J. Phys. Chem. B 2005, 109, 12337-12346
12337
Carbon Nanotube Formation and Growth via Particle-Particle Interaction Murray J. Height,†,§ Jack B. Howard,*,† Jefferson W. Tester,† and John B. Vander Sande‡ Department of Chemical Engineering and Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts AVenue, Cambridge, Massachusetts 02139-4307 ReceiVed: September 3, 2004; In Final Form: February 4, 2005
Carbon nanotubes are observed to form under a wide range of temperatures, pressures, reactive agents, and catalyst metals. In this paper we attempt to rationalize this body of observations reported in the literature in terms of fundamental processes driving nanotube formation. Many of the observed effects can be attributed to the interaction of three key processes: surface catalysis and deposition of carbon, diffusive transport of carbon, and precipitation effects. A new nanotube formation mechanism is proposed that describes the nanotube structures observed experimentally in a premixed flame and can account for certain shortcomings of the prevailing mechanism that has been repeatedly applied to explain nanotube formation in nonflame environments. The interacting particle model (IPM) attributes the initiation of nanotube growth to the physical interaction between catalyst particles. Coalescence of two (or more) catalyst particles leads to partial blocking of the particle surface, causing a disparity in carbon deposition over the particle surface. The resulting concentration gradient generates a net diffusive flux toward the interparticle contact point. Dimers that separate in this condition can support continuous nanotube growth between the particles. The model can also be extended to multiple particles to account for more complex morphologies. The IPM is consistent with many of the structures observed in the flame-produced material. The validity of the model is evaluated through analysis of diffusion dynamics and a force analysis of particle binding and separation. The IPM is also discussed in relation to identifying the requirements and best conditions to support nanotube growth in the premixed flame. The formation of nanotubes between particles as described by the IPM indicates that a single mechanism cannot completely describe nanotube synthesis; more likely, multiple pathways exist with varying rates that depend on specific process conditions.
Introduction Carbon nanotubes, by virtue of their curved graphitic structure, small diameter (1 nm to e 100 nm), and high aspect ratio, possess many appealing properties including semiconducting or metallic electrical behavior, high mechanical strength, and interesting chemical and surface properties. Potential applications include mechanical actuators,1 electronics,2 catalysis,3 sensors,4 high-strength composites,5 and adsorbents.6 Many techniques have been developed for nanotube synthesis including plasma-arc,7 laser ablation,8 chemical vapor deposition (CVD),9 fluidized bed reactors,10 and combustion synthesis.11,12 Despite the wide range of both synthesis techniques and conditions, there are three common elements required to form carbon nanotubes in most processes: (1) a source of carbon, (2) a source of heat to give an appropriate temperature, and (3) the presence of certain metals. The mechanism for how these components interact is understood to be a dissociation-diffusionprecipitation process where elemental carbon is formed on the surface of a metal particle followed by diffusion and precipitation in the form of cylindrical graphite (Figure 1). The effect of various process parameters on nanotube growth has been studied extensively in the literature and these observations provide additional insight into the mechanism of nanotube growth. The first part of this paper examines many of the key * Corresponding author. E-mail:
[email protected]. † Department of Chemical Engineering. ‡ Department of Materials Science and Engineering. § Present address: Particle Technology Laboratory, Institute of Process Engineering, ETH Zu¨rich, Sonneggstrasse 3, CH-8092 Zu¨rich, Switzerland.
