Carbon Nanotube Growth by Catalytic Chemical Vapour Deposition: A General Kinetic ModelJournal: The Journal of Physical ChemistryManuscript ID: jp-2009-06893m Manuscript Type: Article Date Submitted by the Author: 21-Jul-2009 Complete List of Authors: Monzon, Antonio; University of Zaragoza, Che mical and Environmental Engineering Romeo, Eva; University of Zaragoza, Chemical and Environmental Engineering Latorre, Nieves; University of Zaragoza, Chemical and Environmental Engineering Cazaña, Fernando; University of Zaragoza, Chemical and Environmental Engineering Royo, Carlos; University of Zaragoza, Chemical and Environmental Engineering Villacampa, Jose; University of Zaragoza, Chemical and Environmental Engineering Ubieto, Teresa; University of Zaragoza, Chemical and Environmental Engineering ACS Paragon Plus Environment Submitted to The Journal of Physical Chemistry
Carbon Nanotube Growth by Catalytic Chemical VapourDeposition: A General Kinetic Model
Journal: The Journal of Physical Chemistry
Manuscript ID: jp-2009-06893m
Manuscript Type: Article
Date Submitted by theAuthor: 21-Jul-2009
Complete List of Authors: Monzon, Antonio; University of Zaragoza, Chemical andEnvironmental EngineeringRomeo, Eva; University of Zaragoza, Chemical and EnvironmentalEngineeringLatorre, Nieves; University of Zaragoza, Chemical andEnvironmental EngineeringCazaña, Fernando; University of Zaragoza, Chemical andEnvironmental EngineeringRoyo, Carlos; University of Zaragoza, Chemical and EnvironmentalEngineeringVillacampa, Jose; University of Zaragoza, Chemical andEnvironmental EngineeringUbieto, Teresa; University of Zaragoza, Chemical andEnvironmental Engineering
Carbon Nanotube Growth by Catalytic Chemical Vapour Deposition: A General
Kinetic Model
N. Latorre, E Romeo, F. Cazaña, T. Ubieto, C. Royo, J.I. Villacampa and A. Monzón*
Institute of Nanoscience of Aragon. Department of Chemical and EnvironmentalEngineering. University of Zaragoza. 50009 Zaragoza. Spain.
Abstract
A General Kinetic Model has been developed that includes all the relevant stepsinvolved in CNT growth: hydrocarbon decomposition, catalytic nanoparticlecarburization, carbon diffusion, CNT nucleation and growth, catalyst deactivation and
self-regeneration, and/or growth termination by the effect of steric hindrance.Here we emphasize the importance of a suitable kinetic description of all the
stages, in particular the initial carburization-nucleation and the growth cessation. Wehave discussed the different mechanisms proposed to explain the critical step of CNTnucleation and have used an autocatalytic kinetic equation to describe it. The twoparameters involved in this autocatalytic equation allow a very good fit of the initialinduction period usually observed during the growth of CNTs. In addition, rigorous
formulations of the main causes of CNT growth cessation (catalyst deactivation andsteric hindrance) have been proposed.
The General Model as developed is shown to be a potentially versatile tool of general application. In this paper we have applied it to fit data obtained in our lab, andalso to super growth of VA-SWNT experimental data published in the literature. In allcases the values obtained for the kinetic parameters have realistic physical meaning ingood agreement with the mechanism of CNT formation.
Corresponding author: Prof. A. Monzon,e-mail: [email protected], Tel: +34 976 761157; Fax.: +34 976 762142
The attractive possibilities of using the outstanding properties1,2 of carbonnanotubes and other new carbonaceous nanomaterials in a broad range of new
applications3-5
is motivating substantial research effort in practically all the fields of nanoscience and nanotechnology. However, extensive use of these materials requiresthe development of scalable and selective production processes. Catalytic chemicalvapour deposition (CCVD) has become probably the main technique for the synthesis of carbon nanotubes, including selective production of single-walled nanotubes (SWNTs)using many carbon sources and catalysts6,7. In addition to the usual CCVD method, thatuses large surface area porous supported metallic catalysts8-10, the production of layers
of vertically aligned VA-SWNT is assuming increasing importance11,12
. VA-SWNTscan also be produced by CCVD if the catalyst composition and the operating parametersare optimized for the synthesis conditions13,14. Furthermore, this technique can beimproved, for example combining a dip-coat catalyst loading process15 with the alcoholcatalytic chemical vapour deposition (ACCVD) method12,16-18. Other methods used arewater-assisted CVD13,19, oxygen assisted CVD20, point-arc microwave plasma CVD21,molecular-beam synthesis22, and hot-filament CVD23. These new advances havesucceeded in significantly increasing the overall yield, but improvements in SWNTquality and control over chirality are still necessary, particularly when consideringelectrical and optical applications18.
