Model of carbon nanotube growth through chemical vapor deposition

Article abstract of DOI:10.1016/S0009-2614(99)01216-6

This Letter outlines a model to account for the catalyzed growth of nanotubes by chemical vapor deposition. It proposes that their formation and growth is an extension of other known processes in which graphitic structures form over metal surfaces at moderate temperatures through the decomposition of organic precursors. Importantly, the model also states that the form of carbon produced depends on the physical dimensions of the catalyzed reactions. Experimental data are presented that correlate nanotube diameters to the size of the catalyst particles. Nanotube stability as a function of nanotube type, length and diameter are also investigated through theoretical calculations.

Full text of DOI:10.1016/S0009-2614(99)01216-6

17 December 1999
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Chemical Physics Letters 315 1999 25–30
www.elsevier.nlrlocatercplett
Model of carbon nanotube growth through chemical vapor
deposition
a,b
a
a
a
S.B. Sinnott a,), R. Andrews , D. Qian , A.M. Rao b,c, Z. Mao , E.C. Dickey ,
a,b
F. Derbyshire
a
Department of Chemical and Materials Engineering, UniÕersity of Kentucky, Lexington, KY 40506, USA
b
The Center for Applied Energy Research, UniÕersity of Kentucky, Lexington, KY 40506, USA
Department of Physics and Astronomy, UniÕersity of Kentucky, Lexington, KY 40506, USA
c
Received 14 July 1999; in final form 6 October 1999
Abstract
This Letter outlines a model to account for the catalyzed growth of nanotubes by chemical vapor deposition. It proposes
that their formation and growth is an extension of other known processes in which graphitic structures form over metal
surfaces at moderate temperatures through the decomposition of organic precursors. Importantly, the model also states that
the form of carbon produced depends on the physical dimensions of the catalyzed reactions. Experimental data are presented
that correlate nanotube diameters to the size of the catalyst particles. Nanotube stability as a function of nanotube type,
length and diameter are also investigated through theoretical calculations. q 1999 Elsevier Science B.V. All rights reserved.
Ž
.
Nanotubes have attracted much interest since their
walled nanotubes MWNTs are grown almost exclu-
w x
w x
discovery in 1991 1 because of their high modulus
sively 1 . While this progress is encouraging, there
in the direction of the nanotube axis, electrical con-
ductivity that could render them useful as nanome-
ter-scale wires, and hollow structures that could be
exploited in tailored membranes and molecular sieves
w x
2 . Since their initial discovery, researchers have
made tremendous progress in learning to synthesize
carbon nanotubes in gram quantities. Nanotubes can
w x
be synthesized using arc-discharge 1 , laser vapor-
w x
ization 3 , or catalytic decomposition of hydrocar-
w x
bons 4 . By adding the appropriate metal catalyst
single-walled nanotubes SWNTs can be preferen-
tially grown 5,6 while under other conditions multi-
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.
w
x
It is postulated that the formation and growth of
nanotubes is an extension of other known processes
in which graphitic structures are formed over metal
)
Corresponding author. Tel.: q1-606-257-5857; fax: q1-606-
323-1929; e-mail: sinnott@engr.uky.edu
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.
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PII: S0009-2614 99 01216-6

