Role of surface energy in the growth of carbon nanotubes via catalytic pyrolysis of hydrocarbons

Article abstract of DOI:10.1134/S0020168511020105

We report an experimental study of carbon nanotube (CNT) growth via catalytic pyrolysis of acetylene. Surface free energy is shown to play a key role in determining the catalytic activity of the liquid droplet on the CNT tip and to be responsible for the constant nanotube diameter. A vapor-liquid- nanotube model is proposed for CNT growth.

Full text of DOI:10.1134/S0020168511020105

ISSN 0020ꢀ1685, Inorganic Materials, 2011, Vol. 47, No. 2, pp. 128–132. © Pleiades Publishing, Ltd., 2011.
Original Russian Text © V.A. Nebol’sin, A.Yu. Vorob’ev, 2011, published in Neorganicheskie Materialy, 2011, Vol. 47, No. 2, pp. 168–172.
Role of Surface Energy in the Growth of Carbon Nanotubes
via Catalytic Pyrolysis of Hydrocarbons
V. A. Nebol’sin and A. Yu. Vorob’ev
Voronezh State Technical University, Moskovskii pr. 14, Voronezh, 394026 Russia
eꢀmail: vcmsao13@mail.ru
Received October 22, 2009; in final form, May 27, 2010
Abstract—We report an experimental study of carbon nanotube (CNT) growth via catalytic pyrolysis of acetꢀ
ylene. Surface free energy is shown to play a key role in determining the catalytic activity of the liquid droplet
on the CNT tip and to be responsible for the constant nanotube diameter. A vapor–liquid–nanotube model
is proposed for CNT growth.
DOI: 10.1134/S0020168511020105
INTRODUCTION
roidal nickel particles ranging in diameter from 2 to
6 nm. The nanoparticles were spaced 5 to 10 nm apart.
The special mechanical, electrical, thermal, and
magnetic properties of carbon nanotubes (CNTs) make
them attractive candidates for applications in nanoelecꢀ
tronic devices, composite materials, sorbents, etc.
However, advances in understanding the properties of
CNTs and fabricating prototype devices and materials
are highly dependent on the development of techniques
for controlled growth of nanotubes. Unfortunately, the
mechanism of their growth is still poorly understood
and requires further research [1].
Acetylene was pyrolyzed at temperatures from 600
to 1300 K. The gaseous carbon precursor was delivered
to the reaction zone by a carrier gas: nitrogen, argon, or
hydrogen. The flow rate of the gas mixture was varied in
the range 0.5–1.5 l/min, and the Н2/С2Н2 molar ratio
was varied from 1 : 2 to 10 : 1. The pyrolysis time was
several minutes to 0.5 h. The carbon deposit, containing
nanotubes, was examined by scanning and transmission
electron microscopy and Xꢀray microanalysis.
Despite the large number of reports concerned with
the controlled growth of CNTs by various techniques
[1–3], the role of the catalyst droplet in the mechanism
of CNT growth remains unclear. In particular, it is not
yet clear what role is played by the free energy of the
interfaces related to the liquid droplet residing on the
CNT tip.
RESULTS AND DISCUSSION
Our experiments showed that CNTs formed only in
the presence of catalyst particles (Fig. 1a). If there were
no metal particles, only amorphous carbon spheres
were formed (Fig. 1b). The CNTs ranged in diameter
from 10 to 100 or 200–250 nm. The nanotubes grown
on the glassꢀceramic plates with Ni/MgO nanogranules
were more evenly distributed over the substrate surface.
The purpose of this work is to accurately assess the
role of the vapor–liquid–solid interface energy in the
mechanism of CNT growth via thermocatalytic
decomposition of hydrocarbons.
The iron, cobalt, and nickel nanoparticles were
found to be situated on the nanotube tips during CNT
growth. Examining the shape of the CNT tips, we estabꢀ
lished the following:
EXPERIMENTAL
First, the catalyst nanoparticles on the nanotube tips
were elongated, and the liquid droplets were encapsuꢀ
lated in the nanotubes (Fig. 2). Second, the opposite
CNTs were synthesized via thermocatalytic decomꢀ
position of acetylene, С2Н2 [1, 2]. The substrates used
were (111) singleꢀcrystal silicon wafers and glassꢀ menisci of each droplet differed in curvature. The curꢀ
ceramic plates. To catalyze the CNT growth process, vature of the outer (upper) surface of the droplet was
cobalt, iron, and nickel nanoparticles produced by therꢀ smaller than that of its inner (lower) surface. The ratio
mal evaporation were applied to the silicon wafers. On of the radii of curvature of the outer and inner menisci
the working surface of the glassꢀceramic plates, of the droplet was 1.2 to 1.5. Third, the CNTs had a cirꢀ
Ni/MgO composite nanogranules were produced by cular cross section and constant diameter throughout
magnetron sputtering: the MgO matrix contained spheꢀ their length (Fig. 3).
128