Figure 1. Illustration of the nanotube formation mechanism showing the consecutive dissociation (1), diffusion (2), and precipitation (3) steps. Adapted from Amelinckx et al.13
parameters influencing nanotube growth as identified in the literature and discusses these observations in relation to the underlying growth mechanism. The second part of the paper proposes a new formation mechanism that accounts for the formation of nanotubes within the flame environment. Influence of Temperature. Temperature has significant influence on nanotube formation and growth. Carbon nanotubes have been observed to form at temperatures from 400 °C14 to 3600 °C,15 with many different synthesis techniques operating in temperature intervals within this broad range. Multiwalled nanotubes (MWNT) are generally favored at temperatures between 500 to 1000 °C while single-walled nanotubes (SWNT) tend to be found at higher temperatures (above 900 °C), although Hornyak et al.16 observed SWNTs to form between 680 °C to 850 °C in a CVD system. Lee and co-workers17 examined the temperature dependence of nanotube growth from 800 °C to
10.1021/jp046021n CCC: $30.25 © 2005 American Chemical Society Published on Web 06/02/2005
12338 J. Phys. Chem. B, Vol. 109, No. 25, 2005 1100 °C and observed an increase of multiwalled nanotube diameter and growth rate with increasing temperature. Lee et al. also estimated the activation energy for nanotube growth as 30 kcal/mol and attributed increasing growth rates to an increased rate of bulk diffusion of carbon in the metal catalyst particle. Influence of Pressure. The effect of pressure on nanotube growth has not been examined in great detail as the bulk of nanotube literature presents studies conducted at ambient pressures. Nonetheless, a few studies report the formation of nanotubes at both sub-atmospheric and high-pressures. For example, the HiPCO (high-pressure carbon monoxide) process uses carbon monoxide pressures of 30 to 50 atm and temperatures between 900 and 1100 °C.18 Higher SWNT yields are generally attributed to enhanced catalytic disproportionation of CO (Boudouard reaction) at higher pressures. Smaller nanotube diameters were also observed at higher pressures.19 Li and coworkers20 studied the variation in morphology for nanotubes synthesized by a CVD technique operated at pressures between 0.6 and 760 Torr and observed nanotube yield to increase with increasing pressure. The influence decreased at pressures above 600 Torr coupled with an increasing proportion of bambootype morphologies. Shi et al.21 operated a plasma-arc process at two atmospheres pressure and observed an enhanced yield of nanotubes. Maser and co-workers22 examined the formation of plasma-arc-derived SWNTs at pressures between 400 and 100 Torr and observed a drop-off of nanotube formation below 100 Torr where amorphous carbon was favored. The source of this influence was attributed to heat transfer effects in the experiment. Saito and co-workers23 varied the helium pressure in a plasma-arc process between 50 and 1520 Torr and observed an increase in nanotube diameter from 1.0 to 1.4 nm as pressure increased, an effect they also attributed to increasing local temperature at higher pressures. Influence of Gas Composition. Carbon nanotubes have been observed to form from numerous sources of carbon. The most commonly reported compounds include CO,19 hydrocarbons such as CH4,24 C2H2,25 C6H6,26 and C8H10.9 Nanotubes have also been observed to form from sources of elemental carbon such as fullerenes27 and carbon black.28,29 Safvi and co-workers30 recognized that the growth rate of carbon filaments from metal catalysts is linearly proportional to the gas-phase carbon activity and proposed a model to account for nanotube growth. Favorable conditions for nanotube growth for each carbon source compound are highly dependent on the associated temperature, pressure, co-reactant species, and choice of catalyst metal. The wide range of reactant mixtures corresponding to specific temperatures, pressures, and catalyst metals reported in the literature reflect the multidimensionality of the nanotube formation parameter space. Influence of Additives. Carbon nanotube formation is sensitive to the presence of hydrogen. Bladh et al.31 investigated the effect of hydrogen content in a reactant mixture of C2H2, CO, and Fe(CO)5 using a floating catalyst CVD technique operated between 700 and 1000 °C. An increase in SWNT yield was observed with increasing hydrogen concentration. The proposed source of this effect is an increased rate of CO dissociation due to hydrogenation, or a catalytic influence of the coadsorbed hydrogen on CO disproportionation. Herreyre and Gadelle32 report hydrogen concentrations as low as 0.2% to be capable of inducing filament morphologies and proposed that the hydrogen could “clean” the metal surface via conversion of coke to methane, or could act more directly by modifying the carbon/metal interaction or metal lattice restructuring.
