Experimental low-temperature heat capacity of one-dimensional xenon adsorbate chains in the grooves of carbon c-SWNT bundles
The experimental studies of the heat capacity of 1D chains of xenon atoms adsorbed in the outer grooves of bundles of closed single-walled carbon nanotubes CXe have been first made at temperature range 2–30 K with the adiabatic calorimeter. The experimental data CXe have been compared with theory...
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irk-123456789-1186612020-11-18T10:02:14Z Experimental low-temperature heat capacity of one-dimensional xenon adsorbate chains in the grooves of carbon c-SWNT bundles Bagatskii, M.I. Manzhelii, V.G. Sumarokov, V.V. Barabashko, M.S. Наноструктуры при низких температурах The experimental studies of the heat capacity of 1D chains of xenon atoms adsorbed in the outer grooves of bundles of closed single-walled carbon nanotubes CXe have been first made at temperature range 2–30 K with the adiabatic calorimeter. The experimental data CXe have been compared with theory [A. Šiber, Phys. Rev. B 66, 235414 (2002)]. The experimental and theoretical heat capacity curves are close below 8 K. Above 8 K the experimental curve CXe (T) exceeds the theoretical one and excess capacity CXe (T) increases monotonously with temperature. We assume that the CXe (T) caused mainly by the increase of the distance between the neighboring xenon atoms in the chain with increasing temperature. 2013 Article Experimental low-temperature heat capacity of one-dimensional xenon adsorbate chains in the grooves of carbon c-SWNT bundles / M.I. Bagatskii, V.G. Manzhelii, V.V. Sumarokov, M.S. Barabashko // Физика низких температур. — 2013. — Т. 39, № 7. — С. 801–805. — Бібліогр.: 35 назв. — англ. 0132-6414 PACS: 65.40.Ba, 65.80.–g, 81.07.De http://dspace.nbuv.gov.ua/handle/123456789/118661 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
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English |
| topic |
Наноструктуры при низких температурах Наноструктуры при низких температурах |
| spellingShingle |
Наноструктуры при низких температурах Наноструктуры при низких температурах Bagatskii, M.I. Manzhelii, V.G. Sumarokov, V.V. Barabashko, M.S. Experimental low-temperature heat capacity of one-dimensional xenon adsorbate chains in the grooves of carbon c-SWNT bundles Физика низких температур |
| description |
The experimental studies of the heat capacity of 1D chains of xenon atoms adsorbed in the outer grooves of
bundles of closed single-walled carbon nanotubes CXe have been first made at temperature range 2–30 K with
the adiabatic calorimeter. The experimental data CXe have been compared with theory [A. Šiber, Phys. Rev. B
66, 235414 (2002)]. The experimental and theoretical heat capacity curves are close below 8 K. Above 8 K the
experimental curve CXe (T) exceeds the theoretical one and excess capacity CXe (T) increases monotonously
with temperature. We assume that the CXe (T) caused mainly by the increase of the distance between the
neighboring xenon atoms in the chain with increasing temperature. |
| format |
Article |
| author |
Bagatskii, M.I. Manzhelii, V.G. Sumarokov, V.V. Barabashko, M.S. |
| author_facet |
Bagatskii, M.I. Manzhelii, V.G. Sumarokov, V.V. Barabashko, M.S. |
| author_sort |
Bagatskii, M.I. |
| title |
Experimental low-temperature heat capacity of one-dimensional xenon adsorbate chains in the grooves of carbon c-SWNT bundles |
| title_short |
Experimental low-temperature heat capacity of one-dimensional xenon adsorbate chains in the grooves of carbon c-SWNT bundles |
| title_full |
Experimental low-temperature heat capacity of one-dimensional xenon adsorbate chains in the grooves of carbon c-SWNT bundles |
| title_fullStr |
Experimental low-temperature heat capacity of one-dimensional xenon adsorbate chains in the grooves of carbon c-SWNT bundles |
