Longer Nanotubes at Lower Temperatures: The Influence of Effective

J. Phys. Chem. C 2007, 111, 17705-17712

17705

Longer Nanotubes at Lower Temperatures: The Influence of Effective Activation Energies on Carbon Nanotube Growth by Thermal Chemical Vapor Deposition† Michael J. Bronikowski* Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak GroVe DriVe, Pasadena, California 91109 ReceiVed: February 7, 2007; In Final Form: March 29, 2007

Growth of carbon nanotubes (CNTs) by metal-catalyzed thermal chemical vapor deposition (CVD) upon flat silicon substrates is studied as a function of growth temperature. It is found that the CNT growth rate at a given temperature is constant for a certain amount of growth time, after which growth ceases; the product of the growth rate and the growth time gives the ultimate length of the CNTs. Both the growth rate and the growth time are found to depend on the CVD temperature, and this dependence is such that the ultimate CNT length increases as temperature decreases; that is, longer CNTs can be grown at lower temperatures than at higher temperatures. This surprising and counter-intuitive result reflects the interaction of competing factors affecting the CNT growth: the rate at which carbon is incorporated into growing CNTs versus the rate at which catalytic metal particles become inactive. Both of these rates are found to have an Arrhenius form of temperature dependence, with activation energies of 2.0 and 3.4 eV, respectively, when an Al2O3 diffusion barrier layer is used. These energies are interpreted as “effective” activation barriers arising from activation energy contributions from multiple chemical processes. CNT bundles as long as one millimeter have been grown at a temperature of 600 °C.

1. Introduction Carbon nanotubes (CNTs) have many exceptional properties that make them attractive for a variety of applications. In particular, CNTs have been suggested for a variety of materials applications because of their expected exceptional materials properties including mechanical strength and thermal and electrical conductivity.1 For example, a great deal of previous work has been done to investigate the possibility of incorporating CNTs into materials such as ceramics, metals, and polymers/ plastics in such a way that the outstanding properties of the CNT are transferred to the composite material.2-4 One factor currently limiting the utility of CNTs in materials applications is the limit on the lengths to which CNTs can be currently grown. Ideally, one would wish to be able to grow CNTs to arbitrary lengths, for example, to make CNT-based ropes or fibers with lengths of meters or longer. However, current CNT growth technologies do not yield CNTs with lengths in this range. The longest CNTs reported in the literature are a few centimeters for individual CNTs5 and a few millimeters for dense, continuous mats of CNTs.6-13 Clearly, such length limitations will limit the utility of CNTs for many materials applications. Investigations of the growth of CNT by metal-catalyzed chemical vapor deposition (CVD) have generally found that, under any given conditions, there exists some maximum length to which the CNT can be grown. Detailed studies of CNT length versus growth time generally have shown that, at any given temperature, CNTs grow at an approximately constant rate for a certain amount of time (which depends on CVD conditions), after which growth ceases.10-29 CNT nucleation and growth are generally believed to occur when a catalytic metal sample forms into nanometer-sized particles at elevated temperatures; then, †

Part of the special issue “Richard E. Smalley Memorial Issue”. * Corresponding author. Fax: 001-818-393-4663. E-mail: Michael.J. [email protected].

C2H4 or other carbon feedstock molecules decompose upon these particles to release their carbon atoms. If the particle is in the correct size range, the carbon atoms will form into a cylinder of concentric carbon shells, which grows away from the catalytic particle as a carbon nanotube. CNT growth stops when the catalytic particle becomes inactivated: possible mechanisms for this inactivation include overcoating with carbon and conversion of the metal into a metal carbide or other noncatalytic form. Whatever the mechanism, the cessation of growth after a relatively short time, with corresponding short maximum length of producible CNTs, clearly limits the utility of CNTs in many materials applications. What is needed is an understanding of the mechanism(s) CNT growth cessation, how the maximum growth time and length are affected by process parameters, and ultimately whether the mechanism of growth cessation can be overcome, allowing growth of CNT to arbitrary lengths. In this study, CNT growth, growth rate, and ultimate achievable CNT length have been investigated as a function of CVD reaction temperature. It is found that, at any temperature, CNTs grow at a constant rate (which is denoted F), for a certain length of time (denoted τ), after which growth ceases. Both F and τ depend on temperature, and for a given temperature T, the maximum achievable CNT length (denoted λ) is given by λ(T) ) F(T) × τ(T). It is found that, as T increases, F increases while τ decreases, such that λ(T) is larger at lower temperatures and smaller at higher temperatures. This observation implies a temperature-dependent balance between CNT growth and catalyst particle deactivation which favors longer CNTs at lower temperatures (requiring, however, ever increasing growth time to achieve as temperature decreases). This counter-intuitive result indicates the importance of a detailed understanding of the interactions of multiple processes and parameters in CNT growth and suggests that this type of detailed understanding will eventually lead to the production of CNTs of arbitrary