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26
S.B. Sinnott et al.rChemical Physics Letters 315 1999 25–30
surfaces at temperatures below about 11008C from
carbon that is produced by the decomposition of a
carbon-containing precursor. It is also proposed that
the form of graphite that is produced is closely
related to the physical dimensions of the metal cata-
lyst particles. This hypothesis builds on a consider-
able volume of research that has been conducted
over the past two to three decades on the formation
gradient and precipitates on the opposite half, around
and below the bisecting diameter. However, it does
not precipitate from the apex of the hemisphere,
which accounts for the hollow core that is character-
istic of these filaments.
In the filament structure, the graphite crystallites
precipitate with the basal plane tangential to the
Ž
curved surface as opposed to parallel to the surface
w
x
.
of graphitic carbon over metal substrates 14,15 .
for metal substrates with much larger dimensions . In
The most effective metals have been shown repeat-
cross-section, the filaments are composed of a series
w
x
² :
edly to be iron, nickel and cobalt 16 . The peculiar
ability of these metals to form ordered carbons is
thought to be related to a combination of factors.
These include their catalytic activity for the decom-
position of volatile carbon compounds, the fact that
they form metastable carbides, and that carbon is
able to diffuse through and over the metals ex-
of crystallites whose
c
axis tends to follow the
radial vector of the filament and whose basal planes
follow the circumference, approximating the curved
² :
surface of the filament. The
c axis may also be
tilted at an angle to the radial vector, giving rise to a
‘chevron’ type structure. For supported metals, fila-
ments can form either by ‘extrusion’ in which the
fiber grows upwards from metal particles that remain
attached to the substrate, or the particles detach and
move at the head of the growing fibers, labeled
‘tip-growth’. These mechanisms are illustrated
w
x
tremely rapidly 14–16 . The latter property allows
ordered carbon to be produced by a mechanism of
diffusion and precipitation. This also means that
graphitic structures are only formed in proximity to
the metal surface. If there is significant reaction
away from the metal, other undesirable forms of
carbon, such as amorphous carbon nanoparticles,
will be co-produced. Restriction of the reaction to
the surface is controlled through the choice of the
carbon precursor, its partial pressure and the reaction
temperature.
Ž
w
x.
graphically in Fig. 1 after Baker and Harris 14 .
w
x
We have suggested 19 that the catalyst particle
size determines the size of the ‘filament’. As the
particle diameter is reduced, the filament curvature
increases, imposing an increasing strain on the basal
planes of the crystallites. Eventually, a continuous
surface is energetically more favorable and MWNTs
are formed. Logically, if the particle size is reduced
still further, SWNTs will be formed. The rest of this
Letter outlines the experimental and theoretical evi-
dence to support these arguments and hypotheses.
Over thin metal foils, which in the present context
can be considered as bulk metal, carbon dissolves to
w
x
form a solid solution 16 . On cooling, it precipitates
on the surface as a continuous thin film of highly
crystalline graphite in which the graphite basal planes
are oriented parallel to the substrate. The high degree
of crystalline perfection that is obtained in a matter
of seconds demonstrates that carbon atoms are ex-
tremely mobile and can move easily over and through
the metal.
When the metal is present as particles of diameter
in the range of tenths of a micron, the carbon is
w
x
produced as filaments of similar diameter 14,15 .
The metal particles can be supported on a substrate
or introduced as ‘floating’ particles in a gas stream
w
x
that flows through the reactor 17,18 . If the particles
are considered to be spherical or pear shaped, the
deposition of carbon atoms takes place on one half
Ž
of the surface on the lower curvature face for pear
Fig. 1. Schematics of tip-growth and extrusion mechanisms for
.
shapes . The carbon diffuses along the concentration
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w
x.
carbon filament growth after Baker and Harris 14 .

