6.1.1 Definitions

Nanoscience is defined as a research field that encompasses objects having dimensions smaller than 100 nanometers. Nanoscience addresses basic organization principles of the nanoscopic objects and describes their unique properties. Objects at this scale exhibit very different properties and physics than that of the bulk objects of the same material. At this scale, quantum mechanic effects become very important. Nanotechnology deals with synthesis of nanoscopic objects and devices as well as various applications. Nanoscopic objects could be formed from the precursors in various states (atoms, molecules, clusters, exited states, etc.). Plasma nanoscience and nanotechnology deal with synthesis of nanoparticles from the ionized gas or plasma state.

In general, nanoscience and nanotechnology study nanoscopic objects used across many scientific fields, such as chemistry, biology, physics, materials science, and engineering. By encompassing nanoscale science, engineering, and technology, nanotechnology involves imaging, measuring, modeling, and manipulating matter at this length scale.

Historically, many ideas and concepts behind nanoscience and nanotechnology as they are known today started with a talk entitled “There’s Plenty of Room at the Bottom” by physicist Richard Feynman at an American Physical Society meeting at the California Institute of Technology on December 29, 1959, long before the term nanotechnology was used [1]. In that, now famous talk, Feynman described a process in which scientists would be able to manipulate and control individual atoms and molecules.

This section is devoted to description of the plasma-based nanoscience and nanotechnology, which is emerging as one of the promising field.

6.1.2 Plasma-based synthesis of nanoparticles

Deterministic synthesis of nanoparticles and nanodevices is the most pressing demand of today’s nanotechnology. At the elementary level, this means high fidelity control over the precursor density and energy distribution as well as a high degree of control over precursor position. In this respect, presence of the charged particles allows particle manipulation using electric and magnetic fields. As a result, plasma-based nanoparticle synthesis and fabrication could offer a better degree of controllability in the size, shape, and pattern uniformity as compared to neutral-based process such as chemical vapor deposition (CVD) [2]. An observation made in numerical simulations demonstrates this statement (Figure 6.1). One can see that the nanotips grown on plasma-exposed surfaces (plasma-enhanced CVD) are much taller and sharper than those grown by the CVD process under the same deposition conditions.

Plasma-based techniques were demonstrated to be effective in synthesis of various nanomaterials such as carbon nanotubes (CNTs), nanofibers, graphene, graphene nanoribbons, graphene nanoflakes, nanodiamond and related carbon-based nanostructures; metal, silicon, and other inorganic nanoparticles and nanostructures; soft organic nanomaterials; nanobiomaterials; biological objects and nanoscale plasma etching [3]. To this end, various types of plasmas and plasma reactor systems are utilized in nanotechnology, including low-temperature nonequilibrium plasmas at low and high pressures, thermal plasmas, high-pressure microplasmas, plasmas in liquids and plasma–liquid interactions, high-energy-density plasmas, and ionized physical vapor deposition to name just a few.

6.1.3 Synthesis of carbon nanoparticles

Carbon is one of the few elements known from antiquity and the one that is mostly used nowadays. There are several allotropes of carbon in the world, which can be categorized by dimensions, such as diamond and graphite in three dimensions, graphene in two dimensions, CNTs in one dimension, and fullerene in zero dimension. Carbon with sp³ hybridization will form a tetrahedral lattice, thus giving rise to diamond. Carbon with sp² hybridization may form graphite, graphene, CNT, or fullerene, depending on the conditions of their formation. Different structures and hybridizations of carbon atoms can determine the unique properties of each carbon allotropes.

Among possible forms of carbon, CNT and graphene attracted significant interest nowadays. CNT was first discovered in carbon deposits by the arc-discharge method by Iijima in 1991 [4], and the advance of graphene appears when Novoselov et al. [5] were able to extract it from bulk graphite by micromechanical cleavage or the Scotch tape approach in 2004. CNTs have unique structures with cylindrical walls of carbon. According to the number of wall layers, CNT can be categorized as single-walled carbon nanotubes (SWCNTs) and multiwalled carbon nanotubes (MWCNTs), while graphene is one-atom-thick hexagonal-lattice planar carbon layer.

Most SWCNTs have a diameter of around few nanometers, with a tube length that could be millions of times longer. SWCNT can be formed by rolling up a one-layer graphene into a cylinder. The way the graphene sheet is wrapped is represented by a pair of indices (n,m) [6]. The integers of n and m denote the number of unit vectors along two directions in the honeycomb crystal lattice of graphene shown in Figure 6.2. The (n,m) nanotube naming scheme is a vector (C_h) in an infinite graphene sheet that describes how to “roll up” the graphene sheet to make the nanotube as shown in Figure 6.2. An SWCNT can be imagined as graphene sheet rolled at a certain chiral angle with respect to a plane perpendicular to the tube’s long axis. Consequently, SWCNT can be defined by its diameter and chiral angle. The chiral angle can range from 0° to 30°. The SWCNT with index m=0 are named zigzag nanotubes, and the SWCNT with index n=m are called armchair nanotubes. The electrical property of SWCNT is determined by the indices of n and m. If the difference of indices n and m is integral multiple of three, the SWCNTs have metallic properties. The others are semiconducting materials. It will be shown below that various synthesis techniques produce both metallic and semiconductor nanotubes.

The unique structures of SWCNT and graphene lead to excellent mechanical, electrical, and thermal properties. SWCNT and graphene appear to be one of the strongest and stiffest materials in terms of Young’s modulus and tensile strength. This strength results from the covalent sp² bonds formed between the individual carbon atoms. The Young’s modulus of SWCNT and graphene can reach over 1 TPa, which is tens of times higher than that of aluminum [7]. The recent measurements have shown that graphene has a breaking strength which is 200 times greater than steel [8]. Metallic SWCNT can carry an electric current density of 4×10⁹ A/cm² in theory, which is more than 1000 times greater than those of metals such as copper [9]. Intrinsic graphene is a semimetal or zero-gap semiconductor. Experimental results from transport measurements show that graphene has remarkable electron mobility at room temperature, with reported values in excess of 15,000 cm²/V/s. The corresponding resistivity of the graphene sheet would be 10⁻⁶ Ω cm, which is less than the resistivity of silver [10]. SWCNTs have the thermal conductivity of 300 W/(mK) in axial direction. The measurement by a noncontact optical technique demonstrated that the near-room temperature thermal conductivity of graphene was measured to be between (4.84±0.44)×10³ and (5.30±0.48)×10³ W/(mK) [11], which is significantly higher than that of SWNT.

6.1.4 Controlled synthesis of carbon nanostructures in arc plasmas: theoretical premise

Several models of a cathodic carbon arc were developed in past dealing with electrode phenomena [72–74] or interelectrode plasma [75]. A 1D model (in axial direction) of the SWNT formation was developed and the SWNT growth rate in an anodic arc discharge was calculated [76]. According to the existed model predictions, the nanotube formation occurs in the region of relatively small plasma temperature (1300–1800 K [77]) where carbon reacts to form large molecules and clusters. No detailed model for relationship between the discharge parameters and SWNT formation was developed as mentioned in a review paper [78]. A model of SWNT interaction with discharge plasma and SWNT formation in the cathode region (collaret) was developed [79]. It was shown that under certain conditions, SWNT can be deposited on the cathode surface. This process depends on SWNT charging in the arc plasma. In turn, the charging phenomena depend on the electron temperature.

