fullStr |
Radial thermal expansion of pure and Xe-saturated bundles of single-walled carbon nanotubes at low temperatures |
| title_full_unstemmed |
Radial thermal expansion of pure and Xe-saturated bundles of single-walled carbon nanotubes at low temperatures |
| title_sort |
radial thermal expansion of pure and xe-saturated bundles of single-walled carbon nanotubes at low temperatures |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2009 |
| topic_facet |
Наноструктуры при низких температурах |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/117218 |
| citation_txt |
Radial thermal expansion of pure and Xe-saturated bundles of single-walled carbon nanotubes at low temperatures / A.V. Dolbin, V.B. Esel'son, V.G. Gavrilko, V.G. Manzhelii, S.N. Popov, and N.A.Vinnikov, N.I. Danilenko, B. Sundqvist // Физика низких температур. — 2009. — Т. 35, № 6. — С. 613-621. — Бібліогр.: 50 назв. — англ. |
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Физика низких температур |
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Fizika Nizkikh Temperatur, 2009, v. 35, No. 6, p. 613–621
Radial thermal expansion of pure and Xe-saturated
bundles of single-walled carbon nanotubes at
low temperatures
A.V. Dolbin, V.B. Esel’son, V.G. Gavrilko, V.G. Manzhelii,
S.N. Popov, and N.A.Vinnikov
B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine
47 Lenin Ave., Kharkov 61103, Ukraine
E-mail: dolbin@ilt.kharkov.ua
N.I. Danilenko
Frantsevich Institute for Problems of Materials Science of the National Academy of Sciences of Ukraine
3 Krzhizhanovsky Str., Kyiv 03680, Ukraine
B. Sundqvist
Department of Physics, Umea University, SE-901 87 Umea, Sweden
Received February 13, 2009
The radial thermal expansion coefficient � r of pure and Xe-saturated bundles of single-walled carbon
nanotubes (CNT) has been measured in the interval 2.2–120 K. The coefficient is positive above T � 5.5 K
and negative at lower temperatures. The experiment was made using a low-temperature capacitance
dilatometer with a sensitivity of 2·10
–9
cm and the sample was prepared by compacting a CNT powder such
that the pressure applied oriented the nanotube axes perpendicular to the axis of the cylindrical sample. The
data show that individual nanotubes have a negative thermal expansion while the solid compacted material
has a positive expansion coefficient due to expansion of the intertube volume in the bundles. Doping the
nanotubes with Xe caused a sharp increase in the magnitude of � r in the whole range of temperatures used,
and a peak in the dependence � r T( ) in the interval 50–65 K. A subsequent decrease in the Xe concentration
lowered the peak considerably but had little effect on the thermal expansion coefficient of the sample out-
side the region of the peak. The features revealed have been explained qualitatively.
PACS: 74.70.Wz Fullerenes and related materials.
Keywords: single-walled carbon nanotubes, bundles of carbon nanotubes, radial thermal expansion.
Introduction
Since the discovery of carbon nanotubes (CNTs) in
1991 [1], this novel class of physical objects has been
stimulating intense experimental and theoretical research
activities. The diversity of CNT types and the problems
encountered in obtaining pure CNT material in quantities
needed for experimental investigations make it rather dif-
ficult to trace the basic trends in the behavior of carbon
nanotubes (e.g., see the text and references in [2]). Ther-
mal expansion is one of the least studied properties of
CNTs. The currently available experimental evidence
on the thermal expansion of single-walled nanotubes
(SWNTs) and their bundles is confined to the region near
and above room temperature, whereas low-temperature
data are essential for understanding the CNT dynamics.
The theoretically estimated thermal expansion coeffi-
cients (TEC) of SWNTs [3–9] vary appreciably both in
magnitude and sign.
Owing to their unique geometry, CNTs can be a basis
for forming novel low-dimensional systems. For exam-
ple, bundles can be used as templates to form one-dimen-
sional chains or two-dimensional surfaces consisting of
condensed impurity molecules.
