NANO
LETTERS
Kinetics for the Synthesis Reaction of
Aligned Carbon Nanotubes: A Study
Based on in situ Diffractography
2004
Vol. 4, No. 9
1613-1620
Ludovico M. Dell’Acqua-Bellavitis,* Jake D. Ballard, Pulickel M. Ajayan, and
Richard W. Siegel
Department of Materials Science and Engineering and Rensselaer Nanotechnology
Center, Rensselaer Polytechnic Institute, Troy, New York 12180-3590
Received May 20, 2004
ABSTRACT
Single-slit laser diffractography was used to image the growth of carbon nanotubes. A silicon dioxide slit with a minimum width of 150 µm
was prepared and positioned inside a chemical vapor deposition (CVD) reactor in alignment with a laser source. Carbon nanotubes were
grown inside the slit width, producing corresponding changes in the diffraction pattern due to the optical opacity of these structures and to
their high density and alignment. Changes in the diffraction pattern were recorded and used for the direct measurement of nanotube growth.
The results show an exponential increase of length vs time for 45 min experiments, best fit with a double exponential function, which is
interpreted in terms of the concurrence of base-growth and tip-growth modes for successive catalyst particles. Scanning electron microscopy
confirms the diffractographic data at a high level of precision. The innovation brought by this in situ method to the kinetic study of nanotube
synthesis is discussed and compared to a posteriori studies based solely on microscopy for a range of different nanotube lengths.
Introduction. Since the discovery of carbon nanotubes by
S. Iijima in 1991,1 the scientific community has initiated a
new endeavor in both fundamental and applied science. This
laborious exertion is aimed at characterizing the unique
electrical, chemical, and mechanical properties of this highly
versatile carbon phase. If on one hand the characterization
effort for finished nanotubes has been overwhelming, on the
other hand nanotube science suffers from a serious lack of
knowledge on the kinetics that rules the synthesis of these
structures. This is so for a number of reasons, the primary
one of which consists of the prohibitive conditions of the
synthesis reaction, undertaken within the temperature range
800-1200 °C. This high-temperature range is essential to
nanotube synthesis, but it impedes direct imaging of their
growth, heretofore reducing every experiment to a blind
experiment. The limitations in direct imaging of nanotube
growth are also due to the small size of these structures; if
on one hand the use of high energy beams would be ideal to
image nanotube synthesis over time, these methodologies
are found to interfere with the synthesis of carbon bonds
and are therefore not viable.
The paucity of knowledge on the reaction kinetics ruling
carbon nanotube synthesis was here effectively addressed
by real-time in situ monitoring of a variable closely correlated
to carbon nanotube growth, which can be measured continu* Corresponding author. Ph.:
E-mail: [email protected].
10.1021/nl0492335 CCC: $27.50
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© 2004 American Chemical Society
ously over a much broader scale. This type of method has
been successfully used in the past for time-dependent or
temperature-dependent measurements on vacancy concentration for bulk solids. The variables used in these types of
experiments are density, in the case of differential dilatometry, or resistivity, in the case of differential resistometry.
In the former case, the problem to measure vacancy
concentration directly is bypassed by measuring corresponding variations in density for the bulk solids, where infinitesimal variations in volumetric mass can be imaged over
three dimensions and for large atomic quantities, therefore
obtaining appreciable measurements.2-3 In the latter case,
resistivity allows the amplification of incremental temperature-dependent changes over 27 orders of magnitude.4-6 In
the case of differential dilatometry, macroscopic and microscopic measurements are taken simultaneously, while in
differential resistometry they are taken sequentially.