Gamaly and Ebbesen [80] proposed that the bimodal carbon velocity distribution (ions with drift velocity and isotropic neutrals) determines the nanotube creation process near the cathode. They suggested that isotropic distribution leads to fullerene formation, while directed flux results in nanotubes. Iijima et al. [81] proposed an open-ended growth model. In this model, carbon atoms and small carbon clusters add on to the reactive dangling bonds at the edges of the open-ended nanotubes. Other researchers argue that CNTs are elongated by electrostatic forces along the electric field near the cathode [82,83]. However, it seems like a high-resolution transmission electron microscopy (TEM) analysis does not support this hypothesis. Alternatively, a two-step growth model has been proposed [84]. According to this model, different carbon structures are formed first. Then, during the cooling process, the graphitization occurs from the surface toward the interior of the assemblies. Several workers developed a growth model of SWNT explaining the root growth of nanotube bundles emerging from catalyst particles [85]. These models include a catalyst phase diagram of carbon metal. The investigation of mechanism for the catalytic synthesis methods of CNTs in arc plasma is still subject to ongoing research. The vapor–liquid–solid (VLS) mechanism was first proposed by Wagner and Ellis and can be utilized to demonstrate the growth model of SWCNT [86]. According to the VLS framework, Ding et al. [87] simulated the nucleation processes of SWCNT associated with catalyst particles by molecular dynamics method, presenting the dependent relationship between diameters of SWCNT and catalyst particles theoretically. Based on the analysis of diffusion model of carbon atom and calculation by Monte Carlo technique, Keidar et al. [88] also demonstrated that the SWCNT diameter is determined by the size of the molten catalyst core in arc discharge. Chiang and Sankaran [89] reported the very important experimental results suggesting that the variation of the element composition of Ni_xFe_1-x catalyst particles strongly affects the SWCNT chirality. The link between the composition-dependent catalyst structure and the chirality of SWCNT would improve the in situ controllability of SWCNT synthesis. The results indicate the important role of the catalyst particles in the SWCNT synthesis.

6.2.1 Arc-discharge plasma system for synthesis of SWNT

A typical arc-discharge system consists of anode–cathode assembly installed in a stainless steel flanged chamber capped at both ends as shown in Figure 6.5. The arc discharge is sustained with a constant power supply, using a feedback connected to the linear drive of the anode and the power supply generating the arc. Linear drive allows to keep constant interlectrode gap of about 1 mm during the arcing time. The anode hole is packed with various metal catalysts. Quanta sizing and microscope examinations of arc-discharge products for equal arc runtime has revealed that the catalyst combination yielding the largest amount of nanotubes was Y–Ni in a 1–4 ratio [91]. The nanotube samples are typically produced at constant helium pressures ranging from 500 to 700 Torr and arc current ranging between 70 and 80 A. Magnetic field can be used to enhance arc-discharge technique. Schematically application of a nonuniform magnetic field is shown in Figure 6.6. Photos show that magnetic field modifies arc discharge. Magnetic field leads to formation of a plasma jet that will be describe below.

6.2.2 Synthesis of SWCNTs in a magnetic field

Permanent magnets (5×5×2.5) cm³ with different strengths were used to create and vary the strength of a nearly axial magnetic field in the discharge gap of about 0.5 cm as shown schematically in Figure 6.6. Magnetic field varies in the range of 0.2–2 kG. Samples with SWCNTs collected from locations were subsequently analyzed in the solid state with SEM and Raman spectroscopy, and postprocessing into aqueous dispersion by ultraviolet–visible–near infrared (UV–Vis–NIR) and PL spectroscopy techniques.

Collected samples were analyzed under SEM and the length distribution of individual SWNT was measured from SEM images. SEM data indicate that the presence of a magnetic field makes a significant difference in the average length of the SWNTs produced by the arc discharge as shown in Figure 6.7. Typical SEM image used for length measurements is shown in the inset in Figure 6.7. It should be pointed out that in many cases, it was confirmed that we measured length of a single nanotube, while in other cases we refered to an image of SWNT bundle. Left inset shows a typical SEM image used for length measurements; right inset shows the TEM image of the SWNT and bundle of SWNT. TEM image also indicates that SWNTs in a bundle have the same length. Of the entire measurements of SWNT length taken without the magnetic field, 50% were under 600 nm and 90% were under 1300 nm; while 50% of the measurements taken from samples with the magnetic field were under 1100 nm and 90% were under 2600 nm. Thus, the presence of the magnetic field seemingly doubles the length of SWNTs produced [39].

A mathematical model describing the very complicated problem of the SWNT formation in arc plasma was developed [39,78,79,97,98]. It has been shown that the electrical charges influence the growth of nanostructures [2,99]. In the following, we outline the principle points of these models to explain the SWCNT length increase in the strong magnetic-field-enhanced arc plasmas. The detailed description of the SWCNT growth will be presented in the next section.

A nanotube immersed in the plasma accumulates an electric charge on its surface and eventually encloses by the sheath which thickness can be estimated as where ε₀ is the dielectric constant, T_e is the electron temperature, n_p is the plasma density, e is the electron charge, and γ is a constant in the range of 1–5 [100]. In the sheath, there is an uncompensated electric charge which induced an electric field between the plasma bulk and the SWNT surface. In the calculations considered, it was assumed a maximum SWNT length of 5 μm that is in accordance with experimental data (Figure 6.7). Thus, for the typical plasma density (10¹⁷–10¹⁸ m⁻³) and electron temperature (up to 1 eV) in the arc plasma, the sheath thickness is in the range of 15–25 μm that significantly exceeds the SWNT length. While magnetic field can affect the sheath width [101], it does not affect the current collection and thus SWCNT growth. During the process of SWNT formation, the orientation of the nanotube is chaotic and changing in time, so the magnetic field cannot significantly decrease the electron current to the SWNT surface. As a result, the influence of the magnetic field on the sheath is moderate in this case.

In the sheath around SWNT, the ion motion is determined by the electrical field between SWNT and plasma bulk. The electric field is described by the Poisson equation for the electric potential Δφ=ρ_e/ε₀, where ρ_e is the density of electrical charge in the sheath. As a boundary condition for the Poisson equation, an equipotentiality of the entire SWNT surface was assumed, i.e., φ(x,r,α)|_(x,R,α)=Ψ_SWNT, where R is the SWNT radius. Ions enter the sheath with the Bohm velocity where m_i is the ion mass. An ion trajectory in the sheath can be obtained by integrating a motion equation. More details on the electric field and ion motion influence on nanostructures can be found elsewhere [102,103].

