The heat capacity of nitrogen chain in grooves of single-walled carbon nanotube bundles
The heat capacity of bundles of closed-cap single-walled carbon nanotubes with one-dimensional chains of nitrogen molecules adsorbed in the grooves has been first experimentally studied at temperatures from 2 to 40 K using an adiabatic calorimeter. The contribution of nitrogen CN₂ to the total heat...
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Bagatskii, M.I. Barabashko, M.S. Sumarokov, V.V. 2017-05-30T11:49:48Z 2017-05-30T11:49:48Z 2013 The heat capacity of nitrogen chain in grooves of single-walled carbon nanotube bundles / M.I. Bagatskii, M.S. Barabashko, V.V. Sumarokov // Физика низких температур. — 2013. — Т. 39, № 5. — С. 568–573. — Бібліогр.: 65 назв. — англ. 0132-6414 PACS: 65.40.Ba, 65.80.–g, 68.65.–k, 81.07.De https://nasplib.isofts.kiev.ua/handle/123456789/118457 The heat capacity of bundles of closed-cap single-walled carbon nanotubes with one-dimensional chains of nitrogen molecules adsorbed in the grooves has been first experimentally studied at temperatures from 2 to 40 K using an adiabatic calorimeter. The contribution of nitrogen CN₂ to the total heat capacity has been separated. In the region 28 K the behavior of the curve CN₂(T) is qualitatively similar to the theoretical prediction of the phonon heat capacity of 1D chains of Kr atoms localized in the grooves of SWNT bundles. Below 3 K the de-pendence CN₂(Т) is linear. Above 8 K the dependence CN₂(Т) becomes steeper in comparison with the case of Kr atoms. This behavior of the heat capacity CN₂(Т) is due to the contribution of the rotational degrees of free-dom of the N₂ molecules. The authors are indebted to V.G. Manzhelii, M.A. Strzhemechny, K.A. Chishko, S.B. Feodosyev, E.S. Syrkin, E.V. Manzhelii, and I.A. Gospodarev for helpful discussions. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур 9th International Conference on Cryocrystals and Quantum Crystals The heat capacity of nitrogen chain in grooves of single-walled carbon nanotube bundles Article published earlier |
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The heat capacity of nitrogen chain in grooves of single-walled carbon nanotube bundles |
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The heat capacity of nitrogen chain in grooves of single-walled carbon nanotube bundles Bagatskii, M.I. Barabashko, M.S. Sumarokov, V.V. 9th International Conference on Cryocrystals and Quantum Crystals |
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The heat capacity of nitrogen chain in grooves of single-walled carbon nanotube bundles |
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The heat capacity of nitrogen chain in grooves of single-walled carbon nanotube bundles |
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The heat capacity of nitrogen chain in grooves of single-walled carbon nanotube bundles |
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The heat capacity of nitrogen chain in grooves of single-walled carbon nanotube bundles |
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heat capacity of nitrogen chain in grooves of single-walled carbon nanotube bundles |
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Bagatskii, M.I. Barabashko, M.S. Sumarokov, V.V. |
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Bagatskii, M.I. Barabashko, M.S. Sumarokov, V.V. |
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9th International Conference on Cryocrystals and Quantum Crystals |
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9th International Conference on Cryocrystals and Quantum Crystals |
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Физика низких температур |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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The heat capacity of bundles of closed-cap single-walled carbon nanotubes with one-dimensional chains of nitrogen molecules adsorbed in the grooves has been first experimentally studied at temperatures from 2 to 40 K using an adiabatic calorimeter. The contribution of nitrogen CN₂ to the total heat capacity has been separated. In the region 28 K the behavior of the curve CN₂(T) is qualitatively similar to the theoretical prediction of the phonon heat capacity of 1D chains of Kr atoms localized in the grooves of SWNT bundles. Below 3 K the de-pendence CN₂(Т) is linear. Above 8 K the dependence CN₂(Т) becomes steeper in comparison with the case of Kr atoms. This behavior of the heat capacity CN₂(Т) is due to the contribution of the rotational degrees of free-dom of the N₂ molecules.