10.1021/jp071079y CCC: $37.00 © 2007 American Chemical Society Published on Web 06/19/2007

17706 J. Phys. Chem. C, Vol. 111, No. 48, 2007

Bronikowski

length. Dense CNT bundles and mats up to 1 mm in length have been grown in this way, and greater lengths appear possible. 2. Experimental Section The CNT growth procedure has been described in detail elsewhere.14 Briefly, CNTs are grown on catalyst-coated silicon substrates in a tube furnace containing a 2 in. diameter quartz tube, using ethylene (C2H4) as the carbon source gas. CNT growth conditions for this study were: C2H4 flow, 500 sccm; pressure, 200 Torr; temperature, 600-700 °C. Our silicon substrates were photolithographically patterned with a 2.5 nm thick film of e-beam evaporated iron, which serves as a catalyst for CNT growth: CNT will grow upon the substrates only in the areas patterned with iron. Figure 1a shows a scanning electron microscope (SEM) image of an array of bundles of CNTs grown from an array of circular dots of Fe catalyst with dot diameter of 5 µm and edge-to-edge dot spacing of 5 µm. From such catalyst dots, CNTs will grow to form dense bundles. Figure 1b shows a close-up of one nanotube bundle in which the individual nanotubes are visible. Figure 1c,d shows transmission electron microscope (TEM) images of individual CNTs grown using two different types of barrier layer between the iron catalyst and the silicon substrate, Al2O3 and SiO2, respectively. From Figure 1c,d, it is apparent that the CNTs are multiwalled nanotubes; these CNTs have diameters in the range of 10-20 nm, typically, with 5-10 walls. Figure 1c,d also shows that there is no significant difference in the quality of the CNT grown using the two different barrier layers. For these studies, the iron catalyst was patterned in arrays of circular dots with various diameter and edge-to-edge dot separation. The dot size and spacing of the various samples were chosen to cover a wide range of possible CNT feature sizes for different CNT applications: dot sizes were 5 µm (small dot), and 50, 100, 200, and 500 µm (large dots, the final size of 0.5 millimeter essentially is a “continuous” CNT mat of macroscopic size). The 5 µm dots were grown in arrays with a variety of dot spacings, while the larger dots were grown in arrays with the dot spacing set to 1.5 times the dot diameter. Growing CNTs in these bundle arrays rather than as continuous mats allowed easier CNT height measurement using SEM and also readily showed any unevenness in CNT growth across a sample. For convenience, the discussions below will use the notation “(X µm-Y µm) bundles” to refer to bundles of diameter X µm in an array with edge-to-edge bundle spacing of Y µm. The catalyst dot array samples were heated to the selected CVD growth temperature in the quartz tube in flowing argon. Once at the growth temperature, the Ar was shut off, and C2H4 was introduced and flowed for a predetermined time interval. After the growth, the C2H4 was flushed out with argon, and the tube furnace was cooled. The CNT bundles grown on the substrates were examined by SEM to determine the height of the bundles (i.e., the length of the CNT). 3. Results 3.1. CNT Growth Substrate: Barrier Layers. As has been discussed previously,15 attempts to grow CNTs directly upon Si substrates were unsuccessful, probably because of the alloying of the iron catalyst with the underlying Si and consequent deactivation of the catalyst. This problem was solved by using a barrier layer between the iron and the Si surfaces. Two different types of barrier layer were employed, both of which have been described previously.14,15 These were a thick continuous layer of SiO2 (thermal oxide, 400 nm thick14) and a thin

Figure 1. Electron micrographs of carbon nanotube bundles. (a) SEM micrograph of an array of 700 µm tall CNT bundles grown from 5 µm diameter dots of iron catalyst with 5 µm edge-to-edge spacing. (b) Close-up of one nanotube bundle, in which the individual nanotubes are visible. (c) TEM micrograph of individual CNTs grown using Al2O3 barrier layer, showing multiwalled structure (scale bar is 5 nm). (d) CNTs grown using SiO2 barrier layer.

layer of Al2O3 (∼5 nm thick15). The Al2O3 layer was created by evaporating 3 nm of aluminum onto the lithographically patterned Si substrates, then exposing them to air for approximately 10 min to allow the Al to oxidize, after which the

Longer Nanotubes at Lower Temperatures

Figure 2. CNT length vs growth time for CNT bundle arrays grown at 675 °C. (a) Results for CNT grown using 5 nm thick Al2O3 barrier layer from 5 µm diameter catalyst dots with a range of dot separation as indicated. (b) CNT grown using 5 nm thick Al2O3 barrier layer from large (50-500 µm) catalyst dots as indicated. (c) CNT grown using 400 nm thick SiO2 barrier layer from 5 µm diameter catalyst dots. (d) CNT grown using 400 nm thick SiO2 barrier layer from large catalyst dots.