ROLE OF SURFACE ENERGY IN THE GROWTH OF CARBON NANOTUBES
129
5 μm
(а)
10 μm
(b)
Fig. 1. (a) CNT array grown on a silicon wafer in the presence of Ni nanoparticles; (b) amorphous carbon spheres formed on a silicon
wafer in the absence of metal nanoparticles.
The elongated teardrop shape of the catalyst particle coldest surface layer of the droplet increases. The soluꢀ
tion becomes supersaturated, and carbon precipitates in
the form of a solid shell on the liquid surface.
on the CNT tip indicates that the particle was in a liquid
state during nanotube growth at 890 K (Fig. 2a). The
liquid nanoparticle obviously consisted of a carbon
solution in the molten metal. The presence of carbon in
the liquid droplet is evidenced by the formation of a
crystalline carbon shell on the outer surface of the dropꢀ
let, which insures its encapsulation in the nanotube.
The shell may result from the cooling of the carbon
That the nanotubes have a constant diameter
throughout their length indicates that the volume of the
catalyst droplet remains constant during the CNT
growth [3].
Consider a catalyst droplet at mechanical equilibꢀ
solution in the melt after the nanotube growth. As the rium on the tip of a CNT (Fig. 4). We assume that both
temperature is lowered, the carbon concentration in the the inner and outer surfaces of the CNT are poorly wetꢀ
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130
NEBOL’SIN, VOROB’EV
(b)
(а)
Fig. 2. TEM images (200 000
×
) of CNTs containing encapsulated nickel particles: nanotubes grown at (a) 890 and (b) 1070 K.
ted by the liquid on the nanotube tip and that the dropꢀ R2 and the contact angles
ϕ
and γ of the outer and inner
let is anchored to the rim of the CNT of radius r and is
in a stable mechanical equilibrium. The shape of the
droplet is characterized by the radii of curvature R1 and
surfaces of the nanotube, respectively.
Let the threeꢀphase line of contact adjoin the circuꢀ
lar rim of the nanotube. As a first approximation, we
neglect the effect of the line tension at the threeꢀphase
boundary. The mutual arrangement of the vectors of the
forces α1 and α2 corresponding to the free energies of
the outer and inner surfaces of the droplet at point А on
the CNT rim is shown in Fig. 4. Because the droplet
wets only the rim of the nanotube, without wetting its
inner and outer surfaces, the droplet should be in
mechanical equilibrium along the nanotube rim. The
equilibrium of the liquid on the nanotube tip during
CNT growth in the vapor–liquid–solid system is set by
the condition that, upon all possible variations in the
shape of the liquid droplet (with no changes in its volꢀ
ume), the free energy of the system,
Ф, remains conꢀ
stant (minimal for stable equilibrium, that is,
[5, 6],
dФ = 0)
2
1
2
2
⎡
⎤
(1)
Φ = 2π R 1 + sinϕ α + R 1 − cosγ α = min,
(
)
(
)
1
2
⎦
⎣
where the first term in brackets is the surface free energy
of the outer meniscus of the droplet and the second
term is the free energy of the meniscus in the nanotube.
In (1), α1 and α2 are the free energies of the outer
and inner surfaces of the droplet (Fig. 4) (it is reasonꢀ
able to assume that α1 < α2 because of the adsorption
Fig. 3. TEM image of CNTs grown in the presence of iron parꢀ
ticles; 200 000×.
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ROLE OF SURFACE ENERGY IN THE GROWTH OF CARBON NANOTUBES
131
from the gas phase on the outer surface of the dropꢀ
let) [7, 8].
For a hemispherical shape of the parts of the droplet
bounded by the surfaces with α1 and α2, the nanotube
radius
r
is related to the droplet radii R1 and R2 by
ϕ
(2)
r = R1cosϕ, r = R2sinγ.
α1
Substituting in (1), taking its derivative, and equating
it to zero, we obtain
R1
R2
2
α1 sin ϕ
γ
2tan .
(3)
=
A
α2 sin γ
2
r
Relation (3) describes the equilibrium shape of the
catalyst droplet on the CNT tip, corresponding to the
minimum interfacial free energy. When condition (3) is
met, the droplet is in mechanical equilibrium in the
plane of the nanotube rim. There is then a capillary
γ
pressure difference Pn in the droplet, or an uncomꢀ
Δ
α2
pensated surface tension force applied to the wetting
line in the nanotube growth direction (represented by
the heavy arrow in Fig. 4):
2r
⎛
⎞
α2 α1
(4)
Pn
ΔPn = 2
−
.
⎜
⎟
R
2
R
1
⎝
⎠
To eliminate the capillary pressure difference
Δ
,
the droplet tends to reduce the surface energy α2 by
moving adsorbed carbon atoms from the outer surface
of the droplet to its inner surface. This is accompanied
by the formation of a network of sixꢀmembered rings
along the rim of the nanotube. In addition, the droplet
tends to reduce the radius R2 and increase the radius R1
(to increase the outer surface area of the liquid phase
and reduce the inner surface area). This is achieved by
periodic contraction of the elongated droplet and its
displacement in the nanotube growth direction.
Fig. 4. Schematic illustrating the equilibrium position of a catꢀ
alyst droplet on the tip of a CNT.
Thus, the tendency of the droplet to reach thermoꢀ
dynamic equilibrium leads to its spheroidization, that
is, minimization of the surface area on the tip of the
growing nanotube. The droplet spheroidization is
accompanied by a displacement of the threeꢀphase line
of contact and release of the excess energy due to the
reduction in surface area. The mechanical equilibrium
of the droplet on the CNT rim, due to a combination of
surface tension forces, is responsible for the circular
cross section of the nanotube, which reflects the shape
of the threeꢀphase boundary and the constancy of the
CNT diameter.
When the liquid moves during CNT growth, the
capillary pressure can be thought of as a capillary potenꢀ
tial, Ψк, and the difference Δ Ψк
– Pn can be thought
Δ
of as a driving force acting on the catalyst droplet during
CNT growth. The capillary potentials on the opposite
menisci of the liquid droplet differ in direction and
magnitude. As a result, the liquid moves along the formꢀ
ing wall of the nanotube until the potentials become
equal (R1 = R2 and α1 = α2). The movement of the dropꢀ
let results in spontaneous CNT growth.
α
1
To evaluate the parameters in Eq. (3), we take
=
α
The above view that surface energy plays a key role in
determining the catalytic activity of the liquid phase on
the CNT tip fits well with results reported by Lin et al.
[3] and Hofmann et al. [4], who used frameꢀbyꢀframe
photography to follow the evolution of the droplet
shape during nanotube growth (Fig. 5).
0.8. With the observed angles
ϕ
31
°
and
γ
74°
,2we
, we have
. These numerical relationships agree
ꢀ
ꢀ
R1
obtain
1.2. At α1
=
α2 and
ϕ
=
γ
= 45
°
R2
R1 = R2 = 1.41
r
with experimental values.
INORGANIC MATERIALS Vol. 47
No. 2 2011

