Copyright © 2006 American Scientific Publishers
All rights reserved
Printed in the United States of America
Journal of
Nanoscience and Nanotechnology
Vol. 6, 1–12, 2006
Role of the Catalyst in the Growth of
Single-Wall Carbon Nanotubes
Perla B. Balbuena,1 ∗ Jin Zhao,1 Shiping Huang,1 † Yixuan Wang,1
Nataphan Sakulchaicharoen,2 and Daniel E. Resasco2 ∗
2
1
Department of Chemical Engineering, Texas A&M University, College Station, TX 77843, USA
School of Chemical Engineering and Materials Science, University of Oklahoma, Norman, OK 73019, USA
Classical molecular dynamics simulations are carried out to analyze the physical state of the catalyst, and the growth of single-wall carbon nanotubes under typical temperature and pressure conditions of their experimental synthesis, emphasizing the role of the catalyst/substrate interactions. It is
found that a strong cluster/substrate interaction increases the cluster melting point, modifying the
initial stages of carbon dissolution and precipitation on the cluster surface. Experiments performed
on model Co–Mo catalysts clearly illustrate the existence of an initial period where the catalyst is
formed and no nanotube growth is observed. To quantify the nature of the Co–Mo2 C interaction,
quantum density functional theory is applied to characterize structural and energetic features of
small Co clusters deposited on a (001) Mo2 C surface, revealing a strong attachment of Co-clusters to
the Mo2 C surface, which may increase the melting point of the cluster and prevent cluster sintering.
Keywords: Catalyst–Substrate Interaction, Catalyzed Carbon Nanotube Growth, Molecular
Dynamics Simulations, Model Catalysts, Melting Points of Nanocatalysts.
The presence of a transition metal has been found a necessary condition for the synthesis of single-wall carbon
nanotubes (SWNTs) using arc discharge,1 pulsed laser
vaporization,2 or any of the chemical vapor deposition
(CVD) techniques.3 It is interesting to notice that the first
two methods use a form of pure carbon (graphite) that
after vaporization produces SWNTs among other carbon
structures, whereas CVD methods use a carbon-containing
source that generates C atoms after catalytic decomposition. In both cases, transition metal nanoparticles
are needed to generate SWNTs. Moreover, the best of
those transition metal catalysts are the ones able to form
metastable carbides (such as Co, Ni, and Fe), instead of
those that form very stable carbides (such as Mo and others from groups IV to VI), or those that do not form carbides at all (for example Pt, Pd, Rh, Ru, Ir, Cd).4 Thus,
it could be inferred that such metal nanoparticle is most
likely the catalyst that promotes the formation of singlewall carbon nanotubes in a variety of synthesis processes
at temperatures in the order of 1000 K for CVD processes
and 1200 K for carbon vaporization processes.
∗
Authors to whom correspondence should be addressed.
Present address: Beijing University of Chemical Technology, Beijing,
P. R. China.
†
J. Nanosci. Nanotechnol. 2006, Vol. 6, No. 4
But the specific role of the catalyst in the nanotube
growth process is not clear. Several growth mechanisms
have been proposed, among them those where growth is
expected to take place at “base” and “tip” locations with
respect to the nanotube, have received partial evidences
from experimental and theoretical studies. The main difference between them is given by the behavior of the C-metal
nanoparticle during the growth process. If the particle
remains attached to the substrate, new carbon will be
added to the nascent nanotube edge in contact with the
substrate (base growth),5 but if the catalyst separates from
the substrate being lifted up to the top of the nanotube
then a “kite” or “tip” growth is most likely found.6 Further, it has been reported that it is possible to change the
growth mechanism from ‘tip’ mode to ‘base’ mode just by
changing the substrate properties.4 Detailed reviews and
analyses of the various growth modes have been reported
recently.7–9
Integration of theoretical and experimental information
provides the best route to identify reaction mechanisms in
complex processes. Here we address several topics related
to the understanding of the physical state of the catalyst
and its interactions with the substrate in relation to the
SWNTs growth process. Using classical molecular dynamics (MD) simulations, we analyze the effect of the substrate on the shape and morphology of metal nanoparticles
1533-4880/2006/6/001/012
doi:10.1166/jnn.2006.141
1
RESEARCH ARTICLE
1. INTRODUCTION
Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes
at the CVD synthesis temperature and pressure, and discuss how this morphology would affect the SWNT growth
process. New experimental data of the rate of growth for
the CoMoCAT process10 illustrates aspects of the sequence
of events preceding and during the nanotube growth. To
further understand the nature of the catalyst, we report
density functional theory calculations of the structure of a
Mo2 C surface and its interactions with small Co clusters.
2. METHODOLOGY
2.1. Classical MD Simulations
RESEARCH ARTICLE
2.1.1. MD Simulation of Nanotube Growth
Classical MD simulations are carried out in a periodic
box of fixed volume, at temperatures in the range of the
experimental synthesis,11 between 800 K and 1300 K.
