Magnetic-field-enhanced synthesis of single-wall carbon nanotubes in arc dischargeMichael Keidar, Igor Levchenko, Tamir Arbel, Myriam Alexander, Anthony M. Waas, and Kostya Ken Ostrikov

Citation: Journal of Applied Physics 103, 094318 (2008); doi: 10.1063/1.2919712 View online: http://dx.doi.org/10.1063/1.2919712 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/103/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Effect of oxygen plasma on field emission characteristics of single-wall carbon nanotubes grown by plasmaenhanced chemical vapour deposition system J. Appl. Phys. 115, 084308 (2014); 10.1063/1.4866995 Increasing the length of single-wall carbon nanotubes in a magnetically enhanced arc discharge Appl. Phys. Lett. 92, 043129 (2008); 10.1063/1.2839609 High-yield synthesis of single-walled carbon nanotubes by gravity-free arc discharge Appl. Phys. Lett. 79, 2967 (2001); 10.1063/1.1413960 Production of thick single-walled carbon nanotubes by arc discharge in hydrogen ambience AIP Conf. Proc. 590, 7 (2001); 10.1063/1.1420044 Production of fullerenes and single-wall carbon nanotubes by high-temperature pulsed arc discharge J. Chem. Phys. 112, 6000 (2000); 10.1063/1.481172

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Magnetic-field-enhanced synthesis of single-wall carbon nanotubesin arc discharge

Michael Keidar,1,a� Igor Levchenko,2 Tamir Arbel,3 Myriam Alexander,4 Anthony M. Waas,3

and Kostya Ken Ostrikov2,b�

1Department of Mechanical and Aerospace Engineering, The George Washington University, Washington,DC 48109, USA2School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia3Department of Aerospace Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA4Department of Geophysical Science, University of Chicago, Chicago, Illinois 60637, USA

�Received 31 January 2008; accepted 6 March 2008; published online 9 May 2008�

The ability to control the properties of single-wall nanotubes �SWNTs� produced in the arcdischarge is important for many practical applications. Our experiments suggest that the length ofSWNTs significantly increases �up to 4000 nm�, along with the purity of the carbon deposit, whenthe magnetic field is applied to arc discharge. Scanning electron microscopy and transmissionelectron microscopy analyses have demonstrated that the carbon deposit produced in themagnetic-field-enhanced arc mainly consists of the isolated and bunched SWNTs. A model of acarbon nanotube interaction and growth in the thermal plasma was developed, which considersseveral important effects such as anode ablation that supplies the carbon plasma in an anodic arcdischarge technique, and the momentum, charge, and energy transfer processes between nanotubeand plasma. It is shown that the nanotube charge with respect to the plasma as well as nanotubelength depend on plasma density and electric field in the interelectrode gap. For instance, nanotubecharge changes from negative to positive value with an electron density decrease. The numericalsimulations based on the Monte Carlo technique were performed, which explain an increase in thenanotubes produced in the magnetic-field-enhanced arc discharge. © 2008 American Institute ofPhysics. �DOI: 10.1063/1.2919712�

I. INTRODUCTION

Recently, several advanced techniques were developedfor carbon nanotube �CNT� synthesis such as arc discharge,chemical vapor deposition, and laser ablation.1–4 Amongthem, plasma-enhanced methods are one of the most efficientand precise tools for the fabrication of various carbon-basednanostructures including nanotubes.5,6 Among other plasma-aided techniques, arc discharge is the most practical methodof CNT synthesis.7

The main feature of the arc discharge is that the CNTsproduced by the arc discharge technique have fewer struc-tural defects than those produced by low temperature tech-niques probably due to the fast growth that prevents defectformation. In addition, it was shown that among severalmethods of CNT production, nanotubes produced by the arcdischarge have the lowest time degradation of emissioncapability8 that is very important for field emission applica-tions.