132
NEBOL’SIN, VOROB’EV
ϕ
ϕ
γ
γ
10 nm
(b)
10 nm
(а)
Fig. 5. Shape of the catalyst droplet after (a) 948 and (b) 960 s of CNT growth catalyzed by nickel nanoparticles at 920 K in an acetylene
(C H ) atmosphere [3].
2
2
2. Kayastha, V. and Khin, Y., Controlling Dissociative
Adsorption for Effective Growth of Carbon Nanotubes,
Appl. Phys., 2004, vol. 85, no. 1511, pp. 3265–3267.
3. Lin, M., et al., Dynamical Observation of BambooꢀLike
Carbon Nanotube Growth, Nano Lett., 2007, vol. 8, no.
4, pp. 908–914.
4. Hofmann, S., et al., In Situ Observations of Catalyst
Dynamics during SurfaceꢀBound Carbon Nanotube
Nucleation, Nano Lett., 2007, vol. 7, no. 3, pp. 602–608.
5. Voronkov, V.V., On the Thermodynamic Equilibrium at a
ThreeꢀPhase Line of Contact, Fiz. Tverd. Tela (Leninꢀ
grad), 1963, vol. 5, no. 2, pp. 570–574.
CONCLUSIONS
The present results demonstrate that, during CNT
growth in the vapor–liquid–nanotube system via therꢀ
mocatalytic decomposition of hydrocarbons, the role of
interfacial free energy is to create conditions under
which a capillary potential difference arises in the liquid
droplet and acts as a driving force for displacement of
the droplet. The catalyst droplet on the nanotube tip is
then in stable equilibrium, which insures a circular cross
section and constant diameter of the CNT.
6. Nebol’sin, V.A. and Shchetinin, A.A., Role of Surface
Energy in the Vapor–Liquid–Solid Growth of Silicon,
Neorg. Mater., 2003, vol. 39, no. 9, pp. 1050–1055
ACKNOWLEDGMENTS
We are grateful to A.V. Sitnikov and O.V. Stognei for
their assistance in substrate preparation.
[Inorg. Mater. (Engl. Transl.), vol. 39, no. 9, pp. 899–
903].
7. Missol, W., Energia powierzchni rozdzialu faz w metalach
,
'
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INORGANIC MATERIALS Vol. 47
No. 2
2011