The same methodology is used in this study to image
infinitesimally small incremental changes in nanotube length
over time via a setup inspired by a landmark experiment on
the imaging of mercury whiskers by Sears.7-8 The nanotubes
are allowed to grow inside a single-slit and corresponding
changes in the single-slit diffraction pattern are imaged over
time. As the nanotubes are opaque, their growth will
progressively decrease the width of the slit, therefore
increasing the distance between adjacent maxima on the
diffraction pattern. This variable is then used to image the
change in nanotube length at sufficiently long distances from
the nanotubes sample. Due to its extensive use of diffraction,
this method can be considered to be based on differential
diffractography. The diffractographic measurements on
growth are subsequently calibrated a posteriori via microscopy and found to be in good agreement with the final
length of the nanotubes grown inside the slit. This control
allows one to gain insight on nanotube growth rates by
calculating the ratio between a range of final nanotube
lengths obtained in a series of separate experiments and the
respective exposure times.
Differential diffractography is a way to add growth rate
information to a series of otherwise static micrographs taken
at the end of individual synthesis experiments. The positive
implications of this methodology are apparent in its capability
to determine the ideal growth conditions for specific nanotube
morphologies, or in relaxing the stringent conditions that are
currently used for synthesis-a major endeavor in the future
transition from nanotube science to a nanotube technology
widely accessible to masses.
Materials and Method of Procedure. The methods
described in this work comprise five fundamental processes: (i) single-slit substrate fabrication in a clean-room
environment, (ii) synthesis of carbon nanotubes (CNTs) by
chemical vapor deposition (CVD), (iii) in situ measurements
of the kinetics underlying the CNTs synthesis reaction, by
single-slit laser diffractography, (iv) image processing of
diffraction patterns, (v) scanning electron microscopy preceding and after CNTs synthesis reaction.
Single-Slit Substrate Fabrication. Wet thermal oxidation
was initially used on silicon due to its unparalleled capability
to create micron-thick layers of thermal silicon dioxide. This
would subsequently be used as a template to selectively direct
tetramethylammonium hydroxide ((CH3)4NOH) etching
through the silicon wafer. Photolithography was subsequently
performed on the silicon wafer to define the slit width, and
buffered oxide etch (BOE) maintained at ambient temperature
was then used to remove the oxide across the demarcated
slit width. After a silicon dioxide template was created on
the silicon wafer, the photoresist was removed. The patterned
SiO2 was then used as a template to direct subsequent (CH3)4NOH etching of the underlying Si wafer throughout its
thickness. The etching action of (CH3)4NOH is highly
anisotropic and is directed at an angle R ) 54.7°, corresponding to the angular distance between the (100) and the
(111) planes in the silicon unit cell. This process therefore
yields pyramidal pits etched into (100) planes, bounded by
(111) crystal planes.9 Finally, the silicon dioxide template
was removed by BOE, as previously explained.
Carbon nanotubes synthesized by xylenes-ferrocene in a
chemical vapor deposition environment have been shown to
nucleate selectively on silicon dioxide. Conversely, bare
silicon has been shown as an inhibitor of CNT nucleation,
as reported by Zhang et al.10 For this reason, the wafer was
uniformly oxidized on all surfaces of the slit by thermal
oxidation. The final architecture comprised a 200 µm thick
rectangular slit; all the slit sides were covered in SiO2,
allowing CNT nucleation and growth throughout the slit
1614
Figure 1. Diagram representing the main components of the CVD
setup utilized in this study. (A) Diffraction pattern recorded on the
projection screen. Changes in the distance between the primary and
the secondary maxima or, alternatively, between adjacent minima,
map directly to changes in the geometry of the slit. (B, F) Polished
quartz portholes. (C) Sample with horizontal slit. (D) Surface
delimiting the heating zone. (E) Surface of the furnace. (G) Laser
source.
surface and therefore averaging carbon nanotubes growth
over two surfaces, obtaining higher accuracy and consistency
of diffractographic measurements.
Synthesis of Carbon Nanotubes by Chemical Vapor
Deposition. In this study, oriented carbon nanotubes were
synthesized by catalytic pyrolysis of a carbon source.
Ferrocene (C10H10Fe) was used as the catalyst precursor,
while xylenes (C6H4(CH3)2) were used as the carbon source.
