Influence of the gas pressure on single-wall carbon
nanotube formation
I.Hinkov a ,S.Farhat
a,*
,C.D.Scott
b
a
Chemical Engineering Department,LIMHP,Universite
´Paris 13,Avenue J.B.Cle ´ment,93430Villetaneuse,France b
NASA,Lyndon B.Johnson,Space center ES3,Houston,TX 77058,USA
Received 7September 2004;accepted 26April 2005
Available online 24June 2005
Abstract
Experiments and modeling are performed to predict the effect of gas pressure on species distributions and nanotube growth rate under specific conditions of synthesis of single-wall carbon nanotubes (SWCNTs)by arc discharge.Numerical results are compared with experiments in order to find a consistent correlation between the nanotube growth and the pressure.We use argon and helium as buffer gases with a total pressure varied between 0.1and 1bar.We experimentally observe that both the anode erosion rate and the Brunauer–Emmett–Teller (BET)surface area of the as-produced nanotube soot material are very sensitive to the total gas pres-sure in the reactor.
Ó2005Elsevier Ltd.All rights reserved.
Keywords:Carbon nanotubes;Arc discharge;Modeling;BET surface area
1.Introduction
There are a large number of works describing the ef-fect of individual process parameters on the yield of car-bon nanotubes for arc,laser and solar processes.Nevertheless,the relevant processes of nucleat
ion and growth of nanotubes,as well as growth precursors are still not completely elucidated.For the arc process,a key parameter for the nanotube growth is the erosion rate of the anode,which depends primarily on the sur-face temperature.The temperature depends on the input power,the chemical composition of the anode,the length of the arc,the nature of the inert gas,the pres-sure,the cooling of electrodes as well as the geometry of the reactor.Not all of these parameters are indepen-dent,increasing the complexity of the problem.Since nanotube formation is a rate limited process [1],total
gas pressure must play an important role in gas kinetics as well as in species and energy transport.For the arc process,Saito et al.[2]demonstrated that helium was more effective for yielding fullerenes than argon.More recently,Park et al.[3]reported high yield of SWCNTs synthesized by arc discharge under low helium pressure (from 130to 400mbar)with a small amount of a mix-ture of nickel and iron powder.In the same direction,Journet [4]suggested an optimal pressure of 100mbar for argon and 660mbar for helium when bicatalyst mix-ture of nickel and yttrium were used.Our group has also reported recently the effect of the type of inert gas on carbon nanotube diameter and bundle arrangements [5].The current work focuses on the specific role of total pressure on nanotube yield as determined experimen-tally and by modeling.For the experiments,single-walled carbon nanotubes wer
e produced at different pressures by DC arc-discharge method in argon and he-lium atmospheres.Characterization of the as-produced nanotubes was performed by nitrogen adsorption iso-therms and by BET surface area measurements.The
0008-6223/$-see front matter Ó2005Elsevier Ltd.All rights reserved.doi:10.1016/j.carbon.2005.04.026
*
Corresponding author.Tel.:+33149403418;fax:+33149403414.
E-mail address:farhat@limhp.univ-paris13.fr (S.
Farhat).
Carbon 43(2005)
2453–2462
www.elsevier/locate/carbon
measured BET surface area was experimentally corre-lated with the nanotube contents in the sample and can be used as a relative measurement of SWNT con-tents.In addition to these experiments,a modeling approach developed originally to calculate plasma char-acteristics in the inter-electrode space[6,7],was used to quantify the role of the total pressure on calculated spe-cies distributions and nanotube growth rate.Indeed,for specific conditions of the arc process,the high energy densities deposited from the arc insure a total atomiza-tion of the anode material to form atoms of carbon and catalysts.When the temperature decreases in the cold region of the reactor,carbon reacts to form large molecules and clusters.We believe that it is the overall relative concentration of carbon species,not the specific buffer gas,that is critical in nanotube growth.Hence, following Krestinin and MoravskyÕs[8,9]chemical model for fullerenes,we considered a similar gas phase chemical model in the specific conditions of nanotube growth.Theflow from the anode is idealized by a mass flux containing chemical species with concentrations calculated at the thermodynamic equilibrium at the tem-perature of the vaporization of the graphite estimated at $4000K[10]and leaving the anode in the direction of the cathode with an initial velocity estimated from the measured erosion rate of the anode.The model com-putes species,temperature and velocity profiles and incorporates temperature dependantfluid properties in a steady-state one-dimensional stagnation-pointflow between the anode and the cathode with a gap consid-ered constant[10].This one-dimensional model is a clas-sical bound
ary value problem consisting of a set of ordinary differential equations,solved by afinite differ-ence procedure and described in detail in[11]with kine-tics rate constant data from[12].