© A.V. Dolbin, V.B. Esel’son, V.G. Gavrilko, V.G. Manzhelii, S.N. Popov, N.A.Vinnikov, N.I. Danilenko, and B. Sundqvist, 2009
In recent years much experimental effort has been de-
voted to the study of structural and thermal properties of
such systems and a number of theoretical models have
been advanced to predict these properties [10–23]. How-
ever, the thermal expansion behavior of SWNT–gas im-
purity systems still remains obscure.
In this study the radial thermal expansion was measured
on a sample consisting of bundles of single-walled
nanotubes closed at the ends (c-SWNT) in the range
T � 2 2. –120 K and on bundles of SWNTs saturated with Xe
at T � 2.2–75 K. The sorption properties of bundles of
SWNTs with closed (c-SWNT) and open (o-SWNT) ends
were investigated using the technique described below.
1. Radial thermal expansion of pure single-walled
carbon nanotubes
1.1. Measurement technique and investigated sample
The sample for thermal expansion measurements was
prepared using a procedure for ordering the SWNT axes
by applying a pressure of 1 GPa, as described by Bendiab
et al. [24]. These authors showed that in SWNT plates of
up to 0.4 mm thickness, such a pressure aligned the CNT
axes in the sample such that their average angular devia-
tion from a plane normal to the pressure vector was ~ .4�
The starting material was a CNT powder (CCVD me-
thod, Cheap Tubes, USA) which according to the manu-
facturer contained over 90% of SWNTs. The main charac-
teristics are given in the Table 1.
Table 1. Characteristics of carbon nanotube powder given by the
manufacturer
Diameter 1–2 nm
Length 5–30 �m
SWNT fraction > 90 wt %
Amorphous carbon fraction < 1.5 wt %
Co catalyst fraction 2.9 wt %
Specific surface > 407 m
2
/g
Electrical conduction > 102 S/cm
The quality of the powder was confirmed by Raman
analysis performed both by the supplying company and at
Umea University, Sweden. According to the manufac-
turer, the average outer diameter of the tubes was 1.1 nm
but no information is available about the chirality distri-
bution. From our own Raman data, obtained using four
different excitation lasers with wavelengths in the range
541–830 nm, we find that the radial breathing modes indi-
cate a wide range of tube diameters, 0.8–2.1 nm. All sam-
ples studied show typical SWNT G-bands and only weak
disorder bands. Although multi-wall tubes may also be
present, judging from the spread in diameters, the Raman
spectra are completely dominated by the response from
single (or possibly few) wall nanotubes. However, a small
fraction of SWNTs might be invisible due to their large
diameters and possibly lower Raman cross sections.
The starting SWNT powder was also investigated
by high-resolution transmission electron microscopy
(HRTEM) at both the Institute of Problems of Material
Science, NAS of Ukraine (Fig. 1,a) and at Umea Univer-
sity, Sweden (Fig. 1,b). The pictures show that large sam-
ple fractions contain little amorphous carbon or residual
catalyst. By measuring the bundle diameters we estimate
that in the starting powder each bundle contains 7 to 600
SWNTs.
614 Fizika Nizkikh Temperatur, 2009, v. 35, No. 6
A.V. Dolbin, V.B. Esel’son, V.G. Gavrilko, V.G. Manzhelii, S.N. Popov, N.A.Vinnikov, N.I. Danilenko, and B. Sundqvist
a
b
Fig. 1. TEM images of the starting SWNT powder.