Fe catalyst was deposited. This preparation gives Si surfaces where the Al2O3 layer is present only directly underneath the Fe dots, not over the entire surface, which is desirable for applications requiring electrical contact between substrate and CNT bundles. Both types of barrier layer were found to enable reproducible growth of CNTs on Si wafer surfaces, although the details of the growth differed somewhat for the different barrier layers, as discussed below. 3.2. CNT Growth Versus Time. For all temperatures investigated, CNT bundle arrays were grown on substrates using both barrier layers for a selection of different growth times. The

J. Phys. Chem. C, Vol. 111, No. 48, 2007 17707 pattern observed was the same at all temperatures: CNTs grew at an approximately constant rate for a definite, reproducible interval of time, after which no additional growth occurred. This is the same pattern that has been observed in previous studies10-29 and is shown graphically in Figure 2. Shown here are the measured heights of CNT bundles versus growth time, for CNTs grown in a series of CVD runs carried out at 675 °C in which the growth time was systematically varied. Results for a total of nine different bundle size-spacing array parameters are given for CNTs grown on Si surfaces with each of the two different barrier layers. Figure 2a shows results for CNTs grown using the 5 nm Al2O3 barrier layer, from small (5 µm) catalyst dots with a range of dot separation: (5 µm-2 µm), (5 µm-5 µm), (5 µm-10 µm), (5 µm-20 µm), and (5 µm-50 µm) bundle arrays. Figure 2b shows growth of large CNT bundles using the 5 nm Al2O3 barrier layer: (50 µm-75 µm), (100 µm-200 µm), (200 µm-300 µm), and (500 µm-750 µm) bundle arrays. Figure 2c,d shows the same CNT bundle arrays grown on Si samples using the continuous 400 nm SiO2 barrier layer. Each graph in Figure 2 also shows a linear fit (solid line) to the CNT length-versus-time data for growth times that are short compared with the time required to reach the final length, showing that the growth is approximately linear in time for this time regime. R2 values for this linear fit are as indicated. For all CNT bundles, the results are the same: the CNTs grow at an approximately constant rate for approximately 1 h, after which time growth ceases and the CNT height remains constant despite additional growth time. The CNT growth rate can be computed by averaging the observed growth rate (CNT length/growth time) for growth times that are small compared with the time required to reach the final CNT length. Averaging the growth rate data for times e30 min for all bundle sizespacing arrays grown on the Al2O3 barrier yields a growth rate, denoted F, of 5.2 µm/min at this temperature. Similar averaging for CNTs grown on the SiO2 barrier gives F ) 4.7 µm/min. The final CNT length can be computed by averaging the observed CNT length for growth times that are larger than the time required for growth to cease. Averaging the CNT length data for growth times g60 min for all bundle size-spacing arrays grown on the Al2O3 barrier yields an ultimate CNT length, denoted λ, of 304 µm at this temperature. Similar averaging for CNT bundles grown on SiO2 gives λ ) 307 µm. Observation of a constant growth rate which terminates at a certain given length implies a constant growth time for which the CNTs grow before growth ceases; this time, denoted τ, is just the final length divided by the growth rate. On the Al2O3 barrier, this growth time is determined to be τ ) λ/F ) 58.7 min at this temperature. On SiO2, τ ) 65.9 min. Note that no significant dependence of F, τ, or λ on the size-spacing parameters of the bundle array was observed. 3.3. Dependence of CNT Growth on Temperature. Experiments similar to those described above, carried out at other temperatures, yielded similar results. For example, Figure 3 shows CNT bundle height versus growth time for CNTs grown on the SiO2 surface at 700 °C. Here again, we see growth at an approximately constant rate for a certain growth time, with CNT length constant for longer growth times. As in Figure 2, the solid line shows a linear fit to the length-versus-time data for growth times small compared with τ, with R2 for this fit as indicated. Once again, no dependence of F, τ, or λ on the array size-spacing parameters was found. Importantly, it was observed that F, τ, and λ all varied as the temperature was varied. This is illustrated graphically in Figure 4, which shows a comparison between observed CNT length (averaged over all nine investigated size-spacing arrays) versus time for CNTs grown on the

17708 J. Phys. Chem. C, Vol. 111, No. 48, 2007

Bronikowski

Figure 3. CNT length vs growth time for CNT bundle arrays grown at 700 °C on SiO2 layer from large catalyst dots.

Figure 4. Observed CNT length, averaged over all nine investigated size-spacing arrays, vs time for CNT grown on Al2O3 layer at 675 and 700 °C.

