Nanotube formation on catalytic surface in plasma discharge
The expression for number of layers of multilayered nanotube, which have been generated during the time of its growth in the plasma discharge, is derived. Отримано вираз для кількості прошарків багатошарової нанотрубки, що встигає сформуватися за час її росту в плазмовому розряді. Получено выражение...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Cite this: | Nanotube formation on catalytic surface in plasma discharge / V.I. Maslov, V.N. Tretyakov, N.A. Azarenkov, A.M. Yegorov, I.N. Onishchenko // Вопросы атомной науки и техники. — 2005. — № 2. — С. 188-190. — Бібліогр.: 2 назв. — англ. |
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Maslov, V.I. Tretyakov, V.N. Azarenkov, N.A. Yegorov, A.M. Onishchenko, I.N. 2015-04-04T19:45:20Z 2015-04-04T19:45:20Z 2005 Nanotube formation on catalytic surface in plasma discharge / V.I. Maslov, V.N. Tretyakov, N.A. Azarenkov, A.M. Yegorov, I.N. Onishchenko // Вопросы атомной науки и техники. — 2005. — № 2. — С. 188-190. — Бібліогр.: 2 назв. — англ. 1562-6016 PACS Ref: 52.27.Lw https://nasplib.isofts.kiev.ua/handle/123456789/79796 The expression for number of layers of multilayered nanotube, which have been generated during the time of its growth in the plasma discharge, is derived. Отримано вираз для кількості прошарків багатошарової нанотрубки, що встигає сформуватися за час її росту в плазмовому розряді. Получено выражение для количества слоев многослойной нанотрубки, которое успевает сформироваться за время ее роста в плазменном разряде. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Low temperature plasma and plasma technologies Nanotube formation on catalytic surface in plasma discharge Формування нанотрубок на каталітичній поверхні в плазмовому розряді Формирование нанотрубок на каталитической поверхности в плазменном разряде Article published earlier |
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Nanotube formation on catalytic surface in plasma discharge |
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Nanotube formation on catalytic surface in plasma discharge Maslov, V.I. Tretyakov, V.N. Azarenkov, N.A. Yegorov, A.M. Onishchenko, I.N. Low temperature plasma and plasma technologies |
| title_short |
Nanotube formation on catalytic surface in plasma discharge |
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Nanotube formation on catalytic surface in plasma discharge |
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Nanotube formation on catalytic surface in plasma discharge |
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Nanotube formation on catalytic surface in plasma discharge |
| title_sort |
nanotube formation on catalytic surface in plasma discharge |
| author |
Maslov, V.I. Tretyakov, V.N. Azarenkov, N.A. Yegorov, A.M. Onishchenko, I.N. |
| author_facet |
Maslov, V.I. Tretyakov, V.N. Azarenkov, N.A. Yegorov, A.M. Onishchenko, I.N. |
| topic |
Low temperature plasma and plasma technologies |
| topic_facet |
Low temperature plasma and plasma technologies |
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2005 |
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English |
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Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Формування нанотрубок на каталітичній поверхні в плазмовому розряді Формирование нанотрубок на каталитической поверхности в плазменном разряде |
| description |
The expression for number of layers of multilayered nanotube, which have been generated during the time of its growth in the plasma discharge, is derived.
Отримано вираз для кількості прошарків багатошарової нанотрубки, що встигає сформуватися за час її росту в плазмовому розряді.
Получено выражение для количества слоев многослойной нанотрубки, которое успевает сформироваться за время ее роста в плазменном разряде.
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1562-6016 |
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https://nasplib.isofts.kiev.ua/handle/123456789/79796 |
| citation_txt |
Nanotube formation on catalytic surface in plasma discharge / V.I. Maslov, V.N. Tretyakov, N.A. Azarenkov, A.M. Yegorov, I.N. Onishchenko // Вопросы атомной науки и техники. — 2005. — № 2. — С. 188-190. — Бібліогр.: 2 назв. — англ. |
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2025-11-24T15:58:12Z |
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2025-11-24T15:58:12Z |
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| fulltext |
NANOTUBE FORMATION ON CATALYTIC SURFACE IN PLASMA
DISCHARGE
V.I.Maslov, V.N.Tretyakov*, N.A.Azarenkov*, A.M.Egorov, I.N.Onishchenko
NSC Kharkov Institute of Physics & Technology, Kharkov, Ukrain,
e-mail: vmaslov@kipt.kharkov.ua;
*V.N. Karazin Kharkov National University, Kharkov, Ukraine
The expression for number of layers of multilayered nanotube, which have been generated during the time of its
growth in the plasma discharge, is derived.