The compacted sample used was prepared at Umea
University (Sweden) by first compacting pressure-ori-
ented (P � 1.1 GPa) SWNT plates (an individual plate was
up to 0.4 mm thick), then pressing several stacked plates
together at a ten percent higher pressure to form a cylin-
der 7.2 mm high and 10 mm in diameter with a density of
1.2 g/cm3. The sample was made in a special cylindrical
segmented die designed for compacting CNT powder un-
der effective pressures 0.5–2 GPa, consisting of a ring
with a cylindrical channel and a conical outer surface,
which was inserted into a hardened-steel cylinder sup-
ported inside a larger pressure vessel. The structure so ar-
ranged was resistant to internal stresses. The 10 mm in di-
ameter piston was made from sintered tungsten carbide
(WC). The pressures used were high enough to consoli-
date the powder into a solid with well oriented tubes [24],
but still low enough to keep the integrity and structure of
the tubes and avoid tube collapse, and Raman spectra
taken on pressed plates showed no systematic changes
relative to spectra taken on the pristine powder. The sam-
ple prepared by this technology has a pronounced aniso-
tropy of properties in the directions perpendicular and
parallel to the sample axis. In the direction perpendicular
to the applied pressure the axes of the SWNT bundles are
disordered. The compaction aligns the axes of the SWNT
bundles in the plane perpendicular to the sample axis
[24]. As a result the radial component of the expansion of
the SWNT bundles makes a dominant contribution to the
thermal expansion of the sample in the directional parallel
to the sample axis. If the axial component of the thermal
expansion coefficient has a magnitude comparable to that
of the radial one, an angle of typically 4 � implies that the
typical contribution to the total coefficient from the axial
component is about 7 % of the magnitude of the radial
component.
The radial thermal expansion of the sample was investi-
gated using a capacitance dilatometer (its design and the
measurement technique are described in Ref. 25). The
linear thermal expansion coefficient (LTEC) was measured
in the direction of the applied compacting pressure, i.e., ra-
dially to the SWNT bundles. Prior to measurement, the gas
impurities were removed from the sample by dynamic
evacuation for 72 h at 10–3 mm Hg and room temperature.
Immediately before dilatometric investigation, the measur-
ing cell with the sample was cooled slowly (for 8 h) down
to liquid helium temperature (4.2 K) and the sample was
held at this temperature for about 4 h. The cooling and in-
vestigation were made in vacuum down to 10–5 mm Hg.
1.2. Experimental results and discussion
The temperature dependence of the LTEC in the inter-
val 2.2–120 K is shown in Fig. 2. The curves were ob-
tained by least-square averaging over several series of
measurement.
Curve 2 was taken on the first heating of the sample
from T � 2.2 K. Curve 1 data were measured in the sub-
sequent heating–cooling process. The nonequilibrium
LTECs obtained on the first heating from T � 2.2 K may
account for heating-induced alignment and ordering of
the bundles and the nanotubes in them, which causes a
compression of bundles and, as a result, negative thermal
expansion.
The equilibrium radial LTEC � r (curve 1) is positive
above 5.5 K and negative at lower temperatures.
Assuming that the impurity effect is negligible, �r com-
prises two components �d and �g accounting for tempera-
ture-induced changes in the CNT diameters and the inter-
tube gap. From a simple Gr�neisen-type model it might be
expected that �d should be similar to the in-plane thermal
expansion of graphite, and thus probably small and negative
well below room temperature. Because the sample is a
Radial thermal expansion of pure and Xe-saturated bundles of single-walled carbon nanotubes at low temperatures
Fizika Nizkikh Temperatur, 2009, v. 35, No. 6 615
5 10 15 20
–1
0
1
2
3
4
5
T, K
1
2
20 40 60 80 100 120
–60
–40
–20
0
20
40
60
80
100
T, K
1
2
a
b
Fig. 2. LTECs of pressure-oriented SWNT compacted sample
in the direction perpendicular to the SWNT bundle axes: a) T �
= 2.2–120 K; b) T � 2.2–25 K (curve 1 — heating and cooling,
curve 2 — first heating from T � 2.2 K).
mixture of all chiralities, the average �d should also be very
similar to the average axial expansion coefficient of the
tubes. The thermal expansion of a bundle should thus proba-
bly be dominated by � g , which should be similar to the
out-of-plane thermal expansion of graphite or, considering
the curvature, to the thermal expansion of fullerenes or lin-
ear fullerene polymers [26].