Even though the formation and growth mechanisms of carbon nanotubes byCCVD have been extensively studied in the past24-35, there is no general agreementabout what the critical steps are. Most authors propose that this mechanism includes thestages of hydrocarbon (or another carbon source such as CO) decomposition over themetal surface, carbon diffusion through the particles27,31-35and/or atomic carbon surfacetransport36,37 and finally carbon precipitation forming CNTs. Although this form of carbon accumulation allows the catalyst to maintain its activity for an extended periodof time, catalyst deactivation can occur through the formation of encapsulating carbonover the surface of the metal particles34,36. The deactivation phenomenon can bereversible as a consequence of gasification of this type of carbon by oxygen19, water38,39 or hydrogen40-43 that can be added, or be present, in the feed. Additionally to catalystdeactivation, other causes of carbon growth cessation such as steric hindrance44 ordefect diffusion to the growth front45 have been considered. Other phenomena such as
initial catalyst activation can also occur if the catalyst is not previously reduced beforethe reaction44,46.
The physical-chemical description of the steps involved in the CNT growth
process has usually been tackled by kinetic models that take into account only some of the stages (e.g. nucleation and initial growth,47). Other proposed models describe theprocess in steady state31,33,48, without considering that it is strongly time-dependent.These models are usually used to fit experimental data of: i) stationary carbonformation rate as a function of the operating conditions40,41,33,48; ii) evolution over timeof the carbon formation rate49,50,51; and iii) evolution over time of mass (or length of CNTs) of carbon accumulated15-18,42-44,52.
Obviously, a rigorous description of all these stages necessarily implies obtainingvery complex mathematical models with too many parameters, which eventuallyhinders their application for the analysis of kinetic data. On the other hand, the simplestmodels are frequently used owing to the fact that they are easy to apply and understand,although obviously these models are unable to describe the complete process accurately.A compromise solution is to find models that consider the main critical stages of theprocess without excessively increasing its mathematical complexity and therefore the
number of parameters.In any case, it is necessary to have a sufficient quantity of precise experimental
data, for whichin situ techniques are especially suitable. Among thein situ techniques,the most commonly used to follow the growth of carbon nanotubes are: i)environmental HR-TEM35-37,52-55; ii) optical absorbance15-18,45; iii) RAMAN scattering56;iv) time-resolved reflectivity (TRR) of laser beams52,57; v) gas analysis by massspectrometry of time-evolved gases44,58, vi) thermogravimetric techniques42,43,51,59,60. In
addition, SEM images taken after different reaction times have also been used to followthe kinetics of VA-SWCNT growth61,62.
Recently, our group has developed kinetic models to investigate the growth of carbon nanotubes. These models were successfully applied to studying the data obtainedwith in situ thermogravimetric systems in reactions with different carbon sources andcatalysts42-44,59-63. In the different examples studied, we have considered the steps of deactivation-regeneration43,60, catalyst activation, or growth termination by steric
In spite of these efforts, an adequate description of the critical initial inductionperiod of time has not been attained. In fact, the evolution of the rest of the steps isdetermined by this initial period, when some surface carburization of the metallicnanoparticles and carbon nanotube nucleation takes place. It has been observed that thelength of this period is strongly dependent on the operating conditions42,56. Thus, it hasbeen found that the induction period becomes longer as the partial pressure of thecarbon source diminishes42,56,58,60,63, indicating that the initial carburization-nucleationstep is controlled by the feeding of carbon atoms. With the aim of obtaining a morecomplete description of the growth process, in this work we present a kinetic modelincluding all the above considerations, considering especially the initial carburization-nucleation step and the growth termination, by catalyst deactivation and/or by the effectof steric hindrance. However, we have tried to reduce the number of empirical equationsusing parameters with a physical-chemical meaning. In order to show that the developedmodel could be a versatile tool for general application, we have used it not only to fitdata from our lab, but also other data as for example super growth of VA-SWNTexperimental data.