The growth process occurred inside an alumina reaction tube
that was housed horizontally inside a muffle furnace. The
specific setup that was used for this study is represented in
Figure 1. The inlet and the outlet featured in this setup were
lateral with respect to the longitudinal axis of the alumina
tube reactor. This requisite was of fundamental importance,
as it permitted the positioning of polished quartz portholes
along the two extremities of the alumina tube, with an
uninterrupted line of sight through the whole length of the
reactor tube.
The operating temperature of the furnace was equal to 800
°C, and the reactor was purged with argon throughout the
run, in the attempt to achieve an oxygen-free atmosphere in
which carbon oxidation would not impair the synthesis of
the carbon nanotubes or their integrity after completion of
the synthesis reaction. Additionally, argon was used as an
inert gas to drive the flow of xylenes-ferrocene solution
inside the reactor during the synthesis process. The xylenesferrocene solution was initially prepared in the liquid phase;
subsequently it was injected inside a preheating stage (T )
250 °C) by means of a volumetric pump. Finally the solution
was flowed to the heating zone, where the nanotube synthesis
occurred. As explained above, the main effort involved in
this study consisted in the concurrent optimization of the
CVD system for growth of carbon nanotubes and for
transmittance of light through the reactor, in order to perform
accurate in situ diffractography of the carbon nanotube
synthesis reaction.
The silicon-silicon dioxide single-slit sample previously
manufactured was loaded vertically in the reactor tube of
the CVD system. The slit main axis was positioned in the
Nano Lett., Vol. 4, No. 9, 2004
P0Pm
for any given minimum. In this method, a is a
OPm
function of θ, λ, and m, which are all experimentally
measurable quantities. Although the geometry here represented drastically simplifies the real geometric conditions,
the level of accuracy obtained by this approximation is
adequate for the overall experimental setup used in this study.
The laser source used in the present study was a 25 mW
He-Ne Laser System, with a certified wavelength of 633
nm. The high precision in the calibration of the wavelength
(λ) for this laser source allowed an accurate determination
of the changes in a.
Trigonometric Correction for the Geometry of the Slit. The
walls of the slit used in this experiment were not orthogonal
with respect to the slit plane, but were oriented at an angle
of 54.7° with respect to the normal to the slit plane - the
angle between the (100) and the (111) planes in the Si unit
cell. Due to the particular slit geometry, the results had to
be corrected with a trigonometric function of the angle R̂ )
54.7°. Additional corrections of the diffraction data had to
be considered due to the combined growth of carbon
nanotubes on both sides of the slit. This was to average the
measurement of nanotube growth rate on two surfaces instead
of one, therefore obtaining more precise measurements. The
resulting correction factor for the interpretation of the
diffraction data is reported in the following equation:
)
Figure 2. Diagrams representing the Fraunhofer condition. P1, P2,
Pn represent the position of n-order secondary minima. When the
Fraunhofer condition is assumed valid, the rays are approximated
to be parallel, at an angle θ from the central axis. The path
difference between r1 and r2 is given by (a/2)sin θ.
horizontal orientation. A laser beam was aligned along the
plane that connects the slit to the portholes on the two
extremities of the reactor tube. The diffraction pattern was
projected on a screen at a distance of 3.42 m from the plane
of the slit sample and the evolution of the diffraction peaks
was recorded by a CCD camcorder. The alignment of the
CCD camcorder allowed the measurement of the variation
of distances on the diffraction pattern in a fashion that was
maximally precise, considering the given geometrical constraints.
The experimental equipment and the process parameters
that were utilized in this study reinterpret conditions already
documented in the published literature for the growth of
aligned carbon nanotubes.11-14 The optimization of such a
CVD system was achieved by the definition of a multidimensional parametric design of experiment (DOE) matrix.
