Quantum phenomena in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with ³He. A giant isotope effect
The radial thermal expansion αr of bundles of single-walled carbon nanotubes saturated with ³He up to the molar concentration 9.4% has been investigated in the temperature interval 2.1–9.5 K by high-sensitivity capacitance dilatometry. In the interval 2.1–7 K a negative αr was observed, with a magni...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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| Цитувати: | Quantum phenomena in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with ³He. A giant isotope effect / A.V. Dolbin, V.B. Esel'son, V.G. Gavrilko, V.G. Manzhelii, N.A. Vinnikov, S.N. Popov, B. Sundqvist // Физика низких температур. — 2011. — Т. 37, № 6. — С. 685–687. — Бібліогр.: 16 назв. — англ. |
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irk-123456789-1185892017-05-31T03:03:52Z Quantum phenomena in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with ³He. A giant isotope effect Dolbin, A.V. Esel'son, V.B. Gavrilko, V.G. Manzhelii, V.G. Vinnikov, N.A. Popov, S.N. Sundqvist, B. Краткие сообщения The radial thermal expansion αr of bundles of single-walled carbon nanotubes saturated with ³He up to the molar concentration 9.4% has been investigated in the temperature interval 2.1–9.5 K by high-sensitivity capacitance dilatometry. In the interval 2.1–7 K a negative αr was observed, with a magnitude which exceeded the largest negative αr values of pure and ⁴He-saturated nanotubes by three and two orders of magnitude, respectively. The contributions of the two He isotope impurities to the negative thermal expansion of the nanotube bundles are most likely connected with the spatial redistribution of ⁴He and ³He atoms by tunneling at the surface and inside nanotube bundles. The isotope effect turned out to be huge, probably owing to the higher tunneling probability of ³He atoms. 2011 Article Quantum phenomena in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with ³He. A giant isotope effect / A.V. Dolbin, V.B. Esel'son, V.G. Gavrilko, V.G. Manzhelii, N.A. Vinnikov, S.N. Popov, B. Sundqvist // Физика низких температур. — 2011. — Т. 37, № 6. — С. 685–687. — Бібліогр.: 16 назв. — англ. 0132-6414 PACS: 64.70.Tg, 65.40.De, 65.60.+a, 65.80.–g http://dspace.nbuv.gov.ua/handle/123456789/118589 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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English |
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Краткие сообщения Краткие сообщения |
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Краткие сообщения Краткие сообщения Dolbin, A.V. Esel'son, V.B. Gavrilko, V.G. Manzhelii, V.G. Vinnikov, N.A. Popov, S.N. Sundqvist, B. Quantum phenomena in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with ³He. A giant isotope effect Физика низких температур |
| description |
The radial thermal expansion αr of bundles of single-walled carbon nanotubes saturated with ³He up to the molar concentration 9.4% has been investigated in the temperature interval 2.1–9.5 K by high-sensitivity capacitance dilatometry. In the interval 2.1–7 K a negative αr was observed, with a magnitude which exceeded the largest negative αr values of pure and ⁴He-saturated nanotubes by three and two orders of magnitude, respectively. The contributions of the two He isotope impurities to the negative thermal expansion of the nanotube bundles are most likely connected with the spatial redistribution of ⁴He and ³He atoms by tunneling at the surface and inside nanotube bundles. The isotope effect turned out to be huge, probably owing to the higher tunneling probability of ³He atoms. |
| format |
Article |
| author |
Dolbin, A.V. Esel'son, V.B. Gavrilko, V.G. Manzhelii, V.G. Vinnikov, N.A. Popov, S.N. Sundqvist, B. |
| author_facet |
Dolbin, A.V. Esel'son, V.B. Gavrilko, V.G. Manzhelii, V.G. Vinnikov, N.A. Popov, S.N. Sundqvist, B. |
| author_sort |
Dolbin, A.V. |
| title |
Quantum phenomena in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with ³He. A giant isotope effect |
| title_short |
Quantum phenomena in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with ³He. A giant isotope effect |
| title_full |
Quantum phenomena in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with ³He. A giant isotope effect |