A progress in arc discharge method of CNT synthesiswas motivated by Journet et al.,9 who showed that the single-wall nanotubes �SWNTs� can be produced in large quantitiesby the arc discharge. The production of high-purity multiwallnanotubes �MWNTs� in the magnetically enhanced arc dis-charge �MEAD� was also reported.10 It should be mentionedthat the SWNT and MWNT have quite different mechanical,

electrical, and chemical properties.11 The SWNTs usuallydemonstrate high flexibility and a lower level of the struc-tural defects, thus eventually demonstrating higher strengthcharacteristics.12

One important issue related to SWNT synthesis is theability to control SWNT properties, such as radius, chirality,and length. It was demonstrated that the SWNT radius can becontrolled by the type of the gas in the chamber while thegas pressure leads to a fairly constant radius �although sometendencies of radius increase with the pressure were recentlyreported�.13 Recently, some ideas regarding the control of thechirality were suggested.14 There is a tremendous interest insynthesis long SWNT, which will enable new types ofmicro-/nanoelectromechanical system systems, such as mi-croelectric motors, and can act as a nanoconducting cable.15

Recently, the growth of a 4 cm long SWNT was reported.15

In general, while arc discharge technique is considered tooffer poor flexibility, it is primarily a result of limited under-standing of the SWNT synthesis mechanism.16

Despite the significant progress in synthesis techniques,the nucleation and growth of CNTs in the arc discharge arestill not completely understood. In this paper, we mainly con-centrate on the SWNT synthesis in the arc plasmas. A devel-opment of the full picture of SWNT synthesis mechanism inarc discharge goes beyond the frameworks of this paper, andwe will concentrate on several aspects of the SWNT synthe-sis and peculiarities of the arc discharge technique as well aspossible SWNT-plasma interactions. In our preliminary in-vestigation, we have demonstrated17 that the length and pu-

a�Electronic mail: keidar@gwu.edu.b�Also at CSIRO Materials Science and Engineering, West Lindfield, New

South Wales 2070, Australia.

JOURNAL OF APPLIED PHYSICS 103, 094318 �2008�

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rity of the arc-produced CNTs can be significantly improvedby the application of a magnetic field to the arc discharge. Inthis paper, we show a detailed investigation on the magnetic-field-enhanced synthesis of the single-wall carbon nanotubes�SWCNTs� in the arc discharge and propose a model thatallows numerical simulation of the process of nanotubegrowth in the discharge plasma. The experiments show thatthe magnetic field ensures a significant enlargement of thehigh-density plasma area; as a result, the longer SWNT ofbetter quality �lower density of the structural defects� can besynthesized. Besides, this method ensures greater productiv-ity �higher number of nanotubes in the carbon deposit� andbetter purity �higher concentration of nanotubes in the car-bon deposit�. The proposed model makes it possible to un-derstand the main processes responsible for the SWNT pro-duction in the MEAD and calculate the most importantprocess characteristics such as nanotube growth rate in plas-mas of various densities.

II. EXPERIMENTAL SETUP AND PROCEDURES

The arc discharge system consists of an anode-cathodeassembly installed in a stainless steel flanged chambercapped at both ends �Fig. 1�a��. A linear drive connected tothe bottom of the chamber acts as the anode feed system.Two portholes on the vertical sides of the chamber are con-nected to a digital pressure transducer and a constant pres-sure control system. The arc discharge is sustained with aconstant power supply, using a LABVIEW feedback programconnected to the linear drive of the anode and the powersupply generating the arc. The anode is a pure carbon rod,while the cathode is a stainless steel rod, where the anode ishollow and the cathode is solid. The cathode has a length anda diameter of 1.5 and 0.5 in., respectively, while the anodehas a length of 3 in. and outer and inner diameters of 0.25and 0.125 in., respectively. The anode hole is packed withvarious metal catalysts. Previous quanta sizing and micro-scope examinations of arc discharge products for equal arcrun time has revealed that the catalyst combination yieldingthe largest amount of nanotubes was Y–Ni in a 1:4 ratio.13,18

The nanotube samples were produced at constant heliumpressures ranging from 500 to 700 Torr. The magnetic fieldwas applied to confine the discharge plasma. The samplescontaining SWNTs were collected after 180 s run of the arcdischarge under various conditions—with and without mag-

netic field. The produced samples were examined underscanning electron microscopy �SEM� and high resolutiontransmission electron microscopy �HRTEM�. The averageablation rate of the anode was determined by measuring theinitial and final anode geometries. From these measurements,the dependency of the anode material consumption on the arccurrent with and without magnetic field was determined.