A metal nanoparticle (Ni80 or Ni48 ) deposited on a substrate is placed in the simulation box. We have chosen Ni
as a typical good catalyst for this reaction, to capture the
main features of the process. The Langevin equations of
motion are integrated according to the Verlet algorithm,12
with a time step of 0.5 fs. In Langevin dynamics two terms
are added to Newton’s second law in order to account for
neglected degrees of freedom.12 The first term is a frictional force and the second term is a random force. For
the stage of nanotube growth it was found that Langevin
dynamics can search conformations more efficiently that
Newtonian molecular dynamics, and thus help to overcome
barriers generating stable growth patterns.
The initial configuration of the metal nanoparticle is a
local minimum generated via energy minimization of
the structure. The rest of the volume is occupied with
molecules of the precursor gas initially randomly distributed, at a constant density in the range from 0.0001 to
0.0004 molecules/Å3 . Assuming ideal gas conditions, such
gas densities are equivalent to pressures in the range
14–71 atm for temperatures between 800 and 1300 K (typical experimental pressures in the CoMoCAT synthesis are
in the range of 1–5 atm).11 The temperature is kept constant with a simple thermostat where atomic velocities of
the precursor phase, the metal cluster, and the catalyzed
carbon are separately rescaled to the target temperature at
every step of the simulation. It is assumed that as soon
as the precursor gas is in contact with the metal particle,
it is catalyzed and converted into carbon atoms. Together
with the high density condition, this assumption greatly
accelerates the simulated growth process, making possible
to observe the nanotube growth process at the same temperature of the experiment, in tens of nanoseconds at the
lowest density (0.0001 molecules/Å3 ), and even in shorter
times at the highest density (0.0004 molecules/Å3 ).
We have developed a set of effective force fields to
describe C–C, C–Ni, and Ni–Ni interactions, incorporating information from density functional theory (DFT) calculations of model systems to already existent potentials.
2
Balbuena et al.
A detailed description of our force fields is reported
elsewhere;1314 here we briefly describe the main interaction potentials and provide their physical meaning in relation to the simulated synthesis process.
For the C–C interactions, we have adopted the recently
revised second-generation reactive empirical bond order
(REBO) potential developed by Brenner et al.15 However,
we have introduced a weighting factor to describe the relative weakness of the C–C interactions inside the metal
cluster obtained from DFT results.13 14 Such weighting
factor varies according to the coordination number of C
with respect to the metal atoms. Metal–metal interactions are described using a many-body potential including
Morse-type repulsive and attractive terms.16 The distance
parameters were taken from published data16 and the
energy parameters were fitted to the description given by
the Sutton-Chen potential17 for Ni clusters14 Probably the
most crucial potential for this system is that representing metal–carbon interactions. We adopted a many-body
Morse-type potential similar to that used for metal–metal
interactions, as originally proposed by Maruyama et al.,16
where crossed-terms were used to account for the influence
of the number of C atoms surrounding a metal atom. Additionally, we included the dependence on the presence of
metal atoms surrounding a C atom, which may be singleor double-bonded to other C atoms, as determined by DFT
calculations.13 14 Further refinements of the potential were
done considering the effect of the sp2 -carbon/metal bond
on the formation of caps evaluated from analyses of MD
trajectories. For the metal-substrate interactions we use a
Lennard-Jones potential, the strength of the energy parameter was varied in order to represent different substrates.
2.1.2. MD Simulation of Physical Properties of
Metallic Nanoclusters
Classical MD simulations are also used to determine the
effects of size and shape on melting points, structural transitions, and atomic diffusion coefficients of Pt clusters
with initial cube-octahedral, cubic, and spherical structures. The Sutton-Chen many-body potential is used for
the Pt–Pt interactions with parameters as published in the
original references.17 18 The simulations are carried out
in a weak coupling heat bath system with constant temperature using the Berendsen thermostat,19 the temperature relaxation time is 0.4 ps for the simulation system
to approach the canonical ensemble,20 constant number of
particles N , constant volume V , without periodic boundary
conditions. The cubic simulation box has a volume (6L),3
where L is the nanocluster side based on a cubic shape.
Simulations are performed at temperatures in the range of
0 K–1400 K, with temperature increases every 100 K, but
close to the melting point the increments are reduced to
10 K. The Newton equations of motion were integrated
using the Verlet leapfrog method12 with a time step of 1 fs,
with equilibration times of 400 ps at each temperature and
J. Nanosci. Nanotechnol. 6, 1–12, 2006
Balbuena et al.
Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes
200 ps for production time when data is collected for analyses, using the DL_POLY code.21 In order to determine
the melting temperature, the heat capacity Cv in a weak
coupling heat bath system can be written as20
Cv =
kB Ep 2 kB T 2 − 2Ep 2 /3N
(1)
3. RESULTS AND DISCUSSION
where represents the time average. Thus, Cv is related
to fluctuations in the potential energy Ep . is the ratio
of the fluctuation of the kinetic and potential energies, and
approaches zero when the simulation system is close to
the canonical ensemble.20 The self-diffusion coefficient D
is obtained from
Di =
1 ri t + s − ri s2
6t
(2)
where ri t + s is the vector position of the i-th atom, the
average is over atoms of type i and over choices of the
time origin s.