Here, the following scenario of the SWNT growth in a plasma was implemented. It was assumed that the SWNT grow on the partially molten metal catalyst particle supplied to the plasma from ablated electrode. In plasma, the metal catalyst particle is a subject to the additional heating and ablation, which reduce the catalyst size, and then condition and molten the external layer creating a liquid shell. The carbon atom flux gets to the catalyst surface, diffuse through it, and eventually incorporate into the SWNT structure. An ion flux supplies carbon atoms to the SWNT and catalyst. Upon recombination, carbon adatoms migrate about the SWNT surface, eventually reach the molten catalyst shell or reevaporate to the plasma bulk (Figure 6.8). Today, the two main growth scenarios are mostly accepted: the VLS [104] and solid–liquid–solid (SLS) [105]. Both scenarios involve the carbon atom diffusion in the metal catalyst particle, and thus the process of the carbon supply to the external catalyst surface is a decisive factor that determines the SWNT growth kinetics. To calculate the carbon supply to the catalyst surface, we implemented a diffusion model which was used for simulation of the diffusion-driven growth of carbon nanostructures on surface [106]. For the ion motion calculations, a Monte Carlo technique to obtain an ion flux distribution over the SWNT–catalyst surface was used. The diffusion model is used to calculate adatom migration about SWNT surface and the carbon atoms diffusion in the molten catalyst [107].

Obtained ion flux distributions over the nanotube were used for simulation of the SWNT growth rates η (μm×s⁻¹). The results of the calculations are shown in Figure 6.9, with the plasma density as a parameter. We should point out that the SWNT growth rate strongly decreases with the SWNT length and increases with the plasma density. Let us try to interpret the results shown in Figure 6.9. Note that formation of new layers is not considered here; thus, the growth rate of the nanotube depends only on the total influx of the carbon atoms to the surface of catalyst particle, which in turn depends on the total carbon influx to the SWNT and catalyst surfaces, as well as on the influx distribution over the SWNT and catalyst. When an SWNT is short, its growth rate is determined by the total carbon influx and the adaom migration kinetics. An essential part of the carbon atoms gets into the catalyst shell and participate in the SWNT growth. With the SWNT length increasing, the carbon flux to catalyst decreases due to increased carbon loss by evaporation, thus causing the decrease in the SWNT growth rate.

6.2.3 Effect of magnetic field on SWNT chirality

Since the discovery of SWCNTs [4], significant efforts have been directed toward attempts to synthesize SWCNTs of controlled chiral angle as discussed in Section 6.1. In particular, interest in chirality control is driven by the strict requirement to have a narrow distribution of SWCNT diameters, or a small number of chiralities, for enabling nanoelectronic applications [108–110]. Recent works indicate that one of the key parameters for SWCNT chirality control is the initial characteristics of catalyst particle [89,111]. For CD techniques, Li et al. [111] demonstrated that changing the size of their Co-MCM-41 catalyst particle (by altering the synthesis temperature through the range of 550–950 °C) allows for control of the produced SWCNT diameters over the range from 0.6 to 2 nm. Chiang and Sankaran [89] reported that varying the composition of Ni_xFe_1−x catalyst particle strongly affects distribution of produced SWCNT chiralities, namely a decrease of x leads to narrower distribution of produced chiralities and a decrease in the mean SWCNT diameter. However, fine control of the chirality distribution through manipulation of the catalyst has proven to be highly demanding, and so alternative techniques for shaping the distribution during the production process are desirable.

Below tuning of the distribution of produced SWCNTs for the anodic arc production method using an applied magnetic field is described. As it was mentioned above, SWCNTs synthesized in anodic arc have properties superior to those produced by CVD, including on the typical measures for quality of nanotubes (smaller defects, higher flexibility and strength) as well as a significantly higher production rate and should thus be more advantageous for practical applications [78,112–114].

Recently, different methods for control of anodic arc synthesis have been reported. It was shown that the anode composition and structure [115], background gas composition and pressure [25,116], and electric field [117] affect the production yield, diameter range, and aspect ratio of the synthesized SWCNTs. Particularly significant progress in control of arc synthesis was demonstrated using the application of external magnetic fields to the arc [39,118]; this magnetically enhanced discharge was demonstrated to be able to control the aspect ratio of SWCNTs [39]. Nanotubes synthesized in magnetically enhanced arc were two times longer than those produced without magnetic field. By changing the strength of the applied static magnetic field, the diameter distribution of the arc product can be controlled as shown schematically in Figure 6.6. The SWCNT samples synthesized at different magnetic fields were analyzed using scanning electron microscopy (SEM), photoluminescence (PL), UV–Vis–NIR absorbance and Raman spectroscopy.

Produced materials were analyzed both as -produced and as an aqueous dispersion. Figure 6.10A shows Raman spectra and SEM images of the as-produced samples (not purified) obtained with and without magnetic field. The SEM images show that both samples are enriched with SWCNTs ropes. Raman spectra of the samples with (B=1.2 kG) and without magnetic field had similar shapes. Detailed comparison of spectra, however, shows that a slight 1D peak was observed at about 1330 cm⁻¹ in the nonzero B sample, while no such peak was observed for the B=0 sample [119,120]. Separately, the 1G line is observed to be located at different wave number shifts in the two samples, with the primary peak at 1580 cm⁻¹ and a shoulder at 1557 cm⁻¹ for the B=0 sample and slightly upshifted peaks at 1585 and 1562 cm⁻¹ for the nonzero B samples. The presence of 1G indicates that the excitation at 514 nm is predominantly in resonance with the E₃₃ semiconducting transitions and not metallic nanotubes [121]. 2D peaks were observed around 2665 cm⁻¹ for both samples. Full range UV–Vis–NIR spectra are shown in Figure 6.10B.

Detailed comparison of SWCNTs synthesized with and without magnetic field was carried out using UV–Vis–NIR and NIR fluorescence spectrometry. The evolution of UV–Vis–NIR and PL spectra of the purified samples produced at different magnetic field strengths from 0 to 2 kG is shown in Figure 6.11A and B.

The UV–Vis–NIR spectrum of the B=0 sample shows spectra typical for arc-produced SWCNTs with peaks observed in the optical absorption bands corresponding to metallic (in vicinity of 650 nm) and semiconducting (around 900 nm) SWCNTs respectively. As is typical for many synthesis methods, the B=0 sample was enriched with semiconducting tubes around the roughly 2:1 ratio expected from the combinatorial probabilities when wrapping the graphene sheet. The apparent purity by the Haddon method, revised denominator=0.141 [122], was ≈72% for this sample, indicating that the dispersed SWCNTs are well purified by the dispersion and centrifugation process steps. It should be noted that the spectrofluorometer used in this study is unable to detect SWCNTs produced by the arc without a magnetic field due to their relatively large diameter, ≈1.5 nm typical for arc method production [116], which fluoresce from their S₁₁ transitions at wavelengths beyond the long wavelength range of the InGaAs array detector (≈1600 nm).