| title_full_unstemmed |
Experimental low-temperature heat capacity of one-dimensional xenon adsorbate chains in the grooves of carbon c-SWNT bundles |
| title_sort |
experimental low-temperature heat capacity of one-dimensional xenon adsorbate chains in the grooves of carbon c-swnt bundles |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2013 |
| topic_facet |
Наноструктуры при низких температурах |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118661 |
| citation_txt |
Experimental low-temperature heat capacity
of one-dimensional xenon adsorbate chains
in the grooves of carbon c-SWNT bundles / M.I. Bagatskii, V.G. Manzhelii, V.V. Sumarokov, M.S. Barabashko // Физика низких температур. — 2013. — Т. 39, № 7. — С. 801–805. — Бібліогр.: 35 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT bagatskiimi experimentallowtemperatureheatcapacityofonedimensionalxenonadsorbatechainsinthegroovesofcarboncswntbundles AT manzheliivg experimentallowtemperatureheatcapacityofonedimensionalxenonadsorbatechainsinthegroovesofcarboncswntbundles AT sumarokovvv experimentallowtemperatureheatcapacityofonedimensionalxenonadsorbatechainsinthegroovesofcarboncswntbundles AT barabashkoms experimentallowtemperatureheatcapacityofonedimensionalxenonadsorbatechainsinthegroovesofcarboncswntbundles |
| first_indexed |
2025-07-08T14:24:32Z |
| last_indexed |
2025-07-08T14:24:32Z |
| _version_ |
1837089080516542464 |
| fulltext |
© M.I. Bagatskii, V.G. Manzhelii, V.V. Sumarokov, and M.S. Barabashko, 2013
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 7, pp. 801–805
Experimental low-temperature heat capacity
of one-dimensional xenon adsorbate chains
in the grooves of carbon c-SWNT bundles
M.I. Bagatskii, V.G. Manzhelii, V.V. Sumarokov, and M.S. Barabashko
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: sumarokov @ilt.kharkov.ua
Received March 19, 2013
The experimental studies of the heat capacity of 1D chains of xenon atoms adsorbed in the outer grooves of
bundles of closed single-walled carbon nanotubes CXe have been first made at temperature range 2–30 K with
the adiabatic calorimeter. The experimental data CXe have been compared with theory [A. Šiber, Phys. Rev. B
66, 235414 (2002)]. The experimental and theoretical heat capacity curves are close below 8 K. Above 8 K the
experimental curve CXe (T) exceeds the theoretical one and excess capacity CXe (T) increases monotonously
with temperature. We assume that the CXe (T) caused mainly by the increase of the distance between the
neighboring xenon atoms in the chain with increasing temperature.
PACS: 65.40.Ba Heat capacity;
65.80.–g Thermal properties of small particles, nanocrystals, nanotubes, and other related systems;
81.07.De Nanotubes.
Keywords: heat capacity, nanotubes, 1D chain.
The unique structure of bundles of the single-walled
carbon nanotubes (SWNTs) permits obtaining quasi-one,
two and three-dimensional structures formed by adsorbates
[1,2]. Technologically, most of the tubes in the prepared
bundles have closed ends unless special steps are taken to
open them. The possible sites of adsorption of relatively
small impurity atoms or molecules in a bundle of closed
SWNTs (c-SWNTs) are interstitial channels (IC), grooves
at the outer surface (G) and the outer surface (OS) (see
Fig. 1). These positions differ in geometrical size and
energy of adsorbate binding to c-SWNT bundles [3]. Phys-
ical properties (adsorption, thermal and structural) of sim-
ple gas admixtures deposited in c-SWNT bundles were
investigated in experimental and theoretical works [1–26].
The heat capacity of
4
He adsorbed on c-SWNT bundles
was investigated at temperatures below 6 K [19,20]. It was
observed [20] that the heat capacity of the adsorbed helium
exhibited the behavior of 1D and 2D structures depending
on the technique of sample preparation (laser evaporation
or arc discharge).