III. RESULTS

In this section, we present experimental results related tothe study of the effect of a magnetic field on the arc dis-charge and SWNT synthesis. Several interesting effects wereobserved with the application of the magnetic field. First ofall, we should mention that the magnetic field applied to thedischarge significantly changes the mode of arcing, as de-scribed elsewhere.19,20 The discharge becomes brighter,while the discharge current and plasma density increase. Themagnetic field strongly confines the plasma causing brighterdischarge in the smaller zone. Here, we recall that the appli-cation of the magnetic field to the similar discharges usuallycauses a strong change in the plasma density.21,22 In our pre-vious works, we have also demonstrated that the applicationof magnetic field to the arc discharge leads to the significantchange in the cathode and anode erosion rates.17 It is naturalthat the carbon deposit produced in the magnetic-field-applied discharge is different from those produced withoutthe magnetic field. In Fig. 2, one can see the SEM images ofsamples synthesized without �a� and with �b� magnetic field.The purity of the sample produced in the magnetic field �b� isquite remarkable especially in comparison with the samplesynthesized without magnetic field. The sample synthesizedwithout the magnetic field consists of a large amount of by-products, its structure is less pronounced, and the nanotubesare not visible; conversely, the sample produced in the mag-netic field �b� demonstrated a large amount of the nanotubesand a very low fraction of carbon by-products. These resultsshow that the application of an axial magnetic field signifi-cantly improves the purity of anodic SWNT-containing de-posits.

A detailed analysis and HRTEM images of the carbondeposits have demonstrated that the samples produced in themagnetic field mainly consist of isolated SWNTs andbundles. In Fig. 3, we show TEM images of various magni-fications that demonstrate a 6 nm bundle of several SWCNTs

FIG. 1. �Color online� �a� Setups for the MEAD, cathode diameter of 0.5 in. and anode diameter of 0.25 in.; �b� photograph of the setup; �c� scheme of theanodic arc discharge, ablated flux, and helium supply for SWCNT synthesis.

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�a�, bundle and isolated SWCNT �b�, as well as a largebundle where the individual nanotubes are perfectly visible�c�. The detailed studies, along with the radius measure-ments, have proved that the nanotubes produced in themagnetic-field-assisted discharge are mostly single walled.

We recall again that just the length of the SWCNT is ourmain focus; thus, we have made a measurement of the nano-tubes collected from the deposits producing with and withoutthe magnetic field, and the obtained results are presented inFig. 4 where we show the distribution of SWCNT length. Itcan be seen from this graph that the maximum of the distri-bution of SWCNTs that are produced without the magneticfield corresponds to 400 nm; for the SWCNTs that are pro-duced in the magnetic field enhanced discharge, the maxi-

mum of the length distribution corresponds to 1000 nm, andthe deposit contains nanotubes with 4 µm length, with themaximum length of 2 �m found in the deposits producedwithout magnetic field.

IV. MODEL OF ARC PLASMA/SWNT INTERACTION

A. Model of SWNT movement and charging

According to existing model predictions, the nanotubeformation occurs in the region of relatively small plasmatemperature �1300–1800 K �Ref. 23�� where carbon reacts toform large molecules and clusters. Regarding the anode tem-perature, some models assume the anode temperature,22

while recent work showed that the anode temperature de-pends on the gas pressure.24 No detailed model for the rela-tionship between the discharge parameters and SWNT for-mation was developed, as mentioned in a recent reviewpaper.25 A model of SWNT interaction with discharge plasmain the cathode region �collaret� was developed.26 It wasshown that the plasma-SWNT interactions depend on SWNTcharging in the arc plasma. It is known that charging in thearc plasmas strongly depends on the SWNT residence time.27

In this section, we briefly review the model for SWNT charg-ing and transport in the plasma that affect the SWNT resi-dence time in the plasma region.

FIG. 2. SEM images of the carbon deposit produced: �a� without magneticfield �B=0� and �b� with magnetic field, B=0.4 T, applied to the anodic arcdischarge.

FIG. 3. �a� TEM image of the bundleof SWCNTs at high magnification, �b�TEM image of the bundle of CNTsand individual nanotube in parallel tothe bundle at lower magnification, and�c� SEM image of the large bundle ofSWCNTs.

FIG. 4. Distribution of nondimensional SWNT lengths/nanotube length indeposits produced with and without magnetic field. The magnetic field is0.4 T.

094318-3 Keidar et al. J. Appl. Phys. 103, 094318 �2008�

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The charge transfer from the plasma to SWNT is due toelectron and ion fluxes to SWNT seed and due to thermionicemission from the hot SWNT,

dQSWNT

dt= Ii − Ie + Iem, �1�

where QSWNT is the SWNT charge and Ii, Ie, and Iem are ion,electron, and thermionic currents, respectively. Densities ofthe carbon species �ions and atoms� are determined by theanode ablation rate. The maximum density of carbon atoms/molecules in the interelectrode gap can be estimated from thevapor pressure. For instance, in the case of He pressure ofabout 500 Torr, the resulting anode temperature is about3270 K and the anode erosion rate is about 3 mm3 /s.13,16

