ARTICLE pubs.acs.org/IECR
Modeling the Growth of Carbon Nanotubes in a Floating Catalyst Reactor Leila Samandari-Masouleh,† Navid Mostoufi,*,† Abbasali Khodadadi,† Yadollah Mortazavi,† and Morteza Maghrebi‡ †
Oil and Gas Processing Centre of Excellence, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran ‡ Department of Chemical Engineering, Faculty of Engineering, Ferdowsi University, Mashhad, Iran ABSTRACT: An improved model for growth of multiwall carbon nanotube (MWCNT) arrays in a floating catalyst (FC) reactor is developed. The model predicts the height of MWCNT arrays produced from xylene as a carbon source and ferrocene as the catalyst precursor. Based on this model, growth of CNTs was studied at various operating conditions, such as temperature, catalyst concentration in the feed, and xylene concentration. It was shown that the longest carbon nanotubes can be achieved in the temperature range 825875 °C. Increases in the concentrations of both xylene and ferrocene increase the average height of CNTs. During the FC process, catalyst deactivation was observed due to formation of amorphous carbon on the surface of CNTs. Effect of deactivation on the model was empirically correlated with a simple first order deactivation rate.
1. INTRODUCTION Carbon nanotubes (CNTs) have attracted considerable attention due to their outstanding physical and chemical properties.1 Various synthesis methods have been developed for the production of CNTs, including electric arc discharge,2 laser vaporization,3 and catalytic chemical vapor deposition (CVD)47 of which the last has been the method of focus by researchers. Among the available CVD processes, the floating catalyst (FC) method is economic and wellsuited for scaling up to mass production of CNTs with a defined nanotube diameter distribution. FCCVD has especially attracted considerable attention because it ensures continuous growth of aligned and high purity nanotubes at a low reaction temperature and low cost compared with the traditional CVD method. Understanding the parameters affecting the growth rate of CNTs in a CVD reactor is essential when the reactor is to be scaled up and its operational conditions are to be optimized. Mechanisms of CNT growth involve the dissociation of hydrocarbons catalyzed by transition metals and saturation of carbon in a metal nanoparticle. Carbon precipitates from saturated metal nanoparticles and forms nanotubes.8 The CNT deposition profiles inside a CVD reactor strongly depend on the reaction temperatures, feed gas flow rates, carrier gas flow rates, and reactor geometry.9,10 Previously, computational fluid dynamics (CFD) has been used to predict the production rate of CNTs synthesized by the CVD method.1113 Kuwana et al.11 proposed a model to predict the formation process of iron nanoparticles from ferrocene fed into a CVD reactor including the mechanism of nucleation and surface growth of an iron particle and biparticle collision. Wasel et al.14 measured the axial and radial temperature distributions and major species concentrations in the CVD reactor and calculated the overall rate constants for the gas-phase reaction based on the measured species concentration. Ma et al.15 developed a CNT growth model that contains the detailed gas-phase reactions of acetylene pyrolysis and the surface catalytic reactions as well as the influence of C4H4 on the CNT growth. Lee et al.16 r 2011 American Chemical Society
investigated the effect of temperature on the growth rate and the structure of CNTs, which were grown using the pyrolysis of ferrocene/acetylene over the temperature range 7001000 °C. Darvishi Kamachali17 investigated the catalytic growth of multiwall carbon nanotubes (MWCNTs) by the CVD method and observed that the calculated growth rate of CNTs strongly depends on temperature and the diameter of the carbon nanotubes. Gurujicic et al.18,19 developed a reactor-scale model for carbon nanotube fabrication via CVD. Their model was utilized to optimize the process of CNT fabrication in order to determine the process parameters which maximize the CNT yield while minimizing the amount of amorphous carbon codeposited with the CNTs. In the present work, experimental data were used to model the growth of CNTs on a quartz rod at the center of a floating catalyst reactor which was used as a substrate for CNT growth. The model for prediction of the growth of CNTs was developed by which the relationship between the reaction conditions such as temperature, catalyst, and carbon source concentration in the feedstock and the height of CNTs was calculated and compared with the experimental results.