2. Kinetic model of CNT growth.
A) Hydrocarbon (carbon source) decomposition over the catalytic surface.
As an example, here we take the case of catalytic methane decomposition; one of the most commonly used CCVD process. Other carbon sources can also be consideredin the same way. The mechanism of methane decomposition can be expressed throughthe following individual steps32,33:
Atoms of carbon and gaseous hydrogen are then released over the catalyst surface.In this case it is assumed that the number of active sites “l” involved in the controllingstep (named asm) of the methane decomposition is 2 (m=2 )32,33. The step of reversibleformation of encapsulating coke, which deactivates the catalyst, goes through parallelreactions of condensation-oligomerization, and can be expressed as64:
22)( H hPllCH h h x +↓⇔− (vii)
Pl h is the encapsulating coke andh is the number of active sites involved in theabove reaction of coke formation64.
B) Formation of surface carbide and carbon nanotube nucleation.
According to the mechanism proposed by Alstrup29
, after hydrocarbon decompositionthe remaining carbon atoms react with the metallic nanoparticles at the surface forminga metastable carbide, that in the reaction conditions decomposes leaving carbon atomsat the metallic subsurface. After this decomposition-segregation step, the carbon atomsare introduced inside the metal particles29, determining in this way the value of thecarbon concentration at the carbide-metallic nanoparticle interphase. However, for thisstage Puretzki et al.52 consider that the carbon atoms are dissolved on the metallicnanoparticles forming a highly disordered ‘molten’ layer on their surface. Because of much higher carbon diffusivity in the disordered layer compared to the ordered solidphase, the carbon atoms diffuse along this layer and precipitate into a nanotube. Helveget al,36, based on density-functional theory calculations and on “in situ” TEMobservations, propose that the growth of CNFs on a Ni-Mg-Al catalyst involves surfacediffusion of both carbon and nickel atoms. Thus, the graphene layer nucleation andgrowth is explained as a dynamic formation and restructuring of mono-atomic stepedges at the nickel surface.
In the case of SWNT growth, in a recent paper44 we have considered that the carbonatoms enter into the metallic nanoparticles through the clean surface (interface 1), andthat they leave the metallic phase throughinterface 2 when forming the SWNT. Thedriving force for the surface or bulk diffusion from interface 1 tointerface 2 is thedifference in chemical potential between the two interfaces. Comparing these twodiffusion pathways, Lin et al.37 consider that the surface diffusion is dominant due to its
lower activation barrier, as a consequence of a lower coordination number. After the
In the above expression X CH4 represents the methane conversion,(F CH 4)0 the massflowrate of methane fed to the reactor andW the catalyst weight. The solution of thisdifferential equation allows the calculation of methane conversion, hydrogen productionand of the total amount of carbon nanotubes produced along the reactor and over time.Bearing in mind the deactivation produced the formation of encapsulating coke,equation 8 can be expressed in terms of catalyst activity,a, 64,68:
000
)()(;)()())((
)(4
4
4 C t C C t C CH
CH t CH r r aar r
F W d
dX r =⋅===− (9)
The term(r C )0 corresponds to the CNT growth rate, in the absence of deactivation,which can be expressed in terms of difference of chemical potential force between the
interfaces 1 and225,26,32,33,44:
)()(0
0 F S C t
C C C C k
dt dm
r −⋅===
(10)
The term C k is the effective coefficient of carbon transport, has units of time-1,
and depends on the average size of the metallic crystallites, the metallic exposed area,and the carbon atom diffusivity on the metallic nanoparticles25,26,32,33,44:
C) Catalyst deactivation
The main causes of catalyst deactivation are fouling by encapsulating coke,sintering (or thermal aging), and poisoning68. Therefore, the deactivation rate,
dt dar d −= , must be described according to an appropriate deactivation kinetic model
related to the deactivation cause68-71. Thus, if the formation of encapsulating coke ispartially reversible, the catalyst does not suffer a complete deactivation, maintaining aresidual level of activity at steady state. In these conditions, the net rate of activityvariation can be expressed as71:
)( aaadt da
r md r
d d d −⋅−⋅=−= ψ ψ (11)
The terms d ψ and r ψ are respectively the “deactivation and regeneration kinetic
functions” , and both also depend on the operating conditions. If the activity decay is
irreversible,ψ r =0, the deactivation rate will be64,68:
It should be noted that, in equation 11 or 12, the values of the kinetic ordersd andd m depend on the reaction mechanism, i.e. the number of sites involved in thereactions71:
mmd mhmd m )1(;)1( −=−+= (13)Thus, only values with a real physical meaning form and h, i.e. 1 or 2, were
assessed. In fact, cases involving 3 or more active sites in an elemental step were notconsidered since they are quite improbable72. This means thatm and h are not fittingparameters, and therefore their values must be selected before the data fitting.
