The effect of O₂ impurities on the low-temperature radial thermal expansion of bundles of closed single-walled carbon nanotubes
The effect of oxygen impurities upon the radial thermal expansion αr of bundles of closed single-walled carbon nanotubes has been investigated in the temperature interval 2.2–48 K by the dilatometric method. Saturation of bundles of nanotubes with oxygen caused an increase in the positive αr-values...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2011
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| Цитувати: | The effect of O₂ impurities on the low-temperature radial thermal expansion of bundles of closed single-walled carbon nanotubes / A.V. Dolbin, V.B. Esel'son, V.G. Gavrilko, V.G. Manzhelii, S.N. Popov, N.A.Vinnikov, B. Sundqvist // Физика низких температур. — 2011. — Т. 37, № 4. — С. 438–442. — Бібліогр.: 14 назв. — англ. |
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irk-123456789-1185402017-05-31T03:08:14Z The effect of O₂ impurities on the low-temperature radial thermal expansion of bundles of closed single-walled carbon nanotubes Dolbin, A.V. Esel'son, V.B. Gavrilko, V.G. Manzhelii, V.G. Popov, S.N. Vinnikov, N.A. Sundqvist, B. Наноструктуры при низких температурах The effect of oxygen impurities upon the radial thermal expansion αr of bundles of closed single-walled carbon nanotubes has been investigated in the temperature interval 2.2–48 K by the dilatometric method. Saturation of bundles of nanotubes with oxygen caused an increase in the positive αr-values in the whole interval of temperatures used. Also, several peaks appeared in the temperature dependence αr(T) above 20 K. The low temperature desorption of oxygen from powders consisting of bundles of single-walled nanotubes with open and closed ends has been investigated. 2011 Article The effect of O₂ impurities on the low-temperature radial thermal expansion of bundles of closed single-walled carbon nanotubes / A.V. Dolbin, V.B. Esel'son, V.G. Gavrilko, V.G. Manzhelii, S.N. Popov, N.A.Vinnikov, B. Sundqvist // Физика низких температур. — 2011. — Т. 37, № 4. — С. 438–442. — Бібліогр.: 14 назв. — англ. 0132-6414 PACS: 65.80.+n http://dspace.nbuv.gov.ua/handle/123456789/118540 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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English |
| topic |
Наноструктуры при низких температурах Наноструктуры при низких температурах |
| spellingShingle |
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. Sundqvist, B. The effect of O₂ impurities on the low-temperature radial thermal expansion of bundles of closed single-walled carbon nanotubes Физика низких температур |
| description |
The effect of oxygen impurities upon the radial thermal expansion αr of bundles of closed single-walled carbon nanotubes has been investigated in the temperature interval 2.2–48 K by the dilatometric method. Saturation of bundles of nanotubes with oxygen caused an increase in the positive αr-values in the whole interval of temperatures used. Also, several peaks appeared in the temperature dependence αr(T) above 20 K. The low temperature desorption of oxygen from powders consisting of bundles of single-walled nanotubes with open and closed ends has been investigated. |
| format |
Article |
| author |
Dolbin, A.V. Esel'son, V.B. Gavrilko, V.G. Manzhelii, V.G. Popov, S.N. Vinnikov, N.A. Sundqvist, B. |
| author_facet |
Dolbin, A.V. Esel'son, V.B. Gavrilko, V.G. Manzhelii, V.G. Popov, S.N. Vinnikov, N.A. Sundqvist, B. |
| author_sort |
Dolbin, A.V. |
| title |
The effect of O₂ impurities on the low-temperature radial thermal expansion of bundles of closed single-walled carbon nanotubes |
| title_short |
The effect of O₂ impurities on the low-temperature radial thermal expansion of bundles of closed single-walled carbon nanotubes |
| title_full |
The effect of O₂ impurities on the low-temperature radial thermal expansion of bundles of closed single-walled carbon nanotubes |
| title_fullStr |
The effect of O₂ impurities on the low-temperature radial thermal expansion of bundles of closed single-walled carbon nanotubes |
| title_full_unstemmed |
The effect of O₂ impurities on the low-temperature radial thermal expansion of bundles of closed single-walled carbon nanotubes |
| title_sort |