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https://nasplib.isofts.kiev.ua/handle/123456789/118457 |
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The heat capacity of nitrogen chain in grooves of single-walled carbon nanotube bundles / M.I. Bagatskii, M.S. Barabashko, V.V. Sumarokov // Физика низких температур. — 2013. — Т. 39, № 5. — С. 568–573. — Бібліогр.: 65 назв. — англ. |
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2025-11-25T22:46:31Z |
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© M.I. Bagatskii, M.S. Barabashko, and V.V. Sumarokov, 2013
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 5, pp. 568–573
The heat capacity of nitrogen chain in grooves
of single-walled carbon nanotube bundles
M.I. Bagatskii, M.S. Barabashko, and V.V. Sumarokov
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: bagatskii@ilt.kharkov.ua
Received November 2, 2012
The heat capacity of bundles of closed-cap single-walled carbon nanotubes with one-dimensional chains of
nitrogen molecules adsorbed in the grooves has been first experimentally studied at temperatures from 2 to 40 K
using an adiabatic calorimeter. The contribution of nitrogen CN2 to the total heat capacity has been separated. In
the region 2 8 K the behavior of the curve CN2(T) is qualitatively similar to the theoretical prediction of the
phonon heat capacity of 1D chains of Kr atoms localized in the grooves of SWNT bundles. Below 3 K the de-
pendence CN2(Т) is linear. Above 8 K the dependence CN2(Т) becomes steeper in comparison with the case of
Kr atoms. This behavior of the heat capacity CN2(Т) is due to the contribution of the rotational degrees of free-
dom of the N2 molecules.
PACS: 65.40.Ba Heat capacity;
65.80.–g Thermal properties of small particles, nanocrystals, nanotubes, and other related systems;
68.65.–k Low-dimensional, mesoscopic, nanoscale and other related systems: structure and nonelec-
tronic properties;
81.07.De Nanotubes.
Keywords: heat capacity, single-walled carbon nanotubes bundles, one-dimensional periodic phase of nitrogen
molecules.
1. Introduction
Since the discovery of carbon nanotubes in 1991 [1],
investigations of the physical properties of these novel ma-
terials have been rated as a fundamentally important trend
in physics of condensed matter [2,3]. The immense prac-
tical and scientific interest in carbon nanostructures stems
from their unique physical (mechanical, electrical, magnet-
ic, optical and so on) [3–19] characteristics.
Carbon nanotubes have a large specific surface and are
promising as adsorbents for solving several technical prob-
lems such as storage of gaseous and condensed substances
or separation of isotopes and gas mixtures [20,21].
The adsorption of gases and the physical properties
of gases adsorbed by bundles of closed carbon nanotubes
(c-SWNT) are of fundamental interest in the physics of
low-dimensional systems [22–27]. The structure of c-SWNT
bundles enables formation of 1-, 2- and 3-dimensional
systems.
Technologically, most of the tubes in as-prepared bun-
dles have closed ends unless special steps are taken to open
them up. Owing to Van der Waals attractive forces, nano-
tubes can unite into bundles. Within a bundle the nano-
tubes form a close-packed two-dimensional (2D) triangular
lattice [28].
The possible sites of adsorption of gas impurities in
c-SWNT bundles are interstitial channels (IC), grooves (G)
and the outer surface (OS) (see Fig. 1). These sites differ in
geometric size and binding energy [29–32]. At low adsorbate
concentrations, one-dimensional (1D) chains of impurity mo-
lecules (atoms) are formed in the IC- and G-sites. One or se-
veral layers of molecules (atoms) adsorbed at the outer sur-
face of the c-SWNT bundle form quasi-two-dimensional (2D)
or quasi-three-dimensional (3D) systems. The 1D, 2D and
3D systems have different properties at low temperatures
[6,33–39].