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S.B. Sinnott et al.rChemical Physics Letters 315 1999 25–30
27
furnace. At this temperature, liquid exiting the capil-
lary is immediately volatilized and swept into the
reaction zone of the furnace by a flow of argon with
10% hydrogen. Various parameters, such as the fur-
nace temperature, ferrocene to xylene ratio, feed
rate, reaction time, and sweep gas flow rate were
adjusted to obtain growth conditions for high purity
w
x
aligned MWNTs 19 . Carbon nanotube deposits were
formed on the walls of the quartz furnace tube and
on plain quartz substrates placed within the furnace.
Nanotubes were grown at two Fe:C atomic ratios,
0.75 and 0.075 at%. At the higher ratio, nanotubes
were formed with an average diameter of about 33
nm and a diameter distribution as shown in Fig. 2a.
The lower Fe:C ratio produced nanotubes with a
smaller average diameter of about 28 nm and a
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.
noticeably narrower diameter distribution Fig. 2b .
The data in Table 1 shows that the smaller aver-
age nanotube diameter obtained at the lower Fe:C
ratio is directly related to the generation of smaller
iron clusters. Under these conditions, a lower iron
concentration in the vapor phase will limit the ability
of the iron atoms to agglomerate into large clusters
Fig. 2. Diameter distributions for MWNTs produced by chemical
Ž
.
giving larger nanotube diameters , leading to the
Ž .
Ž .
vapor deposition under a 0.75 at% Fe:C and b 0.075 at% Fe:C
ratios.
formation of smaller iron clusters on the quartz
substrate. It may be further supposed that the proper-
ties and temperature of the substrate will also influ-
ence the iron particle size. The selection of a sub-
strate on which the metal is more mobile, andror
increasing the substrate temperature, will enhance
the processes of nucleation and growth. This will
lead to the formation of larger size particles and
In our experiments, aligned MWNTs were pro-
duced at high selectivity by the catalytic decomposi-
tion of a hydrocarbon feedstock, as described in
w
x
detail elsewhere 19,20 . Briefly, about 6.5 mol% of
ferrocene was dissolved in xylene and fed continu-
ously into a two-stage quartz tube reactor. The liquid
feed mixture was passed through a capillary tube and
preheated to ;1758C prior to its entry into the
w
x
hence larger diameter nanotubes 19 , ultimately af-
fecting a transition to the growth of filaments rather
than MWNTs. These suppositions will be examined
in a continuing experimental program.
Table 1
Analytical results of as-grown MWNT samples
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.
FerC at%
Average nanotube
Average nanotube
Average Fe particle
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.
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.
Ž
.
inner diameter nm
outer diameter nm
diameter nm
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.
.
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.
Ž
35.3 12.6
.
.
0.75
0.075
5.8 3.0
33.6 13.5
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Ž
.
Ž
4.3 2.3
28.3 9.9
28.2 12.9
The reactor was operated for 2 h at 6758C, with 20 mbar partial pressure of xylene and gas flows of 675 SCCM Ar and 75 SCCM H2.
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Nanotube lengths were determined from images obtained using a scanning electron microscope Hitachi, 3200N, 5 kV , while nanotube and
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Fe particle diameters were determined from images obtained using a transmission electron microscope Hitachi, H-800 NA, 200 kV . The
average nanotube and Fe particle diameters were obtained by fitting the raw data to a Gaussian normal distribution function. The data in
parentheses are the standard deviations.

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S.B. Sinnott et al.rChemical Physics Letters 315 1999 25–30
Transmission electron microscope images of the
filament diameter relates to the metal particle size
Ž
nanotubes formed at the two Fe:C ratios are shown
in Fig. 3. The metal particles appear at the ends of
the MWNTs and are of similar diameter to the
where the limit is thought to be around 1 nm
.
diameter for the SWNTs and it also accounts for the
hollow core in both structures.
Ž
nanotube, which supports the tip-growth detached
Theoretical calculations were used to shed light
on the relative stability of SWNTs, MWNTs and
graphene as a function of size. The reactive empiri-
.
particle model. The tip growth mechanism is further
supported by the fact that once the nanotubes are
detached from the quartz with a razor blade, the
nanotube root ends appear to be open. However, it
should be pointed out that the open ends could also
be due to the ends being sheared off during their
removal from the substrate. It is also possible that
the nanotubes are directly attached to the substrate
and do not possess the normal hemispherical end
cap. Thus the growth mechanism is equivalent to that
known for carbon filaments in which the nanotube or
Ž
.
cal bond-order REBO potential developed by Ter-
w
x
soff 21 and parameterized for carbon and hydrogen
by Brenner 22,23 is used in the calculations that
consists of two-body and many-body terms. A long-
w
x
w
x
range Lennard–Jones potential 24 is included that
is only non-zero after the short-range covalent poten-
tial goes to zero. The REBO potential accurately
models the energies, bond lengths, and lattice con-
stants of both solid-state and molecular carbon mate-
rials, a crucial condition for the calculations pre-
sented below. It has therefore been used frequently
w
x
to study carbon nanotubes 9,12,25–29 . However,
like most empirical potentials the electrons are not
treated explicitly so forces arising from effects such
as orbital resonances and symmetry that could influ-
ence the stability of small structures are not ad-
dressed. However, it is used here because the size of
some of the systems under considerations is pro-
Ž
.
hibitively large ;10 000 atoms for the use of more
accurate quantum-mechanics-based methods.
It should be emphasized that the REBO potential
cannot model carbon–metal interactions, so only pure
carbon systems are examined in the calculations. The
goal is to determine the most stable configuration of
carbon for a limited size, defined as the number of
atoms in the system. It is proposed that in the
experiments this limited size would come about
through a combination of reaction conditions and the
size and shape of the metal catalyst particles.
The calculations confirm the trends discussed
above of graphitic carbon structures having varying
stability as a function of size. Fig. 4 shows the
Ž
. Ž .
. Ž
energy of a graphene sheet and 10,0 , 19,0 , 5,5
Ž
.
and 10,10 SWNTs as a function of the number of
atoms in each system. For systems smaller than
Ž
.
Ž
.
about 400 atoms, the 5,5 and 10,0 nanotubes,
those with the smallest diameter, are the most stable
Ž
.
see the inset in Fig. 4 . This is because the smaller
Ž
Fig. 3. Images from a transmission electron microscope Hitachi,
nanotubes are longer and thus have a smaller per-
centage of edge atoms than the larger nanotubes.
Above about 1000 atoms, the 10,10 and 19,0
.
H-800 NA, 200 kV of as-grown MWNTs with Fe catalyst
particles at the tube ends. a 0.75 at% Fe:C and b 0.075 at% Fe:C
ratios.
.
.
Ž
.
Ž
.