| title_fullStr |
Quantum phenomena in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with ³He. A giant isotope effect |
| title_full_unstemmed |
Quantum phenomena in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with ³He. A giant isotope effect |
| title_sort |
quantum phenomena in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with ³he. a giant isotope effect |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2011 |
| topic_facet |
Краткие сообщения |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118589 |
| citation_txt |
Quantum phenomena in the radial thermal expansion of bundles of single-walled carbon nanotubes doped with ³He. A giant isotope effect / A.V. Dolbin, V.B. Esel'son, V.G. Gavrilko, V.G. Manzhelii, N.A. Vinnikov, S.N. Popov, B. Sundqvist // Физика низких температур. — 2011. — Т. 37, № 6. — С. 685–687. — Бібліогр.: 16 назв. — англ. |
| series |
Физика низких температур |
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© A.V. Dolbin, V.B. Esel'son, V.G. Gavrilko, V.G. Manzhelii, N.A. Vinnikov, S.N. Popov, and B. Sundqvist, 2011
Fizika Nizkikh Temperatur, 2011, v. 37, No. 6, p. 685–687
Short Notes
Quantum phenomena in the radial thermal expansion of
bundles of single-walled carbon nanotubes doped with
3He. A giant isotope effect
A.V. Dolbin, V.B. Esel'son, V.G. Gavrilko, V.G. Manzhelii, N.A. Vinnikov, and S.N. Popov
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
B. Sundqvist
Department of Physics, Umea University, SE - 901 87 Umea, Sweden
Received February 16, 2011
The radial thermal expansion αr of bundles of single-walled carbon nanotubes saturated with 3He up to the
molar concentration 9.4% has been investigated in the temperature interval 2.1–9.5 K by high-sensitivity capa-
citance dilatometry. In the interval 2.1–7 K a negative αr was observed, with a magnitude which exceeded the
largest negative αr values of pure and 4He-saturated nanotubes by three and two orders of magnitude, respective-
ly. The contributions of the two He isotope impurities to the negative thermal expansion of the nanotube bundles
are most likely connected with the spatial redistribution of 4He and 3He atoms by tunneling at the surface and in-
side nanotube bundles. The isotope effect turned out to be huge, probably owing to the higher tunneling proba-
bility of 3He atoms.
PACS: 64.70.Tg Quantum phase transitions;
65.40.De Thermal expansion; thermomechanical effects;
65.60.+a Thermal properties of amorphous solids and glasses: heat capacity, thermal expansion, etc;
65.80.–g Thermal properties of small particles, nanocrystals, nanotubes, and other related systems.
Keywords: Radial thermal expansion, single-walled carbon nanotube, helium, quantum effects, isotope effects.
Introduction
Since their discovery by Prof. Iijima in 1991 [1], carbon
nanotubes (CNTs) have been attracting intense interest
from scientists owing to their unique geometry and ex-
traordinary physical properties. The very high length-to-
diameter ratios and the capability of CNTs to form bundles
of several tens or even hundreds of tubes make it possible
to form low-dimensional, ordered impurity phases at the
bundles' surfaces [2,3]. Such phases consist of impurity
molecules or atoms forming one-dimensional chains in the
intertube grooves or in the interstitial channels in the bun-
dles. They can also form two-dimensional layers at the
bundle surface. It has been found experimentally [4–7] that
the radial thermal expansion coefficients αr of nanotube
bundles are negative in the region of liquid helium temper-
atures. Gas impurities usually suppress the magnitudes of
these negative values of αr and reduce the temperature re-
gion where they exist. The 4He impurity is an exception:
when 4He is introduced both the magnitude of the negative
αr values and the temperature region of the negative ther-
mal expansion increase [7]. This effect was attributed to a
tunneling redistribution of the 4He atoms at the surface and
inside CNT bundles. It is known [8,9] that the processes of
tunneling gives a negative contribution to the thermal ex-
pansion of a system. It is then reasonable to expect that
saturation of CNT bundles with 3He would enhance the
above effect because the smaller masses of 3He atoms must
increase the probability of tunneling.