PACS Ref: 52.27.Lw
INTRODUCTION
Controllable formation of nanotubes, superlong
nanotubes, nanotubes with the necessary properties are the
very important and now intensively investigated problems
(see, for example, [1, 2]). In this paper the formation of
carbon nanotubes in the plasma discharge is considered,
when on catalytic surface or surface with defects the
nanotubes under effect of the flow of carbon plasma,
bombarding the surface, are formed. The universal
expression for number of layers of multilayered
nanotubes, which have been generated during the time of
its growth in the plasma discharge, is derived.
THE DESCRIPTION OF NANOTUBE
GROWTH
Let us consider the nanotube formation, built in the
lattice ordered in an electric field of the nanotubes,
perpendicular to the catalytic surface. Atoms of carbon,
colliding with a lateral surface of a tube and getting in
area of a shadow concerning bombarding plasma stream,
are quickly cooled, cease to join to nanotubes and "are
blown" from a wood of the nanotubes as a result of
bombardment by the following atoms of their stream. That
is in the region of a shadow, closer to the basis of the
nanotube, layers do not grow on of the nanotubes. In other
words, layers of nanotube grow on some distance from its
head. We name this interval area outside of a shadow and
equal to the length of free run ℓfr of carbon atom
concerning collisions with nanotube walls. As
probabilities of connection of atoms to the top and lateral
side are practically identical, speeds of lengthening of a
lateral side and length of nanotube are identical. Then
during lengthening of nanotube on ℓfr its lateral side also
to be extended on ℓfr. Then the amount of nanotube layers
is equal Nmax=ℓfr/2πR at spiral nanotube which cross-
section, perpendicular to tube axes, represents an
untwisted spiral. Here R is the average radius of nanotube.
For first layer R it is approximately equal to fullerene
radius. Thus ℓfr≈Vz(ℓnan/Vthc ). Here ℓnan is the average
distance between nanotubes, Vz is the longitudinal
lengthways of the nanotube velocity of carbon ions and
atoms, Vthc is the thermal velocity of carbon atoms. If
Vz≈Vthc, then ℓfr≈ℓnan. Thus ℓnan≈(nfs)-1/2 . Here nfs is the
superficial density of the nanotubes. Nmax≈1, if ℓnan≈2πR.
The surface density of the nanotubes σ is derived
from that during lengthening with speed V nz of the
nanotubes on ℓfr the density of the particle flow nc V z
fall on the surface, which with probability ωz engenders
nanotubes. Thus,
σ=
ℓ fr
V nz
ncV z ωz = nc V z
2ωz
V nz V thc
2/3
(1)
One mechanism of the growth of the nanotube side is
its bombardment by carbon atoms and ions of a plasma
flow. The second mechanism of the nanotube growth is
the following one. Fallen on the nanotube and sorbed on
its surface carbon atom diffuse on its surface up to a
growing side, that is growth of a side is reduced to its
lengthening with some speed V nz .
Now we show, that can arise as spiral, and
azimuthally symmetric nanotubes. Also we find quantity
of layers of the azimuthally symmetric nanotube.
For last carbon atom getting between two next carbon
atoms and to form closed cluster, which is the basis of the
azimuthally symmetric nanotube, it should overcome a
power barrier εз on some tens percents higher than to
overcome a barrier εпр for carbon atom to join border
open-ended spiral cluster. Probabilities to join to open-
ended circular wпр or to close wз it are proportional to
wпр~exp(-εпр/T), wз~exp(-εз/T). Hence, the probability to
close wз of open-ended circular cluster is less than
probability to join wпр to open-ended circular cluster
wз<wпр. Thus, the probability of origin of spiral cluster is
more than probability of origin of closed circular cluster.
However, the spiral nanotube (Figure a) is less
favourable from the power point of view, because there
are many nonsaturated connections. Hence, if during the
nanotube growth the bombardment is intensive the part of
the spiral nanotubes decreases due to "heating".
Probability to arise new layer - cluster around
azimuthally symmetric nanotube is small. It is
proportional to nanotube radius. The factor of diffusion of
carbon atoms on the nanotube surface is also proportional
to nanotube radius. Thus, at formation of multilayered
azimuthally symmetric nanotube the distribution on radius
r lengths of layers along z-axis has qualitatively kind
submitted in Figure b.