The physical adsorption of gases by c-SWNT bundles
and the adsorbate dynamics have been the subject of nume-
rous theoretical and experimental investigations. The ad-
sorption of nitrogen by c-SWNT bundles was considered
in [14,31,40–42]. The low-temperature thermodynamics of
helium adsorbed in the G of c-SWNT bundles was ana-
The heat capacity of nitrogen chain in grooves of single-walled carbon nanotube bundles
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 5 569
lyzed theoretically using the lattice gas model [27,43]. The
quantum states and the heat capacity of low-density
4
He
gas adsorbed in the interstitial channels of c-SWNT bun-
dles were studied theoretically in [36,44,45]. The heat ca-
pacity of c-SWNT bundles with adsorbed Ne and Xe atoms
was investigated by the Monte Carlo method [46]. The
phonon heat capacity of 1D chains of inert gases atoms
(Xe, Kr, Ar, Ne) and CH4 molecules adsorbed in the G at
the OS of c-SWNT bundles, was calculated in Refs. 47,48.
The authors of article [48] also calculated the phonon heat
capacity at a constant volume for three chains of CH4 mo-
lecules adsorbed in the grooves.
Experimental investigations of the thermal properties of
c-SWNT bundles containing adsorbed gases are only at
the initial stage. For the most part the results obtained re-
fer to the coefficients of the radial thermal expansion αr of
c-SWNT bundles saturated with gases (
3
Не,
4
Не, Н2, N2,
О2, Хе) [49–55] above 2 K. It is found that in the investi-
gated temperature intervals αr increases sharply in c-SWNT
bundles saturated with Н2, N2, О2, Хе [49–51,53] and the
dependences αr(T) exhibit maxima. It was assumed that the
maxima in the dependences αr(T) account for the spatial re-
distribution of adsorbate particles at the surface of c-SWNT
bundles. The saturation of c-SWNT bundles with helium
isotopes (
4
He [52] and
3
Не [54]) causes a dramatic in-
crease in the magnitude of the negative thermal expansion
in the interval 2.1–7 K. It is believed that the effect can be
induced by the tunneling motion of helium atoms during of
their spatial redistribution [52,54]. The detected great iso-
tope effect is due to the fact that
3
Не atoms have a smaller
mass than
4
He and hence a higher probability of tunneling
[19,54].
The heat capacity of
4
He-saturated SWNT bundles was
investigated below 6 K [56,57]. The heat capacity of the
adsorbed
4
He exhibited a 2D behavior (Сads Т
2
) in the
sample of SWNT bundles prepared by laser vaporization
technique and a 1D behavior (Сads Т) in the sample pre-
pared by the arc-discharge method [57].
Recently, precise measurements of heat capacities have
been performed for the first time on c-SWNT bundles with
adsorbed 1D chains of Xe atoms in the G at temperature
range from 2 to 30 K [58,59]. The experimental heat ca-
pacity agrees, within the measurement error, with the theo-
retical curve [47] at T < 8 K.
This study continues the series of calorimetric experi-
ments carried out in the same adiabatic calorimeter and on
the same sample of c-SWNT bundles saturated with dif-
ferent gases. The heat capacity of bundles of closed-cap
single-walled carbon nanotubes with 1D chains of nitrogen
molecules adsorbed in the G has been first experimentally
studied at temperatures from 2 to 40 K using an adiabatic
calorimeter. Behavior of simple molecular adsorbates, such
as N2 under similar conditions can be interesting for a few
reasons. First, will 1D N2 chains demonstrate alike ther-
modynamic properties and, second, are one to expect cer-
tain peculiarities related to fact that the dopant particle is a
molecule. In addition, the nitrogen molecule has a quadru-
pole moment, which can enrich the emerging picture.
2. Experiment
The adiabatic calorimeter and the measurement tech-
nique have been reported in Ref. 60. The temperature of
the calorimeter was measured with a calibrated CERNOX
resistance thermometer (Lake Shore Cryotronics). Precise
measurements of the heat capacity of the calorimetric ves-
sel with a sample of pure c-SWNT bundles (“addenda”)
were made in Ref. 6.