Now let us consider the evolution of spectra with increase of magnetic field. Firstly, the UV–Vis–NIR spectrum of the nonzero B sample demonstrates overall decrease of peak intensities corresponding to decrease of SWCNT production yield of both metallic and semiconducting nanotubes. Secondly, both UV–Vis–NIR and PL spectra indicate that increase of B-field leads to production of greater variety of semiconducting SWCNT diameters with an overall shift to smaller diameters. This is evidenced by the appearance of new peaks in the nonzero B samples with peak positions around 800 nm on UV–Vis–NIR spectra and new chiralities observed on PL spectra.

To better characterize the produced materials, an additional processing to separate enriched semiconducting and metallic fractions [123] was performed. Below results obtained using separation of semiconducting and metallic SWCNTs are described.

Three layers formed in the test tube after electronic type separation are schematically shown in Figure 6.12C and D by green (bottom layer containing mostly semiconducting SWCNTs), blue (upper layer—metallic SWCNTs), and red (medium—mixture) colors.

UV–Vis–NIR spectra of three layers are also presented in Figure 6.12C and D (green curve from semiconducting SWCNTs layer, blue—metallic SWCNTs layer, and red—from mixture layer). It is seen in Figure 6.12C (B=0 sample) that well pronounced peaks in semiconducting and metal SWCNT bands were observed in corresponding layers of the test tube. In contrast, the UV–Vis–NIR spectrum of the nonzero B sample showed reduced peak features in the layer where the typical metallic arc was separated and was similar to that from graphenic-like structures [125]. This indicates that the population of typical arc diameter metallic SWCNTs was significantly reduced by the application of the magnetic field. The spectrum from semiconducting layer had greater variety of peaks in comparison with the B=0 sample, which correspond to production of semiconducting SWCNTs with smaller diameter.

Thus both UV–visible–NIR and PL indicate that magnetically enhanced anodic arc yields broader spectrum of diameters of synthesized SWCNTs and smaller diameters compared with that without magnetic field. Such behavior is closely related to the change of catalyst particle motion in the presence of magnetic field. One possible pathway that can explain effect observed is the effect of magnetic field on catalysis particle nucleation [126]. The mechanism leading to catalyst nanoparticle diameter decrease is related to acceleration of the nickel-contained (magnetic) particles by the magnetic force toward the magnet when the temperature drops below the Curie point. In the center of the arc, the temperature is about 3000 K, while in the catalyst particle growth region the temperature is below 1800 K and can reach the Curie point toward the outer region.

Upon reaching the temperature below the Curie point, catalyst particles are accelerated toward the magnet thus reducing the residence (i.e., growth) time. As a result, catalyst particle diameter is expected to be smaller in the case of a magnetic field as compared to the case without a magnetic field as shown in Figure 6.13.

6.2.4 Synthesis of graphene in arc plasmas

With an external magnetic field applied to the discharge, the plasma temperature and density significantly increase. The plasma density strongly increases due to the effect of the magnetic-field-related focusing of the plasma jet. Indeed, magnetic confinement restricts the plasma boundaries and prevents the plasma from expansion. Another reason is the magnetization of plasma electrons which leads to more effective ionization of the neutral gas atoms by electron impact. The plasma temperature, in turn, increases in the magnetic field due to the stronger electric field in the magnetized plasma, in contrast to the nonmagnetic conditions [39,127]. Schematically, the magnetically controlled process is shown in Figure 6.14. The carbon samples were collected from the discharge enhancing/separating magnet unit (DESMU) side and top surfaces, and from the chamber walls.

In the growth zone, the ambient temperature is much higher than the Curie point of the catalyst nanoparticles which therefore remain hot and nonmagnetic. This is why the growth conditions are determined by the high catalyst temperature and also a strong incoming flux of carbon material. Outside of the optimum growth zone, the plasma temperature and hence the catalyst temperature decrease sharply. Further away, the temperature decreases below the Curie point, the catalyst particles become ferromagnetic, respond to the magnetic field, and the separation process starts. Thus, the boundary between the growth and the magnetic separation zones is determined by the catalyst alloy and the plasma parameters. Indeed, in the high-density plasma, the catalyst is hot and nonmagnetic; both graphene particles and CNT are developing in the optimum growth zone with no magnetic separation [71,128].

In the separation zone, the plasma density and the temperature are low, and the catalyst is cold. Hence, while the growth is disabled, the magnetic separation starts. To this end, the optimized composition of the two transition metals, yttrium (which is paramagnetic) and nickel (ferromagnetic with the Curie temperature of about 350°C), was used. Nickel exhibits very high carbon solubility but does not form carbon-containing compounds without oxygen, thus ensuring an efficient carbon supply to the nanostructures [129]. On the other hand, yttrium easily forms carbides and as such enables a very quick nucleation of the carbon nanostructures. Note that the melting points for both these metals are very close, so the catalyst alloy nanoparticles have a stable aggregate structure. In this way, the Y–Ni catalyst alloy was customized to exhibit the excellent nucleation/growth support ability when hot (in the optimum growth zone) and the ferromagnetic response when cooled down below 350°C (in the magnetic separation zone). Experiments have proven the effectiveness of this catalyst alloy for the large-scale carbon nanostructure production [39].

Figure 6.15 shows the images of the representative structures produced. The nanostructured carbon (nanotubes and graphene flakes) could be found on the magnet surfaces only, whereas lacey carbon was found only on the chamber walls. The carbon samples were collected and then analyzed with the SEM, TEM, atomic force microscopy (AFM), and micro Raman techniques. In Figure 6.15, we show representative SEM and TEM images of carbon samples collected from various parts of the setup. Figure 6.15A–C shows the low-, medium-, and high-magnification SEM images, respectively, of the samples containing graphene layers, collected from the top and side surfaces of the magnet (see Figure 6.15).

The estimated size of the graphene flakes is approximately 500–2500 nm, with up to 10 graphitic layers. Some graphene flakes show explicit crystallographic faceting (e.g., clearly visible hexagon sections in Figure 6.15C). It is also seen that the graphene flakes are surrounded and partially covered by loose carbon. Figure 6.15D and E shows TEM images of folded graphene layers in the carbon samples collected from the top and side surfaces of the magnet, respectively. It is seen that these fragments contain a few flake-like graphene layers, up to 3. In Figure 6.15F, it is shown the TEM image of the sample containing CNTs, collected from the side surfaces (remote from the discharge) of the DESMU. It should also be pointed out that a typical catalyst size found by the TEM was approximately 2–10 nm. The SEM analysis of the deposits found on the magnet allows a rough estimate of the production rate to be about 1 cm² of graphene per hour of operation.

The results that characterize the samples collected at the top surface of the DESMU by the AFM, Raman, and selected area electron diffraction (SAED) techniques are shown in Figure 6.16. The AFM clearly revealed the presence of flake-like structures with the surface size of around 1 µm and a height variation of 1–5 nm (Figure 6.16A and B). The Raman characterization of the specimens collected from the side surfaces of the magnet showed the occurrence of a weak D-peak at around 1325 cm⁻¹, which is related to the amount of defects in sp² bonds (Figure 6.16C) [130]. The SAED TEM pattern from a similar specimen collected from the top surface of the magnet is shown in Figure 6.16E. It reveals the pattern expected for a hexagonal close-packed crystal with the incident beam close to (0001) plane.