Each dimension of this matrix represented a variable in the
CVD system. CVD optimization for CNT growth alone was
found to be satisfied by several CVD process recipes, each
one consisting of a specific combination of unique values
for each variable. A subsequent set of pilot experiments was
performed in order to optimize the transmittance of light
through the reactor. The feeding rate of xylenes-ferocene
solution inside the reactor was highlighted as the variable
that was most responsible for the deterioration of light
transmittance inside the reactor. After manipulating each
variable separately in a vast number of individual experiments, in the pursuit of satisfactory samples, a single CVD
recipe was selected with which to perform in situ measurements of CNTs synthesis using laser diffractography.12
Single-Slit Fraunhofer Diffractography. The Fraunhofer
condition is shown in Figure 2. The simplifying trigonometric
geometry represented in Figure 2 leads to the following
solution for the diffractographic measurements used in this
study:
a sin θ ) mλ
(1)
with m ) 1, 2, 3 ... (minima - dark fringes), where λ refers
to the wavelength of the incident laser radiation and sin θ
Nano Lett., Vol. 4, No. 9, 2004
leffective ) 1.730*lmeasured
(2)
Image Processing of Diffraction Patterns. The changes
in the diffraction patterns were recorded by means of a
camcorder. Each resulting film sequence consisted of 45 min
of video (frame rate of 15.00 fps, image size of 640×480
pixels, depth of 24 bits), which was subsequently digitized
and then converted into individual picture files (frame rate
of 1.00 fps, image size of 320×240 pixels, depth of 24 bits).
On each of these files, a subsequent spectrographic analysis
was conducted. This analysis was performed on the PC-based
Scion Image software, by Scion Image Corporation (based
on NIH Image, by Wayne Rasband of National Institutes of
Health). Figure 3A documents this step in the image
processing, which led to precise measurements in terms of
pixel positions and distances. These were subsequently
converted to SI metric measurements. The distances OM1,
OM2, OM3 were measured with a frequency of 30 Hz over
the entire 45 min duration of the video. All the diffraction
data were compiled into an electronic spreadsheet.
Scanning Electron Microscopy. Scanning electron microscopy studies were performed on the slit samples both
preceding CVD growth and after it. A JSM 840 scanning
electron microscope by JEOL, Inc. was used for this purpose.
The microscopy studies confirmed carbon nanotube growth
both qualitatively and quantitatively, as documented in the
following section on the experimental results.
Results. Previous experiments in our laboratory revealed
a disproportion between the nanotube lengths synthesized
over a small duration ∆t1 and the nanotube lengths synthe1615
Figure 3. (A, left) Spectrographic analysis for an individual photogram and quantitative identification of the diffraction maxima and
minima. (B, center) Diffraction pattern at 00:00 s. (C, right) Distance between individual minima and absolute maximum vs time plot,
measured during CVD growth of carbon nanotubes on sample Ψ.
sized over longer durations ∆tn ) n∆t1. This nonlinear
relationship justifies the need to base any further discussion
of nanotube growth on growth rates, here referred to as the
infinitesimal and ever slightly changing ratio: ∂l/∂t. The
distinction between growth hodometry, the static measurements of the length of grown nanotubes attained by postexperimental microscopy for different exposure times, and
growth tachometry, the dynamic measurements of nanotube
growth rates, is here used to denote this concept.
Carbon Nanotube Growth Tachometry by Single-Slit Laser
Diffractography. In situ diffractography measurements were
calculated as explained in the Methods section. The experimental data are reported in Figure 3B,C for an individual
diffractographic experiment; similar results were obtained
for a total of three individual experiments.
Figure 3C clearly shows that the third-order secondary
minimum is more accurate in detecting differences in slit
width and ultimately in nanotube growth, as it varies more
rapidly than the first- and second-order minima and over a
larger distance, in accordance with eq 1. However, the
intensity of the maxima decreases as their n-order increases,
namely, the distance from the absolute maximum. This
makes the third-order secondary minimum, when present,
also the most difficult to detect, due to the progressive local
diminution in contrast. The results obtained in Figure 3B,C
were replicated for three individual experiments and subsequently averaged arithmetically between minima of the same
order across subsequent experiments. Figure 4A illustrates
this statistical analysis: each series from this figure represents
the average of the displacement vs time plots for each
individual minimum (i.e., first-order secondary minimum)
measured across three different experiments.