effect of o₂ impurities on the low-temperature radial thermal expansion of bundles of closed single-walled carbon nanotubes |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2011 |
| topic_facet |
Наноструктуры при низких температурах |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118540 |
| citation_txt |
The effect of O₂ impurities on the low-temperature radial thermal expansion of bundles of closed single-walled carbon nanotubes / A.V. Dolbin, V.B. Esel'son, V.G. Gavrilko, V.G. Manzhelii, S.N. Popov, N.A.Vinnikov, B. Sundqvist // Физика низких температур. — 2011. — Т. 37, № 4. — С. 438–442. — Бібліогр.: 14 назв. — англ. |
| series |
Физика низких температур |
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© A.V. Dolbin, V.B. Esel'son, V.G. Gavrilko, V.G. Manzhelii, S.N. Popov, N.A.Vinnikov, and B. Sundqvist, 2011
Fizika Nizkikh Temperatur, 2011, v. 37, No. 4, p. 438–442
The effect of O2 impurities on the low-temperature radial
thermal expansion of bundles of closed single-walled
carbon nanotubes
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
B. Sundqvist
Department of Physics, Umea University, SE - 901 87 Umea, Sweden
Received September 17, 2010
The effect of oxygen impurities upon the radial thermal expansion αr of bundles of closed single-walled car-
bon nanotubes has been investigated in the temperature interval 2.2–48 K by the dilatometric method. Saturation
of bundles of nanotubes with oxygen caused an increase in the positive αr-values in the whole interval of tem-
peratures used. Also, several peaks appeared in the temperature dependence αr(T) above 20 K. The low tempera-
ture desorption of oxygen from powders consisting of bundles of single-walled nanotubes with open and closed
ends has been investigated.
PACS: 65.80.+n Thermal properties of small particles, nanocrystals, nanotubes.
Keywords: Single-walled carbon nanotubes, O2, bundles of carbon nanotubes, radial thermal expansion.
1. Introduction
Carbon nanotubes (CNT) rank among the most promis-
ing objects of fundamental and applied research. Owing to
their unique structures and extraordinary mechanical, elec-
tric and thermal properties, CNTs hold a considerable po-
tential for extensive applicability in various fields of hu-
man activity — from high-speed nano-dimensional
electronics and biosensors to hydrogen power engineering
and developments for ecological purposes. It is known that
doping of carbon nanomaterials (fullerites [1] and nano-
tubes [2]) with impurities, including gaseous ones, has a
considerable effect on their properties and hence on the
characteristics of products and devices based on these ma-
terials. The penetration of O2 molecules into bundles of
single-walled nanotubes (SWNTs) affects drastically the
properties of these SWNT systems, changing, for example,
their conductivity by several orders of magnitude [2].
However, the influence of the O2 impurity on the thermal
properties of SWNT bundles, in particular their thermal
expansion, still remains obscure.
It has been shown [3–6] that doping a system consisting
of SWNT bundles with gases causes sharp changes in both
the magnitudes and the sign of its radial thermal expansion
αr(T). This is due to the joint effect of several factors.
Firstly, the impurity molecules sitting at the surface and
inside the CNTs suppress the lowest-frequency transverse
vibrations of the quasi-two-dimensional carbon walls of
the nanotubes. These vibrations are characterized by nega-
tive Grüneisen coefficients [7], which determines their
dominant negative contribution to the thermal expansion at
low temperatures. The suppression of the transverse vibra-
tions by gas impurity molecules reduces the negative con-
tribution and increases the radial thermal expansion of the
SWNT bundles. Another factor affecting the thermal ex-
pansion of gas-doped SWNT bundles is connected with
temperature variations that provoke a spatial redistribution
of the gas impurity molecules localized in different areas
of the SWNT bundles and having different energies of
binding to the CNTs. This shows up as peaks in the tem-
perature dependence of αr. The saturation of SWNT bun-
dles with He impurities increases the negative values of
αr(T) below 3.7 K, which is due to the tunneling character
of the positional rearrangement of the He atoms [6].
