Nucleation Of Single-walled Carbon Nanotubes Research Articles

Nanocatalyst shape and composition during nucleation of single-walled carbon nanotubes.

The dynamic evolution of nanocatalyst particle shape and carbon composition during the initial stages of single-walled carbon nanotube growth by chemical vapor deposition synthesis is investigated. Classical reactive and ab initio molecular dynamics simulations are used, along with environmental transmission electron microscope video imaging analyses. A clear migration of carbon is detected from the nanocatalyst/substrate interface, leading to a carbon gradient showing enrichment of the nanocatalyst layers in the immediate vicinity of the contact layer. However, as the metal nanocatalyst particle becomes saturated with carbon, a dynamic equilibrium is established, with carbon precipitating on the surface and nucleating a carbon cap that is the precursor of nanotube growth. A carbon composition profile decreasing towards the nanoparticle top is clearly revealed by the computational and experimental results that show a negligible amount of carbon in the nanoparticle region in contact with the nucleating cap. The carbon composition profile inside the nanoparticle is accompanied by a well-defined shape evolution of the nanocatalyst driven by the various opposing forces acting upon it both from the substrate and from the nascent carbon nanostructure. This new understanding suggests that tuning the nanoparticle/substrate interaction would provide unique ways of controlling the nanotube synthesis.

Key roles of carbon solubility in single-walled carbon nanotube nucleation and growth

Elucidating the roles played by carbon solubility in catalyst nanoparticles is required to better understand the growth mechanisms of single-walled carbon nanotubes (SWNTs). Here, we highlight that controlling the level of dissolved carbon is of key importance to enable nucleation and growth. We first performed tight binding based atomistic computer simulations to study carbon incorporation in metal nanoparticles with low solubilities. For such metals, carbon incorporation strongly depends on their structures (face centered cubic or icosahedral), leading to different amounts of carbon close to the nanoparticle surface. Following this idea, we then show experimentally that Au nanoparticles effectively catalyze SWNT growth when in a face centered cubic structure, and fail to do so when icosahedral. Both approaches emphasize that the presence of subsurface carbon in the nanoparticles is necessary to enable the cap lift-off, making the nucleation of SWNTs possible.

Atomic Resolution Single Walled Carbon Nanotube Nucleation Steps on Faceted Catalyst Particle Reveal Potential for Chirality Control

Atomic Resolution Single Walled Carbon Nanotube Nucleation Steps on Faceted Catalyst Particle Reveal Potential for Chirality Control

Chirality-specific growth of single-walled carbon nanotubes on solid alloy catalysts.

Carbon nanotubes have many material properties that make them attractive for applications. In the context of nanoelectronics, interest has focused on single-walled carbon nanotubes (SWNTs) because slight changes in tube diameter and wrapping angle, defined by the chirality indices (n, m), will shift their electrical conductivity from one characteristic of a metallic state to one characteristic of a semiconducting state, and will also change the bandgap. However, this structure-function relationship can be fully exploited only with structurally pure SWNTs. Solution-based separation methods yield tubes within a narrow structure range, but the ultimate goal of producing just one type of SWNT by controlling its structure during growth has proved to be a considerable challenge over the last two decades. Such efforts aim to optimize the composition or shape of the catalyst particles that are used in the chemical vapour deposition synthesis process to decompose the carbon feedstock and influence SWNT nucleation and growth. This approach resulted in the highest reported proportion, 55 per cent, of single-chirality SWNTs in an as-grown sample. Here we show that SWNTs of a single chirality, (12, 6), can be produced directly with an abundance higher than 92 per cent when using tungsten-based bimetallic alloy nanocrystals as catalysts. These, unlike other catalysts used so far, have such high melting points that they maintain their crystalline structure during the chemical vapour deposition process. This feature seems crucial because experiment and simulation both suggest that the highly selective growth of (12, 6) SWNTs is the result of a good structural match between the carbon atom arrangement around the nanotube circumference and the arrangement of the catalytically active atoms in one of the planes of the nanocrystal catalyst. We anticipate that using high-melting-point alloy nanocrystals with optimized structures as catalysts paves the way for total chirality control in SWNT growth and will thus promote the development of SWNT applications.