The number of carbon atoms getting in time unit on
the external surface of the nanotube we estimate as
follows:
188 Problems of Atomic Science and Technology. Series: Plasma Physics (11). 2005. № 2. P. 188-190
dNcmax/dt=npvp2πRmaxH
Here H is the height of the nanotube, np, Vp are the density
and velocity of carbon ions in the flow (plasma)
accordingly, 2πRmax is the length of "circle" of an external
layer of the nanotube.
a b
a) Origin spiral nanotube; b)distribution on radius r of
lengths of nanotube layers
The nanotube growth rate upwards due to carbon
atom connection, which are placed on the nanotube
surface, to a face edge is determined by the following
expression:
V||
(1)=dH(1)/dt=(aw0 dN||/dt)/Na (2)
Here a is the size of internuclear distance in nanotube
structure, w0 is the atom, diffused from the nanotube
surface, probability of connection to the edge, dN||/dt is
the number of carbon atoms getting in time unit on a face
edge, Na is the number of carbon atoms on a face edge.
Taking into account that
dN||/dt=w||dNcmax/dt (3)
and
Na=L/a (4)
we derive the following expression:
dH(1)/dt=(a2w0w||dNcmax/dt)/L (5)
Here w|| is the probability of that the carbon atom, which
is placed on the nanotube surface, diffuse on the face
edge, L is the length of the lateral face edge. With the
account (1) the expression (5) has the following kind:
dH(1)/dt=(a2w0w||npvp2πRmaxH)/L (6)
Now we take into account direct hits of carbon ions
from the discharge plasma flow on a face edge of the
nanotube:
V||
(2)=dH(2)/dt=(aw00 dNc/dt)/Na (7)
Here w00 is the probability of connection of a carbon ion
to a face edge at direct hit from the plasma flow, dNc/dt is
the number of carbon ions getting from the plasma flow
on the end face in time unit. It can be estimated as
follows:
dNc/dt=npvpLΔR (8)
Here R is the nanotube "thickness". Then, with the
account (4) and (8) the equation (7) can be presented as:
dH(2)/dt=a2 w00npvpΔR (9)
Then the full growth rate of the face edge is equal
V||=dH/dt=dH(1)/dt+dH(2)/dt=
=a2npvp(w00ΔR+w0w||2πRmaxH /L) (10)
Let us estimate the growth rate of the nanotube
surface sideways:
Vθ=dL/dt=(aw0dNθ/dt)/Naθ (11)
Here dNθ/dt is the number of atoms, diffused from the
nanotube surface on the lateral edge in time unit, Naθ is the
number of carbon atoms on the lateral edge. In our case
dNθ/dt=wθdNcmax/dt=wθnpvp2πRmaxH (12)
and
Naθ=H/a (13)
Then with the account (12) and (13) the equation (11) we
present in the following kind:
dL/dt=a2w0wθnpvp2πRmax (14)
Here wθ is the probability of that the carbon atom, which
is placed on the nanotube surface, is diffused on the
lateral edge.
As a result we have derived the following system of
the equations describing the nanotube growth upwards
and sideways:
dH/dt=a2npvp(w00ΔR+w0w||2πRmaxH /L) (15)
dL/dt=a2npvpw0wθ2πRmax (16)
It is necessary to take into account, that in system of the
equations (15) - (16 three values, namely w||, Rmax and wθ
are the functions of variables H and L.
The length of an external lateral surface of the
nanotube can be found from the assumption that it can be
presented as Arhimed’s spiral. Then
L=δRφ2/4π (17)
Thus, we derive
2πRmax=L(φ)–L(φ-2π)=δR(φ2–(φ-2π)2)/4π=
=δR(φ-2π)/2 (18)
Here δR is the distance between layers of the nanotube, φ
is the angular coordinate. From (17) we obtain
dependence φ=φ(L):
φ=2(πL/δR)1/2 (19)
From here, using (17) and (19), we find
2πRmax=δR((πL/δR)1/2-π) (20)
Taking into account, that L>>δR, we have from (20) the
following expression:
2πRmax=δR(πL/δR)1/2=(πLδR)1/2 (21)
Then the system of the equations (15) - (16) becomes:
dH/dt=a2npvp(w00ΔR+w0w||(πδR/L)1/2H ) (22)
dL/dt=a2npvpw0wθ(πδRL)1/2 (23)
QUANTITY OF LAYERS IN GROWING IN
THE DISCHARGE MULTILAYERED
NANOTUBE
Under a shadow we believe that part of the nanotube
surface on which bombarding carbon ions and atoms get
only after collision with another nanotube. We believe
that on the nanotube surface, located outside of the
shadow there appears fast (induced) surface diffusion. We
believe that the atom, which is placed on the nanotube
surface, diffuses with equal probability in any direction.