Al2O3 surface at 675 °C and at 700 °C. CNT length increases more rapidly with time at 700 °C than at 675 °C [F(675 °C) < F(700 °C)], but growth also stops sooner at 700 °C [τ(675 °C) > τ(700 °C)], and the relationship is such that the final length achieved by the CNT is greater at 675 °C than at 700 °C [λ(675 °C) > λ(700 °C)]. These trends were followed generally as the growth temperature was varied. CNT growth was studied at a number of temperatures between 600 and 700 °C, and in all cases, the CNT growth curve versus time was observed to be of the same form as in Figures 2-4, that is, well-characterized by the parameters F, τ, and λ. These parameters were found to depend generally on temperature in the same manner as described above: F decreases with decreasing temperature but τ and λ both increase with decreasing temperature. For example, Figure 5 shows CNT length versus time for several size-spacing arrays for CNTs grown on a substrate with an Al2O3 barrier layer at temperatures of 600, 625, and 650 °C. The above trends are readily discerned in this figure. Note that at all temperatures CNT growth is observed to be linear in time even for very short growth times: the curve of CNT length-versus-growth time passes approximately through the origin (zero growth at zero time), with no delay between “turn-on” of growth conditions (introduction of ethylene) and start of CNT growth. This implies that the formation of the catalytic particles and nucleation of CNTs occur very quickly on the time scale of these experiments. It may also be that the formation of metal particles occurs during the heating period in argon and is already completed by the time ethylene is introduced. The global maximum CNT length observed was approximately 1mm (1000 µm), achieved at 600 °C, the lowest temperature at which growth was carried out in this study. This length is reached after approximately 26 h of CVD growth time. Figure 6 shows examples of millimeter-long CNT bundles grown at 600 °C. Table 1 summarizes the measured values of F, τ, and λ at all temperatures investigated, for Si substrates with both the Al2O3 and the SiO2 barrier layers. Figure 7 shows the values of F, τ, and λ plotted versus temperature for both barrier layer types;

Figure 5. CNT length vs time for CNT grown on Al2O3 layer at 600, 625, and 650 °C. (a) 5-50 µm CNT bundle arrays. (b) 500-750 µm CNT bundle arrays.

Figure 6. Millimeter long CNT bundles grown on Al2O3 layer at 600 °C. (a) 5-50 µm CNT bundle array. (b) 500-750 µm CNT bundle array.

in these plots, the F, τ, and λ values have been normalized relative to the maximum values observed for the respective barrier type, for ease of comparison. The data and graph for

Longer Nanotubes at Lower Temperatures

J. Phys. Chem. C, Vol. 111, No. 48, 2007 17709

Figure 7. Relative values of CNT growth rate (F), growth time (τ), and final length (λ) vs temperature. (a) CNT growth on Al2O3 layer. (b) CNT growth on SiO2 layer.

TABLE 1: Measured G, τ, and λ Values at Various Temperatures

Figure 8. Arrhenius plots, ln(rate) vs 1/T, for the CNT growth rate F and catalytic particle deactivation rate Fd ) 1/τ. (a) CNT growth on Al2O3 layer. (b) CNT growth on SiO2 layer.

TABLE 2: Activation Energies for CNT Growth and Growth Cessation barrier layer

∆Eg (eV)

∆Ed (eV)

Al2O3/Si SiO2/Si

2.00 2.16

3.40 2.08

Al2O3 barrier T (°C)

F (µm/min.)

τ (min.)

λ (µm)

600 625 650 675 700

0.64 1.33 3.50 5.18 9.89

1550 600 129 58.7 14.7

1000 800 450 304 145

temperature; this rate could, for example, represent an average rate at which catalytic particles become deactivated. The exponential temperature dependence of the rates of both CNT growth and growth cessation suggests an Arrhenius form for this temperature dependence:

R ) ARe(-∆E/kT)

SiO2 barrier T (°C)

F (µm/min.)

τ (min.)

λ (µm)

600 625 650 675 700

0.50 1.17 3.50 4.66 9.96

400 348 129 65.9 25.8

200 400 450 307 257

the Al2O3 barrier suggest that F and τ vary approximately exponentially with temperature: as temperature decreases from 700 to 600 °C, F decreases by approximately a factor of 2 for every 25 °C interval while τ increases by approximately a factor of 3 over every such interval (the exact values, obtained by averaging the ratios of the data in Table 1, are 1.94 and 3.34, respectively). Because the growth time τ increases faster than the growth rate F decreases, the final CNT length λ increases as temperature decreases by approximately a factor of 3/2 ) 1.5 for every 25 °C decrease over the entire investigated temperature range (exact average value from Table 1 is 1.65). The behavior of the F, τ, and λ parameters is qualitatively similar but quantitatively different for CNTs grown on the SiO2 barrier layer. In this case, as above, F decreases and τ increases with decreasing temperature. However, here the increase in τ is not great enough to offset the decrease in F below 650 °C, so the ultimate length λ decreases for temperatures below 650 °C. On the SiO2 barrier layer, there is thus a global maximum in achievable CNT length, 450 µm, which is achieved at 650 °C. The growth time τ can be interpreted as a growth cessation rate, defined as Fd ) 1/τ, which increases with increasing

(1)