In Situ TEM Observations on the Sulfur-Assisted Catalytic Growth of Single-Wall Carbon Nanotubes

The effect of sulfur on the catalytic nucleation and growth of single-wall carbon nanotubes (SWCNTs) from an iron catalyst was investigated in situ by transmission electron microscopy (TEM). The catalyst precursor of ferrocene and growth promoter of sulfur were selectively loaded inside of the hollow core of multiwall CNTs with open ends, which served as a nanoreactor powered by applying a voltage inside of the chamber of a TEM. It was found that a SWCNT nucleated and grew perpendicularly from a region of the catalyst nanoparticle surface, instead of the normal tangential growth that occurs with no sulfur addition. Our in situ TEM observation combined with CVD growth studies suggests that sulfur functions to promote the nucleation and growth of SWCNTs by forming inhomogeneous local active sites and modifying the interface bonding between catalysts and precipitated graphitic layers, so that carbon caps can be lifted off from the catalyst particle.

Theoretical investigation on carbon nucleation on nickel carbides at initial stages of single-walled carbon nanotube formation.

It is a long-standing controversy whether metal carbide clusters do exist during the nucleation and growth process of single-walled carbon nanotubes (SWCNTs). In the current work, we are trying to elucidate the carbon nucleation on nickel carbides during the initial stages based on density functional theory calculated formation energy and chemical potential for a series of Ni55Cn carbides (n is the number of carbon atoms dissolved in the Ni55 cluster). It is found that the formation energies of the Ni55Cn carbides decrease gradually with an increase of dissolved carbon atomic numbers, meaning the Ni55Cn carbides are thermodynamically stable. Meanwhile, the calculated chemical potentials indicate that not only nickel carbides are preferentially formed during the initial stage of the SWCNT nucleation, but also saturated nickel carbides may be able to exist during the nucleation and growth process of SWCNTs. In addition, the nickel carbides have a high selectivity for the formation of the carbon pentagon and carbon structures with pentagon-incorporated end-edge according to the adsorption energies. All of these findings provide opportunities in controlling the growth of the SWCNTs.

Towards a ‘catalyst activity map’ regarding the nucleation and growth of single walled carbon nanotubes

Quantification using scanning electron microscopy (SEM) of single walled carbon nanotubes (SWNTs) grown per unit area using a Co-Fe (50:50) catalyst system, prepared by the incorporation of the appropriate metal salts into a Spin-On Glass substrate, at 900°C. The effects of substrate, as well as catalyst precursor concentration, were investigated. SWNT growth density is maximised with a catalyst precursor concentration of ≥2.5 mM, associated with the formation of catalyst nanoparticles of a critical size for SWNT nucleation. Samples were subjected to secondary growth, using a range of H2:CH4 ratios to determine the optimum precursor composition. It was found that nucleation and growth stages are optimal under different conditions. Optimum conditions for nucleation resulted in >10× increase in SWNT density. Optimisation is dependent on temperature and the partial pressure of reagent gas species.

Carbon Coating Precedes SWCNT Nucleation on Silicon Nanoparticles: Insights from QM/MD Simulations

Nucleation of single-walled carbon nanotubes (SWCNTs) from C2 molecules adsorbed on silicon nanoparticles (SiNPs) has been investigated using quantum chemical molecular dynamics (QM/MD) simulations. The SWCNT nucleation mechanism was observed to be strikingly different from that of traditional, transition metal catalyzed SWCNT growth. Most notably, neither a bulk Si carbide phase nor the precipitation of carbon from the nanoparticle bulk was observed to precede SWCNT nucleation on SiNPs. Instead, the intermediate stage during SWCNT nucleation featured the formation of a “carbon-coated” Si surface, i.e., one covered with networks of sp2-hybridized carbon. In addition, the QM/MD simulations indicate that the growth of these sp2-carbon networks was dependent exclusively on the dynamic motion of the polyyne chains formed on the catalyst surface. Analysis of the SiNP phase during SWCNT nucleation also indicated that nucleation proceeded while the Si catalyst remained in the solid phase. Thus, it is concluded that the SWCNT nucleation mechanism presented here was consistent with a vapor–solid–solid mechanism, rather than a vapor–liquid–solid mechanism. This conclusion correlates with recent findings concerning SWCNT nucleation on SiO2 catalyst nanoparticles (Page et al. J. Am. Chem. Soc. 2011, 133, 621).