2. EXPERIMENTS The CNT growth experiments were conducted using the reactor system shown in Figure 1, previously described by Maghrebi et al.20 Ferrocene, the Fe catalyst particle source, was dissolved in xylene, the hydrocarbon source, to obtain a feed solution with 0.1 g/mL solution of ferrocene in xylene. A mass flow controller (MFC) was used to introduce 900 sccm argon as the carrier gas to the reactor at atmospheric pressure. A 21.7 mm i.d., 100 cm long quartz tube reactor was placed in a two-zone furnace. Received: May 26, 2011 Accepted: December 19, 2011 Revised: November 25, 2011 Published: December 19, 2011 1143
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5. Amorphous carbon is formed on the surface of the nanotubes by a first-order reaction. Based on the above assumptions, mass balance equations for the main components in the reactor, i.e., xylene, iron, and ferrocene, were developed as follows: (a) Ferrocene. Little is known about the chemical kinetic behavior of ferrocene. Lewis and Smith21 measured the rate of the homogeneous gas-phase thermal decomposition: FeðC5 H5 Þ2 f Fe þ 2C5 H5 Figure 1. Schematic of CNT growth apparatus.
Figure 2. Schematic diagram of cylindrical reactor for carbon nanotube growth using floating catalyst.
The liquid feed was pumped into the preheater zone, where it was preheated to 300 °C prior to its entry into the growth window of the reactor. The liquid was immediately volatilized and swept into the reaction zone of a furnace maintained at 850 °C. The temperature in the annular region between the reactor and the furnace tubes along the system was monitored during the CNT synthesis. A condenser was used to trap heavy byproducts. A 4.0 mm o.d., 25.0 cm long quartz rod at the center of the second zone of the reactor was used as a substrate for CNT growth. Following the injection of 10 mL of xylene solution in 30 min, the reactor was cooled to room temperature under argon atmosphere.
3. MODELING The liquid feed evaporates in the preheater before entering the heating zone in which the CNTs are formed. The CNTs grow on the rod and wall of the reactor while amorphous carbon is deposited on the CNT arrays. A schematic of the section of the reactor considered in the model is shown in Figure 2. The following assumptions were considered in developing the model: 1. The gas is in plug flow in the annular region along the reactor. This can be justified by the fact that the rate of mass transfer of iron particles from the bulk to the surface of the substrate was found to be 2 orders of magnitudes greater than the rate of decomposition of xylene. In other words, the rate of mass transfer is considerably faster than the rate of reaction and the process is mainly controlled by the reaction of nanotube formation on the surface of the substrate. As a result, all gradients in the radial direction were neglected. 2. The temperature profile in the reactor was predetermined; thus, heat balance in the reactor was not necessary. 3. Experimental results show a base growth mechanism for MWCNT arrays.20 The transfer of xylene molecules from the top of the nanotube arrays to the surface of the substrate occurs only by molecular diffusion, through the nanopores between the arrays. 4. Carbon nanotubes are formed on the surface of the substrate by a first-order reaction.