Based on these calculations, one can estimate the upper limitof the carbon species density as nC= Pv / �kT�, where Pv is thevapor pressure at the anode. The density decreases due toplasma expansion in the radial direction and, typically, theplasma density has its highest value along the arc dischargecenterline.28 Typically, the ionization degree is about 10−3

and the electron temperature Te is about 0.5 eV.SWNT interaction with plasma in the interelectrode re-

gion leads to momentum transfer so that SWNT trajectoriescan be calculated as follows:

MSWNTd2rSWNT

dt2 = FD + QSWNTE , �2�

where FD is the drag force, FD=�dSWNT�Vi−VSWNT�2,16 � isthe plasma density, and E is the electric field in the region ofSWNT formation. Momentum transfer depends on theplasma and neutral density in the interelectrode gap.

The calculated SWNT charge is shown in Fig. 5 as afunction of plasma density. One can see that a higher plasmadensity leads to a negative charge due to the increased elec-tron flux to SWNT from the plasma. These simulations showthat SWNT accumulates negative or positive charge depen-dent on the electron density in the SWNT formation region.Based on this prediction, different strategies of manipulationof SWNT growth by electric field can be implemented, assuggested earlier.16

B. Model of SWNT growth: Effect of electric field

Now, we attempt to explain the features of SWNTgrowth in the MEADs. We recall that the application of mag-netic field, first of all, strongly increases the plasma densityand electron temperature of the discharge. Together with theelectric field related effects, this should strongly affect theSWNT growth.29 We have already shown in our previousworks that ion focusing in nanoscaled systems can play avery important role.30,31 Now, we present a model that helpsdescribe a SWNT growth in the dense plasma.

Let us first consider in detail the SWNT-plasma interac-tion. As any object immersed in the plasma, SWNT esquiresan electric charge �dependent on plasma density, as shown inFig. 5� and eventually encloses by the plasma-surface sheathwhich thickness can be estimated as few Debye lengths,

� = ���0Te/enp, �3�

where �0 is the dielectric constant, np is the plasma density,and � is a constant in the range of 1–5.32 The plasma isquasineutral outside the sheath, and the electrical field isclose to zero. In the sheath, there is a noncompensated elec-tric charge which created an electric field applied to theSWNT surface �Fig. 6�.

It was shown that in the process with pure helium, theSWNT length reaches several microns;33 so in our calcula-tions, we have assumed the maximum SWNT length of5 �m. Thus, for the typical plasma density �1017–1018 m−3�and electron temperature �1–5 eV� in the arc discharge, wecan estimate the sheath thickness in the range of 15–50 �m.This estimate shows that the sheath thickness well exceedsthe SWNT length � and, hence, the shape of the sheathenvelope does not significantly depend on it.

FIG. 5. SWNT charge as a function of electron density in plasma calculatedby the model of SWCNT/plasma interaction.

FIG. 6. �Color online� SWNT on the metal catalyst particle in plasma. In thepractically interesting condition of large sheath �����, the shape of thesheath weakly depends on the SWNT length. Electric field is applied be-tween SWNT/C and plasma bulk border. Carbon ion flux is mainly depos-ited on SWNT tip and on catalyst particle.

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In the vicinity of SWNT, the ion motion is determinedby the electrical field between the SWNT surface and plasmabulk boundary. The electric field is described by the Poissonequation for the electric potential �=�e /�0, where �e is thedensity of electrical charge on the sheath. As a boundarycondition for the Poisson equation, we assumed the equipo-tentiality of the entire SWNT surface �thus, we assumed thatthe SWNT is well conductive�: ��x ,r ,���x,R,�=�SWNT,where �SWNT is the electric potential of the SWNT/catalystsystem and R is the SWNT radius. With the electric field inthe sheath calculated, the ion trajectories can be obtained byintegrating the motion equation. More details on the electricfield and ion motion calculations on nanostructures can befound elsewhere.34,35