A cylindrical sample of c-SWNT bundles (7.2 mm high,
10 mm in diameter, of 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
SWNT powder (“Cheap Tubes”) also under the pressure
1.1 GPa. The powder was prepared by chemical catalytic
vapor deposition. It contained over 90 wt% of SWNT bund-
les, 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 SWNT bundles was
15 µm. The number of nanotubes in the bundles varied
within 100–150 (estimated from high-resolution TEM pic-
tures). The mass of the sample of c-SWNT bundles was
716.00 0.05 mg [6].
This experiment was made after measuring the heat ca-
pacity of c-SWNT bundles with 1D chains of Xe atoms in
the G at the OS of the bundles [58,59]. Before starting the
experiment, the vacuum chamber of the calorimeter with a
c-SWNT bundle sample at room temperature was washed
several times with pure N2 gas and the sample stayed in
dynamic vacuum (~5·10
–3
Torr) for about 12 h. Then test
measurement of the “addenda” heat capacity was per-
formed. The results coincided with the data of Ref. 6. After
completing the “addenda” measurement, the vacuum
chamber of the calorimeter was filled with nitrogen at
Fig. 1. Possible sites of adsorption of relatively small impurity
atoms or molecules in a c-SWNT bundle.
M.I. Bagatskii, M.S. Barabashko, and V.V. Sumarokov
570 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 5
room temperature. The quantity of nitrogen was found by
the PVT method (µN2 = 3.81·10
–4
6·10
–6
mol). The
chemical purity of N2 was 99.997% (O2 0.003%). The
sample of c-SWNT bundles was saturated with N2 directly
in the vacuum chamber of the calorimeter by cooling the
calorimeter cell. The ratio of the number of NN2 molecules
adsorbed by the c-SWNT bundles to the number of carbon
atoms NC in the sample of c-SWNT bundles was estimated
to be ξN2 = NN2/NС 0.0066. The parameter ξN2 characte-
rizes the occupancy of c-SWNT bundles with nitrogen.
The quantity of N2 required to form one chain in all G
of the c-SWNT bundles was estimated in advance. The
calculation using a geometric model and assuming that the
average tube diameter was 11 Å and the average number of
tubes in a bundle was 127. We also assumed that the dis-
tance between the N2 molecules in the 1D chains was
a = 3.994 Å, which corresponds to the nearest neighbor
distance in the Pa3 lattice of solid N2 at T = 0 K [61].
On cooling the calorimeter cell the N2 molecules are
adsorbed first of all in the G because at these sites their
binding energy is higher than at OS of the bundles [31]. N2
molecules are unable to penetrate into the interstitial chan-
nels because their cross-section sizes are smaller than the
size of N2 molecules [29,62]. During N2 adsorption the
temperature distribution in the vacuum chamber of the ca-
lorimeter together with calorimetric cell must be maintain-
ed at the level permitting the c-SWNT bundles to adsorb
all the nitrogen available in the vacuum chamber.
After filling the vacuum chamber of the calorimeter with
N2 (µN2 = 0.000381 mol) at room temperature the pressure
of the N2 gas in the chamber was ~ 16 Torr. As follows from
the equilibrium vapor pressure above solid nitrogen [63],
this value corresponds to T ~ 56 K of solid N2.
Since the moment of filling the N2 bath of the cryostat
with liquid N2, the calorimeter cooled down from 289 to
90 K during ~8 h. Then, the temperature Tvc of vacuum
chamber walls was decreased by blowing cold
4
He gas
through the helium bath of the cryostat. To increase the
“effective” enthalpy of the
4
He gas in the helium bath,
before the experiment the lower part of the helium bath
was filled with adsorbent Al2O3 (500 cm
3
). This permitted
us to reduce the derivative dТvc/dt almost by an order of
magnitude in the process of blowing cold
4
He gas through
the helium bath of the cryostat and cool the calorimeter
from 90 to ~60 K during ~5 h. Then the helium bath of
cryostat was filled with liquid
4
He.