So far there has been only one study [27] in which both
�d and �g were measured by the x-ray diffraction
method in the interval 300–950 K. At T � 300 K �r =
= (0.75 ± 0.25)·10–5 K–1, �d = (–0.15 ± 0.2)·10–5 K–1
and �g = (4.2 ± 1.4) · 10–5 K–1. Another measurement, of
�r only, by the same method [28] arrived at negative val-
ues in the whole range of measurement temperatures
(200–1600 K). We are not aware of further experimental
attempts to directly investigate the thermal expansion of
SWNT bundles, but some experiments have been made to
estimate the thermal expansion from the temperature de-
pendence of the radial breathing Raman modes of
nanotubes. Although these modes shift down rapidly with
increasing temperature, indicating a large strong positive
thermal expansion coefficient, it was concluded by
Raravikar et al. [7] that this effect is almost completely
caused by changes in intra- and intertube interactions,
and that �d is very small.
It is rather problematic to compare our results with the-
oretical data quantitatively, mainly because the available
theoretical studies are concerned with the radial and axial
thermal expansion of individual CNTs. Some of them of-
fer general conjectures on how thermal expansion can be
affected by the interaction of nanotubes in a bundle (e.g.,
see Ref. 8). Also, there is little agreement between the
theoretical conclusions from different groups about the
TEC magnitude, sign and temperature dependence, about
the effect of chirality and CNT diameter upon thermal ex-
pansion, and about the correlation between the radial and
axial components of the thermal expansion of nanotubes.
For example, the thermal expansion is negative in a wide
temperature interval (0–800 K) in Ref. 4, changes from
negative magnitudes at low temperatures to positive ones
at moderate and high temperatures in Ref. 8 or is positive
at all the temperatures investigated in Ref. 6.
The qualitative interpretation of our results is based on
the Gr�neisen coefficients calculated [8] for carbon modi-
fications — diamond, graphene, graphite and nanotubes. It
is found [8] that the Gr�neisen coefficients and the radial
thermal expansion of CNTs are negative at relatively low
temperatures, an effect caused mainly by the contribution
from transverse acoustic vibrations perpendicular to the
CNT surface. However, our measurements show that a
negative thermal expansion coefficient exists only in a
temperature interval much more narrow than found in the
calculations [8]. We believe that the main reason for this is
that the calculations were performed for individual
nanotubes only [8]. Our sample is clearly dominated by
CNT bundles (Fig. 1), and in this case additional factors
contributing to the thermal expansion come into play.
Firstly, there appears a positive contribution � g caused by
variations of the intertube gaps with temperature. Sec-
ondly, the nanotube interaction in the bundles suppresses
the negative contribution of the transverse acoustic vibra-
tions perpendicular to the nanotube surfaces [8]. These two
positive contributions to the thermal expansion of SWNT
bundles decrease both the magnitude and the temperature
region of the total negative thermal expansion. If we use
this model and assume � d to vary slowly with temperature
over a wide temperature interval we can use the data shown
in Fig. 2,b to estimate � d = (–4 ± 1)�10–8 K–1 at T � 2.2 K.
Assuming further that the temperature dependent part of �
at low temperatures is dominated by a positive coefficient
� g , we see from Fig. 2,b that a polynomial of the third or-
der in T is a good approximation to � g T( ) up to about
25 K. Although the scatter in the data is somewhat high it
is clear that to get a good fit it is necessary to include one
term in T 3 and one term linear (or, with a less good fit, qua-
dratic) in T . In a Gr�neisen model, the thermal expansion
coefficient of a bundle is closely related to its specific heat
capacity, and it is well known that the experimentally
found low-temperature specific heat of nanotube bundles
shows a similar behavior above 2 K [29]. In that case the
experimental behavior c T aT bTp ( ) � �
3 could be fitted
by an anisotropic two-band Debye model with weak cou-
pling between tubes in the bundle by adding a contribution
from the first optic branch. It thus seems quite reasonable
to attribute the strongly temperature dependent positive
component of the total thermal expansion to � g . The data
in Fig. 2,a also shows a noticeable plateau-like structure
between 40 and 60 K. We point out that the intermolecular
interaction in C60, which should be similar in magnitude to
the inter-tube interaction, corresponds to an effective
Debye temperature near 50–60 K which gives rise to a pla-
teau in the specific heat in this range for both molecular
and polymeric C60 [30]. The plateau structure observed
here might thus indicate the cross-over between the acous-
tic modes and the lowest optical/molecular 3D modes in
the bundle lattice.