2.Experiments
Single-wall carbon nanotubes were produced by DC arc-discharge technique described in detail in our earlier paper[7].For this study,we used argon or helium as buffer gases and nickel and yttrium as catalysts.Due to its efficiency in nanotube yield,the bicatalyst nickel–yttrium was used with the relative atomic percent proposed by Journet et al.[13]C(94.8);Ni(4.2);Y(1). The electric current intensity wasfixed at100A,and a constant gap of3±0.2mm was maintained between the electrodes during all the experiments.The plasma was observed through a quartz window in the reaction chamber.A magnified image of the luminescent plasma was projected from this window on a screen and allows us to adjust the distance between the anode and the cathode.Different experiments were carried out by vary-ing the total gas pressure of the inert gas from0.1to 1bar.The different products obtained after synthesis were always a hard deposit on the cathode,a rubber-like collaret formed around the cathode,and the soot depos-ited on the reactor walls.The percentage of these com-ponents ranges broadly depending on the production conditions.Quantitative characterization was systemati-cally made on the collaret because it contained the larg-est fraction of nanotubes.The BET surface area of as obtained collaret s
amples was determined by nitrogen adsorption at77K using a BET COULTER SA3100 instrument.The sample wasfirst evacuated of all gases at393K for at least1h and then cooled to a tempera-ture of77K.At this temperature,nitrogen is physically adsorbed on the surface of the sample.The adsorption isotherms were hence recorded as a specific volume (cm3/g)of gas adsorbed at standard temperature and pressure(STP)versus relative pressure calculated from sample pressure divided by the saturation vapor pres-sure.The BET equation[14]is used to give the specific surface area.Different values of carbon nanotubes BET surface area were found in the literature,depend-ing of the type of synthesis process and the operating conditions.For multi-wall carbon nanotubes synthe-sized by CVD process the values ranges between120 and425m2/g[15–17].For the arc process,Li et al.[18] measured42m2/g while Tang et al.[19]reported 856m2/g for purified carbon nanotubes.This large gap between measured data could be explained by the strong effect of the impurities on carbon morphology at micro-scopic and macroscopic levels.Indeed,depending on the synthesis conditions and post-synthesis purification technique,a large variety of carbon impurities could re-main with the nanotubes at different concentrations. These impurities include amorphous carbon,graphitic nanoparticles,polyhedral carbon particles,carbon nanoonions,single-wall nanohorns(SWNHs),fulle-renes,and some other forms of carbon with metal cata-lyst enclosed.For an individual carbon nanotube,the calculated surface area is1315m2/g[20].For a bundle of single-walled carbon nanotubes,Peigney et al.[21] demonstrated that t
he specific surface area decreases with the number of nanotubes per bundle,ranging from 751m2/g for seven nanotubes per bundle to484m2/g for 19nanotubes per bundle.A compilation of BET mea-surements performed at different conditions of input power,arc length and total pressure,show that as-produced samples obtained with helium have always a higher BET surface area than those obtained with argon (Fig.1).This suggests that:(i)helium is more efficient than argon to vaporize the anode material,and(ii)when the anode erosion rate is increased,BET surface area is also increased.
In order to correlate BET surface area to nanotube yield,we used a scanning electron microscopy(SEM) technique to estimate qualitatively the amount of nano-tubes.We also compared purified and non-purified BET surface area of our samples.Typical nitrogen adsorption
2454I.Hinkov et al./Carbon43(2005)2453–2462
isotherms at77K and(SEM)pictures of collaret ob-tained with helium and argon are shown in Fig.2.These isotherms showed a Type II adsorption isotherms behavior in the IUPAC classification.
From SEM pictures associated with these adsorption isotherms,we can qualitatively see that nanotube den-sity decreases drastically when argon is used instead of helium as a buffer gas;this suggests that BET surface area is a relative measurment of SWNT contents.More recently,a quantitative correlation
between BET surface area and SWNT contents was demonstrated by Li et al.
[22].By mechanically mixing purified SWNT with MWNT and by comparing measured(wt.%)nanotube contents to microscopic pore size distribution(PSD) peak height and area with BET surface area,Li et al.
[22]demonstrated the superiority of PSD peak criteria on the as-measured BET surface area and proposed a correction for BET area ratio for a quantitative estima-tion of SWNT contents in their samples.In Li et al.[22] method,corrected BET area ratio(a c),is calculated from measured BET area(a)and two references accounting for purified SWNT nanotubes(a100= 619.1m2/g)and purified MWNT(a0=240.1m2/g)with
the following formula:a c¼aÀa0
1000Â100.This correction
permits the prediction of the percentage of SWNT
within5wt.%limit.