D) Steric hindrance.
For the SWNT it has also been considered that the growth on porous catalysts can beslowed down as a consequence of the steric hindrance44. In this case, as carbonaccumulates within the internal porous structure, physical hindrance for the freeenlargement of the growing nanotubes may occur. This fact constrains SWNT growth,delaying the insertion of new carbon atoms atinterface metal-SWNT . The degree of interaction of a growing SWNT with the catalyst support, and/or with other nanotubes,depends on the catalyst pore sizes. The larger the available space on the catalyst, theless hindered will be the insertion of new carbon atoms at the interface. Similarconsiderations have been made to explain the deactivation of catalytic carbonaceousmaterials used to produce hydrogen by methane decomposition73,74.We assume here that this hindrance effect can be expressed as a potential function of theaccumulated mass of carbon:
pC H F mC ⋅=ξ (14)
In this equation, the termξ H is called the “hindrance factor ”. In addition, the
value of the hindrance kinetic order, p, determines if this effect is progressive over time, p>1 , or decays over time, p<1 . As commented above, the values of both parametersdepend on the catalyst texture.
Finally, substituting equations 2, 10 and 14 into equation 9, the amount of CNTsformed can be calculated integrating the following expression:
jC0 has units of (g C/g cat.min ) and can be considered as the intrinsic CNT growthrate for the fresh catalyst. Similarly, the termξ HC represents the intrinsic constant rate of steric hindrance, and has units of (g cat (1-p) /g C (1-p) .min ). The differential equations 11and 15 can be considered as a general kinetic model for studying the growth rate and theamount of CNTs formed over the reaction time, as a function of the operatingconditions, and of the potential effects of catalyst deactivation and/or steric hindrance.The parameters involved are:ξ HC and p, accounting for the steric hindrance,ψ d and ψ r relating to catalyst deactivation and jC0 , that is the intrinsic growth rate. This generalmodel can be simplified into many particular cases; some of them are described in thefollowing paragraphs.
On the other hand, one of the most original aspects of this model is the
description, by means of parametersψ S and K S in equations 1 and 2, of thecarburization-nucleation stage. Figures 1 to 3 show some examples of the effect of theseparameters on the CNT growth. In Figures 1 and 2 it can be seen that as the value of K S increases, the induction period becomes longer, indicating that the more demanding theautocatalytic effect, the more time is needed to achieve the initial stage of nucleation. Incontrast, if K S is zero or takes a low value, the induction period is not appreciablebecause the carburization-nucleation steps occur very quickly.
As regards the catalyst deactivation, this causes a diminution in the reaction rateand then on the mass of CNTs accumulated over the catalyst. Furthermore, themaximum rate of reaction appears later, and with a lower value (Figure 1). In relation to
the evolution of mC , an increase inK S produces a decrease in the amount of CNTsformed because the catalyst deactivation occurs before the carburization-nucleation stephas been completed and the nanoparticles can transport the carbon atoms. On the otherhand, if there is no catalyst deactivation, after the initial induction period the reactionrate increases until it reaches a constant final value (Figure 2). Consequently, theinduction periodmC subsequently increases linearly over the reaction time (Figure 2). In
Figure 3 the results relating to the impact of the parameterψ S are presented. Thus, an
increase inψ S causes a shortening of the induction period and simultaneously anincrease in the maximum reaction rate. Both phenomena are the result of the fact that
the termination of the carburization-nucleation stage occurs before the deactivation of the catalyst is advanced. The results in Figures 1 to 3 correspond to the case where thereis no effect of steric hindrance (ξ HC =0 ). However, qualitatively similar results will beobtained if the growth termination is caused by steric hindrance, or by both causesacting simultaneously.