Height et al. Alternatively, Nolan et al.33 assert that hydrogen plays a crucial role in satisfying the valences (stabilizing “dangling bonds”) at the free edge of graphite planes. The observation of clean, openended nanotubes in a hydrogen arc-discharge process by Wang et al.34 tends to support the stabilizing influence of hydrogen. A similar stabilizing influence is observed with bonds derived from inclusion of alcohol with the reactant stream.35 Bethune36 reports a dramatic increase (up to an order of magnitude) in SWNT production efficiency with the addition of sulfur (or bismuth) to a plasma-arc process using a cobalt catalyst. A broadening of nanotube diameter distribution was observed when using sulfur, bismuth, and also lead additives. Cheng et al.,26 using a floating catalyst technique based on iron metal, benzene, and hydrogen gases, and temperatures of 1100 °C to 1200 °C, report a SWNT promoting effect of adding thiophene (0.5-5 wt %). Sulfur is generally attributed to impart a stabilizing influence on dangling graphitic bonds, while Alvarez et al.37 also suggest that sulfur may enhance nanotube growth by lowering the eutectic temperature of the metal/carbon mixture in the catalyst particle. The presence of nitrogen can induce a number of interesting effects on nanotube growth. Choi et al.38 co-injected ammonia with acetylene using a CVD technique with nickel metal catalyst and temperatures between 600 and 950 °C and observed a marked increase in nanotube alignment. Inhibition of amorphous carbon was the suggested mechanism for this effect. Jung and co-workers39 attributed the growth of aligned nanotubes to the interaction of NH3 with the catalyst surface and suggest that free nitrogen atoms enhance formation of graphitic carbon and also improve separation kinetics of the graphitic layer from the surface. Lee et al.40 observed the formation of “bamboo” structures with internal compartments during pyrolysis of ammonia, iron pentacarbonyl, and acetylene mixtures between 750 and 950 °C. Influence of Catalyst Metal. Although multiwalled nanotubes have been reported to form both with and without the presence of metals, the synthesis of single-walled nanotubes requires the use of catalyst metals. Numerous metals have been identified as catalysts capable of forming single-walled nanotubes, with the most commonly used metals being iron,19 nickel,41 and cobalt.42 Other metals that have also found use include molybdenum,43 rhodium, platinum,23 vanadium,44 yttrium,45 magnesium,46 tungsten,47 and copper;48 however, these metals are generally used in conjunction with Fe, Ni, or Co. Nanotubes have also been observed to form from other metalbased structures such as Fe2O3,49 Fe-Al2O3,50 and LaFeO3.51 Greatly improved yields of nanotubes have been observed for mixtures of catalysts such as Fe/Ni and Co/Ni.46 Nanotube crystallinity, chirality, diameter, and growth rate are all influenced by the type of metal catalyst employed.52 Different substrates for catalyst particle support have also been examined with catalyst particles in surface deposition CVD studies, with typical substrates including quartz,9 silica, zeolites and alumina.53 The effectiveness of various catalysts for nanotube synthesis is a function of temperature, pressure, gas-phase composition, substrate type, catalyst composition, and particle size. The optimal catalyst choice under one set of experimental conditions may therefore be ineffective at different conditions. Influence of Particle Size. The size of the catalyst particles is often cited as a having a large influence on the nature of synthesized nanotubes. Li and co-workers49 synthesized Fe2O3 particles with well-defined diameter distribution between 1 and 5 nm and observed close correlation of nanotube diameter to catalyst particle size during CVD synthesis in CH4/H2 at 900
CNT Formation and Growth via Particle-Particle Interaction
J. Phys. Chem. B, Vol. 109, No. 25, 2005 12339