In the present study,Table1summarizes the mea-
sured BET surface area of some arc samples.For quan-
titative estimates of SWNT contents,the Li et al.[22]
criteria were adapted with the specific conditions.For
the upper limit a100,BET surface area of498m2/g ob-
tained with purified helium products was taken as refer-
ence.The purification technique consists of an oxidation
of the collaret in air for40min at425°C,followed by a
chemical treatment with hydrochloric acid,HCl(6M)
for24h.Since,as demonstrated by Peigney et al.[21],
the specific surface area is sensitive to the number of
nanotubes per bundle,the difference with Li et al.[22]
value could be attributed to a different bundle organiza-
tion in the purified samples.For the lower value a0,the
BET surface area of109m2/g obtained for soot collected
on the reactor wall,where very few nanotubes are pres-
ent,was considered.In order to study the specific effect
of the pressure,we conducted two series of experiments
with argon and helium as inert gases.We varied the
pressure from100to800mbar.The other parameters
held constant were the electric current I=100A and
the anode to cathode distance ACD=3mm.The mea-
sured and corrected BET surface area are plotted versus
the pressure in Fig.3.From thisfigure,it can be noted
that the gas pressure has an effect on SWNT contents
with an optimum yield obtained respectively at
100mbar for argon and at660mbar for helium.
The evolution of the anode erosion rate versus the
pressure,plotted in Fig.4,confirms the correlation be-
tween BET surface area and the anode erosion rate.
The anode erosion rate is higher with helium than with
argon;and the maximum BET surface area corresponds
to the maximum erosion rate.The relationship between
measured BET surface area,and the anode erosion rate
suggests that the kinetics of condensation of carbon into
soot,is encouraged by the weakfluxes of carbon species
which depend on the pressure.
Fig.2.N2adsorption isotherms of as-produced collaret obtained with helium(top)and argon(down)and their respective SEM pictures.Table1
Typical BET surface area of several nanotube samples Sample BET surface
area(m2/g) Non-purified collaret(prepared
with helium at660mbar)
274
Purified collaret by oxidation
(He at660mbar.After40min
oxidation with air at425°C)
470
Chemically purified collaret
(He at660mbar.After oxidation
and24h chemical treatment
with HCl(6M))
498
Deposit(He at660mbar)14
Soot collected on reactor wall
(helium at660mbar)
109
Non-purified collaret(prepared
with argon at100mbar)
185
I.Hinkov et al./Carbon43(2005)2453–24622455
3.Modeling
The effect of the pressure on chemical species distri-bution and nanotube growth rate was simulated using the SPIN and surface CHEMKIN[23]program package under a stagnation-flow configuration.We solved stea-dy-state axial and radial momentum,species and energy equations in one spatial dimension between the anode and the cathode as shown in Fig.5.
单reactor和主从reactorEven though,growth chemistry and surface site den-sity are very different when SWCNT growth in the coll-aret or MWCNT formation in the hard deposit are considered,the formalism developed in this paper re-mains valid and could take into account simultaneous growth of these species in2D.The gas kinetics and ther-modynamic properties of species were taken from Kres-tinin et al.[12]and the transport properties were estimated from the CHEMKIN thermodynamic data-base and transport library[24].3.1.Governing equations
The governing equations include continuity,radial momentum,species,and thermal energy conservation equations:
Continuity:
1
q
o q
o t
¼À
o u
o x
À2VÀ
u
q
o q
o x
¼0
Radial momentum:
q
o V
o t
¼À
o
o x
l
o V
o x
Àq u
o V
o x
Àq V2À
1
r
o p
o r
¼0 Species:
q
o Y i
o t
þ
oðq Y i V iÞ
o x
þq u
o Y i
o x
¼M i x iði¼1;...;n gÞEnergy:
q c p
o T
o t
¼
o
o x
k
o T
o x
Àq c p u
o T
o x
À
X n g
i¼1
c pi q Y i V i
o T
o x
þx i h i
þS qðxÞÀQ rad¼0
where u is the axial,V is the radial velocity,T is the gas temperature,Y i are the gas-phase species mass fractions, q is the mass density and c p is the specific heat at constant pressure.In the radial momentum equation,p is the spa-tially varying component of the pressure.The molecular weight and specific enthalpy of each species i is given by M i and h i respectively.The viscosity and thermal conduc-tivity are l and k.The net chemical production rate of species i by gas-phase reaction is x i.In the above equa-tions,the independent variables are the radial position r,the distance normal to the cathode x and the time t. The species diffusion velocity V i is calculated from mix-ture diffusion coefficient and species gradient.The source term S q(x)in the energy equation accounts for the electri-
cal energy dissipated in the arc.It was assumed that it is distributed in the form of Gaussian centered at x s with a half-width of w s by the equation:
S qðxÞ¼q
1
w s
ffiffiffi
3
p
r
exp
À3ðxÀxsÞ2
w2
s
"#
2456I.Hinkov et al./Carbon43(2005)2453–2462
Here,q accounts for the total power integrated over its full spatial extent q ¼R þw s