The error bars present in this plot represent the standard
error of the mean. This is defined only for those cases when
all measurements were readable for each minimum in each
experiment. Due to the increasing diminution in contrast
coupled with the migration of the minima outside the field
of view, the standard error of the mean was not defined for
experiments longer than 15 min.
1616
When the correction reported in eq 2 to compensate for
the nonorthogonal slit walls was put in place, the nanotube
length calculated from the changes in slit width varied in
the range 65-75 µm. This result was subsequently compared
to the nanotube length measured by scanning electron
microscopy (SEM), as described below.
After the diffractographic data were corrected in order to
represent nanotube growth, the displacement of the second
order minima was averaged arithmetically for any instantaneous measurement within each experiment and not between
individual ones, as was the case in Figure 4A. The results
are here reported in the form of a growth vs time plot for
one individual experiment in Figure 4B. This figure shows
two distinct data ranges with a rather large gap in data
acquisition for intermediate times. This was caused by the
need to evacuate the chamber during the experiment, in the
attempt to maximize laser transmission. For this reason, the
data sets on these graphs are represented in different colors,
as they belong to methodologically distinct populations.
However, these datasets are plotted within the same graph
as the single experiment they derive from was performed
on the same sample. Accurate experimental controls were
undertaken to compare the overall growth rate for nanotubes
synthesized in the absence of chamber evacuations with the
growth rates measured in the presence of chamber evacuations, and the two rates were found to be identical.
Each dataset was initially regressed with a set of exponential and sigmoidal models across two stages described
below. Nonlinear curve fitting was performed using Origin
7.0 software and computing 1000 simplex iterations for each
model. In the first stage, the dataset was regressed using a
variety of models previously selected among a very wide
variety of possible regression equations, in light of the higher
value of the respective correlation coefficient. The function
that more accurately regressed the series of data presented
above was a double exponential y ) y0 + A1e(x-x0/t1) +
A2e(x-x0/t2) (R2 ) 0.98241), where y represents nanotube
Nano Lett., Vol. 4, No. 9, 2004
Figure 4. (A, left) Statistical analysis of displacement vs time for secondary minima. The error bars present in this plot represent the
standard error of the mean. (B, right) Carbon nanotube growth vs time plot for two data ranges within the same experiment performed on
sample Ψ. The gap of data for intermediate time values is attributable to the diminution in light transmission through the reactor tube. This
was due to the increase in carbon source and catalyst within the reactor. After chamber evacuation was performed, the diffraction peaks
reappeared and further tracking was possible, therefore allowing the monitoring of nanotubes growth rates for longer time intervals. The
three exponential regression models used are: y ) (a1/a1 - a2)(e-a2x - e-a1x) (red), y ) y0 + A1ex/t1 + A2ex/t2 (blue), y ) y0 + A1e(x-x0)/t1
+ A2e(x-x0)/t2 (green).
Figure 5. (A) Slit specimen geometry before exposure to CNT growth. (B, C, D) Slit specimen geometry after exposure to CNT growth.
Carbon nanotubes grow on all surfaces of the slit and progressively shutter the slit width, altering the corresponding diffraction pattern. The
laser was focused in the central portion of the slit length (B), eliminating the distortion of nanotube growth due to edge effects, illustrated
on (C). The high magnification micrograph (D) shows the alternation of sections, respectively, exhibiting a degree of cyclical growth in
subsequent stages or uninterrupted nanotube growth.
length, x is time, and the remaining symbols are parameters.