2. Xe sorption in the powder of carbon nanotubes
with closed and open ends
2.1. Measurement technique and investigated samples
Carbon nanotubes prepared by standard methods (elec-
tric-arc, laser evaporation of carbon, or CCVD method) are
arranged into bundles. Inside a bundle the CNTs form a
close-packed two-dimensional triangular lattice [31]. Nor-
mally, CNTs have fullerene-like semispheres at the ends
(CNTs with closed ends, or c-SWNT). The final CNT
product can contain large amounts of amorphous carbon,
616 Fizika Nizkikh Temperatur, 2009, v. 35, No. 6
A.V. Dolbin, V.B. Esel’son, V.G. Gavrilko, V.G. Manzhelii, S.N. Popov, N.A.Vinnikov, N.I. Danilenko, and B. Sundqvist
fullerenes and other carbon modifications [2,31–37]. The
currently used methods of cleaning CNT materials involve
oxidative treatment with acid-oxidant mixtures, ozone [38],
etc. They lead to partial or complete opening of the CNT
ends and produce defects at the lateral surfaces.
The possible sites for sorption of gas impurity molecules
in bundles of infinite, open and equal-diameter SWNTs are
shown in Fig. 3. However, in practice such SWNT systems
can have additional zones of impurity sorption. For exam-
ple, nanotubes of different diameters form rather large chan-
nels parallel to the nanotube axes, which can be occupied by
impurity molecules [39]. Besides, oxidation can produce in-
terstices between the nanotubes in a bundle [18].
We investigated Xe sorption in c-SWNT and o-SWNT
powders at T � 78–200 K. The choice of the temperature
interval and the impurity was dictated by the following
considerations. The interaction of gas impurities with dif-
ferent parts of the CNT surface is most evident at low tem-
peratures. Owing to their geometric configuration, SWNT
bundles ideally (Fig. 3) have favorable sites where sorp-
tion of impurity molecules is energy-advantageous. A
number of theoretical models were proposed [39–43] to
describe the physical sorption and dynamics of admixed
gas molecules at the surface and in the interstitial channels
of SWNT bundles. According to mathematical simulations
[43], the inner CNT surfaces and the interstices between
the neighboring tubes at the surface of SWNT bundles (the
grooves — G, Fig. 3) are the most energy-advantageous
sites for sorbing impurity gas molecules. Xe was used
because the SWNT–Xe system is already a well-studied
«model» system [44–47]. A Xe atom is too large to pene-
trate into the interstitial channels (IC) of close-packed bun-
dles of identical nanotubes whose energy of binding to im-
purity molecules is comparable to that at the inner surface
[20]. Therefore, the Xe impurity is sorbed inside a na-
notube (I), in a groove between two neighboring tubes at
the outer surface of a bundle (G) and at the surface of the
individual tubes forming the outer surface of a bundle (S)
(see Fig. 3).
To obtain the necessary information about gas im-
purity desorption from CNT materials, a laboratory test
bench (Fig. 4) was constructed for investigating the pro-
cess of Xe sorption and desorption in a CNT powder at
T � 78–200 K.
The measuring cell V1 containing a CNT sample was
filled with Xe at 12 torr and cooled slowly to T � 78 K. At
this temperature the xenon available in the cell was sorbed
by the CNT powder and condensed on the cell walls. The
cell temperature was then increased in steps of 5 K. The Xe
evaporated from the cell surface and was desorbed from
different sites of the SWNT bundle surface. The evapo-
rated Xe was condensed in the vessel V2 cooled with liquid
nitrogen. When the stepwise heating brought the pressure
in the V1–V2 system to a constant value, the cell V1 with
the sample was separated from the vessel V2. The Xe con-
densed in the vessel V2 was evaporated and its pressure in
the system was measured with the capacitive pressure
transducer 5. With the volume of the system known, we
could estimate the quantity of Xe desorbed from the sam-
ple at a particular temperature. To reduce the error due to
the temperature gradient over the vessel V2, the vessels V2
and V3 were minimized to the form of capillaries 1 mm in
diameter. After each measurement run, Xe was recon-
densed from vessel V2 to vessel V3.