In this study the radial thermal expansion of O2-saturated
bundles of single-walled carbon nanotubes with closed ends
(c-SWNTs) was investigated in the interval T 2.2–48 K by
The effect of O2 impurities on the low temperature radial thermal expansion
Fizika Nizkikh Temperatur, 2011, v. 37, No. 4 439
the dilatometric method. To interpret the results obtained,
we needed some information about the concentration and the
spatial arrangement of the O2 molecules in the SWNT bun-
dles. Such information was obtained by investigating the
temperature dependence of O2 desorption from bundles of
closed and open SWNTs saturated with oxygen.
2. Low-temperature desorption of oxygen impurities
from carbon nanotubes
The O2 desorption from the SWNT powder was inves-
tigated in the temperature interval 50–133 K using a spe-
cial cryogenic device whose design is described elsewhere
[3] together with the measuring technique used. Two sam-
ples were used — the starting SWNT powder (CCVD me-
thod, Cheap Tubes, USA) and SWNT powder after an
oxidative treatment was applied to open the ends of the
nanotubes. The oxidative treatment is detailed in [3]. It
should be noted that the oxidative-treated sample was used
only to investigate desorption. The samples of c-SWNT
and o-SWNTs were saturated with oxygen by the same
procedure. The used O2 gas was 99.98% pure and con-
tained ≤ 0.02% N2 as an impurity. The starting masses of
the c-SWNT and o-SWNT samples were 41.6 and
67.4 mg, respectively. Prior to measurement, each sample
was evacuated for 72 hours directly in the measuring cell
of the device to remove possible gas impurities. Then the
cell with the sample was filled with oxygen at room tem-
perature to the pressure 23 Torr and cooled slowly (for 10
hours) down to 46 K. In the process of cooling the O2 gas
was fed to the cell in small portions as soon as the previous
portion was absorbed by the SWNTs. Thus, the pressure in
the cell remained no higher than the equilibrium pressure
of O2 vapor at each temperature. This saturation procedure
allowed the maximum possible filling of all saturation-
accessible positions in the SWNT bundles and on the other
hand it prohibited condensation of O2 vapor on the cell
walls. At T = 46 K the equilibrium pressure in the cell with
the sample was 0.01 Torr, which was considerably lower
than the equilibrium pressure of O2 vapor at this tempera-
ture (0.04 Torr [8]). After this, the O2 desorption from the
nanotubes was investigated. The quantities of desorbed gas
were measured during stepwise heating of the SWNT
powder. The oxygen released on heating was taken to an
evacuated calibrated vessel whose internal pressure was
measured using a capacitive MKS-627B pressure trans-
ducer. The gas was withdrawn at each temperature of the
sample until the gas pressure over the sample decreased to
0.01 Torr. Then the measurement procedure was repeated
at the next temperature point.
A diagram of the desorbed O2 quantities (mole per mole
of SWNT powder, i.e. the number of O2 molecules per
carbon atom) is shown in Fig. 1.
It should be noted that the quantities of O2 desorbed
from the SWNT samples were equal, within the experi-
mental error, to the quantities of O2 sorbed by the samples
on saturation, which points to a practically complete re-
moval of the O2 impurity from the sample. The reversibili-
ty of the sorption is conclusive evidence for its non-
chemical origin because complete desorption of oxygen at
temperatures below 110 K can only occur with physical
sorption.
It was found previously [3,5] that the air-oxidative
treatment of a powder of SWNT bundles led to opening the
CNT ends and thus enhanced the sorptive capacity of the
bundles for Xe atoms [3] and N2 molecules [5]. A similar
effect of such treatment might be expected for O2 sorption
as well. Indeed, the investigation of the sorptive capacity
of the oxidized SWNTs showed that the absorbed quantity
of O2 increased almost threefold (see Fig. 1). The quantity
of O2 desorbed from the treated SWNT powder increased
sharply in the temperature interval 57–63 K. A similar
growth of the low temperature maximum in the desorption
diagram was also observed for the N2- saturated o-SWNT
sample [5]. This is most likely because, firstly, the oxida-
tive treatment separates nanotubes in the bundle [9] and
thus increases the sorption-accessible area at the outer sur-
face of the SWNT bundles where the energy of binding to
the impurity molecules is lower in comparison with the
grooves at the CNT surface [10]. Secondly, after the oxida-
tive treatment the O2 molecules are able to penetrate into
the internal cavities of the CNTs through their open ends
or through holes formed in the cylinder walls. It is shown
theoretically [10] that the O2 molecules that are located in
the internal cavity along the nanotube axis and do not con-
tact the CNT walls have much lower binding energies than
the molecules localized near the inner walls. The binding
energy of the O2 molecules localized inside the CNTs and
having no contact with the internal surface is comparable
to that of the molecules forming the first layer at the outer
surface of the bundles, which accounts for the highest peak
of O2 desorption from the o-SWNT bundles at low tem-
peratures (57–63 K).