SWCNT Networks on Nanoporous Silica Catalyst Support: Morphological and Connectivity Control for Nanoelectronic, Gas-Sensing, and Biosensing Devices

Effective control of morphology and electrical connectivity of networks of single-walled carbon nanotubes (SWCNTs) by using rough, nanoporous silica supports of Fe catalyst nanoparticles in catalytic chemical vapor deposition is demonstrated experimentally. The very high quality of the nanotubes is evidenced by the G-to-D Raman peak ratios (>50) within the range of the highest known ratios. Transitions from separated nanotubes on smooth SiO(2) surface to densely interconnected networks on the nanoporous SiO(2) are accompanied by an almost two-order of magnitude increase of the nanotube density. These transitions herald the hardly detectable onset of the nanoscale connectivity and are confirmed by the microanalysis and electrical measurements. The achieved effective nanotube interconnection leads to the dramatic, almost three-orders of magnitude decrease of the SWCNT network resistivity compared to networks of similar density produced by wet chemistry-based assembly of preformed nanotubes. The growth model, supported by multiscale, multiphase modeling of SWCNT nucleation reveals multiple constructive roles of the porous catalyst support in facilitating the catalyst saturation and SWCNT nucleation, consistent with the observed higher density of longer nanotubes. The associated mechanisms are related to the unique surface conditions (roughness, wettability, and reduced catalyst coalescence) on the porous SiO(2) and the increased carbon supply through the supporting porous structure. This approach is promising for the direct integration of SWCNT networks into Si-based nanodevice platforms and multiple applications ranging from nanoelectronics and energy conversion to bio- and environmental sensing.

Nanoscale Plasma Chemistry Enables Fast, Size-Selective Nanotube Nucleation

The possibility of fast, narrow-size/chirality nucleation of thin single-walled carbon nanotubes (SWCNTs) at low, device-tolerant process temperatures in a plasma-enhanced chemical vapor deposition (CVD) is demonstrated using multiphase, multiscale numerical experiments. These effects are due to the unique nanoscale reactive plasma chemistry (NRPC) on the surfaces and within Au catalyst nanoparticles. The computed three-dimensional process parameter maps link the nanotube incubation times and the relative differences between the incubation times of SWCNTs of different sizes/chiralities to the main plasma- and precursor gas-specific parameters and explain recent experimental observations. It is shown that the unique NRPC leads not only to much faster nucleation of thin nanotubes at much lower process temperatures, but also to better selectivity between the incubation times of SWCNTs with different sizes and chiralities, compared to thermal CVD. These results are used to propose a time-programmed kinetic approach based on fast-responding plasmas which control the size-selective, narrow-chirality nucleation and growth of thin SWCNTs. This approach is generic and can be used for other nanostructure and materials systems.

In situ evidence for chirality-dependent growth rates of individual carbon nanotubes

Chiral-selective growth of single-walled carbon nanotubes (SWNTs) remains a great challenge that hinders their use in applications such as electronics and medicine. Recent experimental and theoretical reports have begun to address this problem by suggesting that selectivity may be achieved during nucleation by changing the catalyst composition or structure. Nevertheless, to establish a rational basis for chiral-selective synthesis, the underlying mechanisms governing nucleation, growth, and termination of SWNTs must be better understood. To this end, we report the first measurements of growth rates of individual SWNTs through in situ Raman spectroscopy and correlate them with their chiral angles. Our results show that the growth rates are directly proportional to the chiral angles, in agreement with recent theoretical predictions. Importantly, the evidence singles out the growth stage as responsible for the chiral distribution-distinct from nucleation and termination which might also affect the final product distribution. Our results suggest a route to chiral-selective synthesis of SWNTs through rational synthetic design strategies based on kinetic control.

Thermal annealing of SiC nanoparticles induces SWNT nucleation: evidence for a catalyst-independent VSS mechanism

Density-functional tight-binding molecular dynamics (DFTB/MD) methods were employed to demonstrate single-walled carbon nanotube (SWNT) nucleation resulting from thermal annealing of SiC nanoparticles. SWNT nucleation in this case is preceded by a change of the SiC structure from a crystalline one, to one in which silicon and carbon are segregated. This structural transformation ultimately resulted in the formation of extended polyyne chains on the SiC nanoparticle surface. These polyyne chains subsequently coalesced, forming an extended sp(2)-hybridized carbon cap on the SiC nanoparticle. The kinetics of this process were enhanced significantly at higher temperatures (2500 K), compared to lower temperatures (1200 K) and so directly correlated to the surface premelting behavior of the nanoparticle structure. Analysis of the SiC nanoparticle Lindemann index between 1000 and 3000 K indicated that SWNT nucleation at temperatures below 2600 K occurred in the solid, or quasi-solid, phase. Thus, the traditional vapor-liquid-solid mechanism of SWNT growth does not apply in the case of SiC nanoparticles. Instead, we propose that this example of SWNT nucleation constitutes evidence of a vapor-solid-solid process. This conclusion complements our recent observations regarding SWNT nucleation on SiO(2) nanoparticles (A. J. Page, K. R. S. Chandrakumar, S. Irle and K. Morokuma, J. Am. Chem. Soc., 2011, 133, 621-628). In addition, similarities between the atomistic SWNT nucleation mechanisms on SiC and SiO(2) catalysts provide the first evidence of a catalyst-independent SWNT nucleation mechanism with respect to 'non-traditional' SWNT catalyst species.