In this work, we have implemented the following sce-nario of the SWNT growth in plasma. We assume that theSWNT grows on the partially molten metal catalyst particlesupplied to the plasma from the ablated electrode �below, wewill term the SWNT growing on the catalyst particle as theSWNT/C system�. In the plasma, the metal catalyst particleis subject to additional heating and ablation, which reducethe catalyst size, and then condition and molten the externallayer creating an external liquid shell. The carbon atom fluxgets to the catalyst surface, diffuses through it, and eventu-ally incorporates into the SWNT structure. The ion flux at thesheath border-SWNT/C surface supplies carbon atoms to theSWNT/C system. Upon recombination, carbon adatoms mi-grate about the SWNT/C surface and eventually reach themolten catalyst shell or re-evaporate to the plasma bulk �themain processes are schematically shown in Fig. 7�. Today,the two main growth scenarios are mostly accepted: thevapor-liquid-solid36,37 and solid-liquid-solid.38 Despite thedifferent initial stages, both scenarios involve the carbonatom diffusion in the molten metal of the catalyst particleand, thus, the process of the carbon supply to the externalcatalyst surface is a decisive factor that determines theSWNT growth kinetics. To calculate the carbon supply to thecatalyst surface, we implemented a diffusion model that wasused for the simulation of the diffusion-driven growth ofcarbon nanostructures on surface.30,31,35

The above described model was used to simulate theSWNT growth on a metal catalyst particle in plasma. For theion motion calculations, we used a Monte Carlo �MC� tech-nique to obtain the ion flux distribution over the SWNT-

catalyst surface.34 The adatom migration in the collisionlessapproximation about SWNT surface was simulated also bythe MC method, and the carbon atom diffusion in the moltencatalyst was calculated by the diffusion equation.39 The de-tailed description of the numerical method and boundaryconditions can be found elsewhere.35

The calculated distributions of the ion flux on theSWNT/C system surface with the plasma density and SWNTlengths as parameters are shown in Fig. 8. It can be seenfrom the graphs that the plasma density strongly affects thedistributions. In the plasma of lower density �1�1017 m−3�,the ion flux is distributed nearly uniformly over the entireSWNT/C surface, with a slight increase at the SWNT tip andcatalyst particle. For the plasma density of 1�1018 m−3, thedistribution becomes strongly nonuniform, with the densityof ion flux strongly reduced at the middle part of the SWNT.The further increase in the plasma density of up to 3�1018 m−3 does not change the distribution but makes it yetmore nonuniform, with the density at the middle part ofSWNT tending to zero. The distributions are similar for bothSWNT lengths but the longer SWNT exhibits stronger non-uniformity �Figs. 8�a� and 8�b��.

Obtained ion flux distributions were used for the simu-lation of the SWNT growth kinetics. First, we have calcu-lated the ratio of carbon flux through the catalyst �incorpo-rated into the SWNT structure� to the total flux of carbonatoms �,

� = C

�i + �a, �4�

where C is the total flux of carbon atoms through the cata-lyst, �i is the total flux of carbon ions deposited on thesurface of SWNT/C system, and �a is the total flux of car-bon atoms deposited on the surface of SWNT/C system. We

FIG. 7. �Color online� Growth of SWNT on the molten metal catalyst par-ticle in plasma. Carbon flux from plasma is nonuniformly distributed aboutSWNT and catalyst particle surface. Carbon adatoms diffuse to the catalystend and then incorporate into the SWNT structure through the molten cata-lyst shell. The SWNT diameter is determined by the size of the moltencatalyst core.

FIG. 8. �Color online� Distribution of carbon ion flux on SWNT/C surfaceswith plasma density and SWNT length as parameters. The SWNT lengthsare �a� 2 �m and �b� 1 �m, the diameter is 2 nm, and the catalyst particlediameter is 10 nm.

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did not assume carbon re-evaporation from the molten cata-lyst shell, thus assuming that the carbon atoms that get to thecatalyst dissolve in the molten metal and migrate to theSWNT through it. The results of calculations are presented inFig. 9 as a function of plasma density, with the SWNT lengthas a parameter. The ratio � increases with the plasma density,reaching 0.5 for a SWNT length of 2 �m and 0.8 for aSWNT length of 0.5 �m, for the plasma density of 5�1018 m−3.

Then, we used the obtained flux ratio � in calculatingthe SWNT growth rates � ��m s−1�. The results of the cal-culations are shown in Fig. 10, with the plasma density as aparameter. We should point out that the SWNT growth ratedecreases with the SWNT length and increases with the pres-sure.

V. DISCUSSION

In this section, we will try to interpret the obtained re-sults. The experimental results show that the purity andlength of the SWNT significantly increase with the applica-tion of the magnetic field. Our previous studies suggest thatthe application of an axial magnetic field leads to the in-crease in the relative density of the plasma and also electrontemperature.40 Given that the purity of the SWNTs increaseswith application of a magnetic field, this means that someparticular ratio between ion and neutral density may be op-timal for the SWNT growth. Also, this fact demonstrates animportance of the high-energetic ions versus neutral speciesin the process of the nanotube synthesis in the discharge.This suggests that MEAD, which provides wide possibilitiesfor controlling the discharge parameters, might be the moreefficient system for SWNT synthesis.