Fig. 1. The relative (mol/mol) O2 quantity desorbed from c-SWNTs
(solid columns) and o-SWNTs (empty columns) saturated with
oxygen.
0
0.005
0.010
0.015
0.020
0.025
0.1
0.2
0.3
0.4
0.5
c-SWNT
o-SWNT
50 60 70 80 90 100
T, K
n
,
m
o
l
/m
o
l
O
C
2
A.V. Dolbin, V.B. Esel'son, V.G. Gavrilko, V.G. Manzhelii, S.N. Popov, N.A.Vinnikov, and B. Sundqvist
440 Fizika Nizkikh Temperatur, 2011, v. 37, No. 4
The total quantities of O2 desorbed from the starting
O2-saturated SWNT powder and from the oxidative-treated
SWNT powder are given in Table 1.
Table 1. The total quantities of gases desorbed from c-SWNTs
and o-SWNTs (mole per mole and mass.%)
Impurity
c-SWNT о-SWNT
mol/mol, % mass % mol/mol, % mass %
H2 [4] 10.0 1.67 8.07 1.35
Xe [3] 1.64 7.38 4.71 21.2
N2 [5] 11.2 26.1 46.4 108
O2 18.1 42.27 56 149.4
The somewhat higher concentration of the sorbed O2 im-
purity can be attributed to the higher energies of the O2– O2
interaction (9.2 kJ/mol [8]) in comparison with the N2–N2
one (6.8 kJ/mol [11]). This difference gives the O2 molecules
more chances to form a second and subsequent layers at the
bundle surface in comparison with N2 molecules.
3. Radial thermal expansion of oxygen-saturated
bundles of closed single-walled carbon nanotubes
The radial thermal expansion of O2-saturated closed sin-
gle-walled carbon nanotubes was investigated using a low-
temperature capacitance dilatometer with a 0.02 nm sensitiv-
ity [12]. The sample was prepared by layer-by-layer com-
pressing [13] a SWNT powder (Cheap Tubes,USA) at the
pressure 1.1 GPa. The technique used aligned the CNT axes
in the plane perpendicular to the sample axis, which was
attested by an x-ray investigation. The preparation technique
is detailed in [14]. The sample was a cylinder ~7.2 mm high
and ~10 mm in diameter. Prior to measurement, the cell with
the sample of pressure-oriented CNTs was evacuated at
room temperature for 72 hours. Then the CNTs were doped
with oxygen using the procedure described in Section 1.
When the saturation process was completed, the measuring
cell was cooled to liquid helium temperature. The thermal
expansion was measured in vacuum down to 1·10–5 Torr.
The obtained temperature dependence of the radial
thermal expansion coefficient αr(T) of the c-SWNT bun-
dles saturated with oxygen is shown in Fig. 2 (curve 1).