It should be pointed out that the magnetic field strongly enhances the arc discharge. Indeed, with the DESMU installed, the plasma arc (normally confined between the cathode and the anode) is stretched toward the magnet as shown in Figure 6.17. In the video snapshots shown in Figures 6.17, it can be noted that the presence of the magnet results in deviation of arc plasma in the direction of J×B force. It was also observed that the geometry of arc plasma column did not change by removing the nickel catalyst from the anode. This means that the influence of magnetic field on nickel catalyst particles motion does not affect overall geometry of plasma column. It is possible to control distribution of magnetic field by changing the position of permanent magnet, and consequentially the growth region of carbon nanostructures can be easily manipulated according to the J×B direction. SWCNT and graphene flakes are collected in the different areas. The sample collected from the surface of Mo sheet where the arc plasmas jet was directed contains high-quality and large-scale graphene. Experimental observations suggest that the graphene is growing by a surface precipitation mechanism [131].

6.2.5 Current state of the art of plasma-based synthesis of carbon nanostructures

In this section, we describe most pressing issues and current state of the art associated with synthesis of carbon nanoparticles in plasma-based synthesis technique.

6.3.1 Arc-discharge plasma

It was already mentioned above that the arc-discharge synthesis of carbon nanoparticles is a very promising plasma-based technique [117]. On the other hand, the controllability and flexibility of the arc-plasma-based process may be significantly improved by the use of a magnetic field (Section 6.2), which strongly influences the plasma parameters [127]. In fact, it was shown that the high-purity MWNTs can be grown in the magnetically enhanced arc discharge [38] and it was demonstrated that the use of the magnetic-field-enhanced arc discharge is very promising for the production of the long SWNTs [39].

Experimental efforts to understand the arc plasma mechanism of synthesis concerned with anode erosion mechanism [152], current–voltage characteristics of the arc discharge [153], and cathode deposit mechanism [154]. In particular, it was demonstrated that anode erosion increases with anode radius decrease, current–voltage characteristics have typical V-shape, and radius of the cathode deposit increases with arc current as shown in Figure 6.18.

CNT synthesis is a relatively recent application of the anodic arc discharge and only few theoretical models related directly to this application were developed. A 1D model (in axial direction) of the SWNT formation was developed and the SWNT growth rate in the anodic arc discharge was calculated [76]. In that model, some simplified gas phase analysis was employed to calculate the nanotube growth rate. The axial velocity of the carbon outflow from the anode was estimated from the measured erosion rate and thus such model is not predictive. Moreover, the temperature of the anode was given a priori, while another work showed the anode temperature dependent on the gas pressure [79]. In all existing models, there is no coupling between the interelectrode plasma and electrode phenomena such as ablation and electron emission.

6.3.2 Experimental studies of the arc-discharge plasmas for nanoparticle synthesis

Plasma diagnostics is an essential tool for the in situ studies of nanostructures formation during the synthesis processes. Combining with the postsynthesis characterizations of the nanostructures, it can establish the important correlations between external arc-discharge parameters and intrinsic nanostructure properties, thus allowing ultimate control of the synthesis process.

Several experimental techniques can be utilized to investigate the plasma and nanostructures in arc discharge. We will start with description of the Langmuir probe. In addition, a nondestructive optical spectrometry technique will be described. UV–Vis emission spectra of arc in different locations under various magnetic conditions will be analyzed to provide an in situ investigation for transformation processes of evaporated carbon and catalyst species into growing carbon nanostructures. Based on the arc spectra of carbon diatomic Swan bands, vibrational temperature in arc is determined.

6.3.3 Two-dimensional simulation of atmospheric arc plasmas

The purpose of the multidimensional simulation of the arc plasma is to obtain plasma parameters of the discharge relevant for CNT synthesis, which are very difficult to measure. To be useful, the numerical models should combine various phenomena such as arc operation, electrode heating, sublimation, flow expansion, species diffusion, plasma generation, and finally, nanostructure growth.

In order to obtain the temperature and species distribution, the numerical simulation of carbon arc discharge was performed [172] and will be described in this section. Electrode heating and ablation rate were coupled with flow expansion to evaluate the instantaneous mass rate of ablation self-consistently. Conservative form of Navier–Stokes equations with electromagnetic source and energy equation are solved using SIMPLER algorithm [173]. Species diffusion is solved separately for C, Ni, and Y to obtain the respective mass fractions inside the fluid domain. Ionization fractions are calculated for the individual species using Saha equation with LTE plasma assumption. Momentum and energy equations are solved using finite-volume discretization and SIMPLER algorithm to obtain velocity distribution. Power law scheme is used to obtain the fluxes on the cell faces. Energy equation is then solved to obtain the temperature distribution. Using the equation of state, overall density distribution is obtained. This order is repeated until convergence is achieved at any time step. This procedure is repeated at all time steps to obtain the transient results. Further details of modeling, boundary conditions, and the simulation are found in Ref. [172].

Axisymmetric formulation is adapted here. Formulation can be divided into five major areas: arc, sublimation, flow expansion, species transport, and ionization. The domain and boundary conditions are shown in Figure 6.40.

Current continuity in electric potential form is solved to obtain the potential field and then current is obtained. Where, σ is the electrical conductivity and φ is the electric potential.

(6.22)

Electrical conductivity of weakly ionized plasma in DC field is obtained using the Chapmann–Enskog equation

(6.23)

where, e, n_e, and m_e are unit charge, number density, and mass of electron, respectively. ν_e,a and ν_e,i are collision frequency of electron–neutrals and electron–ions, respectively, as given by:

(6.24)

where K_B, T, n_a, and n_i are Boltzmann constant, temperature, neutrals density, and ion density, respectively. Q_m is momentum transfer cross section for electrons and neutrals collision varying with temperature [161]. Coulomb logarithm, ln(Λ) of Eq. (6.25) is given in Eq. (6.26) for T_i=T_e and n_i=n_e:

(6.25)

(6.26)

where and ln(γ)=0.577 [174]. The momentum transfer cross section Q_m is species dependent. The collision frequencies of all the electron–neutral interactions should be added. Here the collision cross section of helium is considered for all neutrals. In general, the collision cross sections of metallic species are about two orders of magnitude greater than that of noble gases. In the present case, the evaporated material vapor density is one to two orders of magnitude less than that of He.

The azimuthal component of self-induced magnetic field is obtained using Ampere’s law. B_θ is azimuthal component of magnetic field, μ₀ is permittivity of vacuum, r is spatial coordinate in radial direction, j_z is axial component of current flux, and R is radius of chamber.

(6.27)

Initially, arc concentrates near the axial region and the catalyst-filled core intensively evaporates. Due to this intensive evaporation, the gap between electrodes increases near the catalyst core, and hence, the arc shifts toward the enclosed carbon shell. This transition in arc position is expected to alternate between the catalyst core and enclosed carbon shell throughout the experiment. Simulation of this transition is complicated and not necessary to obtain the overall evaporation rate. Hence, it is assumed that anode is made of single uniform compound material and arc is distributed uniformly throughout the anode tip.