To understand an experimental fact of the nanotubelength increase in the MEAD, we should match and analyzethe experimental and simulative results. Let us consider firstthe short SWNT. At low plasma density, the sheath aroundSWNT is very large, and the ion flux is distributed nearuniformly on the surface. The catalyst particle adsorbs somefraction of the total ion flux deposited on the SWNT �0.6 for1�1017 m−3, Fig. 9�, and the rest atoms are lost due to there-evaporation from the SWNT surface. The evaporationlosses are low in this case since the SWNT is short, and the

time of adatom migration is too short for intensive evapora-tion. At higher plasma densities �up to 5�1018 m−3�, thesheath around SWNT is narrow, and ion focusing becomesmuch stronger �Fig. 8�a��. The number of ions directly de-posited on the catalyst surface increases and the number ofadatoms that should pass a SWNT length decreases. As aresult, the re-evaporation loss decreases, and the ratio � in-creases and approaches 0.8 for the short SWNT we are con-sidering.

This scenario is supported by the quantitative data ob-tained by calculations. Indeed, in the plasma of very lowdensity �1016 m−3�, the ions are uniformly distributed aboutthe SWNT surface, and the rate of losses is about 50% �Fig.9, curve for SWNT length of 0.5 �m�; thus, a half of all ofthe adatoms that migrate about the SWNT are lost. In thesecond ultimate case of the dense �5�1018 m−3� plasma, ionfocusing is very strong and we can assume that the ion flux isdeposited only on the SWNT’s tip and on the catalyst par-ticle �Fig. 8, curve for np=3�1018 m−3�. Thus, at present,50% of the ions that deposited on the SWNT tip �i.e., 25% ofthe total flux� will be lost and 25% should reach the catalystsurface by surface migration. Hence, the total ratio of fluxthrough the catalyst � should approach 75%, which is in agood agreement with the graph �0.78, Fig. 9, upper curve�.

For other SWNT lengths, the same tendency is observed,with larger rate of loss to evaporation for longer SWNTs�Fig. 9, curves for 1 and 2 �m�. It can be noted that � ratiofor long �2 �m� SWNT approaches 0.5; this evidences thaton the long SWNT, almost all adatoms migrating about thelong SWNT are lost by re-evaporation, and only 50% of theions focused on the catalyst participate in the SWNT growth.Indeed, in the conditions of strong ion focusing, the ratio �cannot be less than 0.5 in the dense plasma environment,where the entire ion flux is distributed to the SWNT tip andcatalyst particle.

FIG. 10. Dependence of SWNT growth rate � on the nondimensional nano-tube length/nanotube length with plasma density as a parameter. The SWNTdiameter is 2 nm and the catalyst particle diameter is 10 nm. The graphshows a strong decrease in the SWNT growth rate with the SWNT length.

FIG. 9. Dependence of ratio of the carbon flux through catalyst to the totalflux of carbon ions deposited on the SWNT surface on plasma density, withthe SWNT length as a parameter. The SWNT diameter is 2 nm and thecatalyst particle diameter is 10 nm. No evaporation from surface of moltencatalyst shell.

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Let us now discuss the dependence of SWNT growthrate � on the SWNT length �Fig. 10�. First, we should pointout that the growth rate � of a SWNT in the constant influxconditions �constant carbon flux through catalyst to SWNT�does not depend on the SWNT length since the thickness ofthe SWNT does not depend on its length �single-atom wall�.Thus, the growth rate only depends on the total influx of thecarbon atoms to the surface of catalyst particle, which in turndepends on the total carbon influx to the SWNT/catalyst sys-tem and on the influx distribution over the SWNT/catalyst.We also recall here that in the case considered �SWNT length����, the sheath shape and the size weakly depend on theSWNT length. Thus, the total flux to the SWNT/catalyst isproportional to the area of sheath surface around the SWNT/catalyst system and also proportional to the plasma densitynp; thus, taking into account the sheath size dependence �

=���0Te /enp, we conclude that the total flux to the SWNT/Cin the first approximation does not depend on the plasmadensity and could be estimated as

� = �2�0Te

e�B, �5�

where �B is the Bohm velocity.24 When a SWNT is short, itsgrowth rate is determined by the total carbon influx to theSWNT/catalyst and the adatom migration kinetics; it wasalready mentioned that the carbon flux to the catalyst shelldecreases with increasing SWNT length, as seen in Fig. 9. Inthe case of a short SWNT, an essential part of the carbonatoms �from 80% for higher plasma density to 50% for lowerdensity� gets into the catalyst shell and participates in theSWNT growth. With increasing SWNT length, the carbonflux to catalyst decreases due to increased carbon loss byevaporation, thus causing the decrease in the SWNT growthrate.