In the following sections we present the equations corresponding to someparticular cases of the general model developed here.
Case 1. CNT growth termination by catalyst deactivation alone.
If the CNT growth is not hindered by any steric impediment,ξ HC =0, or the valueof C F is very low compared withC S , equation 15 can be simplified to:
at K
t j
dt dm
r S
C C C ⋅
⋅−⋅+⋅−−
==))exp(1())exp(1(
0
α
α (17)
The value of the catalyst activity,a , is calculated from equation 11, and then the
fitting parameters in this case areψ d , ψ r , jC0, K S and ψ S . The explicit equation for theactivity vs. time relationship depends on the values of m and h. For example, in thesimplest case,m=h=1, the deactivation rate and the catalyst activity are given by the
following expressions:
)1( aadt da
r r d d −⋅−⋅=−= ψ ψ (18a)
)(;))(exp()1( r d r S r d S S at aaa ψ ψ ψ ψ ψ +=⋅+−−+= (18b)
The terma S represents theresidual activity of the catalyst.
Now,mC must be calculated integrating numerically the following equation:
( )))(exp()1())exp(1())exp(1(
0 t aat K
t j
dt dm
r d S S S
C C ⋅+−−+⋅⋅−⋅+⋅−−= ψ ψ
α
α (19)
If the deactivation is irreversible,ψ r =0, and the carburization-nucleation step is
very rapid, i.e.K S 0 andψ S is very high, thenC S =C Sm, In these conditions equation 19results in the most simple case:
Equation 20b is formally equal to that used to describe many studies of the
production of layers of vertically aligned single-walled nanotubes, VA-SWNT,including the so-called super-growth proces17-19, 45, 61:
−−⋅=
00 exp1)(
τ τ β
t t H (21)
The equivalence between the kinetic parameters of both models is given by:
d C
d C C
j H
jt mt H
ψ τ β
τ β
0
0
0max
0 1;;)()(
∝⋅=
=∝∝(22)
In summary, equation 21 can be considered as a particular case of the generalmodel described in this work. It is obvious that for the cases described by equations 15and 20, there are many others that can be easily deduced and applied for each specificparticular study. For example, if the carburization-nucleation step is described byequation 6, instead of considering thatC S =C Sm, the following intermediate case isobtained:
⋅−−−
+⋅+−−=
S
S
S d
S d C C
t t jm
ψ ψ
ψ ψ ψ ψ ))exp(1()))(exp(1(
0(23a)
)exp())exp(1(0
t t jr d S C C ⋅−⋅⋅−−= ψ ψ (23b)
These equations will be applied later in the analysis of VA-SWNT supergrowthdata.
Case 2. CNT growth cessation by steric hindrance only.
If the catalyst does not suffer deactivation, i.e.a=1 , and the growth cessation isonly caused by steric hindrance,r C is calculated as:
))exp(1())exp(1(
0
t K
t jm
dt dm
S
C pC HC
C
⋅−⋅+⋅−−
=⋅+α
α ξ (24)
In the above equation the fitting parameters areξ HC , p, jC0, K S andψ S . Similarly tothe above case, if p=1, the carburization-nucleation step occurs very quickly, i.e.K S
0, ψ S is very high andC S =C Sm, equation 24 is simplified to:
The above equations are identical to equations 20a and 20b, replacingψ d by ξ HC .This result also indicates that by means of kinetic studies alone it is not easy todistinguish what is the true underlying reason, or reasons, for CNT growth decay. Infact, both causes considered here can act simultaneously, clearly complicating theelucidation of the parameters and requiring a previous design of a careful experimentalstudy specifically designed to obtain them.
Case 3. No effect of steric hindrance or catalyst deactivation.
This case corresponds to the simplest situation where the growth rate is maintainedalong the reaction38,47. In this situation equation 15 is simplified to:
⋅−+⋅−−
⋅=)exp(1
)exp(1)(0 t K
t jr
S C t C α
α (26a)
The analytical integration of the above expression gives:
( )
+⋅−+
⋅
+−⋅=
S
S
S
S C C K
t K K
K t jt m
1)exp(1ln1)(
0
α α
(26b)
This solution is represented in the curves corresponding to the evolution of mC inFigure 2.