Àw s S q ðx Þd x and includes 100%of the net power added to the arc.The center of the inter-electrode gap was chosen as the peak in the distribution x s and w s chosen to adjust the flatness of the distribu-tion.In the present calculations w s was 0.15cm,result-ing in a very uniform distribution.The total power per unit area of arc q was calculated from measured electric power dissipated in the arc and corrected by an esti-mated loss from arc plasma due to gas convection.The radiative term Q rad in the energy equation accounts for the net loss of energy by gas radiation.It was esti-mated from a curve fit of Owano [25]in atmospheric argon plasma by:
Q rad ¼1.065Â1014a exp
À141;170T W
m 3 with T ,the gas temperature in K and a ,a non-equilib-rium factor accounting for the deviation from the equi-librium;a =1for local thermal equilibrium (LTE).Gas
radiation is negligible when helium is used.3.2.Kinetics and thermodynamic data
The kinetics of the formation of carbon clusters C n has been studied by various workers and recently r
e-viewed by Scott et al.[26].In 1986,Bernholc and Phil-lips [27]used a general model of cluster formation in the laser vaporization source starting from the atomic vapor C to clusters up to C 25.In the n =1À25range,this model reproduced the experimentally observed clus-ter distributions.Creasy and Brenna [28]used a simple model in which clusters grew by attachment of only the small clusters C,C 2,and C 3.Later,Creasy [29]developed more complex reaction models with clusters up to C 450with the reaction rates independent of tem-perature.More recently,Krestinin et al.[12]developed a temperature dependent reaction scheme for fullerene formation with the following assumptions:
•Carbon clusters up to C 31are assumed to be highly reactive chains,cycles,and polycycles.
•Clusters of size between C 32and C 79are closed shells,where the main growth or decomposition is from C 2attachment or detachment,respectively.
•Due to the resonance stabilization,odd clusters are less stable than even clusters.
•Odd clusters tend to eject C,rather than C 2upon decomposition.
•Clusters greater or equal than C 80are assumed to be soot.They are lumped together as a single species,soot (Z ).
When pure carbon is used as the feedstock for reactions in high temperature processes like the arc,the Krestinin et al.[12]model achieved reasonable agreement with
measured fullerene yield.In the specific single-wall car-bon nanotubes (SWNT)conditions,only few percent of metal is added to the system,and Krestinin et al.[12]model can be used.For example,in our conditions,a typical concentration of metals in evaporated mixture is about 4at.%for nickel and 1at.%for yttrium.After dilution in the inert gas,these concentrations drops down making gas phase dominated by helium and car-bon species.It is assumed in this article that (i)gas phase reactions govern the rate of the formation of fullerenes,(ii)surface phase reactions govern the rate of the forma-tion of SWNTs at the cathode.
The gas phase chemistry used involves neutral carbon species and includes small clusters (C 1–C 10),cycles and polycycles (C 11–C 31),fullerene shells (C 32–C 46),fullerene clusters (C 47–C 79)and two fullerene molecules C 60F and C 70F .In addition,argon and/or helium,as well as nickel and yttrium,are considered as inert chemical species.It is possible to improve this model by considering carbon/metal clusters.Unfortunately,reactions and thermody-namics of carbon/(Ni,Y)clusters are entirely unknown at present [30].Neglecting carbon/metal reactions,there are at least 554chemical reactions that describe chemical kinetics of carbon vapor condensation of clusters of dif-ferent sizes.R
eaction equations and rate coefficients are given in Arrhenius form in Table 2where symbols M and !in each reaction indicates that this reaction is reversible or irreversible respectively.The thermody-namic properties for carbon clusters were determined from existing data for C [31],C 2[32],C 3–C 10[33],and C 60F and C 70F [34].The enthalpy of formation for clus-ters with n =11–59,61–69,and 71–79were estimated by interpolating the values between n =10and 60.The en-tropy of formation was estimated by interpolation be-tween n =5and 60.The thermodynamic properties of all species are fitted in the temperature range of 300–20,000K and given in CHEMKIN (old NASA)format.This format presumes that the standard-state thermody-namic properties as standard state molar heat capacity at constant pressure,standard molar enthalpy,and stan-dard molar entropy are thermally ‘‘perfect’’,in that they are only functions of temperature and are given in terms of polynomial fits.Nickel and yttrium thermodynamic properties are fitted in the temperature range of 300–20,000K from IVTANTHERMO thermodynamic data-base [35].
3.3.Anode boundary conditions
The axial gas velocity at the anode u A was estimated from the measured erosion rate U and the total gas den-sity q by the relation:u A ¼U
q A
where A is the anode sur-face area.This velocity ranged typically from 12m/s for argon at 100mbar to 78m/s for helium at 660mbar in good agreement with the estimated interval of Krestinin and Moravsky from 2to 80m/s [8,9].The initial mole
I.Hinkov et al./Carbon 43(2005)2453–24622457
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