Sublimation is calculated using Langmuir evaporation model (for details see Chapter 1).

(6.28)

Γ is evaporation mass flux rate, p_sat is the saturation pressure, R and M are gas constant and molecular weight, respectively. Equation (6.28) is applied at all radial locations along the anode tip and plasma interface to account for the variation in surface temperature and the subsequent sublimation rate. It has to be noted here that, Langmuir model predicts higher ablation rate compared to model based on Knudsen layer kinetics (see Chapter 1) as the former does not consider the influence of background pressure on the ablation rate.

In order to find the temperature and density of fluid inside the chamber, standard Navier–Stokes equations are solved. Conservative form is used to account for the variations in density:

(6.29)

(6.30)

(6.31)

where u is the velocity, μ is the viscosity, and h is the enthalpy. All the species are combined to obtain overall density and then treated as a single fluid. Velocity is zero on all solid fluid interfaces, due to no-slip, other than at the anode tip. Mass averaged velocity of the sublimated vapor at the interface is given as the boundary condition for axial velocity at the anode tip. The mass averaged velocity is obtained by dividing the evaporation mass rate with sum of vapor density and local density of fluid existing near the interface. Radial velocity and normal gradient of axial velocity are zero along the axis. Vent condition is specified on the whole bottom periphery of the chamber to maintain constant pressure inside the chamber.

Temperature on chamber walls is maintained constant at 350 K and normal gradient along the axis is considered to be zero. The chamber wall temperature 350 K is observed from the experiments. Heat flux boundary condition at the anode tip and plasma interface is given by Eqs (6.14) and (6.15).

Mass diffusion equation (Eq. (6.32)) is employed to find the distribution of individual species inside the chamber. c_l and D_l are the mass fraction and diffusion coefficient of species l, respectively.

(6.32)

Binary diffusion coefficients with hard sphere model [175] are used to account for the influence of temperature on the diffusion:

(6.33)

where D_AB is diffusion coefficient of species A diffusing into species B. M_A and M_B are molecular weights of species A and B. σ_AB is rigid sphere collision diameter.

Assuming that plasma is in LTE, Saha equation is used to obtain the ionization fractions of individual species (see Chapter 1):

(6.34)

where, n_i,l and n_0,l are number density of ions and neutrals of species l, respectively. E_l and h are ionization energy of species l and Planck’s constant. The set of Saha equations with the ionization energies corresponding to each species is solved subjected to charge neutrality condition.

Figure 6.41 shows the direct comparison of temperature contours from the simulation (left-hand side) with the photo of experiments. Total current is 60 A and the electrodes are separated by 4 mm. In the contour plot, the temperature of plasma at the cathode periphery level is greater than 4000 K. This 1:1 comparison is not accurate in terms of plasma emission and has only qualitative character. The similarity in the shape of the temperature contour plot and photo image can be noted here.

The current flux and self-induced magnetic field are shown in Figure 6.42A. The current flux is uniform near the anode tip and self-adjusts to a lower value toward the cathode tip. The maximum value of self-induced magnetic field is 0.0034 T. Pressure and density are shown in Figure 6.42B. Pressure of the gas inside chamber is 68,280 Pa throughout the chamber except in the arc region. Pressure along the axis near the anode tip is 68,480 Pa and decreases to 68,350 Pa in the mid arc region and then increases to 68,390 Pa toward cathode tip, due to flow stagnation. The density is low in the arc region due to high temperatures. Streamlines are shown in Figure 6.42C. The material evaporates from the anode with a velocity of 95 m/s and accelerates to 176 m/s in the mid arc region due to heat addition. The vapor then deflects away from the axis by cathode and velocity decreases gradually due to expansion. Vapor velocity is 20 m/s at a distance of 20 mm from the axis. In addition, the deflected vapor separates into two recirculation regions after hitting the chamber wall. Some of the gas leaves the chamber through the vent to maintain constant pressure.

Figure 6.43A and B shows the density distribution of neutral species C, Ni, Y, and their ions in the arc-discharge chamber. The highest values of density existing at the anode tip are 4.2×10²², 3.2×10²¹, and 7.8×10²⁰ m⁻³ for C, Ni, and Y, respectively. As expected, the quantity of carbon in the plasma exceeds that of the catalyst. The transport of species below the arc is mainly due to diffusion, whereas the diffusion and convection ensure the transport above the arc. The diffusion coefficient increases with the temperature; since the temperature in the fluid below the anode tip is high due to conduction from the anode lateral surface, the downward diffusion of species is observed in this area. Transport in radial direction is mainly due to convection. The highest densities of ions are 1.9×10²⁰, 5.5×10²⁰, and 2.6×10²⁰ m⁻³ respectively for C⁺, Ni⁺, and Y⁺. It is interesting to note that number density of C⁺ is lowest though it has highest neutral density. This is due to its high ionization potential. Out of the three species, Y has the lowest ionization potential and hence more Y⁺ are observed outside the arc, where temperatures are not sufficient to ionize C and Ni. Helium background gas has even higher ionization potential, so its ionization is negligible. Figure 6.43C illustrates the calculated distributions of temperature and electron density in the discharge with the highest numbers, 7020 K and 7.5×10²⁰ m⁻³ respectively, observed in the interelectrode gap. The disk-like radial distribution of temperature is due to convection.

The flow parameter distribution for I=100 A of arc current is shown in Figure 6.44. Anode evaporation rate increases due to higher energy deposition. As a result, the species density and temperature increase inside the chamber. Figure 6.44A shows the increased spreading of neutrals in all directions. The peak density of neutrals is 6.56×10²², 5.02×10²¹, and 1.21×10²¹ m⁻³ for C, Ni, and Y, respectively. The peak densities of C⁺, Ni⁺, and Y⁺ (Figure 6.44B)) are 7.31×10²⁰, 9.89×10²⁰, and 4.25×10²⁰ m⁻³, respectively. A slight reduction in the thickness of the disk-like structure is noted from Figure 6.44C, which is due to the increased flow speed. However, the peak temperature in the core region is 8640 K, which is greater than that observed for I=60 A case. The peak density of electrons, for this case, is 1.6×10²¹ m⁻³.

In the model described, an attempt was made to identify and outline the probable location of nanotube growth, directly from the simulation results. Majority of MWNTs are found in the soft core of the cathode deposit while SWNTs are found in the collaret, lateral surface of the cathode, upper wall of the chamber, and in the web suspended between cathode and chamber walls. It was also observed that, the cathode deposit has negligible amount of Ni, while it is high inside the soot deposited on the electrode lateral surfaces and in the web. The temperature distribution in Figure 6.43C also shows that temperature inside the arc region is high for Ni clusters to form. Three major theories were suggested for the growth of nanotubes: open-ended model [81], two-step growth model [84], and root-growth model [176]. Either one or all of the three mechanisms may contribute for the growth. Nevertheless, the root-growth model alone is considered here, due to the presence of large Ni clusters outside the arc region. It was shown analytically that growth of nanotubes is terminated due to the solidification of Ni clusters [177]. By considering the solidification point of 1730 K and condensation point of 3180 K, the region of nanotube growth can be outlined using the isothermal lines, directly from the simulation.