°C supported on SiO2. The structures were observed to have a closed-cap on the growing tip of the tubes, indicating a basegrowth mechanism with the particle diameter governing the diameter of the associated nanotube. Dal et al.54 observed close correlation between catalyst particle diameter and associated nanotube diameter, and proposed the “yarmulke” mechanism to account for this growth, where a graphitic cap, with size determined by the particle diameter, breaks off the surface and a nanotube forms in the wake of the cap. Wang et al.45 report that, for a plasma-arc process using Y/Ni catalyst, the concentration of catalyst influences the yield of nanotubes but has little effect on nanotube diameter, indicating to some extent an independence of nanotube properties from particle size, although there is no direct measurement of particle size reported in the article. Kukovitsky and co-workers55 report that at lower temperatures (700 °C) nanotube diameters (MWNT) reproduce the original particle size distribution, whereas at higher temperatures (>800 °C) the nanotube diameters follow a Gaussian distribution independent of particle size. While there are certainly many instances where the nanotube diameter is dictated by the catalyst particle size, there are also studies reporting no significant effect of particle size. This range of behavior tends to indicate that a plurality of mechanisms is capable of synthesizing nanotubes and the existence of different nanotube formation mechanisms at various temperatures, pressures, reactant species, and choice of catalyst metal.
disproportionation and hydrogenation (reduction) reactions are the primary pathways for carbon deposition. Geurts and Sacco57 performed measurements on the relative rates of the Boudouard and hydrogenation (reduction) reactions on Fe and Co foils at 900 K and identified hydrogenation as the main reaction for carbon deposition and carbide formation. In systems with low concentrations of hydrogen, disproportionation dominates the carbon deposition flux and is often identified as the dominant reaction driving carbon nanotube growth.19 Disproportionation can also proceed on metal oxides such as Fe2O3 and Fe3O4.59 The kinetics of the Boudouard reaction on metal surfaces has been investigated by a number of authors. CO dissociation on R-iron was investigated by Tsao et al.60 over a temperature range of 903 to 1027 K. Tavares and co-workers61 investigated CO disproportionation on nickel catalysts and evaluated kinetic parameters based on a gravimetric technique. CO disproportion on metals is a very complex system to study as the surface reactions are confounded by transformations of the surface structure and bulk composition of the solid as the reaction proceeds, making kinetics of these reactions difficult and often ambiguous to determine. One of the main features of carbon deposition on metals is the simultaneous migration of carbon into the metal structure, often accompanied by the formation of metal carbides (e.g., Fe3C). The formation of carbides is frequently reported as the cause of nanotube growth de-activation.62 The influence of carbide content on carbon deposition processes is illustrated by Herreyre.32 The deposition of carbon on metal surfaces is also governed by the composition of the gases above the metal. The rate of carbon deposition is proportional to the concentration of carbonbearing species (carbon activity) in the gas mixture;30 however, it can also be influenced by other species. Sacco and co-workers examined the deposition of carbon on metal surfaces for gas mixtures containing CO, H2, CH4, CO2, and H2O and observed that deposition was influenced by the relative proportions of all gaseous species, with carbon deposition occurring only for certain compositions.24 The amount of CO and hydrocarbons available in the gas mixture is obviously a primary factor governing carbon deposition; however, the presence of H2, CO2, and H2O can also have a mediating influence based on the interactions described in the three deposition reactions shown previously. Increasing the level of H2 can increase the flux of the hydrogenation reaction as is seen in many nanotube studies.31 Increasing the concentration of CO by increasing the system pressure can increase the flux of the disproportionation reaction.19 Increasing the amount of H2, CO2, and H2O in the system would also be expected to have an effect in suppressing flux from each of the three reactions. Other species can also impact the deposition rate by occupying surface sites on the catalyst surface and through competing reactions. The importance of gas-phase composition on nanotube growth is illustrated well by the Vander Wal et al. study of nanotube growth on substrates immersed in flames.63 In their study, a limited parameter space of CO and H2 concentrations support nanotube growth, an effect that is likely driven largely by surface reaction chemistry. Carbon Diffusion. Following deposition of the carbon on the surface of the metal, a diffusive process transports the elemental carbon to the opposite side of the particle. This transport may proceed via surface diffusion or internal (bulk) diffusion; however, internal diffusion is generally assumed to be the dominant pathway for nanotube growth.64