2.2. Density Functional Theory Calculations
3.1. Growth of SWNTs on a
Supported Catalyst Nanocluster
Significant effort has been devoted to study the growth of
SWCNTs on metal clusters floating in a vapor of the precursor gas, using classical MD simulations.13 30–32 In all
these simulations it is found that carbon first dissolves into
the metal cluster, and after saturation or oversaturation of
the C inside the cluster, C precipitates on the surface forming various structures ending with the formation of a cap
which evolves separating from the cluster and forming a
single-wall carbon nanotube. In all cases, the simulated
nanotubes are closed by the cap in one end and attached to
the metal cluster in the other end, just like those observed
in base growth mode.4 In our previous work13 we also
reported that the growth process on a weakly interacting
substrate is not significantly altered from that of a nanocatalyst floating in a vapor. However, new simulations done
for a cluster deposited on a strongly interacting substrate
indicate that such interaction modifies the stages of nucleation and growth with respect to those found in identical
metal clusters floating in a vapor phase.
The most significant features are illustrated by snapshots
shown in Figure 1. The strong substrate/cluster interaction
favors a more rigid cluster structure which modifies the
initial stage of C dissolution. Even though C still dissolves
into the cluster, the amount is lower than that obtained
when the metal cluster is completely unrestrained.
Note that the effect is similar to a reduction in temperature. The related literature usually discusses the need
of an initial supersaturation,33 defined as the ratio of the
actual amount of C dissolved in the metal to the equilibrium concentration. However, both the actual and the
equilibrium C concentrations are functions of the metal
particle size, temperature, and pressure, and the simultaneous dissolution and deposition of C on the surface cannot be discarded.34 In fact, supersaturation is a metastable
transient phenomenon, which would be difficult to detect
experimentally and also by simulations, especially if the
simulated rate of C addition is artificially high. Under the
effect of a strong surface-metal cluster interaction, we do
not observe supersaturation, and in addition we observe
simultaneous C dissolution and deposition on the surface.
Thus, C deposits on the surface at the same time that some
atoms dissolve in the interior, initially forming chains that
then interact with each other forming sp2 polygons, and
finally fullerene-type structures partially cover the surface,
and a cap is formed that leads to the nanotube growth.
3
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Periodic density functional theory calculations are performed with the CPMD program, Version 3.9.1.22 The code
implements density functional theory (DFT) in the KohnSham formulation with a plane-wave basis set and a
norm-conserving pseudopotential (PP) for the interactions
between the valence electrons and the ionic cores. The DFT
method and the PPs used through the present simulation
are the PBE type of generalized-gradient approximation
density functional,23 and the Goedecker pseudopotentials,24
respectively. In order to accurately treat open shell systems, spin states are polarized. In the Goedecker scheme,
Mo, Co, and C have 14 (4s2 4p6 4d5 5s1 , 9 (3d7 4s2 ), and
4 (2s2 2p2 ) valence electrons, respectively. The wavefunction is expanded in plane wave basis sets with a kinetic
energy cutoff of 100.0 Ry. Only the -point is used in
the Brillouin zone (BZ) sampling generated from the basis
vectors of the supercell.
In order to validate the employed Goedecker pseudopotentials, density functional theory calculations (PBE,
LANL2DZ ECP and basis set25 ) are also conducted for a
variety of small cluster systems, such as Con (n = 1 − 3),
Mom (m = 3, 4), and Con –Mom , using Gaussian 03.26 The
electronic structures and geometries obtained with CPMD
and Gaussian for the tested clusters are in reasonable
agreement, as discussed in Section 3.5.
The adsorptions of Con (n = 1–3) clusters are investigated on the bulk surface of -Mo2 C(001). To model
the surface, the supercell approach was used, with fourlayer slabs27 and a 11 Å vacuum space between any two
successive slabs. For most of the CPMD optimizations,
the surface was fixed at their experimental bulk lattice
constant of Mo2 C (a = 473 Å, b = 603 Å and c =
520 Å).28 A couple of optimizations performed with a
J. Nanosci. Nanotechnol. 6, 1–12, 2006
totally relaxed surface indicates that surface relaxation
effects are not significant as found by previous calculations for other extended systems.29 Partial atomic charges
for the optimized structures are estimated by the method
of Hirshfeld.21
Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes
Balbuena et al.
RESEARCH ARTICLE
Fig. 1. Time evolution of nanotube growth calculated by classical MD simulations using a reactive force field. Ni48 is interacting with a substrate
via a LJ potential, the density of precursor atoms is 0.0002 molecules/Å3 , and the temperature is 1023 K. Initially the C atoms either dissolve in the
cluster or deposit on the surface, then chains are formed, followed by fullerene structures, and finally a cap is formed that develops into the nanotube.
At the conditions of pressure and temperature shown in
Figure 1, the nanotube formed has several imperfections
and those are most likely due to the fast rate of carbon
addition artificially imposed by our simulations.