SWNT Nucleation from Carbon-Coated SiO2 Nanoparticles via a Vapor−Solid−Solid Mechanism

Since the discovery of single-walled carbon nanotubes (SWNTs) in the early 1990s, the most commonly accepted model of SWNT growth on traditional catalysts (i.e., transition metals including Fe, Co, Ni, etc.) is the vapor-liquid-solid (VLS) mechanism. In more recent years, the synthesis of SWNTs on nontraditional catalysts, such as SiO(2), has also been reported. The precise atomistic mechanism explaining SWNT growth on nontraditional catalysts, however, remains unknown. In this work, CH(4) chemical vapor deposition (CVD) and single-walled carbon nanotube (SWNT) nucleation on SiO(2) nanoparticles have been investigated using quantum-chemical molecular dynamics (QM/MD) methods. Upon supply of CH(x) species to the surface of a model SiO(2) nanoparticle, CO was produced as the main chemical product of the CH(4) CVD process, in agreement with a recent experimental investigation [Bachmatiuk et al., ACS Nano 2009, 3, 4098]. The production of CO occurred simultaneously with the carbothermal reduction of the SiO(2) nanoparticle. However, this reduction, and the formation of amorphous SiC, was restricted to the nanoparticle surface, with the core of the SiO(2) nanoparticle remaining oxygen-rich. In cases of high carbon concentration, SWNT nucleation then followed, and was driven by the formation of isolated sp(2)-carbon networks via the gradual coalescence of adjacent polyyne chains. These simulations indicate that the carbon saturation of the SiO(2) surface was a necessary prerequisite for SWNT nucleation. These simulations also indicate that a vapor-solid-solid mechanism, rather than a VLS mechanism, is responsible for SWNT nucleation on SiO(2). Fundamental differences between SWNT nucleation on nontraditional and traditional catalysts are therefore observed.

QM/MD Simulation of SWNT Nucleation on Transition-Metal Carbide Nanoparticles

The mechanism and kinetics of single-walled carbon nanotube (SWNT) nucleation from Fe- and Ni-carbide nanoparticle precursors have been investigated using quantum chemical molecular dynamics (QM/MD) methods. The dependence of the nucleation mechanism and its kinetics on environmental factors, including temperature and metal-carbide carbon concentration, has also been elucidated. It was observed that SWNT nucleation occurred via three distinct stages, viz. the precipitation of the carbon from the metal-carbide, the formation of a "surface/subsurface" carbide intermediate species, and finally the formation of a nascent sp(2)-hybidrized carbon structure supported by the metal catalyst. The SWNT cap nucleation mechanism itself was unaffected by carbon concentration and/or temperature. However, the kinetics of SWNT nucleation exhibited distinct dependences on these same factors. In particular, SWNT nucleation from Ni(x)C(y) nanoparticles proceeded more favorably compared to nucleation from Fe(x)C(y) nanoparticles. Although SWNT nucleation from Fe(x)C(y) and Ni(x)C(y) nanoparticle precursors occurred via an identical route, the ultimate outcomes of these processes also differed substantially. Explicitly, the Ni(x)-supported sp(2)-hybridized carbon structures tended to encapsulate the catalyst particle itself, whereas the Fe(x)-supported structures tended to form isolated SWNT cap structures on the catalyst surface. These differences in SWNT nucleation kinetics were attributed directly to the relative strengths of the metal-carbon interaction, which also dictates the precipitation of carbon from the nanoparticle bulk and the longevity of the resultant surface/subsurface carbide species. The stability of the surface/subsurface carbide was also influenced by the phase of the nanoparticle itself. The observations agree well with experimentally available data for SWNT growth on iron and nickel catalyst particles.