Radial thermal expansion of pure and Xe-saturated bundles of single-walled carbon nanotubes at low temperatures
Fizika Nizkikh Temperatur, 2009, v. 35, No. 6 617
S
G
G
GG
G
GG
GG
S
S
S
S
S
SS
IC
IC
IC
IC
ICIC
I
I
I
I
I
I
I
IC
S
– interstitial site
– groove site
– bundle surface site
– interior siteI
G
Fig. 3. Sites of possible sorption of gas impurity molecules in
bundles of infinite, open and equal-diameter SWNTs.
1
2
3
4
5 6
7 8 9
10
11
Pump
4He
4He
V2 V3
PC
V1
Fig. 4. Schematic view of the laboratory test bench for investi-
gation of gas sorption–desorption in CNT samples at low tem-
peratures: 1 — sample of nanotubes; 2, 3, 10 — heaters; 4, 11
— temperature sensor (silicone diode DT-470); 5 — pressure
transducer (capacitance manometer MKS Baratron 627B); 6 —
gas input; 7 — digital multimeter (Keithley 2700); 8 — tem-
perature controller (Cryo-Con model 34); 9 — matching de-
vice (Advantech PCI-1670).
2.2. Results and discussion
The sorption properties of the starting pure c-SWNT
powder (0.0416 g) were investigated through thermo-pro-
grammed desorption (see above). Figure 5 illustrates the
temperature distribution of the desorbed impurity. The
greatest quantities of Xe were desorbed at T � 125–135 K.
In the case of close-packed bundles of infinite equal-di-
ameter SWNTs (Fig. 3), the highest desorption of Xe in
this temperature interval is expected from the grooves at
the outer bundle surface (G) and from the interior chan-
nels of some nanotubes (I) because Xe atoms have the
highest and nearly equal binding energies at these sites
[47]. In our powder the desorption can be enhanced con-
siderably by removal of Xe atoms from the axial large-di-
ameter channels (IC). Such channels are possible in bun-
dles of nanotubes of varying diameters. Xenon can
penetrate into interior channels through defects at the
ends or the lateral surfaces that can be present in some
nanotubes of the starting powder. A rather small quantity
of Xe was also desorbed at T � 100–105 K, which may be
due to removal of the layers (S) of Xe molecules that form
at the outer surface of SWNT bundles.
To open the nanotube ends, a portion (0.0705 g) of the
starting powder was placed into a capsule which was then
evacuated for 8 h and heated to 450 �C. At this tempera-
ture the capsule was filled with air for 12 min under atmo-
spheric pressure. According to the literature data, the
ends of over 90% of CNTs can be opened through this
procedure [48]. Thereafter, the capsule was evacuated
again to about 10–3 mm Hg, heated to 750 �C and held at
this temperature for an hour to remove the gaseous oxida-
tion products. The post-treatment weighting showed a
loss of ~ 5% in the powder mass.
The sorption properties of the nanotubes with the
opened ends were then investigated using the same
thermoprogrammed desorption technique (see above).
The oxidation-induced opening of the CNT ends made the
inner CNT surfaces and the intertube interstice in the bun-
dles accessible to Xe sorption [18], which enhanced the
sorption capacity of the SWNT powder almost fivefold as
compared to the starting material (see Fig. 5).
3. Radial thermal expansion of xenon-saturated
single-walled carbon nanotubes. Discussion
The radial thermal expansion of Xe-saturated SWNTs
was also investigated on the compacted sample used previ-
ously to measure the LTECs of pure SWNTs. The measure-
ment technique is described in Sec. 1. Immediately before
measurement, the cell with a pure CNT sample was evacu-
ated at room temperature for 96 h and then filled with Xe at
760 mm Hg. The evacuated measuring cell of the
dilatometer with the sample in the Xe atmosphere was
cooled to 90 K. At this temperature it was evacuated again
and then cooled to liquid helium temperature. The thermal
expansion was measured in vacuum down to 1·10–5 mm Hg.