Component Processes of Nanotube Formation Many techniques, reactants, catalysts, and conditions have been used to synthesize carbon nanotubes. Because many combinations of factors and molecular processes interact during nanotube synthesis, it is difficult to identify underlying mechanisms of nanotube growth. Nonetheless, despite these diverse characteristics, the nanotube formation process for single-walled carbon nanotubes can be considered as the interaction of three fundamental processes: (1) catalytic deposition of carbon on the surface of a metal, (2) diffusion transport of carbon over or through a catalyst particle, and (3) precipitation of the carbon in the form of a hollow graphitic tube (Figure 1). Each of these process steps is discussed below in the context of previously summarized observations. Catalytic Deposition of Carbon on Metals. Deposition of elemental carbon on the surface of a metal particle is often cited as the first step in nanotube formation. Catalytic decomposition of carbon-bearing compounds such as carbon monoxide and hydrocarbons on the surface of metals is generally believed to be the origin of the carbon deposition process. Surface catalysis and carbon deposition have been widely investigated for a number of decades with a focus on the coking of catalysts and reactor walls and chemistry associated with Fischer-Tropsch synthesis. These studies have characterized many aspects of reactions leading to carbon deposition on metal surfaces.56 There are three main reactions that have been identified for deposition of carbon on metal surfaces from hydrocarbons and carbon monoxide: (1) hydrocarbon cracking, (2) CO reduction/ hydrogenation, and (3) CO disproportionation.57,58 metal CxHy 98 xCsolid + 2yH2 cracking metal
CO + H2 98 Csolid + H2O reduction metal
2CO 98 Csolid + CO2 disproportionation
(i) (ii) (iii)
In systems where CO is the main carbon-bearing species, the
12340 J. Phys. Chem. B, Vol. 109, No. 25, 2005 Internal Diffusion. The diffusivity of carbon in iron has been investigated by Tibbetts,65 McLellan et al.,66 Agren,67 and Kucera et al.68 Diffusivity is strongly influenced by temperature, and at temperatures above 1000 °C the diffusivity of carbon in metals can be of order 10-7 cm2/s or more. The characteristic time for diffusion can be determined using the relation L2 ) Dτ, where L is the characteristic length, D is the diffusivity and τ is characteristic time. Assuming a diffusivity of 2.5 × 10-7 cm2/s for carbon in iron at 1000 °C,67 and a particle diameter of 10 nm, the characteristic time for carbon diffusion through the particle is on the order of 0.01 milliseconds. This characteristic time is less than that for surface diffusion (see below), indicating that internal diffusion may be the dominant pathway for the carbon flux. Further support of this theory is provided by Baker et al.62 who compared the activation energies for filament growth and for carbon diffusion and found that these values correlated closely. Furthermore, in a structural sense it is argued that the high degree of order in the nanotube wall can be attributed to the constraining influence of the internal structure of the metal particle whereas growth from surface diffusion would likely lead to more disorder in the nanotube wall.69 While the rapid diffusion of carbon in certain metals can lead to the formation of carbon nanotubes, the nature of this diffusion can also explain additional aspects of nanotube formation. Mixed catalysts have been found to give greatly improved yield of nanotubes.46 This observation could possibly be attributed to reorganization of the metal lattice to give wider spacing of the crystal planes which can in turn allow improved diffusive transport of carbon atoms through the bulk. Another possibility is that the addition of another metal component (or another impurity such as sulfur) can lower the binding energy of the metal with carbon atoms, giving improved diffusivity. Surface Diffusion. Sorescu et al.70 performed ab initio quantum chemical calculations on the adsorption, diffusion, and