In this equation, the parameter ∆E is the activation energy, or activation barrier, for the chemical process in question. The parameter AR is the pre-exponential factor for the rate R, and corresponds roughly to the “attempt frequency” for the reactive system to overcome the reaction barrier. The factors influencing this parameter depend on the details of the reaction and can include such numbers as the concentration of reactive species, their velocities and collision rates, the characteristic frequencies of the vibrational modes of the reactive complex, and the entropy of activation for the reaction. Figure 8 shows Arrhenius plots (ln(R) vs 1/T) for F and for Fd ) 1/τ; the slope of the line in such a plot gives the activation energy ∆E. Table 2 shows the results for the derived activation energies for CNT growth (∆Eg) and particle deactivation (∆Ed) for growth on both the Al2O3 and the SiO2 barrier layers. Equation 1 also implies an ultimate CNT length λ given by:

λ ) Fτ ) F/Fd ) Age(-∆Eg/kT)/Ade(-∆Ed/kT) ) Aλe(∆Ed-∆Eg)/kT (2) If the energy difference in the exponent ∆Ed - ∆Eg is negative, λ will increase with increasing temperature T, while a positive energy difference will imply that λ decreases as T increases. 4. Discussion Both CNT growth and growth cessation depend on a number of different processes, such as decomposition of the carbon

17710 J. Phys. Chem. C, Vol. 111, No. 48, 2007 feedstock molecules upon the catalyst, diffusion of carbon atoms to the edge of the growing CNT (either through the metal particle or on its surface), and formation of a carbon overcoating on the particle’s surface. Each process will have its own rate constant and activation energy ∆Eact. The F, τ, and λ parameters that characterize the growth will depend on the relative rates of these various processes and hence on the various ∆Eact values. Equation 2 shows that, even if growth and growth cessation rates are determined by ∆Eact values from only a single process, the ultimate length depends on the ∆Eact values from multiple processes. However, as discussed below, it is more likely that even the rates of growth and growth cessation depend on multiple processes and thus that the derived ∆Eact values for F and Fd are in fact “effective activation energies” consisting of sums of energy contributions from multiple processes. Previous investigations of the dependence of CNT growth rate on temperature have allowed a number of groups to measure the activation energy for the growth of CNTs by catalytic thermal CVD.12,30-35 It should be noted that all of these studies used acetylene, C2H2, as the carbon source gas, rather than ethylene. Most of these groups30-35 measured activation energies for CNT growth in the range of 1.2-1.6 eV, substantially less than the current result of 2.0-2.2 eV but close to the measured activation energy for diffusion of carbon in bulk (γ phase) iron, 1.52 eV.34 ,36 These groups concluded that the growth of CNTs was limited by the diffusion of carbon through the catalytic particle and ascribed the observed activation energy to the barrier for this carbon diffusion. On the other hand, Puretzky et al.12 estimated an activation energy of 2 eV for CNT growth by thermal CVD using C2H2 over an iron catalyst, in agreement with the current results. Puretzky et al. also reported the dependence of CNT terminal length and growth time on temperature. They found that both λ and τ increase with increasing temperature for temperatures between 575 and 700 °C, in contrast to the decreasing λ and τ found in the present work. Puretzky et al.12 developed a detailed kinetic model of CNT growth and growth termination based on various chemical processes believed to occur in CNT growth. From their kinetic equations, they derived expressions for growth rate, growth time, and ultimate length that were proportional to products and ratios of the rate constants for various processes, where each rate constant had temperature dependence in the form of eq 1. Thus, the temperature dependences of F, τ, and λ were characterized by “effective” activation energies that were the sums and differences of activation energies of various processes. For example, for 575 °C < T < 700 °C, the ultimate length λ was determined to be proportional to ksb/kcl, where ksb and kcl are the rate constants for the surface-to-bulk penetration of C atoms into the Fe particle and for the formation of a carbonaceous overcoating layer upon the particle (which stops the growth of the CNT), respectively. Thus, the temperature dependence of λ was given by λ ) Aλ exp(-(Esb - Ecl)/kT), where Esb and Ecl are activation energies for the respective processes. The positive temperature dependence of λ led Puretzky et al. to conclude that Esb > Ecl, and from their data, they derived a value of Esb ) 2.2 eV in the limit Esb . Ecl. Similarly, their kinetic model predicted a growth time τ proportional to ksb/(kcl × Fcl) or equivalently a growth cessation rate Fd proportional to (kcl × Fcl)/ksb, where Fcl is the flux of carbon-containing molecules onto the surface of the catalytic particle. Fcl had temperature dependence Fc1 ) A exp(-(Ea1)/kT), with Ea1 giving the activation barrier for sticking and catalytic decomposition of the feedstock molecules. Thus, τ has the form τ ) Aτ exp(-