Experimental evidence for the early nucleation of single-walled carbon nanotubes

In situ optical emission spectroscopy (OES) was used to investigate the spatial and temporal evolution of C 2 , the electron density ( N e ) and the electron temperature ( T e ) of laser induced plasmas in the laser-furnace method of synthesizing single-walled carbon nanotubes (SWCNTs). The intensities of the spectral maps of C 2 , N e and T e showed a strong temperature dependence. The frequency of sharp fluctuations which appear as hot spots in the spectral maps of N e and T e increased as the furnace temperature was increased from 1073 to 1273 K. We suggest that the appearance of hot spots is a result of the heat of formation of SWCNTs.

Mechanisms of Single-Walled Carbon Nanotube Nucleation, Growth, and Healing Determined Using QM/MD Methods

Since their discovery in the early 1990s, single-walled carbon nanotubes (SWNTs) have spawned previously unimaginable commercial and industrial technologies. Their versatility stems from their unique electronic, physical/chemical, and mechanical properties, which set them apart from traditional materials. Many researchers have investigated SWNT growth mechanisms in the years since their discovery. The most prevalent of these is the vapor-liquid-solid (VLS) mechanism, which is based on experimental observations. Within the VLS mechanism, researchers assume that the formation of a SWNT starts with co-condensation of carbon and metal atoms from vapor to form liquid metal carbide. Once the liquid reaches supersaturation, the solid phase nanotubes begin to grow. The growth process is partitioned into three distinct stages: nucleation of a carbon "cap-precursor," "cap-to-tube" transformation, and continued SWNT growth. In recent years, molecular dynamics (MD) simulations have come to the fore with respect to SWNT growth. MD simulations lead to spatial and temporal resolutions of these processes that are superior to those possible using current experimental techniques, and so provide valuable information regarding the growth process that researchers cannot obtain experimentally. In this Account, we review our own recent efforts to simulate SWNT nucleation, growth, and healing phenomena on transition-metal catalysts using quantum mechanical molecular dynamics (QM/MD) methods. In particular, we have validated each stage of the SWNT condensation mechanism using a self-consistent-charge density-functional tight-binding (SCC-DFTB) methodology. With respect to the nucleation of a SWNT cap-precursor (stage 1), we have shown that the presence of a transition-metal carbide particle is not a necessary prerequisite for SWNT nucleation, contrary to conventional experimental presumptions. The formation and coalescence of polyyne chains on the metal surface occur first, followed by the formation of the SWNT cap-precursor, "ring condensation", and the creation of an sp(2)-hybridized carbon structure. In our simulations, the nucleation process takes approximately 400 ps. This first step occurs over a much longer time scale than the second stage of SWNT condensation (approximately 50 ps). We therefore observe SWNT nucleation to be akin to the rate-limiting step of the SWNT formation process. In addition to the QM/MD simulation of various stages of SWNT nucleation, growth, and healing processes, we have determined the effects of temperature, catalyst composition, and catalyst size on the kinetics and mechanism of SWNT growth. With respect to temperature dependence, we observe a "sweet-spot" with respect to the efficiency of SWNT growth. In addition, Ni-catalyzed SWNT growth is observed to be 70-100% faster compared to Fe-catalyzed SWNT growth, depending on the catalyst particle size. We also observe a noticeable increase in SWNT growth rates using smaller catalyst particles. Finally, we review our recent QM/MD investigation of SWNT healing. In particular, we recount mechanisms by which adatom defects, monovacancy defects, and a "5-7 defect" are removed from a nascent SWNT. The effectiveness of these healing mechanisms depends on the rate at which carbon moieties are incorporated into the growing SWNT. Explicitly, we observe that healing is promoted using a slower carbon supply rate. From this rudimentary control of SWNT healing, we propose a route towards chirality-controlled SWNT growth.