The probable growth region in vapor is shown in Figure 6.45 for I=20, 60, and 100 A. The outlined region also shows the possibility of nanotube growth on the walls of the electrodes. It can be deduced now that, the clusters grown in this region will be transported away due to convection and buoyancy, and deposited on the chamber walls. The size of growth region decreases with the increase of arc current, which is mainly due to the increases in the flow velocity as a result of increased anode evaporation rate. However, the production rate of nanoparticles does not decrease as the growth depends on the local density of contributing species which increase with the arc current as shown in Figure 6.44. Hence, there exists an optimum value of current for which production rate is the highest.

6.3.4 Model of the CNT synthesis in arc-discharge plasmas

Inside the growth region, vapor flux contributing to the growth consists of neutrals and ions of metal and carbon. The nanoparticles are negatively charged due to high mobility of electrons, creating a sheath of thickness close to Debye length, and hence ions are attracted toward the nanoparticle as shown in Figure 6.46. Nanoparticle of diameter d_np is surrounded by Debye sphere of radius d_np/2+λ_De consisting of nonneutral plasma. Ions enter the sheath with Bohm speed, v_B at the Debye sphere edge, and create a focused flux that contributes to the growth of nanoparticle [178]. Neutrals, on the other hand, attach to nanoparticle with thermal velocity v_th. However, the focusing of ion flux vanishes if the collisions with the neutrals of background gas are dominant inside the sheath, which occurs for smaller mean free paths λ_mf, i.e., λ_De>λ_mf. Besides, the nanoparticle travels at the flow speed macroscopically, which has to be considered to account for the variation in the contributing factors for nanoparticle growth [179]. The flux balance model used in Ref. [177] was for neutral vapor in the exhaust of rocket nozzles. Coming to the specific case of root-growth method of nanotubes, the effect of surface diffusion has to be considered for estimating the flux of carbon atoms. Quasi-steady form of continuum surface diffusion model was used previously for nanotube growth in stationary plasmas with constant properties [177].

Let us describe the mathematical model and prediction related to the growth of CNTs in arc plasmas. The growth of catalyst clusters can be obtained by first finding the critical cluster size using Gibbs free energy of formation of a spherical cluster of radius r given by Eq. (6.35):

(6.35)

where σ_τ is surface energy (surface tension of isotropic materials), V_a is the atomic volume, and S is the saturation ratio given by the ratio of oncoming vapor pressure p_v and equilibrium pressure of the spherical cluster p_sat. Equation (6.35) has maxima at r_c=2σV_a/[k_BT ln(S)] with a maximal energy of Here, r_c is the radius of critical nucleate. The clusters with r≥r_c are stable and grows larger with further addition of vapor atoms. Furthermore, the probable number of critical clusters may be given using Boltzmann like distribution function, as given in Ref. [180].

The growth model for the cluster moving along a random path l is given by [177]:

(6.36)

where r+r_a≈r=(3/4π)1/3N^1/3(2r_a), N is the number of atoms in the cluster, r_a is the radius of atom, r is the radius of nanoparticle, and v_l is the velocity of the cluster. The coefficient β is the ratio of the vapor atoms contributing to the growth of cluster to those arriving on to the cluster’s surface. β is given as (R_arr−R_evap)/R_arr. Since arrival rate (R_arr) and evaporation rate (R_evap) are proportional to pressure of the vapor atoms and equilibrium pressure of the cluster, by assuming bulk vapor and cluster exist at the same temperature, R_evap/R_arr=S. The equilibrium pressure p_sat of the spherical cluster surface can be calculated from its value corresponding to a flat surface (p*) using Kelvin’s equation, p_sat=p* exp[2σV_a/(rRT)]. Here, r is radius of the sphere and R is gas constant. The particle flux Q_Ni is obtained by adding neutral and ion fluxes as

(6.37)

Finally, Q_Ni from Eq. (6.37) is substituted in Eq. (6.35) to obtain the equation for catalyst cluster growth:

(6.38)

where η=[1+(/n)(4v_B/v_th)(1+(λ_De/r))²]. The value of η gives the ratio of total flux to the neutral vapor flux.

The effective flux of carbon atoms j_C directly contributing to the growth of nanotube is estimated using quasi-steady approach of continuum surface [176]:

(6.39)

where x is the length coordinate along nanotube and Q_C is the rate of carbon flux from the bulk vapor arriving on the nanotube surface, D_s is the surface diffusion coefficient, and τ_a is the time required to absorb carbon atoms. Q_C, D_s, and τ_a are estimated using the following system of equations [176]:

(6.40)

(6.41)

(6.42)

where a₀ is the inter atomic distance for carbon 0.14 nm, υ is the vibrational frequency of the atoms=3×10¹³ (value based on thermal vibrations), δE_D is the activation energy for surface diffusion of carbon (0.3−1.8 eV), and E_a is adsorption energy (1.8−3.5 eV) [176].

Equation (6.39) is solved analytically using the following boundary conditions specified at the root (x=0) and closed end (x=L) to obtain the flux distribution:

(6.43)

where L is the instantaneous length of nanotube, is diffusion length, and k=a₀/τ_inc is the kinetic constant of incorporation. The incorporation time τ_inc can be calculated as [176]:

(6.44)

Now, the increase in the length of the nanotube moving along a path l inside the chamber can be estimated using the flux balance as

(6.45)

where Ω is area of one carbon atom in the SWCNT.

Let us now discuss some predictions by the model described. The growth region in plasma is outlined using the isotherms 3180 (inner line) and 1730 K corresponding to the condensation and solidification points of Ni. The outlined region for an arc current of 60 A is shown in Figure 6.46. Now, the path of nanoparticle in the chamber has to be traced in order to extract the vapor density and temperature local to the particle, which contributes to its growth. Since the particle size varies from nanometer to micrometer, they can be conveniently assumed to follow the streamlines of the flow. Three typical streamlines are shown in Figure 6.47. The following calculations are performed along streamline-3, which originates inside the arc core and passes through the growth region. The temperature and species distribution used for these calculations were obtained from detailed simulation of arc discharge.

Electrode heating and sublimation rate were coupled with flow expansion to evaluate the instantaneous mass rate of ablation self-consistently. 2D electric field was considered to simulate the arc. Conservative form of Navier–Stokes equations with electromagnetic source and energy equation were solved. Species diffusion was solved separately for C, Ni, and Y to obtain the respective mass fractions inside the fluid domain. Ionization fractions were calculated for the individual species using Saha equation with LTE plasma assumption. Further details of modeling, boundary conditions, and the simulation are found in Refs [170,176]. For 60 A of arc current, the evaporation model has predicted almost double that of experiment value. Nevertheless, the trend shown the simulation for 10–100 A arc currents was consistent with the experiment values.