It is interesting that above 20 K the radial thermal ex-
pansion of the oxygen-saturated nanotubes (curve 1 in
Fig. 2,a) shows several well defined maxima. It was as-
sumed in [3–6] that the peaks observed in the αr(T) of gas-
saturated SWNT bundles were caused by the positional
redistribution of the gas impurity molecules at the surface
of and inside SWNT bundles due to a change in the tem-
perature. Some impurity molecules can change their ener-
gies as they move from one position to another at the sur-
face and inside the SWNT bundles and the peaks in the
temperature dependence αr(T) account for such rearrange-
ments of the impurity molecules. According to [10], the O2
molecules localized in the grooves between the neighbor-
ing tubes in the c-SWNT bundles have the highest energy
of binding to the bundle surface. The O2 molecules form-
ing a two-dimensional phase (layer) at the lateral surface of
SWNT bundles have somewhat lower energy. The binding
energies of the O2 molecules forming the subsequent
(second, third and so on) layers are even lower. On heat-
ing, the impurity molecules having the lowest energies of
binding to the CNT surface, i.e. the molecules of the two-
dimensional layers (the first and the subsequent ones), at
the bundle surface are excited first. The excited molecules
move from the first layer to the next ones having much
lower energies of binding to the surface of SWNT bundles.
This process increases the energy of the total system
(SWNT bundles plus impurity molecules), which causes a
peak in αr(T). Further heating excites the gas molecules in
the grooves at the lateral surface of SWNT bundles. They
escape from the grooves and form a two-dimensional layer
5 10 15 20 25 30 35 40 45 50
0
20
40
60
80
100
120
140
160
180
1
1
T, K
3
4 5
2
1
�
r,
1
0
K
–
6
–
1
�
r,
1
0
K
–
6
–
1
1.0
0.8
0.6
0.4
0.2
0
2 3 4
1
2 3
4
T, K
5
a
b
Fig. 2. Coefficient of radial thermal expansion of bundles of
closed nanotubes: 1 — saturated with oxygen; 2 — saturated with
nitrogen [5]; 3 — saturated with hydrogen [4]; 4 — saturated
with xenon [3]; 5 — pure nanotubes [14]; (a) in the temperature
interval of 2,2–48 К; (b) in the temperature interval of 2,2–4.5 К.
The effect of O2 impurities on the low temperature radial thermal expansion
Fizika Nizkikh Temperatur, 2011, v. 37, No. 4 441
at the lateral surface of the bundles. Their potential energy
grows, which shows up as peaks in the temperature depen-
dence αr(T). Some of the O2 molecules inside the SWNT
bundles penetrate into the relatively limited number of
nanotubes with open ends available in the starting powder
and the O2 molecules can also move into the comparatively
wide channels formed inside SWNT bundles between na-
notubes having different diameters. Such temperature-trig-
gered positional redistribution of the impurity molecules
inside SWNT bundles can also induce peaks in the depen-
dence αr(T). The nonuniform solution of gases in the
SWNT bundles leads to a considerable smearing and over-
lapping of the peaks in the dependence αr(T). As a result,
the peaks that may appear in the dependence are not all
evident, which makes a detailed interpretation of the re-
sults rather difficult.
Of the gases (He, H2, N2, Xe) investigated previously [3–
6], the effect of O2 upon the thermal expansion is most
closely similar to that of N2. The peaks in the dependence
αr(T) of the N2-SWNT and O2-SWNT systems appear in
very similar temperature intervals (Fig. 2), though in the
case of N2 the interval is somewhat narrower. Because of
the narrower temperature region of the αr(T) peaks in the
N2-SWNT system, more peaks may overlap and therefore
be partly unobservable (Fig. 2). We should also note that the
saturation of SWNT bundles with oxygen led to a practically
complete disappearance of the region of negative αr(T)-
values. This is most likely because the O2 concentration is
relatively higher in the O2-c-SWNT system (Tabl. 1) than in
the other gases, and the interaction between the O2 mole-
cules and the CNT surface is appreciably stronger [10]. To-
gether these factors suppress effectively the low-temperature
transverse vibrations of the quasi-two-dimensional CNT
walls which are responsible for negative αr(T).
It is obvious that the contribution of the positional redi-
stribution of impurity molecules to the thermal expansion
coefficient αr(T) is not proportional to the impurity concen-
tration. Variations of the O2 concentration in the O2-c-SWNT
solution cause nonuniform changes in the positions of the O2
molecules in the SWNT bundles, which correspondingly
affects the temperature dependence of the contribution made
to αr(T) by the positional O2 redistribution. To decrease par-
tially the O2 concentration, the sample was heated to
T = 63 K, which let us remove mainly the O2 molecules
weakly bound to the CNTs (see Fig.1). The sample was held
at T = 63 K until the O2 desorption proceeding at this tem-
perature was completed (i.e., until the pressure in the measur-
ing cell became 1⋅10–5 Torr). The sample was then cooled to
T = 2.2 K and the thermal expansion was measured again
(see Fig. 3, curve 2).