618 Fizika Nizkikh Temperatur, 2009, v. 35, No. 6
A.V. Dolbin, V.B. Esel’son, V.G. Gavrilko, V.G. Manzhelii, S.N. Popov, N.A.Vinnikov, N.I. Danilenko, and B. Sundqvist
100 110 120 130 140 150 160 170 180 190 200
0
1
2
3
4
5
6
7
8
9
0
0,83
1,67
2,50
3,33
4,17
5,00
5,83
6,67
7,50
T, K
c-SWNT
o-SWNT
n
,
1
0
m
o
l/
m
o
l
m
3
n
,
1
0
m
o
l/
g
g
4
Fig. 5. Temperature distribution of Xe impurity (mole per
mole and mole per gram) desorbed from powder samples of
c-SWNTs (dark columns) and o-SWNTs (light columns).
2 3 4 5 6 7
0
0,01
0,02
0,03
0,04
T, K
1, 2
3
0 10 20 30 40 50 60 70
–1
0
1
2
3
4
5
6
7
8
T, K
3
1
2
a
b
Fig. 6. The radial TECs of SWNT bundles: 1 — Xe-saturated
bundles, 2 — after partial Xe removal at T � 110 K, 3 — pure
SWNTs (� r) at T � 2.2–75 K (a) and 2.2–7 K (b), compacted
sample.
The temperature dependence of the LTEC taken on a
Xe–SWNT sample in the interval 2.2–75 K is shown in
Fig. 6 (curve 1). The sharp increase in the LTECs of the
Xe-saturated sample (cf. curves 1, 3) can reasonably be
attributed to the heavy Xe atoms affecting the transverse
vibrations of the nanotubes in the direction perpendicular
to their surface. At low temperatures the Gr�neisen coef-
ficients of such vibrations are negative in two-dimen-
sional (graphene) or quasi-two-dimensional (graphite,
nanotubes) carbon systems [8,49] and positive in a
three-dimensional carbon modification (diamond). The
formation of SWNT bundles and the sorption of impurity
atoms at the surface or inside the nanotubes generate
three-dimensional features in the system. As a result, the
negative Gr�neisen coefficients of such system decrease
in magnitude or become positive. The thermal expansion
coefficients are expected to behave in a similar way. That
is why the negative contribution to the radial thermal ex-
pansion of Xe-saturated SWNT bundles decreases and
shifts towards lower temperatures (see Fig. 6; cf. curves
1, 2 and 3).
In contrast to pure CNTs the thermal expansion of
Xe-saturated SWNTs is similar during the first heating
and in the subsequent heating and cooling runs. It is pos-
sible that the first heating of pure SWNT bundles with xe-
non can make the system more rigid and its geometry in-
sensitive to heating at low temperatures.
It is interesting that the LTECs have maximum values in
the interval 50–65 K, which may be a manifestation of spa-
tial redistribution of the Xe atoms in the SWNT bundles.
The simulation (by Wang–Landau algorithm) [23,50] of
the potential energy for a system of SWNT bundles satu-
rated with inert gases predicted peaks in the temperature
dependence of the heat capacity at T � 50–100 K, attrib-
uted to reordering of the impurity atoms.
To test the prediction, it was necessary to remove the
Xe impurity from the surface of the SWNT bundles. For
this purpose, the sample was heated to T � 110 K. This
temperature causes intensive desorption of Xe from the
sample surface but leaves it undisturbed in the grooves of
the SWNT bundles (G) and the inner interstices (I) of the
nanotubes having surface defects (Fig. 5). The sample
was kept at T � 110 K until the desorbed Xe was entirely
removed and the pressure in the measuring cell reached
~ 1·10–5 mm Hg. The sample was then cooled to T � 2.2 K
and the thermal expansion was measured again (Fig. 6,
curve 2). It is seen that the LTEC peak is much lower after
Xe was removed from the SWNT bundle surfaces. How-
ever, this partial Xe desorption leaves the temperature de-
pendence of the LTEC practically unaffected outside the
interval of the peak. This suggests that the Xe atoms re-
siding on the bundle surface have only a small effect upon
the thermal expansion of SWNT bundles when the pro-
cess of spatial redistribution of atoms are absent.