3. Application of the kinetic model to experimental data.
In Figures 4 to 7 we present different results of the application of the generalkinetic model developed in this contribution and some comparisons with other simplermodels used in the literature. Thus, Figures 4a and 4b show two examples taken from akinetic study of vertically aligned single wall carbon nanotube (VA-SWCNT) growth,synthesized by catalytic chemical vapour deposition of ethanol18. In that paper, the
authors study the effect of the partial pressure of ethanol and of the synthesistemperature over the evolution over time of the VA-SWCNT thickness. The kinetic
the Exponential Model , 2. However, the inclusion of this additional parameter,ψ S , istotally justified from a physical point of view.
The data in Figure 5 corresponds to a study of SWNT synthesis by CCVD
followed by in situ RAMAN spectroscopy56
also carried out by Maruyama’s group. Ascan be seen, the evolution of the G-band signal intensity, proportional to the amount of SWNT formed, shows a very long induction period due to the very low value of thepartial pressure of ethanol (0.1 Torr) used during the experiment. In these operatingconditions the rate of carburization of the metallic particles is low, and therefore thetime needed to complete the nucleation is greater causing an enlargement of theinduction period. Obviously, from figure 5 and the values presented in Table 1 it is clear
that the fitting obtained with the Exponential Model is clearly worse than that obtainedwith the General Model. With respect to the values of the parameters, the fitting of the
long induction period is solved by theGeneral Model giving a low value for theψ S parameter and a high value for theK S parameter, in agreement with the trends presentedin Figures 1 and 3. Figure 5 also shows the evolution of the growth rate of the SWNTcalculated with the values estimated using the General Model. This curve shows clearlythat in the first instants of the reaction (in this case the first minute) the reaction rate isalmost zero, just the contrary of the result obtained with the Exponential Model thatinitially predicts the higher reaction rate.
Finally, the results presented in Figures 6a and 6b correspond to a study of CCVD of CH4 on a Ni-Al catalyst, carried out by our group42. These figures correspond to theresults obtained analyzing the influence of the methane concentration on the CNTproduction and on the reaction rate. Figure 6a shows that the length of the inductionperiod is strongly dependent on the carbon source concentration, increasing as the
partial pressure of CH4 diminishes. This result confirms the conclusions obtained fromFigure 5. Table 2 shows the values of the parameters of the General Model, aftersimultaneous fitting of the experimental data in Figures 6a and 6b. In this case, thevalues of the variable y on equation 27a are carbon concentration, while forSSR2 y corresponds to the growth rate data (equation 27b).
The evolution of the parameters with respect to the methane concentration
indicates that as the CH4 partial pressure increases, the values of 0C j and ψ d also
increase. These results explain that at the end of the experiment the total amount of
all cases the values obtained of the kinetic parameters have realistic physical meaning ingood agreement with the mechanism of CNT formation.
Acknowledgements.
The authors acknowledge financial support from MICINN (Spain)-FEDER, Project
CTQ 2007-62545/PPQ, and the Regional Government of Aragón, Departamento de
Ciencia, Tecnología y Universidad, Project CTP P02/08. Also, the authors thank Prof.
S. Maruyama for sending the experimental data shown in Figures 4 and 5.
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Figure 1. Effect of the parameterK S on the reaction rate and CNT concentration. Case
with catalyst deactivation.
Figure 2. Effect of the parameterK S on the reaction rate and CNT concentration. Casewithout catalyst deactivation.
Figure 3. Effect of the parameterψ S on the reaction rate and CNT concentration.
Figure 4. Fittings comparison of VA-SWCNT film thickness and growth rate data taken
from figures 2a and 2b of reference 18. (Figure 4a) data corresponding toγ0=2.7
µm/min andτ=3.6 min ; (Figure 4b) data corresponding toγ0=5.2µm/min andτ=6 min.Figure 5. General Model fitting of G-band intensity data taken from figure 4b of reference 56.
Figure 6. Simultaneous fitting of CNT concentration (Figure 6a) and growth rate(Figure 6b) data from reference 42.