In the present work we have, therefore, investigated the
radial thermal expansion of single-walled carbon nano-
tubes (SWNTs) saturated with 3He using the dilatometric
A.V. Dolbin, V.B. Esel'son, V.G. Gavrilko, V.G. Manzhelii, N.A. Vinnikov, S.N. Popov, and B. Sundqvist
686 Fizika Nizkikh Temperatur, 2011, v. 37, No. 6
method. The temperature interval studied was 2.1–9.5 K.
As will be shown below, the experimental results verify
our expectation that the addition of 3He should enhance the
negative thermal expansion; in fact the effect is surprising-
ly large, two orders of magnitude larger than for 4He.
Experimental technique
The radial thermal expansion of 3He saturated CNTs
was investigated using a high-sensitivity low-temperature
capacitance dilatometer with 2·10–9 cm resolution. The
technique and the experimental apparatus are presented in
detail elsewhere [10]. The sample was a cylinder 7.2 mm
high and 10 mm in diameter, obtained by compressing a
stack of thin (≤ 0.4 mm) plates consisting of in-plane
oriented CNTs at 1.1 GPa. The plates were prepared by
compressing (1.1 GPa) small amounts of CNT powder
(Cheap Tubes, USA, CCVD method). It is known [11] that
such pressure treatment of a thin CNT layer leads to a pre-
ferred orientation where the CNT axes mainly lie in the
plane perpendicular to the applied pressure, the average
deviation being about 4º. The alignment of CNT axes in
the plane makes it possible to investigate preferentially the
radial component of the thermal expansion of the tubes
[12] and the effect of gas saturation upon the radial thermal
expansion of SWNT bundles [4–7].
Just before starting the investigation, the cell with a
pure CNT sample was evacuated at room temperature for
72 hours to remove possible gas impurities. It was then
cooled to 2.1 K and a series of control measurements was
performed. The results showed that the thermal expansion
of the sample coincided, within the experimental error,
with the values obtained previously for pure CNTs [12]
(see Fig. 1,a, curve 4). 3He gas was then fed to the measur-
ing cell at T = 2.1 K. The 3He was added in small portions
as some quantities were sorbed by the nanotubes. This
permitted us to maintain the pressure in the cell several
times lower than the pressure of saturated 3He vapor at this
temperature (151.112 Torr at T = 2 K [13]). The total
amount of 3He absorbed by the pure CNT sample was
9.4 mol.% (94 3He atoms per 1000 C atoms). At this im-
purity concentration we were able to compare our results
on the thermal expansion of the 3He-SWNT with those
from previous measurements of the radial thermal expan-
sion of CNTs saturated with 4He to the molar concentra-
tion 9.4% [7]. After the sorption was completed, an equili-
brium of ~ 1·10–4 Torr was set in the measuring cell. Since
the rise of the sample temperature in the course of measu-
ring αr could entail some 3He desorption from the sample,
the reproducibility of the results was checked at regular
intervals by heating and subsequently cooling the sample
by ΔT, where ΔT = 0.3–1 K. If the results obtained under
this cycling coincided, within experimental error, the effect
of He desorption was regarded as negligible and the data
were considered to be obtained in equilibrium. The ab-
sence of reproducibility was believed to show that at this
and higher temperatures the desorption of the 3He impurity
from the sample had some effect on the thermal expansion.
The measurement was then stopped. Note that for the radi-
al thermal expansion of the 3He-SWNT the data were ob-
served to be reproducible in the interval T = 2.1–9.5 K, but
no longer reproducible when cooling the sample to 9.7 K.
When reproducibility was no longer observed the sample
was heated to T = 11 K and held at this temperature under
dynamic evacuation until an equilibrium pressure of
7.5·10–2 Torr was achieved in the system. During this
process, a fraction of the 3He impurity was desorbed from
the sample. The sample was then cooled back down to the
lowest temperature, 2.1 K, and the radial thermal expan-
sion was measured again.