This statistical analysis using exponential regression functions
was specifically compared to different models based on
sigmoidal functions, which provided lower R2 values and
which were therefore not considered adequate. The descriptive statistics compellingly demonstrate a strong monotonic
time dependency of carbon nanotube length.
Scanning Electron Microscopy. Scanning electron microscopy was performed both before (Figure 5A) and after
(Figure 5 B-D) exposure of the slit specimens to carbon
nanotube growth, which confirmed the diffractographic
measurements.
Careful SEM measurements on the samples indicated a
nanotube average length of 70 µm, which matches well with
the estimated length based on the measurements of the shifts
in the diffraction peaks. Similar confirmation was made for
the other samples. These results on nanotube growth are
particularly compelling in the light of the absence of any
layer of amorphous carbon observed by scanning electron
microscopy.
Nano Lett., Vol. 4, No. 9, 2004
In all samples observed, the nanotubes grow equally on
both sides and gradually shutter the slit aperture, causing
the change in the diffraction pattern. Although this effect is
slightly impaired on the edges of each slit, nanotube growth
appears uniform for most of the slit length and throughout
its thickness. Finally, high magnification studies of the
nanotubes grown on the slit walls indicate that the nanotubes
exhibit a peculiar type of growth (Figure 5D). On one hand,
some sections exhibit a degree of cyclical growth in
subsequent stages, which is probably caused by the alternation of xylenes-ferrocene exposures with reactor evacuations
- made necessary to prevent deterioration of the diffractive
signal through the reactor. On the other hand, many other
sections exhibit uninterrupted nanotube growth. The alternation of sections exhibiting cyclical growth with sections of
uninterrupted growth in the nanotube array is here interpreted
in terms of cycles where either heterogeneous or homogeneous nucleation are prevalent for individual sections of the
array, due to nonuniform supply of the carbon and of the
catalyst sources.
1617
The quantitative measurements of length and growth rate
for different nanotube arrays respectively obtained by diffractography and by microscopy are found to match. This
proves the accuracy of in situ diffractography as an imaging
method for the monitoring of carbon nanotube growth rates.
Analysis and Discussion. The majority of the published
literature on carbon nanotube growth is based on a posteriori
electron microscopy studies. The growth rates are generally
measured by dividing the length of the nanotubes, as
measured by microscopy, by the time the sample was
exposed to the carbon source and to the catalyst. These a
posteriori techniques are grossly inadequate because they
average the measurements of carbon nanotube growth over
a long time interval-from the onset of the experiment to its
conclusion. On the contrary, measurements that rely on in
situ techniques allow a higher resolution in time for the
measurements being monitored, providing instantaneous
measurements of nanotube growth. The distinction between
these two approaches is here stressed using the terms of
growth hodometry and growth tachometry.
From Growth Hodometry to Growth Tachometry. Kim et
al. describe an in situ method for monitoring plasmaenhanced chemical-vapor deposition (PECVD) growth of
aligned carbon nanotubes based on optical interference
techniques.15-16 The incident angle used by these authors is
higher than the one used in the slit diffractography experiment here reported, and optical interference was measured
by Kim et al. using a focused 650 nm laser diode and a
photodiode detector. The study of interference oscillations
patterns performed by these authors is based on the partial
reflection of the laser light from the top surface of the carbon
nanotubes, the wavelength of which is much larger than the
size of the growing nanotubes, while the transmitted light is
reflected from the substrate surface. The interference oscillation patterns can be affected by experimental conditions
such as laser wavelength, angle of beam incidence, and
growth conditions, and provide a very effective way to
investigate growth behavior.