In situ optical emission study on the role of C2 in the synthesis of single-walled carbon nanotubes

In situ optical emission spectroscopy was used to study the temporal and spatial behavior of laser induced plasmas in the laser-furnace synthesis of single-walled carbon nanotubes (SWCNTs). A graphite composite target located within a sealed quartz tube with a chemical stoichiometric composition of 95:4:1 at. wt % of carbon, yttrium, and nickel, respectively, was ablated by a Q-switched Nd:YAG laser delivering colinear, focused laser pulses of 1064 and 532 nm temporarily separated by 20 ns. The ablation process was done at a furnace temperature of 1273 K in a flow of argon gas at either 150 or 200 SCCM (SCCM denotes cubic centimeter per minute at STP). The pressure was varied (100, 400, and 600 Torr) for each gas flow setting. The temporal and spatial behavior of the emission intensity associated with C2 Swan bands (d Π3g−a Π3u) was investigated and found to be influenced by the pressure and flow rate of the argon gas. At conditions optimal to SWCNT production, a sharp drop in C2 intensity followed by a rise in C2 intensity was observed. The temporal and spatial behavior of the electron density was determined by the Stark broadening profile of the CII emission peak at 283.7 nm and was found to decrease with the adiabatic expansion of the plume. We propose that the sharp drop in C2 intensity and the rise in electron density and electron temperature observed in this study are due to the accompanying rapid nucleation and growth of SWCNTs.

Effect of Manganese Addition to the Co-MCM-41 Catalyst in the Selective Synthesis of Single Wall Carbon Nanotubes

The effect of manganese addition to the Co-MCM-41 catalyst on the synthesis of single wall carbon nanotubes (SWNT) by CO disproportionation was characterized. The ratio between the two metals in the MCM-41 framework was varied, and its effect on the resultant SWNT distribution was studied and compared with the results obtained for the monometallic Co-MCM-41 catalyst. Methods including temperature-programmed reduction, X-ray absorption fine structure, thermogravimetric analysis, TEM imaging, and Raman and fluorescence spectroscopy were employed to characterize the behavior of the catalysts under the SWNT synthesis conditions and the diameter and structure distribution of the resultant nanotubes. We found that addition of Mn to the Co-MCM-41 catalyst promotes the growth of SWNT, leading to synthesis of high yield, small diameter SWNT. Manganese does not act in the nucleation of SWNT but acts as an anchoring site for cobalt particles formed during the synthesis process as shown by X-ray absorption.

Quantum Chemical Molecular Dynamics Simulation of Single-Walled Carbon Nanotube Cap Nucleation on an Iron Particle

The atomic scale details of single-walled carbon nanotube (SWNT) nucleation on metal catalyst particles are elusive to experimental observations. Computer simulation of metal-catalyzed SWNT nucleation is a challenging topic but potentially of great importance to understand the factors affecting SWNT diameters, chirality, and growth efficiency. In this work, we use nonequilibrium density functional tight-binding molecular dynamics simulations and report nucleation of sp(2)-carbon cap structures on an iron particle consisting of 38 atoms. One C(2) molecule was placed every 1.0 ps around an Fe(38) cluster for 30 ps, after which a further 410 ps of annealing simulation without carbon supply was performed. We find that sp(2)-carbon network nucleation and annealing processes occur in three sequential and repetitive stages: (A) polyyne chains on the metal surface react with each other to evolve into a Y-shaped polyyne junction, which preferentially form a five-membered ring as a nucleus; (B) polyyne chains on the first five-membered ring form an additional fused five- or six-membered ring; and (C) pentagon-to-hexagon self-healing rearrangement takes place with the help of short-lived polyyne chains, stabilized by the mobile metal atoms. The observed nucleation process resembles the formation of a fullerene cage. However, the metal particle plays a key role in differentiating the nucleation process from fullerene cage formation, most importantly by keeping the growing cap structure from closing into a fullerene cage and by keeping the carbon edge "alive" for the addition of new carbon material.

DFT and tight binding Monte Carlo calculations related to single-walled carbon nanotube nucleation and growth

Density-functional theory (DFT) calculations for idealized nucleation processes of (5, 5) and (10, 0) single-walled carbon nanotubes (SWCNTs) on a 55 atom nickel cluster (Ni 55) showed that it requires a larger chemical potential to grow a carbon island (which is the simplest structure that can lead to formation of the SWCNTs) on the cluster than to extend the island into a SWCNT or to have the carbon atoms dispersed on the cluster surface. Hence, in the thermodynamic limit the island will only form once the (surface of the) cluster is saturated with carbon, and the island will spontaneously form a SWCNT at the chemical potentials required to create the island. The DFT (zero Kelvin) and tight binding Monte Carlo (1000 K) also show that there is a minimum cluster size required to support SWCNT growth, and that this cluster size can be used to control the diameter, but probably not the chirality, of the SWCNT at temperatures relevant to carbon nanotube growth. It also imposes a minimum size of clusters that are used for SWCNT regrowth.