Structures of
4
He adsorbates in the grooves and at the
outer surface of c-SWNT bundles were measured by the neu-
tron diffraction method [27]. At low coverage, the
4
He atoms
formed a 1D single line lattice along the grooves. As the con-
centration of the adsorbed helium atoms increased, a 2D mo-
nolayer was formed, which covered the whole c-SWNT bun-
dle surface [27]. Antsygina et al. [15–17] suggested a rigor-
ous thermodynamic model describing the multilayered atom-
ic adsorbate in grooves, interstitials and external surface of
Fig. 1. Possible sites of adsorption of relatively small impurity
atoms or molecules in a c-SWNT bundle.
M.I. Bagatskii, V.G. Manzhelii, V.V. Sumarokov, and M.S. Barabashko
802 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 7
bundles. The model [16,17] based on a proper account of the
temperature-dependent adsorbate redistribution between 1D,
2D and 3D subsystems made it possible to explain on a quan-
titative level the adsorption isotherms and isoteric heat of He
deposited on the bundles [15,19]. The thermodynamic re-
search on the neon films adsorbed by HiPco c-SWNT bun-
dles was carried out experimentally in Ref. 28. However, the
behavior of the one-dimensional chains of the adsorbed gas
in the grooves on the outer surface of the bundles has not
been given enough attention in this work. The radial thermal
expansion coefficients of c-SWNT bundles saturated with Xe
atoms to rather high (1.64 mole/mole, %) concentration were
measured in Refs. 18 and 25.
The 1D chains of Xe atoms adsorbed in the grooves at
the outer surface of a c-SWNT bundle are shown schemat-
ically (one in each groove) in Fig. 2.
Low temperature dynamics of inert gas atoms and me-
thane molecules in c-SWNT bundles was considered in
theoretical studies [29–31]. The calculated heat capacities
of 1D chains of inert gas atoms and methane molecules
adsorbed physically in the grooves of c-SWNT bundles are
reported in [29] (Ar, Kr, Xe) and [30] (Ne, CH4).
To our knowledge, no experimental investigations of
the thermal properties of c-SWNT bundles containing 1D
chains of adsorbed classical inert gas atoms (Ar, Kr, Xe)
have been reported so far.
Our goal was to investigate the low-temperature heat
capacity of the 1D chains of xenon atoms adsorbed in the
grooves at the outer surface of c-SWNT bundles. The
choice of the adsorbate was dictated by the following rea-
sons. First, physical adsorption of Xe atoms is possible
only in the grooves and at the outer surface of c-SWNT
bundles. Adsorption in the interstitial channels is prohi-
bited because of the relationship between the geometrical
sizes of channels and Xe atoms [12]. Second, the binding
energy of Xe atoms is higher in the grooves than at the
outer surface [3,8] and Xe atoms are physically adsorbed
primarily in the grooves where they form one-dimensional
chains (see Fig. 2).
The heat capacity of 1D chains of Xe atoms adsorbed in
the outer grooves of c-SWNT bundles has been first meas-
ured in this work at temperature range from 2 K to 30 K
using an adiabatic calorimeter [32].
A cylindrical sample of c-SWNT bundles (7.2 mm high,
10 mm in diameter and 1.27 g/cm
3
density) was prepared by
compressing c-SWNT plates under the pressure 1.1 GPa.
The plates (~0.4 mm thick) were obtained by compacting a
c-SWNT powder (―Cheap Tubes‖) under P=1.1 GPa [33].
The powder was prepared by chemical catalytic vapor depo-
sition (CVD). It contained over 90 wt% of c-SWNT bun-
dles, other allotropic forms of carbon (fullerite, multiwalled
nanotubes and amorphous carbon) and about 2.9 wt% of
cobalt catalyst. The average tube diameter in the sample was
1.1 nm; the average length of the c-SWNT bundles was
15 μm [33]. The number of nanotubes in the bundles varied
within 100–150 (estimated from high-resolution TEM pic-
tures) and was equal to, on the average, 127. The mass of the
c-SWNT bundles sample was equal to 716.00 ± 0.05 mg.
The temperature of the calorimeter was measured with
a calibrated CERNOX resistance thermometer (Lake Shore
Cryotronics).