Therefore on the end face of the nanotube which length is
equal 2π R N , the following part of atoms comes
189
z
r
ωup=
2π R N
2 z sh2π R N .
On the lateral side of the growing nanotube, which length
is equal z sh , the following part comes
ω¿=
z sh
z sh2π R N
Here Ṅ is the number of carbon atoms, settling on the
lateral surface of the nanotube outside of a shadow in time
unit:
Ṅ=2πRmax zsh noV th ωs
R is the average radius of the multilayered nanotube,
N is the quantity of layers in multilayered nanotube,
Rmax is the radius of the multilayered nanotube. Rmax
is possible to express through N and distance between
layers in multilayered nanotube
Rmax=Nr ℓ .
The quasi-stationary density of sorbed carbon atoms
ncs is determined by balance of sorption with
probability ωs and a leaving with probability ωds
ωs no V thс=ωds ncs .
Here no is the plasma density. It is necessary to note,
that ωds depends on induced effective temperature of
sorbed atoms.
Speed of lengthening of growing nanotube is equal
V II=
Ṅ aωo ωup
2π R N /a
Here ωo is the probability of carbon atom connection to
a growing side or the end face of the nanotube.
The growth rate of the lateral side of the nanotube is equal
V ¿=
Ṅ aωo ω¿
z sh /a
V II and V ¿ are connected between themselves by the
following ratio
V II
V ¿
=
zsh
2π R N
From here we find quantity of layers in multilayered of the
nanotube
N= z sh
2πr ℓ
V ¿
V II
The nanotube length, located outside of a shadow, is equal
z sh=Rn
V IIe
V th
Here V IIe is the component of the carbon atom velocity,
directed perpendicularly to the catalytic surface;
Rn=n
sn
−1 /2
is the distance between nanotubes; nsn is
the surface density of the nanotubes.
N=Rn
2πr ℓ
2π R N
z sh
V IIe
V th
ω¿
ωup
=
¿Rn
πr ℓ
V IIe
V th
=1
πr ℓnsn
V IIe
V th
Since π R N≈ z sh , the area of cross-section of
multilayered nanotube is equal Sup=πRmax
2 =4π R2 .
The area of its lateral surface, on which the carbon atoms
are sorbed and fastly diffuse due to surface diffusion, is
equal Sc=2π R NπR min . Taking into account that
R=Nr ℓ /2 , we derive Sc=
4π2 R2 Rmin
r ℓ
. Thus, we
obtain that Sup is not much less Sc , i.e.
S c
S up
=
πRmin
r ℓ
3 .
In the case of azimuthally symmetric nanotube
N=ωln zsh
2πr ℓ
V ¿
V II
ωln is the probability of origin of a new layer.
REFERENCES
1. G.-H.Jeong, R.Hatakeyama, T.Hirata et al. // Proc. of
XXV ICPIG. Nagoya, 2001, v.2, p.155.
2. R.Hatakeyama, Y.Abe, H.Ishida et al. // Proc. of XXV
ICPIG. Nagoya, 2001, v.2, p.159.
ФОРМИРОВАНИЕ НАНОТРУБОК НА КАТАЛИТИЧЕСКОЙ ПОВЕРХНОСТИ В ПЛАЗМЕННОМ
РАЗРЯДЕ
В.И. Маслов, В.Н. Третьяков, Н.А. Азаренков, А.М. Егоров, И.Н. Онищенко
Получено выражение для количества слоев многослойной нанотрубки, которое успевает сформироваться
за время ее роста в плазменном разряде.
ФОРМУВАННЯ НАНОТРУБОК НА КАТАЛІТИЧНІЙ ПОВЕРХНІ В ПЛАЗМОВОМУ РОЗРЯДІ
В.І. Маслов, В.М. Третьяков, М.О. Азаренков, О.М. Єгоров, І.М. Онищенко
Отримано вираз для кількості прошарків багатошарової нанотрубки, що встигає сформуватися за час її
росту в плазмовому розряді.
190
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