Although this study is very valuable from a methodological
point of view, it appears inadequate to measure growth
behavior for long nanotube arrays synthesized over long time
intervals, as it suffers from a gradual diminution in the
intensity of interference oscillations caused by the absorption
of the laser light through the nanotubes, which increases
gradually with nanotube growth. On the contrary, the
capability of the diffractography method used in the present
work to expand the small scale of sample topography into
the large scale of the reciprocal coordinates of the diffraction
pattern enables a resolution in space that is higher than any
other measuring technique. For these two reasons, the
technique described in the present study for the dynamic
monitoring of carbon nanotube growth-based on in situ
diffractography-is considered ideal. When the results based
on the single slit diffractography study here reported are
compared with the results of the study of interference
oscillations reported by Kim et al.,15-16 it is possible to
conclude that the results reported in these two studies are in
agreement with one another. One additional specification is
1618
however necessary, namely that the study here reported was
run for a longer time interval and for longer nanotube lengths
than that of Kim et al.
A control experiment was performed to compare the
consistency of the measurements for nanotube arrays either
grown inside the slit used in this experiment (made of silicon
dioxide) or grown on a standard horizontal sample of silicon
dioxide having equal thickness. The slit geometry used in
this experiment was not found to reduce significantly the
growth rate of the nanotube array. A reduction in the growth
rate of the nanotube array would, however, be expected for
increasingly smaller slit widths due to the increasingly
smaller flow of carbon and catalyst sources.
The matching of the results obtained by diffractography
and by microscopy compellingly demonstrates the rigor of
diffractography as an in situ technique to image carbon
nanotube growth. The consistency in the measurements
obtained respectively by microscopy and by diffractography
is expected to be observed for a wide range of slit widths in
this experiment. For smaller slit sizes, however, it is
reasonable to expect an increase in error due to the
increasingly shorter nanotube lengths.
The results clearly demonstrate that the synthesis reaction
of aligned nanotubes for the xylenes-ferrocene CVD setup
follows a nucleation and growth succession. Several functions
were used to regress the data presented in Figure 4B; among
all the functions considered, double exponential functions
were the ones that had the best r2 values for all the datasets.
The double exponential function was here interpreted as a
proof of the suggestion that nanotube synthesis results from
the combination of two phenomena: base growth and tip
growth for successive catalyst particles.
A Unifying Framework: Concurrent Base and Tip Growth
for SuccessiVe Catalyst Particles. The evidence in support
of the model for nanotube growth here proposed is limited
to scanning electron microscopy performed on nanotube
samples produced with the CVD setup utilized to perform
the experiment of in situ diffractography. No direct transmission electron microscopy was performed on the nanotubes
grown within the slit.
The model proposed here is intended specifically for
catalytically grown multiwall carbon nanotubes. Although
single-wall carbon nanotube catalytic growth can potentially
be reduced to a subset of the multiwall case for nuclei sizes
smaller than 2 nm, this model does not specifically address
the case of single-wall nanotube synthesis.
The main posit underlying the model proposed here
consists of the concurrence of base growth from the nuclei
located on the substrate. From this posit follows that the
concentration of carbon atoms is lower on the sample surface
than in the carbonaceous atmosphere immediately overlying
the sample. During this initial stage of nanotube synthesis,
the tubes grow in random orientation with open tip. The
dangling bonds from the open tip are energetically unstable
until a second particle from the carbonaceous atmosphere
reaches the opened tip of the tube, minimizing the system
free energy. At this occurrence, base growth from the initial
catalyst particles continues and a new synthesis mechanism
Nano Lett., Vol. 4, No. 9, 2004
Figure 6. Diagram representing the proposed model for concurrent
base and tip growth in a catalytically nucleated zigzag single-wall
carbon nanotube (SWCNT).
of tip growth is initiated. The two processes of base and tip
growth continue simultaneously over subsequent iterations
as soon as additional catalyst particles are added to the
nanotube chain. According to this model, after the initial
layer of catalytic particles is deposited on the substrate, each
nanotube is formed by a succession of iterative catalytic steps
that concurrently pyrolize carbon in the upward (in the case
of base growth) and in the downward (in the case of tip
growth) directions (Figure 6).