It is interesting to add that while this report was under
review, we became aware of ab initio molecular dynamics
simulations35 that basically agree with our findings. In the
ab initio MD study,35 the metal cluster is kept fixed, and
hydrogen atoms are added to the bottom part of the metal
structure to emulate the effect of the substrate. It is found
that a cap is formed without carbon atoms being dissolved
in the cluster interior, as expected from our discussion for
a strongly interactive substrate that causes the cluster to
adopt a rigid structure avoiding the penetration of C atoms.
The most significant aspect extracted from these MD
simulations is that the physical state of the cluster and its
interactions with the substrate can significantly influence
the nanotube growth. Thus, in the next sections we focus
on various aspects of the catalyst characterization, using
computational and experimental techniques.
3.2. Physical Properties of Metallic Nanoclusters at
High Temperatures and Pressures
At the high temperature conditions of the SWNT synthesis
process and under the effect of moderate to high pressures,
nanoclusters may have significant changes of morphology
and structure.36 Experimental and theoretical studies have
provided ample evidence that melting points of metallic
nanoclusters are much lower than the melting temperature
4
of the bulk material,37–40 and the change is a function
of cluster size,41 cluster-substrate interactions,42 43 cluster
composition,44 and combinations of these effects.
Figure 2 illustrates the variation of the melting temperature as a function of the cluster size for Pt nanoclusters
of different initial shapes: cubic (fcc), cube-octahedral, and
spherical. The phase transition is characterized both by the
discontinuity in the potential energy versus temperature and
also by the peak in the heat capacity calculated by Eq. (1).
The spherical clusters were built defining a cutoff distance
from a large Pt metal crystal with fcc structure, whereas
the cube-octahedral clusters are a function of R, the ratio
of the number of 111 and 100 exposed faces.
Results summarized in Figure 3 clearly illustrate the
decrease of the melting temperature as the cluster size
decreases, with little dependence on the cluster shape for
small sizes, and slightly larger differences for intermediate
sizes, given by variations in the onset of surface melting
due to the nature of the exposed surfaces.
In conjunction with the melting transition, another property that is clearly relevant to the SWNT synthesis process is the T-dependence of the self-diffusion coefficient
as shown in Figure 4. Very high mobilities are observed in
the liquid phase, in agreement with previous studies.45 46
As discussed in Section 3.1, for catalysts floating in vapor,
or for weak cluster/substrate interactions, at the beginning
of the synthesis process, carbon atoms are dissolved in the
metal cluster and after some time they start depositing on
the surface. The C dissolution continues until the cluster
J. Nanosci. Nanotechnol. 6, 1–12, 2006
Balbuena et al.
Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes
–5.25
(a)
1.0
500
–5.35
Ep (eV/atom)
(b)
256
–5.30
256
864
500
0.8
1372
C (eV/K)
–5.40
–5.45
–5.50
864
1372
0.6
0.4
–5.55
0.2
–5.60
–5.65
0.0
200
400
600
800
1000
1200
1400
1600 1800
200
400
600
800
T (K)
T (K)
–5.20
(c)
(d)
–5.25
341
613
–5.35
1140
–5.40
1287
C (eV/K)
Ep (eV/atom)
–5.30
–5.45
–5.50
–5.55
–5.60
–5.65
200
400
600
800
1000
1200
0.34
0.32
0.30
0.28
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
1400
200
341
613
1140
1287
400
600
800
T (K)
(e)
(f)
–5.25
904
0.3
0.2
2
3
4
–5.65
200
0.4
C (eV/K)
1
266
0.1
400
600
800
1000
1200
1400
T (K)
0.0
200
400
600
800
1000
1200
1400
T (K)
Fig. 2. MD calculated temperature effect on the potential energy (Ep , in eV/atom) and specific heat (C, in eV/K) of Pt nanoclusters of different
number of atoms as indicated in each graph. (a) and (b) correspond to initial cubic shape, (c) and (d) initial cube-octahedral shape, and (e) and (f) are
the results obtained for initial spherical structures. The number of atoms of the nanoclusters in (e) are: (1) 266, (2) 370, (3) 490, (4) 610, (5) 736, and
(6) 904. For clarity, only three of these sizes are included in (f).
reaches saturation at the given temperature. At higher temperatures more carbon atoms are able to be dissolved in
the more open and highly dynamic cluster structures therefore slowing down the process of carbon deposition on the
cluster surface, which in turn permits the continuous growing of the metal cluster. However, as the metal/substrate
interaction strength increases, the melting temperature of
the cluster increases. We note that once carbon is dissolved in the small metal cluster, the formation of a carbide
or simply the physical mixture C-metal would also alter
(usually reducing) the melting temperature of the C-metal
cluster. Thus, a sufficiently strong metal/substrate interaction is needed to control the cluster melting temperature
and cluster growing, and to avoid particle sintering.
We emphasize that although the discussion and results
presented in Sections 3.1 and 3.2 refer to Ni and Pt
J. Nanosci. Nanotechnol. 6, 1–12, 2006
nanoparticles respectively, the conclusions are valid for
other transition metals, in particular for Co and Fe, which
are the most common catalysts in SWNTs synthesis processes. In the next section we provide experimental insights
yielded by experiments in model systems that emulate the
CoMoCAT synthesis, and in the last two sections simulation results related to the Co–Mo system attempt to quantify the strength of the Co–MO2 C interaction.