First, the addenda heat capacity Cad (the heat capacity
of calorimeter with an inserted sample of pure c-SWNT
bundles) was measured in a separate experiment. Then the
calorimeter with sample was warmed to room temperature.
The c-SWNT bundles were saturated with Xe directly in
the calorimeter cell. The vacuum cavity of the calorimeter
was filled with Xe gas: 3.19·10
–4
± 5·10
–6
mole. The ob-
tained ratio is NXe/NC ≈ 0.55%, where NXe, NC is the
number of Xe and C atoms in the SWNT sample, respec-
tively. The quantity of Xe was estimated by PVT-method.
The chemical purity of xenon was 99.98% (0.01% N2,
0.01% Kr).
It was assumed within the employed geometric model
that the distance a between the nearest Xe atoms in the
chain is equal to the distance between the nearest neigh-
bors in the FCC lattice of solid Xe a = 4.336 Ǻ at T = 0 K
[34]. In the case of complete occupancy of the grooves by
Xe atoms (one chain in each groove) we obtained the ratio
nXe/nC ≈ 0.5% (nXe and nC are the number of Xe and
C atoms in the c-SWNT bundles, respectively). This value
is 10–20% lower than in the experiment.
The calorimeter was cooled from room temperature to 90
K for eight hours. During this period Xe atoms were being
adsorbed in the c-SWNT bundles. For the geometrical rea-
sons Xe atoms cannot penetrate into the interstitial channels
[12] under low pressure. Since the binding energy of Xe
atoms is higher in grooves than at the outer surface [3,8], the
Xe atoms are physically adsorbed first of all in the grooves
Fig. 2. One-dimensional chains of Xe atoms adsorbed in the
grooves at the outer surface of a c-SWNT bundle; a is the dis-
tance between the nearest neighboring Xe atoms in the chain.
Experimental low-temperature heat capacity of one-dimensional xenon adsorbate chains
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 7 803
where they form 1D chains. After cooling of the calorimeter
from 90 K to helium temperatures (during 5–6 h), the sam-
ple was thermocycled (about 1 K heating–cooling) several
times and then the heat capacity was measured. The heat
capacity measurement runs were made from the lowest tem-
perature of the run up to 30 K. After each measurement se-
ries up to 30 K the sample was heated to 80 K and then, after
a slow cooling down to helium temperature and thermocycl-
ing, the measurement was repeated. Several measurement
runs were made. The results of different runs coincided
within the measurement error. Other experimental features
have been reported elsewhere [32,35].
The temperature dependencies of the total heat capacity
Cad+Xe and its addenda component Cad are shown in Fig. 3
at the temperature range from 2 to 30 K (Insert: the heat
capacities below 5 K). It is interesting that the introduction
of only 5–6 atoms of xenon per 1000 carbon atoms causes
a significant increase in the heat capacity in the whole
temperature range of the experiment. For example, ratio
(Cad+Xe–Cad)/Cad ≈ 160% and ≈ 20% at T = 2.6 K and at
30 K, respectively. The contribution CXe of xenon atoms to
the total heat capacity Cad+Xe has been separated by sub-
tracting the heat capacity of the addenda from the total heat
capacity Cad+Xe.
Random error in the CXe — value is within ± 20% at
2.2 K and ± 5% at the temperature region 10–30 K. The
systematic error is mainly contributed by inaccuracies con-
cerning the number of SWNTs.
The CXe(T) is shown in Fig. 4 in the coordinates
CXe(T)/(μR), where μ is the number of xenon atoms (in
moles), R is the gas constant. For comparison, Fig. 4 in-
cludes a theoretical temperature dependence of the heat
capacity of 1D chains of Xe atoms adsorbed physically in
the grooves at the outer surface of c-SWNT bundles [29].