Bronikowski (Esb - Ecl - Ea1)/kT). The “effective activation energies” for τ and λ in these equations are thus the sums of contributions from various processes. Note that this effective activation energy sum can be negative in value: Puretzky et al. observe that growth time increases, and hence, growth cessation rate Fd decreases with increasing temperature. This implies a negative effective activation barrier for the growth cessation rate, that is, a positive exponent in eq 1. In a similar vein, a separate model by Kamachali37 predicts a CNT growth rate with an effective activation barrier equal to the sum of the activation energies for carbon dissolution in and diffusion through iron. Using literature values for these numbers,38 ,39 Kamachali predicts an effective activation barrier for CNT growth of 1.9 eV, which is in reasonable agreement with the values measured in this work and by Puretzky et al.12 The dependence of the effective activation barriers for F, τ, and λ on contributions from multiple processes is further suggested by the magnitude of the values derived in Table 2, which are larger than ∆Eact values for typical chemical processes. In particular, a value of 3.4 eV for the deactivation rate upon Al2O3 seems anomalously large for an activation barrier for any single chemical process. Processes associated with CNT growth typically have substantially smaller energy barriers: for example, hydrocarbons like ethylene and acetylene dissociatively adsorb upon iron surfaces with activation energies on the order of 0.87 eV,40 while the energy barriers for carbon surface and bulk diffusion in first row transition metals are on the order of 0.3 eV41and 1.5 eV,36 respectively. Thus, contributions from multiple chemical processes appear necessary to explain the observed effective activation energies of Table 2. The fact that no one reaction or rate governs CNT growth implies that a much better understanding of the processes involved will be necessary in order to fully control this growth. Nevertheless, currently available models do provide some insight into the mechanisms that control CNT growth. The kinetic model of Kamachali37 predicts a CNT growth activation barrier very close to the observed barrier and explains this barrier as the sum of the activation energies for carbon dissolution in and diffusion through the metal catalyst. The model of Puretzky et al.12 predicts a final CNT length proportional to the exponential of the difference in the activation energies for C atom dissolution into the particle and C atom attachment to a growing carbonaceous overcoat. From their observed increase of λ with temperature, Puretzky et al. concluded that the former was greater than the latter. In the current system, however, λ decreases as temperature increases, suggesting that in this case the barrier for formation of an overcoating on a particle is greater than the barrier for carbon dissolution into the particle. This difference between these results and those of Puretzky et al. could arise because of the different feedstock gases used (ethylene vs acetylene) or because of differences in the catalyst: Puretzky et al. used a catalyst containing 17% Mo in addition to Fe, which could lower the barrier for formation of the overcoating relative to the barrier for dissolution. The current results for the two different types of barrier layer also provide insight into the CNT growth process. The effective activation energy for CNT growth is approximately the same on the two surfaces, suggesting that interaction of the C2H4 feedstock molecules with the substrate surface independent of the catalytic particle is not important in the growth of CNTs. On the other hand, the effective energy barrier for catalyst particle deactivation is much greater on Al2O3 than on SiO2. This result indicates substantial differences in the chemistry of catalyst deactivation on the two surfaces. The main difference

Longer Nanotubes at Lower Temperatures between the general chemistries of these two materials is that SiO2 is much more easily reduced (to SiO or Si) than Al2O3 is reduced to the corresponding sub-oxides of aluminum. Specifically, SiO2 is more reactive than Al2O3 with respect to reducing agents like hydrogen, carbon, and hydrocarbons; for example, H2 reduction of SiO2 occurs at a much lower temperature than H2 reduction of Al2O3, 1000 versus 2000 °C.42 Thus, one possible explanation for the difference in catalyst deactivation barriers is that the SiO2 surface interacts much more strongly with C2H4 molecules or their decomposition products than the Al2O3 surface. The complete encapsulation of a surface-bound catalytic particle within a shell of carbon might therefore be a much more facile process (with lower activation barrier) on SiO2 than on Al2O3. Alternately, if catalyst particle deactivation occurs through the loss of Fe atoms by the catalyst particle because of surface diffusion (i.e., atoms from the catalyst particle become bound directly to the substrate and then diffuse away from the particle, which thereby slowly shrinks over time), the more easily reduced SiO2 would bind much more readily to atoms of elemental Fe than would the less-reactive Al2O3 surface, thereby facilitating this catalyst deactivation mechanism. For the case of the Al2O3 layer, the effective energy barrier for particle deactivation is substantially larger than that for CNT growth, hence the monotonic increase in λ with decreasing temperature given by eq 2 and observed in Figure 7. For SiO2, it is found that ∆Ed and ∆Eg are approximately equal, implying an approximately zero exponent in eq 2 and only a weak dependence of λ on temperature. Figure 7 shows that, to a low order of approximation, this is correct: λ varies by only a factor of 2 over the studied temperature range for SiO2, versus a factor of 7 over the same range on Al2O3. However, eq 2 predicts a monotonic dependence of λ on T and fails to predict any maximum in λ versus T of the sort observed in Figure 7b for SiO2. The real temperature dependence of the reaction rates is evidently more complex than the simple form given in eq 1. It is interesting to speculate on how long CNTs could be grown upon the Al2O3 barrier layer. For example, extrapolating Figure 7 down to a temperature of 500 °C predicts 5 mm long CNTs, achieved after a growth time of 2095 h (87.3 days). Clearly, CNT growth times will become prohibitively long for growing extremely long CNTs on this surface. What is more likely, however, is that λ reaches a global maximum upon Al2O3 at some temperature below 600 °C, as occurs at 650 °C on SiO2. Indeed, there is some evidence that this maximum is already being approached at 600 °C: the value of λ on Al2O3 changes by only a factor of 1.25 between 625 and 600 °C, rather than the average ratio of 1.6 per 25 °, so growth at 600 °C may already be approaching the maximum in CNT length achievable on Al2O3. Nevertheless, the temperature dependences of the F, τ, and λ parameters can help to illuminate the mechanisms by which CNTs grow on surfaces and the mechanisms by which this growth ceases. If the mechanism of growth cessation can be better understood, it should even be possible to grow CNTs to arbitrary lengths. Investigations into this possibility are ongoing in this laboratory. 5. Conclusions CNT growth by metal-catalyzed thermal CVD has been studied on Si substrates coated with barrier layers of Al2O3 and SiO2. CNT growth rates, growth times, and ultimate lengths have been investigated as a function of temperature on these surfaces. It was found that, at all temperatures, CNTs grow at an approximately constant rate to a certain ultimate length, after