Conclusions
This is the first time that the temperature dependences
of the radial thermal expansion coefficients � r T( ) of pure
and Xe-saturated SWNT bundles have been investigated
experimentally at low temperatures. The measurements
were made on heating and cooling the samples in the in-
terval 2.2–120 K using a capacitance dilatometer.
The dependence � r T( ) measured on the first heating
showed very strong nonequilibrium effects, and in the in-
terval 3.2–120 K it differed significantly from the well re-
producible equilibrium dependences � r T( ) that were
found on subsequent heating and cooling runs in this mea-
surement.
The equilibrium coefficients of the radial thermal ex-
pansion �r (Fig. 2, curve 1) are positive above 5.5 K and
negative at lower temperatures. The nonequilibrium coef-
ficients of the radial thermal expansion �r (Fig. 2, curve 2)
are negative in the interval 2.2–82 K. It is assumed that the
nonequilibrium �r -values measured on the first heating of
the sample are due to the irreversible alignment and order-
ing of the bundle positions and the nanotubes in the bun-
dles at rising temperature. As this occurs, the density of the
system increases, and the thermal expansion becomes
negative.
The qualitative interpretation of the equilibrium de-
pendence � r T( ) was based on the theoretical conclusions
about the Gr�neisen coefficients for carbon modifications
[8]. The Gr�neisen coefficient and the radial thermal ex-
pansion of nanotubes are negative at reasonably low tem-
peratures [8], which is determined mainly by the contri-
bution of the transverse acoustic vibrations perpendicular
to the nanotube surfaces. However, in the experiment the
temperature interval of the negative thermal expansion is
much narrower in comparison with the theoretical predic-
tions. This is most likely because the cited theory [8] in-
vestigated individual nanotubes. Additional contribu-
tions to the thermal expansion come into play in SWNT
bundles. First, there is a positive contribution � g , gener-
ated by the variations of the intertube gaps with tempera-
ture. In addition, the nanotube interaction in the bundles
suppresses the negative contribution from the transverse
acoustic vibrations perpendicular to the nanotube sur-
faces [8]. These two positive contributions to the thermal
expansion of the SWNT bundles decrease both the magni-
tude and the temperature interval of the negative thermal
expansion.
The saturation of SWNT bundles with xenon brings
about new features in their thermal expansion.
1. The magnitude of � r increases sharply in the whole
range of temperature investigated. This is because the Xe
impurity suppresses the negative contribution to the ther-
mal expansion from the transverse acoustic vibrations
perpendicular to the nanotube surfaces [8].
Radial thermal expansion of pure and Xe-saturated bundles of single-walled carbon nanotubes at low temperatures
Fizika Nizkikh Temperatur, 2009, v. 35, No. 6 619
2. The dependence � r T( ) has a peak in the interval
50–65 K, which appears to be due to the spatial redistribu-
tion of the Xe atoms over the SWNT bundle surfaces. Re-
moval of the Xe impurity from these surfaces decreases
the peak significantly but leaves the temperature depend-
ence of the LTEC practically unchanged outside the inter-
val of the peak. This suggests that the Xe atoms atoms lo-
cated at the bundle surfaces have little effect on the
thermal expansion of SWNT bundles when the processes
of their spatial redistribution are inoperative.
3. For the Xe saturated material there is no nonequilib-
rium thermal expansion behavior such as was observed
during the first heating of the sample and attributed to ir-
reversible alignment and ordering of the bundle positions
and the nanotubes in the bundles at rising temperature. It
is likely that the saturation with Xe makes the system of
SWNT bundles more rigid and its geometry insensitive to
heating in a low-temperature interval.
Finally, the employed technique of thermoprogram-
med desorption has also enabled us to measure the tem-
perature dependence of Xe desorption from both open
and closed SWNT bundles.
We wish to thank Prof. V.M. Loktev for valuable dis-
cussion.
The authors are indebted to the Science and Technol-
ogy Center of Ukraine (STCU) for the financial support
of this study (project No. 4266).
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>>
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|