dissociation of a CO molecule on an Fe(100) surface and predicted an adsorption energy between 44 and 47 kcal/mol, dissociation energy barrier of 24.5-28.2 kcal/mol, and surface diffusion activation energy of 2 to 13 kcal/mol. Xiao et al.71 measured the diffusivity of CO on the surface of Ni(110) subjected to various levels of impurities. The measured diffusion activation barriers were 2 to 3 kcal/mol for a clean surface with CO, and up to 7 or 8 kcal/mol at high impurity coverages, giving values in agreement with the range reported by Sorescu and co-workers.70 A typical prefactor reported by Xiao is 5 × 10-10 cm2/s. Xiao et al.71 also found sulfur to have a greater impeding effect than oxygen. Using the characteristic time relationship described previously and the parameters reported by Xiao et al., a CO molecule diffusing to the opposite side of a 10 nm sphere at 1000 K, the characteristic time is of order 10 ms. The impeding influence of sulfur and oxygen impurities on surface diffusion, as reported by Xiao and co-workers,71 gives us some insight as to why sulfur addition may enhance SWNT formation. The presence of sulfur on the surface of catalyst particles would lower surface diffusion rates, and therefore internal diffusion may be selectively favored as the flux pathway for carbon, enhancing the precipitation of ordered SWNT from the internal lattice structure. Carbon Precipitation. The third process of nanotube formation involves the precipitation of carbon from the particle in the form of a cylindrical graphitic shell. Lucas et al.72 discuss the energy transformations associated with “rolling” a nanotube from a plane of graphite. The strain energy of a graphitic sheet grows significantly as it increases in curvature, yet the closing
Height et al. of the dangling bonds at the edge of the graphene sheet gives a stable tube structure that is similar in stability to the initial graphite. While the formation of a nanotube in this manner under flame conditions is unlikely, this analysis is illustrative of the stability of the curved nanotube structure. The large energy penalty for forming a nanotube from a planar graphene sheet indicates that the most likely means for forming the nanotube is formation directly to the closed shell structure upon precipitation from the metal surface. The “yarmulke” mechanism proposed by Dal et al.54 accounts for the need to stabilize dangling bonds by invoking a hemispherical cap forming on the metal surface initially, followed by lift-off and nanotube growth in the wake of the cap. The curved graphitic structure minimizes dangling bonds, and it has been proposed that additives such as sulfur and alcohol can also have a stabilizing role.36 An alternative view is that carbon atoms diffusing through the metal particle emerge from the lattice in a template fashion, with shape constrained by the internal lattice geometry of the particle, stabilizing the tubular form. The uniform diameter and constant chirality along the length of each single-walled nanotube supports the notion that the metal lattice has a templating influence on nanotube growth. Nanotube Formation Models There are a number of models for nanotube growth that attempt to describe the overall formation process. Tibbetts and co-workers69 proposed an adsorption-diffusion isotherm for filament growth from methane cracking on iron particles and examined the dominant processes in nanotube formation. Tibbetts concluded that temperature difference across the particle is not responsible for carbon diffusion, rather that supersaturation of the metal phase leads to a concentration gradient and diffusive flux, and that the internal (bulk) diffusion flux dominates over surface diffusion. Safvi et al.30 developed adsorption-diffusion models that demonstrated the dependence of growth rate on gasphase carbon activity. Snoeck et al.73,74 developed models incorporating surface catalytic reactions, carbon diffusion, and precipitation and cited supersaturation of the metal and the existence of an internal concentration gradient as origins of the internal diffusive flux. Laplaze et al.15 proposed that the nanotube growth process is strongly related to the nature of liquid-solid transformations and carbon solubility and rationalized nanotube growth using metal-carbon equilibrium phase diagrams. The need for liquid catalyst particles for the formation of SWNT is cited by Gorbunov et al.75 where small particles (