We should also mention that the proposed catalyst core/shell scenario can explain a weak increase of the SWNTdiameter with gas pressure.13 An increase in the gas pressurecauses an increase in the plasma density; this in turn causes aslight decrease of the electron temperature in plasma. As aresult, the catalyst heat exchange conditions change, and alarger solid core �thinner shell� forms; the diameter ofSWNT formed on it increases.

VI. CONCLUSIONS

The obtained results suggest that the magnetic field has aprofound effect on the arc discharge and growth of theSWNTs. In particular, the SWNT purity and length signifi-cantly increase with the magnetic field. The model of SWNTinteraction and growth in the arc discharge plasma was de-veloped and successfully used for analyzing the obtained ex-perimental results. Several effects such as momentum,charge, and energy transfer between SWNT and plasma wereconsidered. The SWNT growth model in the arc plasmabased on MC technique also suggests that a magnetic fieldmay lead to longer nanotubes. In general, trends predicted bythe model are in good agreement with our experimental ob-servations.

It should be pointed out that previous model suggestedvarious scenarios for SWNT growth termination in arc dis-charge. These scenarios tie to the mechanism of the carbonspecies precipitation and chemistry involved in SWNT syn-thesis. In addition to that, in the dynamic system such as arcdischarge, SWNT growth is the function of the SWNT seedmotion along the discharge plasma. Therefore, increase ofthe SWNT residence time and increase of the carbon precipi-tation due to the increase of the plasma density may be con-sidered as an efficient way to control SWNT growth.

ACKNOWLEDGMENTS

M.K. and M.A. thank the National Nanotechnology In-frastructure Network �NNIN�. The work was also supportedin part by the University of Sydney, CSIRO, and the Austra-lian Research Council.

1S. Iijima, Nature �London� 354, 56 �1991�.2Z. Huang, J. Xu, Z. Ren, J. Wang, M. Siegal, and P. Provencio, Appl.Phys. Lett. 73, 3845 �1998�.

3Y. H. Wang, M. J. Kim, H. W. Shan, C. Kittrell, H. Fan, L. M. Ericson, W.F. Hwang, S. Arepalli, R. H. Hauge, and R. E. Smalley, Nano Lett. 5, 997�2005�.

4S. Arepalli, J. Nanosci. Nanotechnol. 4, 317 �2004�.5C. D. Scott, J. Nanosci. Nanotechnol. 4, 368 �2004�.6Z. Markovic, B. Todorovic-Markovic, I. Mohai, Z. Farkas, E. Kovats, J.Szepvolgyi, D. Otaševic, P. Scheier, S. Feil, and N. Romcevic, J. Nanosci.Nanotechnol. 7, 1357 �2007�.

7K. Ostrikov, Rev. Mod. Phys. 77, 489 �2005�.8Y. Okawa, S. Kitamura, and Y. Iseki, Proceedings of the Ninth SpacecraftCharging Technology Conference, Tsukuba, Japan, April 2005 �unpub-lished�.

9C. Journet, W. K. Maser, P. Bernier, A. Loiseau, M. L. de la Chapelle, S.Lefrant, P. Deniard, R. Lee, and J. E. Fischer, Nature �London� 388, 756�1997�.

10K. Anazawa, K. Shimotani, C. Manabe, H. Watanabe, and M. Shimizu,Appl. Phys. Lett. 81, 739 �2002�.

11P. J. F. Harris, Carbon 45, 229 �2007�.12I. Stepanek, G. Maurin, P. Bernier, J. Gavillet, A. Loiseau, R. Edwards,

and O. Jaschinski, Chem. Phys. Lett. 331, 125 �2000�.13E. I. Waldorff, A. M. Waas, P. P. Friedmann, and M. Keidar, J. Appl. Phys.

95, 2749 �2004�.14J. Kunstmann, A. Quanddt, and I. Boustani, Nanotechnology 18, 155703

�2007�.15L. X. Zheng, M. J. O’Connell, S. K. Doorn, X. Z. Liao, Y. H. Zhao, E. A.