The models that have been proposed so far to account for
nanotube synthesis rely on catalytic diffusion and on surface
diffusion. The model on catalytic diffusion is sharply
dichotomized into two opposing theories: (i) the theory of
base-growth synthesis of carbon nanotubes and (ii) the theory
of tip-growth synthesis of carbon nanotubes. The proponents
of the base-growth theory argue for a layer of catalytic
nucleants initially deposited on the substrate, which then
initiates nanotube synthesis. Among many authors, the study
by Bower et al. is here considered prototypical of the model
of base growth and of upward catalysis.17 The proponents
of tip-growth theory argue for a positioning of catalytic
particles at the tip of the nanotubes, which then directs carbon
pyrolysis downward. Ren et al., among many authors,
compellingly defend this theory to account for their experimental data.18 The model of surface diffusion, on the
contrary, finds its strongest proponent in Louchev et al.19-22
The combination of base-growth and tip-growth for a
single nanotube structure has been effectively introduced by
Wang et al.,23 by Li et al.,24 and by Chadderton et al.25,26 for
the case of bamboo-like nanotubes. The power of the models
for nanotube synthesis proposed by these authors consists
of its ability to synthesize base growth or tip growth within
the same model, considering the cases of “pure” base-growth
or “pure” tip-growth as limiting cases of an otherwise
continuum variation from a preponderance of base growth
to a preponderance of tip growth, respectively, for successive
catalyst particles. At the same time, the model here proposed
takes into account the surface diffusion model as an
additional route for carbon atoms to become integrated within
the nanotube structure.
Nano Lett., Vol. 4, No. 9, 2004
Conclusions. This study consists of two different approaches to the measurement of carbon nanotube growth
kinetics. One approach consists of the instantaneous measurement of infinitesimal increments of nanotube length via
in situ diffractography. A second approach consists of the a
posteriori measurement of nanotube length via electron
microscopy. The two approaches are in agreement with each
other and are interpreted in the light of concurrent base and
tip growth modes for successive catalytic particles. The dual
nature of nanotube synthesis is confirmed by the double
exponential regression of growth over time.
Based on unpublished experimental results achieved in our
laboratory, for exposure times longer than 45 min, the growth
acceleration evident in Figure 4B is found to cease and the
growth rate is expected to converge on a constant value.
These observations are in accordance with Zhang et al.,27
who document a steady growth rate up to the value of 50
µm/min, for experiments based on the same catalyst and on
the same carbon source used in the present study.28 The
experiment of single-slit diffractography could therefore be
used in future experimental work to ascertain these semiempirical observations.
Additionally, the relative extent of base and tip growth
could be analyzed by comparing standard growth conditions
to the synthesis of nanotubes occurring when an initially high
catalyst concentration is followed by the absence of catalytic
particles in the chamber (i.e., venting of the reactor). The
performance of an experiment of this kind, accompanied by
a thorough transmission electron microscopy study, should
provide evidence of the relative efficiency of base growth
and of the combination of both base- and tip-growth modes.
The importance of the experiments obtained via in situ
studies in the formulation of an accurate theory of nanotube
growth leads one to compare the breakthrough introduced
by this method over preexisting a posteriori techniques to
the radical innovation brought by kinematics over statics in
mechanics. The best use of this methodology in the foreseeable future lies in the precise monitoring of the experimental
conditions for nanotube synthesis at the locus of initial
nucleation, allowing for in situ control of mechanical or
electrical properties of nanotube arrays.
This effort will ultimately allow us to control the chirality
and the defect density for nanotube arrays while they are
being synthesized, delving into the domain of dynamic
control of the synthesis of nanostructured materials.
Acknowledgment. We thank Chang Ryu for the use of
his laser equipment and Robert Vajtai for technical suggestions. This work was supported by Philip Morris USA and
the Nanoscale Science and Engineering Initiative of the
National Science Foundation under NSF Award No. DMR0117702.
Supporting Information Available: A scanning electron
micrograph of multiwall carbon nanotubes. This material is
available free of charge via the Internet at http://pubs.acs.org.
1619
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