Kinetics for the Synthesis Reaction of Aligned Carbon Nanotubes: A

Aug 21, 2004 - Scanning electron microscopy confirms the diffractographic data at a high level of precision. The innovation brought by this in situ me...
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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 Published on Web 08/21/2004

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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 Rˆ ) 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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