Results and discussion
The temperature dependence of the radial thermal ex-
pansion coefficient αr of the 3He-SWNT system is shown
in Fig. 1,a. Solid circles represent αr of the sample with the
initial 3He concentration 9.4 mol.%, empty circles data for
Fig. 1. The radial thermal expansion coefficient αr as function of
temperature for SWNT bundles saturated with different gases.
Symbols show data from the present study: ● — 3Не–SWNT ,
molar 3He concentration 9.4%; ○ —
3Не–SWNT after partial
removal of the 3He impurity at T = 11 К. Full lines show data
from earlier work: 1. 4Не–SWNT , molar 4He concentration 9.4%
[7], 2. Н2- SWNT [5], 3. Хe- SWNT [4], and 4. data for pure
SWNTs [12].
2 3 4 5 6 7 8 9 10 11
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–10
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0
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4
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,
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b
Quantum phenomena in the radial thermal expansion of bundles
Fizika Nizkikh Temperatur, 2011, v. 37, No. 6 687
the same sample after partial removal of the 3He impurity
by heating at 11 K. The inset in Fig. 1,a shows the low-
temperature data for the partially evacuated sample on an
expanded scale to enable a comparison with earlier studies,
while Fig. 1,b is shown on an intermediate scale for further
comparisons with the saturated sample.
It is obvious from the Fig. 1 that saturating SWNT bun-
dles with 3He causes a dramatic increase in the magnitude of
the negative thermal expansion in the interval 2.1–7 K. The
largest negative αr in the 9.4% 3He-CNT solution exceeds
those of pure CNTs and 4He-saturated CNTs by three and
two orders of magnitude, respectively. As in the case of the
4He-SWNT solution, the negative contribution to the ther-
mal expansion of the 3He-SWNT system is most likely due
to a process of spatial redistribution of the 3He atoms by
tunneling at the surface and inside SWNT bundles. The iso-
tope effect occurs because of the larger tunneling probability
of the 3He atoms, which have a smaller mass than the 4He
atoms, all other things being equal.
The temperature regions for the strong Schottky-like
anomalies observed in the thermal expansion coefficients
for the 3He–SWNT and 4He–SWNT solutions (similar
anomalies have been predicted in specific heat of low-
density He gas adsorbed in the carbon nanotube bundles
[14]) suggest rather low energy barriers impending the
motion of the He atoms in SWNT bundles. Strzhemechny
and Legchenkova [15] have used the potential curves [16]
for a helium atom interacting with the outer surface of a
single-wall carbon nanotube in order to evaluate the tunne-
ling probability of different He isotopes along the nano-
tube. They showed that in this direction a 4He atom propa-
gates in an energy band approximately 10.1 K wide. The
respective band width for 3He is 13.4 K. These values are
quite consistent with the results of this study.
After a partial 3He desorption from the sample the nega-
tive contribution of the impurity to the thermal expansion
decreases and shifts towards higher temperatures (Fig. 1,a).
The reason may be as follows. There are several kinds of
sites where He atoms can reside in SWNT bundles, and the
resulting total tunneling contribution to the thermal expan-
sion is a sum of contributions made by various types of
tunneling motion. On desorption, the He atoms leave first
the sites with a comparatively low energy for the bond
between the He atom and the C framework. As a conse-
quence, the role of different types of tunnel motion chan-
ges, which affects the temperature dependence of the re-
sulting tunneling contribution to the thermal expansion.
The authors are indebted to M.A. Strzhemechny and
Yu.A. Freiman for fruitful discussions and to the National
Academy of Sciences of Ukraine for the financial support of
the study (Program “Fundamental problems of nanostructur-
al systems, nanomaterials, nanotechnologies”, Project “The
quantum phenomena in nanosystems and nanomaterials at
low temperatures”).
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