J. Phys. Chem. C, Vol. 111, No. 48, 2007 17711 which growth ceases. The growth rate, growth time, and ultimate CNT length all depend on temperature. Consideration of the dependence of these parameters on temperature implies that ultimate achievable CNT length is dictated by a competition between faster CNT growth and faster catalyst particle deactivation as temperature increases. This temperature dependence is such that longer CNTs can actually be grown at lower temperatures than at higher temperatures on these substrates: the longest CNTs achieved were grown on the Al2O3 barrier layer at 600 °C, reaching 1 mm in length after approximately 26 h of growth time. Activation energies were derived for the rates of CNT growth and growth cessation. These energies were found to be approximately equal on SiO2 but to differ substantially on Al2O3 and are interpreted as “effective” activation energy barriers that arise because of contributions from multiple processes involved in nanotube growth and growth cessation. Acknowledgment. This research was carried out at the Jet Propulsion Laboratory (JPL), California Institute of Technology, under a contract with the National Aeronautics and Space Administration (NASA). This work was funded by JPL’s Research and Technology Development Fund. The author thanks the following individuals (all from JPL) for their assistance with this work: E. Wong, H. Manohara, and B. Hunt for discussions in the analysis of these data and preparation of this manuscript; E. Luong for assistance in preparation of sample substrates; and C. M. Garland of the California Institute of Technology for TEM imaging. References and Notes (1) Baughman, R. H.; Zakhidov, A. A.; de Heer, W. A. Science 2002, 297, 787. (2) Ishikawa, T. AdV. Compos. Mater. 2006, 15, 3. (3) Coleman, J. N.; Khan, U.; Blau, W. J.; Gun’ko, Y. K. Carbon 2006, 44, 1624. (4) Lau, K. T.; Gu, C.; Hui, D. Composites, Part B 2006, 37, 425. (5) Zheng, L. X.; O’Connell, M. J.; Doorn, S. K.; Liao, X. Z.; Zhao, Y. H.; Akhadov, X. E. A.; Hoffbauer, M. A.; Roop, B. J.; Jia, Q. X.; Dye, R. C.; Peterson, D. E.; Huang, S. M.; Liu, J.; Zhu, Y. T. Nat. Mater. 2004, 3, 673. (6) Deck, C. P.; Vecchio, K. Carbon 2006, 44, 267. (7) Hata, K.; Futaba, D. N.; Mizuno, K.; Namai, T.; Yumura, M.; Iijima, S. Science 2004, 306, 1362. (8) Christen, H. M.; Puretzky, A. A.; Cui, H.; Belay, K.; Fleming, P. H.; Geohegan, D. B.; Lowndes, D. H. Nano Lett. 2004, 4, 1939. (9) Eres, G.; Puretzky, A. A.; Geohegan, D. B.; Cui, H. Appl. Phys. Lett. 2004, 84, 1759. (10) Xiong, G. Y.; Wang, D. Z.; Ren, Z. F. Carbon 2006, 44, 969. (11) Yun, Y. H.; Shanov, V.; Tu, Y.; Subramaniam, S.; Schulz, M. J. J. Phys. Chem. B 2006, 110, 23920. (12) Puretzky, A. A.; Geohegan, D. B.; Jesse, S.; Ivanov, I. N.; Eres, G. Appl. Phys. A 2005, 81, 223. (13) Li, Q. W.; Zhang, X. F.; DePaula, R. F.; Zheng, L. X.; Zhao, Y. H.; Stan, L.; Holesinger, T. G.; Arendt, P. N.; Peterson, D. E.; Zhu, Y. T. T. AdV. Mater. 2006, 18, 3160. (14) Bronikowski, M. J. Carbon 2006, 44, 2822. (15) Bronikowski, M. J.; Manohara, H. M.; Hunt, B. D. J. Vac. Sci. Technol., A 2006, 24, 1318. (16) Futaba, D. N.; Hata, K.; Yamada, T.; Mizuno, K.; Yumura, M.; Iijima, S. Phys. ReV. Lett. 2005, 95. (17) Cassell, A. M.; Raymakers, J. A.; Kong, J.; Dai, H. J. J. Phys. Chem. B 1999, 103, 6484. (18) Hafner, J. H.; Bronikowski, M. J.; Azamian, B. R.; Nikolaev, P.; Rinzler, A. G.; Colbert, D. T.; Smith, K. A.; Smalley, R. E. Chem. Phys. Lett. 1998, 296, 195. (19) Venegoni, D.; Serp, P.; Feurer, R.; Kihn, Y.; Vahlas, C.; Kalck, P. Carbon 2002, 40, 1799. (20) Magrez, A.; Seo, J. W.; Miko, C.; Hernadi, K.; Forro, L. J. Phys. Chem. B 2005, 109, 10087. (21) Singh, C.; Shaffer, M. S.; Windle, A. H. Carbon 2003, 41, 359. (22) Morjan, R. E.; Maltsev, V.; Nerushev, O.; Yao, Y.; Falk, L. K. L.; Campbell, E. E. B. Chem. Phys. Lett. 2004, 383, 385.