Akhadov, M. A. Hoffbauer, B. J. Roop, Q. X. Jia, R. C. Dye, D. E.Peterson, S. M. Huang, J. Liu, and Y. T. Zhu, Nat. Mater. 3, 673 �2004�.

16M. Keidar, J. Phys. D 40, 2388 �2007�.17M. Keidar, I. Levchenko, T. Arbel, M. Alexander, A. M. Waas, and K.

Ostrikov, Appl. Phys. Lett. 92, 043129 �2008�.18M. Keidar, Y. Raitses, A. Knapp, and A. M. Waas, Carbon 44, 1022

�2006�.19I. Levchenko, M. Romanov, and M. Keidar, J. Appl. Phys. 94, 1408

�2003�.20I. Levchenko, M. Romanov, M. Keidar, and I. Beilis, Appl. Phys. Lett. 85,

2202 �2004�.21I. Levchenko and M. Romanov, Surf. Coat. Technol. 184, 356 �2004�.22A. Fruchtman and A. Cohen-Zur, Appl. Phys. Lett. 89, 111501 �2006�.23I. Hinkov, J. Grand, M. L. de la Chapelle, S. Farhat, C. D. Scott, P.

Nikolaev, V. Pichot, P. Launois, J. Y. Mevellec, and S. Lefrant, J. Appl.Phys. 95, 2029 �2004�.

24M. Keidar, A. M. Waas, Y. Raitses, and E. Waldorff, J. Nanosci. Nano-technol. 6, 1309 �2006�; U. Cvelbar, M. Mozetic, and A. Ricard, IEEETrans. Plasma Sci. 33, 834 �2005�.

25S. Farhat and C. D. Scott, J. Nanosci. Nanotechnol. 6, 1189 �2006�.26M. Keidar and A. M. Waas, Nanotechnology 15, 1571 �2004�.27M. Keidar, I. Beilis, R. L. Boxman, and S. Goldsmith, IEEE Trans. Plasma

Sci. 23, 902 �1995�.28I. Beilis, M. Keidar, R. L. Boxman, S. Goldsmith, J. Heberlein, and E.

094318-7 Keidar et al. J. Appl. Phys. 103, 094318 �2008�

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

131.181.251.131 On: Tue, 15 Jul 2014 00:57:12

Pfender, J. Appl. Phys. 86, 114 �1999�.29I. Levchenko, K. Ostrikov, M. Keidar, and S. Xu, J. Appl. Phys. 98,

064304 �2005�; I. Levchenko, K. Ostrikov, J. D. Long, and S. Xu, Appl.Phys. Lett. 91, 113115 �2007�.

30I. Levchenko, K. Ostrikov, M. Keidar, and S. Xu, Appl. Phys. Lett. 89,033109 �2006�.

31I. Levchenko, K. Ostrikov, and E. Tam, Appl. Phys. Lett. 89, 223108�2006�; I. Levchenko, M. Korobov, M. Romanov, and M. Keidar, J. Phys.D 37, 1690 �2004�.

32M. A. Lieberman and A. J. Lichtenberg, Principles of Plasma Dischargesand Materials Processing �Wiley, New York, 1994�.

33F. Du, Y. Ma, Xin Lv, Yi Huang, F. Li, and Y. Chen, Carbon 44, 1327�2006�.

34I. Levchenko and K. Ostrikov, J. Phys. D 40, 2308 �2007�.35I. Levchenko and K. Ostrikov, Phys. Plasmas 14, 063502 �2007�.36J. Gavillet, J. Thibault, O. Stéphan, H. Amara, A. Loiseau, Ch. Bichara,

J.-P. Gaspard, and F. Ducastelle, J. Nanosci. Nanotechnol. 4, 346 �2004�.37B. B. Wang, S. Lee, X. Z. Xu, S. Choi, H. Yan, B. Zhang, and W. Hao,

Appl. Surf. Sci. 236, 6 �2004�.38R. Sen, S. Suzuki, H. Kataura, and Y. Achiba, Chem. Phys. Lett. 349, 383

�2001�.39I. Levchenko, A. E. Rider, and K. Ostrikov, Appl. Phys. Lett. 90, 193110

�2007�.40M. Keidar, I. Beilis, R. L. Boxman, and S. Goldsmith, J. Phys. D 29, 1973

�1996�.

094318-8 Keidar et al. J. Appl. Phys. 103, 094318 �2008�

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

131.181.251.131 On: Tue, 15 Jul 2014 00:57:12