3.3. Experimental Observations of
Model Co–Mo Catalysts
In this section we report electron microscopy and Raman
studies conducted on model Co–Mo catalysts prepared on
TEM grids, in order to obtain direct observations of
the onset of the nanotube growth, as well as the
5
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–5.45
–5.60
1400
490
6
–5.40
–5.55
1200
0.6
0.5
5
–5.35
–5.50
1000
T (K)
–5.30
Ep (eV/atom)
1000 1200 1400 1600 1800 2000
Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes
1150
1.5
Melting Temperature (K)
1100
1.4
0.87
1.3
1050
1.0
1.50
1.2
1000
1.1
950
1.73
900
Cube-octahedral
Cube
Spherical
1.0
850
800
0
200
400
600
800
1000
1200
1400
1600
Number of Atoms in the Cluster
transformations undergone by the catalyst under the precursor gas as a function of time. Although the catalyst
formulation (Co/Mo ratio, support composition) and reaction conditions attempt to mimic those of the CoMoCAT process, the resulting particle size and diameter of
the nanotube produced are not exactly the same as those
obtained on the high-surface area support. Nevertheless,
the observed behavior is expected to be qualitatively the
same as that in the real process. One of the uniqueness
of the CoMoCAT process compared to the rest of the
catalytic decomposition methods is the stabilization of
highly dispersed Co species that are generated under the
reaction on the solid substrate. The effect of the Co
stabilization by the Mo carbide species is dramatic. The
strong interaction between Co and its substrate (oxidic
Mo that becomes Mo carbide under reaction) inhibits the
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
– 0.1
266
370
D (1×10 – 9 m2/s)
RESEARCH ARTICLE
Fig. 3. Melting points as functions of size for Pt nanoclusters of spherical, cube-octahedral, and cubic shape, calculated from MD simulations.
The diameter (in nm) of the spherical cluster is marked by a number in
blue, and the ratio of the number of 111 to 100 exposed surfaces in
the cube-octahedral particle is denoted by a pink number.
200
904
400
600
800
1000
1200
1400
T (K)
Fig. 4. MD calculated atomic self-diffusion coefficient in Pt nanoclusters of initial spherical shape with 266, 370, and 904 atoms, and predicted
melting temperatures of 880, 970, and 1090 K respectively.
6
Balbuena et al.
formation of large metallic aggregates. These large metallic aggregates, present in other CVD methods have the
disadvantage of getting encapsulated in graphite layers,
which remain in the product and are more difficult to
remove. In the development of the CoMoCAT process it
was found that silica-supported Co–Mo catalysts with low
Co:Mo ratio exhibit excellent performance in the temperature range 700–900 C under the CO disproportionation
reaction. We have explained this performance on the basis
of the Co–Mo interaction. Co is stabilized by the Mo in
an oxidized form of the type CoMoO4 and remain as such
even at high temperatures. Only when the carbon containing gas (CO) is contacted with the catalyst, the CoMoO4 is
converted to unstable CoMo carbide; Co is no longer stabilized in this new matrix and starts migrating towards the
surface where gets reduced in the form of very small Co
metallic clusters that start the SWNT growth. That is, there
is an induction period during which carbon is uptaken
by the catalyst and the CoMoO4 species start transforming into Mo carbide and metallic Co, but no nanotube
growth should be observed. We attempt here to have a
direct observation of this induction period.
The real catalyst in the CoMoCAT process is composed
of Co–Mo species supported on high-surface-area silica.
Using a porous high-surface area supports allows for the
stabilization of relatively large amounts of catalytically
active metals in high state of dispersion and facilitates the
scale-up process. However, using porous supports complicates the observation of the catalytic reaction and the evolution of the active species during the various stages of the
process. Model catalysts on flat surfaces provide a more
direct access and have allowed us to directly observing
some of the important transformations that take place.
For example, we have prepared Co–Mo catalysts
directly supported on lacey silicon monoxide membranes
TEM grids. Before reaction, the grid was calcined at
500 C for 5 min in order to generate a silica surface on
the membrane surface. A solution containing Co and Mo
was prepared by dissolving cobalt(II) acetate tetrahydrate
and molybdenum(II) acetate dimer in ethanol. The solution
was then dropped on the calcined grids and further calcined at 400 C for 5 min to decompose the acetate and
form the Co–Mo metallic oxide species. As illustrated in
Figure 5, we have been able to directly observe on these
model catalysts the induction period (nucleation) that we
have previously proposed. Remarkably, during the first
3 min in contact with CO, no nanotubes were observed
on the TEM grid. The TEM/SEM images clearly showed
that after the grid was reduced at 500 C and heated
up to the reaction temperature (850 C), the structure of
the CoMoO4 species was still crystalline. By contrast,
after being in contact with CO for 1 min the particles
start changing their morphology and their surface became
rougher. This transformation clearly indicates that the
CoMoO4 species began to change into a different species.
J. Nanosci. Nanotechnol. 6, 1–12, 2006
Balbuena et al.
Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes
850 C
before
CO
3 min
under
CO
10 min
under
CO
Previous EXAFS, XRD, and XPS studies indicate that the
new species is a carbide. After 5 minutes exposure to CO
a high density of long bundles of SWNTs was detected.
These TEM/SEM observations are in perfect agreement
with the Raman spectroscopy observations. Figure 6 shows
the Raman spectra of the material obtained at 850 C at
different times. The band appearing at about 1580 cm−1
(G band) results from the in-plane stretching mode of
ordered crystalline graphite-like structures, while the band
appearing at around 1340 cm−1 (D band) represents disordered carbon structure. No G band was observed after
1 minute reaction, and only a weak signal corresponding to the G band was present after 3 minutes reaction,
for this particular sample only a few short SWNTs were
observed from TEM/SEM. However, after 5 minutes, the
Raman spectra changed dramatically displaying a typical
Growth vs. time CO 850 C
Growth vs. time CO 850 C
30000
3500
3000
3 min
2500
25000
20000
2000
1 min
15000
1500
10000
1000
1hr
Heat 850 C
5000
500
10 min
5 min
Cal 400 C
0
0
80
580
1080
Wave number (cm–1)
1580
80
580
1080
1580
Wave number (cm–1)
Fig. 6. Raman spectra as function of process time. Nanotube features revealed by the G mode and the radial breathing modes start at about 3 min
and become clear at longer times (right).
J. Nanosci. Nanotechnol. 6, 1–12, 2006
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Fig. 5. Evolution of the Co–Mo species in a model catalyst directly supported on a TEM grid. Left: SEM images. Right: TEM images. Top: Catalyst
heated to 850 C in He, before exposure to CO. Middle: After 3 min in CO at 850 C (induction period); note the change in texture of the catalytic
particles, but absence of nanotubes. Bottom: After 10 min in CO, large number of SWNT bundles.
Balbuena et al.
Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes
Raman G band Signal
25000
20000
15000
10000
5000
0
1
10
100
Time (min)
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Fig. 7. Time evolution of the Raman G signal, indicative of nanotube
growth, shows the existence of an induction period of 3–5 min before a
temperature dependent nanotube growth is detected. Squares: T = 750 C,
Triangles: T = 850 C.
SWNT spectrum with a high G/D ratio, indicative of good
nanotube quality, which correlates very well with the high
density of long SWNT observed by TEM/SEM.
Figure 6 also illustrates the transformation undergone
by the catalyst particles during the initial stages of growth.
It is clear that the Raman bands observed on the catalyst before reaction correspond to CoMoO4 species. After
pretreatment to reaction conditions, the cobalt molybdate
bands become getting distorted; this change in the Raman
spectra might originate from the loss of crystallinity
of CoMoO4 in the first stages of transformation. After
1 minute reaction, the intensity of CoMoO4 band has
greatly decreased, which indicates that the CoMoO4 phase
either becomes more amorphous or starts to transform into
the carbide species. The latter case seems more plausible
as revealed by TEM/SEM, as well as by previous characterization conducted on the high surface area catalysts.
Figure 7 shows the evolution of the G band with reaction time. It can be seen that the G band intensity increased
significantly after the first 3 minutes of induction. As
described above, the G band in the Raman spectra arises
from ordered crystalline graphite-like structures; this is
directly related to the presence of SWNT, as also confirmed by the breathing mode bands. After the nanoclusters of metallic cobalt start being released from the carbide
intermediate, SWNTs can grow very fast via the dissolution of carbon atoms into the cluster and deposition on
the cluster surface as illustrated in Section 3.1. From these
observations, we can conclude that SWNTs grew after the
catalyst was in contact with CO for a period of time. An
induction time is needed for the CoMoO4 species transform into a dual carbide, which decomposes into Mo carbide and Co clusters.
In the last two sections we discuss the morphology of
Co clusters predicted from theoretical calculations when
the Co interactions with substrates (graphite and molybdenum carbide) are taken into account.
3.4. Shape and Morphology of Co Clusters as a
Function of Co-Substrate Interactions
To evaluate the substrate effect on Co-graphite interactions, we analyze the structure obtained from MD simulations of a 48 atom-Co cluster deposited on a graphite
surface. Results are presented as a function of the metal/
substrate interaction represented by a 12-6 LJ potential.
The Sutton-Chen potential was employed for the Co–Co
interactions,47 in two possible structures of the Co cluster,
ε = 3/4 εo
800 K
ε = 1/2 εo
800 K
ε = εo
800 K
ε = εo
1023 K
Fig. 8. Snapshots from MD simulations of hcp Co clusters of 48 atoms deposited on a graphite substrate. The 12-6 LJ potential function is used
to represent the Co–C interatomic interactions; in the top two figures the value of the energy parameter was reduced with respect to the calculated
o = 004475 eV in order to determine its effect on the cluster morphology and structure.
8
J. Nanosci. Nanotechnol. 6, 1–12, 2006
Balbuena et al.
Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes
Fig. 9. The cell and its partial neighbor periodic images for the bulk
surface of -Mo2 C (Mo atoms are blue spheres, C atoms are grey). Top:
Top view. Bottom: Side view.
having two carbon atoms coordinated (Mo2), illustrated in
Figure 9.
The adsorption of one Co atom on the Mo-terminated
-Mo2 C surface was investigated on top, bridge as well as
hollow initial configurations. Such adsorption corresponds
to 1/4 of a monolayer coverage. Co tends to be adsorbed
on both bridge and hollow sites. In the case of bridge
adsorption, the distances from Co to the two Mo atoms
are 2.63 and 2.65 Å, which they are around 2.83 Å for the
hollow adsorption. The adsorption energies are defined as
the difference between the energy of the complex adsorbate/adsorbent minus the energy of the adsorbent (slab)
minus the energy of the adsorbate Con (Co cluster of n
atoms)
E = ECon − Mo2 C complex) − EMo2 C slab − ECon (3)
Such Es are almost the same for the hollow and bridge
different adsorptions for n = 1, −5.80 eV. Charge population analysis indicates that significant charge of ∼0.9 e is
transferred from Mo to Co atoms. As the bulk surface is
relaxed, the energy of the complex decreases only slightly
by ∼0.5 eV. The distances between Co and Mo are very
comparable to the case of the fixed surface.
3.5. Preliminary Ab Initio Studies of the
Mo2 C/Co Interactions
Both experimental and theoretical results show that the
most stable -Mo2 C phase adopts an orthorhombic crystal
structure,27 28 where Mo atoms are in a slightly distorted
close-packed arrangement and carbon atoms occupy half
of the ordered positions in lattice octahedral vacancies.
Such -Mo2 C phase was also identified in the CoMoCAT
process. In the bulk crystal, the coordination of Mo is three
and that of C is six; while in the Mo-terminated surface,
Mo atoms have two types of coordination, the first having
one carbon coordinated (denoted as Mo1) and the second
J. Nanosci. Nanotechnol. 6, 1–12, 2006
Fig. 10. Adsorption of Co3 (left) and Co2 (right) on a Mo2 C carbide
surface calculated with periodic DFT. For clarity, only the unit cell is
shown.
9
RESEARCH ARTICLE
hexagonal close-packed, hcp, and face-centered cubic, fcc.
The Sutton Chen potential for Co–Co was fitted to a
LJ potential to obtain LJ energy and length parameters
for Co–Co interactions. Such LJ parameters were then
used along with the Lorentz-Berthelot mixing rules,12 and
C–C parameters taken from published work,48 to determine the cross-interaction C–Co LJ parameters (
C−Co =
004475 eV and C−Co = 2743 Å).
The stable structure of bulk Co is hexagonal close packing, hcp.49 However, experiments indicate that the fcc
phase is most stable at high temperatures,50 and the stable
phase is a function of the particle size. Kitakami et al.51
reported fcc for average particle diameters below 20 nm,
mixtures of fcc and hcp for diameters of 30 nm, and almost
pure hcp for larger particles, whereas Dassenoy et al.52
found hcp and non-periodic polytetrahedral structure for
Co clusters of 2–4 nm synthesized in the presence of a
polymer template. Our MD simulations showed that Co
clusters of nanodimensions can exist both as fcc or hcp
with very close energies, especially at temperatures close
to its melting point. Although we have not determined
the melting temperature for Co clusters, by analogy with
other transition metals, we speculate that it should be
much lower than Co bulk melting temperature, 1768 K.53
Figure 8 qualitatively shows the effect of the substrate on
the melting temperature of an hcp Co48 structure. When the
substrate-cluster interaction strength is half of that of the
Co-graphite interaction (Fig. 8, top left), both surface
and core atoms have high mobility and the cluster has
a melted appearance at 800 K. As the cluster/substrate
interaction increases, the cluster adopts a much ordered
structure (Fig. 8, top right), and a clear wetting layer is
developed (Fig. 8, bottom left) causing a significant change
on the overall shape of the cluster and on the nature of the
exposed phases. Finally, the structure of Co48 at 1023 K for
an interaction strength corresponding to the Co-graphite
system (Fig. 8, bottom right) reveals much higher atomic
mobility than at 800 K. In relation to the CoMoCAT
synthesis process, we next investigate the strength of
the Co–Mo carbide interaction, assuming that Co clusters are formed on a Mo carbide substrate as discussed in
Section 3.3.
Balbuena et al.
Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes
RESEARCH ARTICLE
Table I. DFT calculated (PBEPBE/LANL2DZ) ground state electronic energies of small clusters of Co, Mo, and Mon Com , with ground state
multiplicities (m) indicated, characteristic bond distances R, and binding energies BE (in eV) for the Mon Com complexes.
m (ground states)
Energy/au
Co
Co2
4
3
−14499340
−29004792
Co3 isosceles triangle
Mo
Mo2
8
7
1
−43514510
−6742057
−13495908
Geometry (Å and degree)
BE/Co atom in
Mon Com (eV)
2.115
2.209, 2.209, 2.441
1.992
Mo3 isosceles triangle
3
−20246427
2.233, 2.233, 2.484
Mo4 rhombus
3
−27000641
1–2 = 2.297, 2–3 = 2.297
3–4 = 2.298, 4–1 = 2.296
1–2–3 = 105.1, 2–3–4 = 74.8,
3–4–1 = 105.1, 1–2–3–4 = 0
Mo4 pyramid
1
−27002325
1–2 = 2.724, 2–3 = 2.128, 3–4 = 2.719,
3–1 = 2.722, 4–1 = 2.128, 4–2 = 2.719
1–2–3 = 67.0, 2–3–1 = 67.0,
1–2–3–4 = −50.3
Mo2 _Co isosceles triangle
2
−28003051
Mo1 –Mo2 = 2.071, Co–Mo1 = 2.411
Co–Mo2 = 2.411
−2.1
Mo3 _Co rhombus
4
−34755842
Mo1–Mo2 = 2.273, Mo2–Mo3 = 2.274
Mo3–Mo1 = 2.434, Mo3–Co = 2.491
Mo1–Co = 2.493,
Mo1–Mo2–Mo3–Co = 0
−2.7
Mo3 _Co pyramid
4
−34755715
Mo1–Mo2 = 2.381, Mo2–Mo3 = 2.297
Mo3–Mo1 = 2.320, Mo1–Co = 2.404
Mo2–Co = 2.426, Mo3–Co = 2.773
Mo1–Mo2–Mo3–Co = 65.3
−2.7
Mo3 _Co2 square-based
pyramida
5
−49268092
Co–Co = 2.271, Mo1–Mo2 = 2.288,
Co1–Mo1 = 2.406, Co2–Mo2 = 2.679,
Co1–Mo3 = 2.584, Co2–Mo3 = 2.331
−2.3
Mo4 _Cob
4
−41509523
Co–Mo1 = 2.309, Co–Mo2 = 2.761,
Co–Mo3 = 2.763, Co–Mo4 = 3.965,
Mo1–Mo2–Mo4–Mo3 = −37
−2.9
Mo4 _Coc trigonal
bipyramid
4
−41512848
Co–Mo1 =2.518, Co–Mo2 = 2.566,
Co–Mo3 = 2.540, Mo1–Mo3 = 2.881
−3.0
Mo4 -Cod2 square-based
bipyramid
5
−56027030
Co–Co = 2.277, Co1–Mo1 = 2.473,
Mo3–Co1 = 2.776, Mo3–Co2 = 2.477,
Mo1–Mo2 = 2.900, Mo2–Co2 = 2.673,
Mo4–Co1 = 2.786, Mo4–Co2 = 2.475
Mo1–Mo2–Co2–Co1 = 0.0
−2.7
a
Mo1, Mo2 and the two Co atoms constitute the base;
Initial geometries could be considered as rhombus Mo4 and Co, yet Mo4 is considerably distorted into a butterfly cluster;
From pyramid Mo4 and Co;
d
It may also be considered as octahedron. Mo1, Mo2, and the two Co atoms form the square.
b
c
Stable adsorption of Co2 on the Mo-terminated -Mo2 C
surface was also found at the bridge site (Fig. 10, right).
The distances between Co and its nearest neighbors are
∼2.65 and 2.75 Å, and the Co–Co bond length is ∼2.37 Å.
The adsorption energy is ∼−5.05 eV/Co atom. The net
charges carried by the two Co atoms are −0.62 e and
−0.45 e.
For Co3 adsorption (Fig. 9, right), the binding energy is
−4.1 eV/Co atom, and the charges on the Co atoms are
−0.68, −0.58, and −0.74 e. To test the performance of the
pseudopotentials regarding binding energies, we used DFT
to calculate structure and binding energies of small clusters
Mon Com using the PBE/PBE functional and the LANL2DZ
10
basis set. Results indicate that although similar bonding
geometries are obtained, the binding energies (Table I) are
approximately half of the values obtained with periodic
DFT, but still in the order of 3 eV/Co atom, indicative of a
Fig. 11. DFT (PBEPBE/LANL2DZ) optimized geometries of clusters.
From left to right: Mo3 –Co2 (m = 5, square-based bipyramid); Mo4 Co
(m = 4, butterfly); Mo4 Co2 (m = 5); Mo3 Co (rhombus, m = 4). See
Table 1 for bond lengths, angles, and binding energies.
J. Nanosci. Nanotechnol. 6, 1–12, 2006
Balbuena et al.
Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes
very strong interaction between small Co clusters and Mo
surfaces. Selected geometries are shown in Figure 11.
4. CONCLUSIONS
(1) the existence of melting and solid–solid structural
transitions in nanoclusters at the temperatures and
pressures of SWNT synthesis;
J. Nanosci. Nanotechnol. 6, 1–12, 2006
Acknowledgment: Financial support from the National
Science Foundation (NER/CTS-04003651) is gratefully
acknowledged.
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RESEARCH ARTICLE
New simulations done for a cluster deposited on a strongly
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Role of the Catalyst in the Growth of Single-Wall Carbon Nanotubes
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RESEARCH ARTICLE
Received: 23 May 2005. Revised/Accepted: 19 October 2005.
12
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