According to the isotherm of N2 adsorption in samples
of SWNT bundles at T = 77 K [31], saturation to ξN2
0.0066 produces the pressure ~10
–4
Torr of the NN2 gas
over the sorbent. In the case of nitrogen adsorption iso-
therm at 60 K the nitrogen gas pressure is ~ 10
–5
Torr.
After filling the helium bath of the cryostat with liquid
4
He
the N2 gas present in the tube of the vacuum chamber of
the calorimeter at P~10
–5
Torr condensed onto the tube
walls. The mass of condensed nitrogen was 10
–9
mol.
Thus, practically all the nitrogen available in the vacuum
chamber of the calorimeter was adsorbed by the c-SWNT
bundles.
3. Results and discussion
The experimental temperature dependence of the total
heat capacity Cad+N2 and its “addenda” part Cad are shown
in Fig. 2 over the temperature ranges 2–40 K (Fig. 2(a))
and 2–6 K (Fig. 2(b)), respectively. As can be seen, that
saturation of the c-SWNT bundles with N2 to the occupan-
cy ξN2 0.0066 caused a significant increase in the heat
capacity over the entire temperature range. The ratio
Cad+N2/Cad is about 1.6 at 2 K < T < 15 K and decreases to
1.2 at 40 K.
The contribution CN2 of nitrogen to the total heat ca-
pacity Cad+N2 was separated by subtracting Cad from
Cad+N2. The heat capacity CN2 was estimated assuming
that the contributions Cad and CN2 are additive because the
influence of the 1D chains of N2 molecules on the phonon
density of the c-SWNT bundles is negligible. The coupling
between the acoustic vibrations of the adsorbate atoms
(molecules) in the chain and the carbon atoms in the nano-
Fig. 2. Experimental temperature dependence of the total heat
capacity Cad+N2 (open circles) and its “addenda” part Cad (solid
circles) in the temperature ranges 2–40 K (a) and 2–6 K (b).
The heat capacity of nitrogen chain in grooves of single-walled carbon nanotube bundles
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 5 571
tubes influences the physical properties of the system at much
lower temperatures than in our experiment (see [48,64,65]).
Figure 3 shows the normalized experimental heat capa-
city (СN2/(μR), where µ is the number of the nitrogen moles
and R is the gas constant) of the 1D chains of N2 mole-
cules adsorbed in G of c-SWNT bundles at T = 2–40 K
(Fig. 3(a)) and 2–8 K (Fig. 3(b)). For comparison, Fig. 3
contains a theoretical curve of the molar heat capacity
(СV/R)Kr of the 1D chains of Kr atoms adsorbed in G of
c-SWNT bundles [47]. It is seen (Fig. 3(b)) that the expe-
rimental heat capacity of nitrogen СN2/(μR) and the theo-
retical phonon heat capacity of krypton (СV/R)Kr [47] are
close within the range T = 2–8 K. Thus, below 8 K the heat
capacity of the 1D nitrogen chains in the G is influenced
predominantly by the phonon modes.
The phonon heat capacity CV of physically adsorbed 1D
chains of Xe, Kr, Ar, Ne atoms [47,48] and CH4 molecu-
les [48] in grooves is determined by the longitudinal acous-
tic L and two transverse optical T1, T2 modes. The contri-
bution of the optical modes decreases exponentially with
lowering temperature. At low temperatures, at which the
contribution of the L mode is dominant, the specific heat
CV(T) can be presented in terms of the Debye model [47]:
,
2.095 2.095
( / )
V B
L D L
C k T T
R q a
, (1)
where kB is the Boltzmann constant, ħ is the Plank con-
stant, L(q= /a) is the highest Brilouin zone edge fre-
quency of the L mode, a is the distance between the adsor-
bate particles in the chain. The Debye temperature D,L is
found using the sound velocity L [48]
, /D L L Bаk . (2)
Equation (1) neglects all contributions other than longitu-
dinal mode, limiting its applicability to an even lower tem-
perature regime than usual DT [48,64,65].