Growth calculations performed for I=60 A and 4 mm interelectrode gap with a background pressure of 68 kPa are shown in Figure 6.48. Mass fractions of C, Ni, and Y in the anode are 0.66, 0.25, and 0.09, respectively. Calculations are performed along streamline-3 shown in Figure 6.47. The mean free path, λ_mf is calculated based on neutral gas density. Here, He neutrals alone are considered as their density is more than three orders of magnitude compared to Ni. Figure 6.48A shows the effect of plasma on the growth of Ni cluster. The abscissa represents the distance along the streamline-3 starting from the isotherm corresponding to 3180 K and ending at the isotherm corresponding to 1730 K. The coefficient η shown on the left ordinate reflects the ratio of ion flux to neutral flux (η−1) contributing to the growth.

The ion density decreases as the particle moves away from the arc and hence η also decreases. Debye sheath thickness, λ_De shown on right ordinate, increases with the reduction in plasma density. The mean free path λ_mf decreases due to reduction in the temperature. At l=6 mm, the ion flux to the Ni cluster ceases completely as λ_De>λ_mf. The resultant growth is shown in Figure 6.48B. Though the flux is high in the region up to l=3 mm, cluster growth is negligibly small due to high rate of evaporation, R_evap. From l=3 to 6 mm, steep increase in the particle diameter d_np is observed due to the dominance of ion flux and beyond this point, the growth rate is low due to the cessation of ion flux. The final size of the Ni cluster is around 9.3 nm. It has to be noted here that, SWCNT starts growing on the Ni cluster simultaneously, which will reduce the Ni vapor flux to the cluster. The maximum reduction in the area may be 50%. It remains relatively unknown, exactly when the nanotube starts growing on the Ni cluster. Hence, on an average, only 75% of the cluster area is considered to receive Ni vapor flux.

Arc-discharge experiment with 60 A current was carried out to measure the Ni particle size. The details are found in Ref. [126]. The diameter distribution of Ni particles in a sample taken at a distance of 20 mm from the arc axis is shown in Figure 6.49. Diameter varies from 2 to 12 nm and the highest number of particles is of 6 nm. The average size of the particles is 7.5 nm. The size of the Ni cluster obtained from the present simulation at this location is 9.2 nm. As mentioned earlier, the rate of evaporation predicted by the simulation was higher compared to experiment. The accurate values of evaporation rate may decrease the Ni concentration in the growth region leading to a reduction in the particle size. But, the flow speed also decreases simultaneously, due to low evaporation rate. The slower flow causes the particle to stay for a longer time in the growth region and eventually increases the particle size.

Figure 6.50A shows that the ratio of total (ions + neutrals) flux to the neutral vapor flux is about 1 throughout the growth region. This means the ion flux no longer contributes to the growth of nanotube, which is evident from Figure 6.50B.

The ratio of ion density to neutrals density of carbon is negligibly small (less than 10⁻¹¹) even when the Debye sheath increases the collecting area. The reason for low ion flux is high ionization potential of carbon. Figure 6.50C shows the length of SWCNT as it travels along the streamline in the temperature range 3180–1730 K. The nanotube grows up to 3.6 μm long mostly due to neutrals flux.

The nanotube growth model, used here, cannot specify the diameter; however, the Ni cluster growth model can be used to specify the range of diameters. In fact it was shown that nanotubes grow as bundles as well on a single catalyst particle [21].

The SWCNT length distribution from the experiments conducted with 70–80 A arc current is shown in Figure 6.51. More details are found in Ref. [39]. The length distribution shows that 50% of the nanotubes are under 0.6 μm length while 90% are less than 1.3 μm. Also, the SEM image from Ref. [39] shows the nanotube grown up to 3.04 μm long. The growth calculations performed for 70 A and 80 A arc current are shown in Figure 6.52. The SWCNT length is 2.2 μm and 2.02 μm respectively for the arc currents 70 A (Figure 6.52A)) and 80 A (Figure 6.52B). The length obtained using the growth model agreed well with experimental data.

It should be pointed out that the growth of nanoparticles can be improved by (1) increasing the size of growth region, (2) increasing the density of contributing species (Ni, Ni⁺, C, and C⁺), and (3) decreasing the velocity of nanoparticle (≈fluid velocity). For a given configuration, contributing species density and velocity are interdependent as velocity is directly proportional to the evaporation rate. Though ion flux has a significant effect on the growth rate, density of C⁺ may not increase without increasing the temperature above 4500 K, at which nanotubes cannot grow [176].

Keeping this in view, parametric studies were carried out by varying the arc current, background pressure, and interelectrode gap. The results are listed in Table 6.3. Columns 2, 3, and 4 represent arc current, interelectrode gap, and background pressure, respectively. The length of path traversed by nanoparticle in the growth region, l, is shown in column 5. The size of Ni cluster, d_np, and length of SWCNT, L, are given in columns 6 and 7, respectively.

The nanoparticle sizes, d_np and L, decrease with the increase of arc current. This is mainly due to the increase in the flow velocity along the growth region. The velocity increases by 40 m/s compared to case-0. Though the density of species Ni, Ni⁺, C, and C⁺ is high due to the increased evaporation, the particles quickly move out of the growth region. On the other hand, reduction in arc current has the exactly opposite effect on the growth of nanoparticles. Reduced background pressure (case-3) and interelectrode gap (case-5) accelerate the flow and decrease the species density as well. Hence the particle sizes also decrease. Increase in background pressure and electrode gap decelerates the flow and also results in the increase of species density along the streamline. The diameter of Ni cluster increases by 1.1 and 2.5 nm, and the length of SWCNT increases by 1.5 and 3.4 μm respectively for the cases 4 and 6 in comparison to case-0. The increment of pressure and interelectrode gap has limitations in terms of transformation to MWCNT growth mode and arc stability. High pressure causes the arrival rate of vapor atoms to exceed the incorporation rate, which may result in the formation of MWCNTs.

1. Calculate charge evolution of a 10 µm long carbon nanotube. Consider 1.5 nm diameter nanotube in carbon plasma electron density of about 10¹⁷ m⁻³ and electron temperature of about 1 eV. Consider collisionless sheath around nanotube and neglect electron emission from the nanotube.

2. Compute SWCNT residence time in the 2 mm plasma region having density of about 10¹⁸ m⁻³ and flow velocity of about 10³ m/s. Consider electric field of about 1 V/m. Use conditions from problem #1 to calculate SWCNT charge in steady state.

3. Taking into account results presented in Section 6.3.2 compute the heat flux to anode and cathode in the case of 100 A arc discharge. Consider pressure of about 300 Torr, the anode diameter of about 6.35 mm, and the cathode diameter of about 12.5 mm. Both cathode and anode are made out of carbon.

4. Compute the conductivity of the weakly ionized 1 eV carbon plasma as a function of pressure. Consider that ionization degree is about 0.001.

5. Calculate the binary diffusion coefficient of carbon into helium as a function of temperature (1000–3000 K) for 1 atm arc.