17712 J. Phys. Chem. C, Vol. 111, No. 48, 2007 (23) Cui, H.; Eres, G.; Howe, J. Y.; Puretkzy, A.; Varela, M.; Geohegan, D. B.; Lowndes, D. H. Chem. Phys. Lett. 2003, 374, 222. (24) De Zhang, W.; Wen, Y.; Liu, S. M.; Tjiu, W. C.; Xu, G. Q.; Gan, L. M. Carbon 2002, 40, 1981. (25) Andrews, R.; Jacques, D.; Qian, D. L.; Rantell, T. Acc. Chem. Res. 2002, 35, 1008. (26) Chakrabarti, S.; Nagasaka, T.; Yoshikawa, Y.; Pan, L. J.; Nakayama, Y. Jpn. J. App. Phys., Part 2 2006, 45, L720. (27) Lin, M.; Tan, J. P. Y.; Boothroyd, C.; Loh, K. P.; Tok, E. S.; Foo, Y. L. Nano Lett. 2006, 6, 449. (28) Zhao, N. Q.; He, C. N.; Jiang, Z. Y.; Li, J. J.; Li, Y. D. Mater. Lett. 2006, 60, 159. (29) Zhu, L. B.; Hess, D. W.; Wong, C. P. J. Phys. Chem. B 2006, 110, 5445. (30) Kim, K. E.; Kim, K. J.; Jung, W. S.; Bae, S. Y.; Park, J.; Choi, J.; Choo, J. Chem. Phys. Lett. 2005, 401, 459. (31) Liu, K.; Jiang, K. L.; Feng, C.; Chen, Z.; Fan, S. S. Carbon 2005, 43, 2850.

Bronikowski (32) Ducati, C.; Alexandrou, I.; Chhowalla, M.; Amaratunga, G. A. J.; Robertson, J. J. Appl. Phys. 2002, 92, 3299. (33) Lee, Y. T.; Park, J.; Choi, Y. S.; Ryu, H.; Lee, H. J. J. Phys. Chem. B 2002, 106, 7614. (34) Baker, R. T. K. Carbon 1989, 27, 315. (35) Baker, R. T. R.; Harris, P. S. The formation of filamentous carbon. In Chemistry and Physics of Carbon; Walker, P. L., Thrower, P. A., Eds.; Marcel Dekker: New York, 1978; Vol. 14; p 83. (36) Smithells, C. J. In Smithells Metals Reference Book; 7 ed.; Brandes, E. A., Brook, G. B., Eds.; Butterworth-Heinemann Ltd.: London, 1992. (37) Kamachali, R. D. Chem. Phys. 2006, 327, 434. (38) Wert, C. A. Phys. ReV. 1950, 79, 601. (39) Klinke, C.; Bonard, J. M.; Kern, K. Phys. ReV. B 2005, 71. (40) Anderson, A. B. J. Am. Chem. Soc. 1977, 99, 696. (41) Mojica, J. F.; Levenson, L. L. Surf. Sci. 1976, 59, 447. (42) Schaefer, H. Chemical Transport Reactions; Academic Press: New York, 1964.