It is seen in Fig. 4 that below 8 K the experimental and
theoretical [29] curves of heat capacity CXe are close. Ac-
cording to the Šiber theory [29], at T < 4 K the heat capaci-
ty is influenced mainly by the longitudinal mode and is
proportional to the temperature. Above 4 K the transverse
optical modes begin to take effect. Figure 5 illustrates the
low temperature part of heat capacity CXe in coordinates
CXe/μRT vs T. The straight line in the same figure shows
the theoretical low-temperature heat capacity of the chain
of Xe adatoms caused by the longitudinal mode [29]. It is
seen that below ≈ 4 K the experimental dependence of CXe
is close to the predicted straight line characteristic for the
low temperature heat capacity of 1D chains. Above 4 K the
experimental points start to deviate from this line. Using
the formula (13) from Ref. 29, we estimated both the pho-
non frequency of the longitudinal mode ħωL ≈ 3.1 meV
which is close to the theoretical value 3.06 meV [29] and
the Debye temperature D,L ≈35.7 K of 1D chains. The
Debye temperatures D,L of one-dimensional Xe and Ne
chains are given in the table. There is good agreement be-
tween theoretical and experimental Debye temperatures of
1D Xe chains. The large discrepancy observed for Ne
chains is somewhat surprising [28,30].
Fig. 3. Experimental temperature dependencies of the total heat
capacity Cad+Xe and its component Cad.
Fig. 4. The heat capacity of 1D chains of Xe atoms adsorbed in the
grooves at the outer surface of c-SWNT bundles. Experiment (this
work): open circles. Theory [29]: solid curve for the L + T1 + T2
modes; solid straight line only for the L mode.
Fig. 5. The dependence of CXe/μRT vs T: circles — experiment,
the straight line — theoretical low temperature asymptotics of the
heat capacity of the longitudinal mode of the chains of Xe ada-
toms [29].
M.I. Bagatskii, V.G. Manzhelii, V.V. Sumarokov, and M.S. Barabashko
804 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 7
At T > 8 K the experimental curve CXe(T) starts to ex-
ceed the theoretical one [29] and the CXe(T) increases
monotonously with the rising temperature. We assume that
the excess caused mainly by the increase of the distance
between the neighboring xenon atoms in the chain with
increasing temperature.
Šiber [29] suggested that the heat capacity of 1D
chains of inert gas atoms adsorbed physically in the
grooves of c-SWNT bundles could be calculated using a
simple model in which for simplicity author assumes that
substrate is rigid, ignores the discrete structure of the tubes
surrounding a groove and neglects all the interactions be-
tween the adsorbates that are not in the same groove. It
should be noted, that the absolute minimum (–225 meV) of
external potential for Xe atom in the groove [29] is higher,
than the experimental binding energy (–282 ± 11 meV) [3].
These values are an order of magnitude smaller than the
binding energy of the adsorbate–adsorbate [29]. He calcu-
lated the temperature dependencies of one-dimensional
chains of inert gas adsorbates (Ar, Kr, Xe) in the interval
2–40 K [29]. Similar results on the heat capacity of the
chains of Ne atoms and CH4 molecules adsorbed physi-
cally in the grooves of c-SWNT bundles were obtained in
a theoretical study [30].
There is surprisingly good agreement between the theo-
retical predictions and experimental results despite signifi-
cant simplification in the theoretical model [29] and possi-
ble deviations from the ideal object.
The discrete structure of nanotubes has little effect on the
transverse modes of Xe atoms beyond the center of the Bril-
louin zone [31], but the longitudinal mode is more sensitive
to the parameters of the models and the chain density.
In this study the heat capacity of one-dimensional chains
of xenon atoms adsorbed in the outer grooves of bundles of
single-walled carbon nanotubes with closed ends has been
first studied in the temperature interval 2–30 K. The experi-
mental and theoretical [29] results are close below 8 K. Ob-
served at higher temperatures, the discrepancy between the
experimental and theoretical heat capacities could be mainly
due to the increase of the distance between the nearest
neighboring xenon atoms in the chain with increasing tem-
perature.
The authors are grateful to Yu. Freiman, M. Strzhe-
mechny, A. Dolbin and K. Chishko for helpful discussions.
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Experiment Theory Experiment Theory
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Ne — — 58 [28] 78 (3.08 Å) [30]
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