It is seen that the partial removal of the oxygen impuri-
ty at T = 63 K resulted mainly in a considerable suppres-
sion of the contribution of the O2 molecules whose posi-
tional rearrangement caused a comparatively small change
in the energy of the system. When the O2 molecules were
removed from these positions, the low temperature peaks
of αr(T) disappeared (at T = 21 K and T = 28 K). As was
expected, the partial desaturation had considerably less
influence on the high-temperature peaks of αr(T). For ex-
ample, at T = 35 K and T = 40 K these peaks transformed
into a single lower peak. The effect of the partial removal
of the O2 impurity upon the temperature dependence αr(T)
of the sample was even weaker outside the peak region
(below T = 9 K). This may indicate that the thermal expan-
sion of the SWNT sample outside the peak region is influ-
enced mainly by the O2 molecules that are localized at the
sites with high binding energies, i.e. in the first layer at the
bundle surface, in the internal voids of the CNTs and in the
grooves between the CNTs at the bundle surface.
Conclusions
The temperature dependence of the radial thermal ex-
pansion coefficient αr(T) of closed single-walled carbon
nanotubes saturated with oxygen has been measured in the
temperature interval 2.2–48 K using the dilatometric me-
thod. Saturation of SWNT bundles with oxygen led to a
sharp increase in the magnitudes of αr in the whole range
of temperatures investigated. The reason may be that the
O2 molecules decrease the negative contribution to the
thermal expansion made by the transverse acoustic CNT
vibrations perpendicular to the nanotube surface. The more
appreciable suppression of the negative contribution in
comparison with other gas impurities is attributed to the
relatively high O2 concentration (18 mol.%) in the SWNT
bundles, as well as to the rather strong interaction between
the O2 molecules and the CNTs.
The temperature dependence αr(T) of the O2-saturated
SWNT bundles has several peaks in the interval T = 20–45 K.
They may be caused by a positional redistribution of the O2
5 10 15 20 25 30 35 40 45 50
0
20
40
60
80
100
120
140
160
180
T, K
3
2
1
�
r,
1
0
K
–
6
–
1
Fig. 3. The radial thermal expansion coefficient of c-SWNT bun-
dles: 1 — saturated with O2, 2 — after a partial removal of oxy-
gen at T = 63 K, 3 — pure CNTs.
A.V. Dolbin, V.B. Esel'son, V.G. Gavrilko, V.G. Manzhelii, S.N. Popov, N.A.Vinnikov, and B. Sundqvist
442 Fizika Nizkikh Temperatur, 2011, v. 37, No. 4
molecules at the SWNT surface and inside some nanotubes.
As the concentration of oxygen was reduced through its par-
tial desorption at T = 63 K, the values of αr(T) decreased at
T > 9 K. The analysis of the O2 desorption effect on the ther-
mal expansion of the O2-c-SWNT solution shows that in the
interval T = 15–45 K the magnitude and the dependence of
αr(T) are mainly determined by the positional rearrangement
of the O2 molecules whose interaction with the CNTs is rela-
tively weak. It is likely that below 9 K the thermal expansion
is mainly contributed by the O2 molecules strongly bound to
the CNTs, i.e. the O2 molecules localized in the grooves of the
bundles and the O2 molecules forming the first layer at the
bundle surface and on the inner CNT walls.
The effects produced by the sorbed oxygen and nitro-
gen upon the radial thermal expansion of SWNT bundles
have been compared qualitatively.
The desorption of oxygen from a powder of SWNTs
with open and closed ends has been investigated in the
temperature interval 50–133 K.
The air-oxidative treatment of SWNT bundles aimed at
opening the CNT ends 3.1 times enhanced the sorptive
capacity of the sample for oxygen in comparison with the
starting SWNT powder.
The authors are indebted to the Science & Technology
Center of Ukraine (STCU) for the financial support of the
study (Project # 5212).
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