The solid lines in Fig. 3(b) demonstrate the linear be-
havior of the specific heat СN2/(μR) of 1D chains of N2
molecules (straight line 1) and Kr atoms (Cv /R)Kr (straight
line 2) [47] below 4 K. Using Eq. (1), we obtain D,L 60 K
for the N2 chains and the highest Brillouin zone edge fre-
quency of the L mode ħ L = 5.2 meV.
Although the theoretical models [47,48] include signifi-
cant simplifications, the experimental results СN2/(μR) and
the theoretical predictions for the phonon heat capacity of
krypton at T < 8 K are in good agreement.
Above 8 K the temperature dependence of the heat ca-
pacity of N2 molecules СN2/(μR) is steeper than that of Kr
atoms (СV(Т)/R)Kr [47] (see Fig. 3). At higher tempera-
tures, the difference С = СN2(Т)/(μR) – (СV(Т)/R)Kr be-
tween the heat capacities of the N2 and Kr chains increases
monotonically. It is reasonable to assume that above 8 K
the difference С is due to a contribution of orientational
vibrations of the N2 molecules (librons).
The temperature dependence of the heat capacity of N2
chains (circles) and the experimental [59,60] (triangles)
and theoretical [47] (solid curve) heat capacities of Xe
chains are compared in Fig. 4. Note that the experimental
data for 1D chains of N2 and Xe have been obtained in the
same adiabatic calorimeter [60] and with the same sample
of c-SWNT bundles [6]. The dependences are qualitatively
similar at T < 12 K.
In the case of 1D Xe chains the experimental curve
CXe(T) goes above the theoretical one for T > 8 K and the
excess ( Сph) increases steadily with temperature going up
(see Fig. 4). It was assumed [60] that Сph is mainly due to
an increasing distance aXe between nearest neighbor Xe
atoms in the chain at higher temperatures. The theoretical
curve for Xe chains was calculated assuming aXe = const.
The effect of the changes in aN2 with increasing tempera-
Fig. 3. The normalized experimental heat capacity СN2(Т)/(μR) of
1D chains of N2 molecules adsorbed in the grooves of c-SWNT
bundles at T = 2–40 K (a) and T = 2–8 K (b). The solid curve is
the theoretical heat capacity (СV/R)Kr of phonon modes (longi-
tudinal acoustic L mode and two transverse optical T1 and T2
modes) of adsorbed 1D chains of Kr atoms [47] in the grooves
of c-SWNT bundles. The solid straight lines (b) show a linear
low-temperature behavior of the heat capacity of the longitudinal
mode L of the 1D chains of N2 molecules (1) and Kr atoms (2).
M.I. Bagatskii, M.S. Barabashko, and V.V. Sumarokov
572 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 5
ture upon the phonon heat capacity should also be ob-
served for 1D chains of N2 molecules above 8 K.
Thus, above 8 K the heat capacity of the 1D chains of
N2 in the G is determined by the translational vibrations of
the centers of gravity of the molecules, the orientational
vibrations of molecules as a whole and by the Cph varia-
tions when the distance aN2 between the nearest neighbor
N2 molecules increases as temperature goes up.
4. Conclusions
The heat capacity of c-SWNT bundles containing one-
dimensional chains of adsorbed N2 molecules in the
grooves of the c-SWNT bundles has been investigated for
the first time. The contribution of N2 molecules CN2 to the
total heat capacity has been separated. The highest Bril-
louin zone edge frequency of the longitudinal phonon
mode has been estimated for 1D chains of N2 molecules in
the grooves ( 5.2 meV)L . The contribution of the
translational vibrations of N2 molecules to the heat capaci-
ty of nitrogen is dominant at 2–8 KT . Above 8 K the
contribution of the orientational vibrations of N2 molecules
becomes significant.
The authors are indebted to V.G. Manzhelii, M.A. Strzhe-
mechny, K.A. Chishko, S.B. Feodosyev, E.S. Syrkin, E.V.
Manzhelii, and I.A. Gospodarev for helpful discussions.
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Dresselhaus, and G. Dresselhaus (eds.), Imperial Colledge
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