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S.B. Sinnott et al.rChemical Physics Letters 315 1999 25–30
29
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. Ž
. Ž
.
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.
Fig. 4. Potential energy of 10,0 , 19,0 , 5,5 and 10,10 SWNTs and a graphene sheet as a function of number of atoms in each system.
nanotubes are preferred due to their lower strain. Fig.
4 also shows that nanotube stability depends on the
diameter rather than on the helical symmetry in
w
x
agreement with previous theoretical studies 30 .
Ž .
Ž
.
Ž
.
Fig. 5. a Potential energy of several MWNTs and SWNTs. v is a MWNT of a 10,0 nanotube within a 12,12 nanotube, l is a MWNT
Ž
.
.
Ž
.
Ž
.
Ž
Ž
.
Ž
.
Ž
of a 5,5 nanotube within a 17,0 nanotube, ' is a MWNT of a 5,5 nanotube within a 10,10 nanotube, B is a 10,0 nanotube within a
U
Ž
Ž
.
Ž
.
.
Ž
.
.
.
19,0 nanotube, = is a 10,0 SWNT, is a 19,0 SWNT, I is a 5,5 SWNT, ` is a 10,10 SWNT, and ^ is a 12,12 SWNT. b
Ž
.
Ž
.
Potential energy of several MWNTs as a function of the number of shells in the nanotube. The shells in the MWNTs of n,0 type are 10,0 ,
. Ž . Ž . Ž
Ž
.
Ž
.
Ž
.
Ž
.
Ž
.
19,0 , 29,0 , and 39,0 . The shells in the MWNTs of n,n type are 5,5 , 10,10 , 15,15 , and 20,20 .

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30
S.B. Sinnott et al.rChemical Physics Letters 315 1999 25–30
The graphene is the least stable structure until
Acknowledgements
about 6000 atoms where it becomes more stable than
Ž
.
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.
the 10,0 and 5,5 nanotubes. At the smaller sizes,
the instability caused by the dangling bonds in the
graphene is greater than the instability in the nan-
otubes due to strain. As the number of atoms contin-
ues to increase, the fraction of edge atoms in the
graphene decreases, which continues to stabilize the
graphene relative to the nanotubes.
This work was supported by a National Science
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.
Foundation MRSEC DMR-9809686 . Z.M. and
S.B.S. also acknowledge support from the NASA-
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.
Ames Research Center NAG 20-1121 .
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the MWNT increase as the nanotube gets longer. A
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