ð1Þ
It was found that the rate of surface growth is considerably slower than the rate of nucleation of Fe particles and reduction of ferrocene was caused mainly by the gas-phase reaction.13 Since detailed kinetic information on reactions between ferrocene and radicals is not available, reaction 1 was considered as a one-step process in the present work. The rate of decomposition of ferrocene is22 0 1 kJ 209 B C B C mol CCfer rA ¼ 1:0 1014 ½s1 expB ð2Þ @ A RT Therefore, the mass balance equation for ferrocene decomposed along the reactor becomes kCfer ¼ Ur z¼0
∂Cfer ∂z
ð3Þ
Cfer ¼ C0fer
ð4Þ
(b) Iron. Iron is produced in the reactor by decomposition of ferrocene and then migrates to the surface of the tubes through mass transfer. Therefore, the mass balance for iron is kCFe
4Kc Din CFe ∂CFe ¼ Ur Dout 2 Din 2 ∂z
z¼0
CFe ¼ 0
ð5Þ ð6Þ
In the above equations, Kc is the mass transfer coefficient, which is calculated from23 Kc d t ¼ 0:0096 þ NRe 0:913 NSc 0:346 ð7Þ D (c) Xylene. Studies have shown that xylene converts to several products such as toluene, benzene, methane, and C2 hydrocarbons as a result of thermal decomposition.11 The contribution of each surface reaction to nanotube formation was calculated by Kuwana et al.11 According to their model, more than 90% of the nanotubes are formed directly from xylene and can be increased to 95% in the experimental conditions of this work due to long reaction time (30 min). Almost the same results were reported by Gail and Dagaut24 and Li et al.25 Therefore, in the present work, all steps from xylene to carbonaceous materials were lumped together and only one step was assumed for this reaction. The inflow of xylene is consumed along the reactor length and converted to amorphous and graphitic carbon.26 Therefore, the mass balance for xylene becomes NSh ¼
ðk0A þ k0CNT ÞCX ¼ Ur z¼0 1144
∂CX ∂z
CX ¼ C0X
ð8Þ ð9Þ
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Table 1. Pre-exponential Factors and Activation Energies Based on the Arrhenius Equation26 pre-exponential
activation
reaction
factor
energy (kJ/mol)
amorphous carbon carbon nanotubes
k0A = 3.28 104 m/s k0CNTs = 1.53 103 m3/g of Fe 3 s
EA = 61.48 ECNTs = 120.16
The values of kA and kCNT were reported initially per amount of iron and per unit surface, respectively.26 However, to be used in eq 8, they should be converted to quantities per unit volume of the reactor as follows: 4ðDout þ Din Þ ECNT j exp ð10Þ k0CNT ¼ k0CNT Dout 2 Din 2 RT k0A ¼ k0A nπDavCNTs lavCNTs
4ðDout þ Din Þ EA exp Dout 2 Din 2 RT
ð11Þ
Pre-exponential factors and activation energies of the formation of carbon nanotubes and amorphous carbon are listed in Table 1. The amount of iron deposited per unit surface of the reactor, j, affects the graphitic carbon formation rate directly because CNTs grow on these nanoparticles. The flux of formation of iron nanoparticles is m0 ¼ MFe Kc CFe
ð12Þ
This flux is based on the cross-sectional area of the flow. Therefore, the rate of transfer of iron nanoparticles, from the bulk of the gas to the surface of the substrate on both inner and outer pipes, can be evaluated from j ¼ MFe Kc CFe
Dout 2 Din 2 4ðDout þ Din ÞL
ð13Þ
The amount of deposited iron nanoparticles on the surface of the substrate is directly proportional to time. Thus, the amount of deposited iron nanoparticles on the surface of the growth window is j ¼ MFe Kc CFe
Dout 2 Din 2 t 4ðDout þ Din ÞL
ð14Þ
Given that the carbon is produced as a result of xylene decomposition (carbon source) according to C8 H10 f 8C ðnanotubesÞ þ 5H2
ð15Þ
The amount of deposited carbon at time t and entrance flow rate of the carbon source can be evaluated and then converted to the length of carbon nanotubes: Z 0 Din 8CAu dt Din þ Dout lCNT ¼ tπ 1 ð16Þ nDCNT 2 FCNT As 4 MC The d iameter of nanoparticles formed along the reactor was estimated from the model proposed by Kuwana and Saito.13 The density of carbon nanotubes was calculated from FCNTs ¼ xg Fg þ xA FA
ð17Þ
Mole fractions of carbon nanotubes and amorphous carbon were determined from the experimental data.
Figure 3. (a) Temperature profile along the reactor and corresponding position of heating zones as well as the growth window. (b) CNT array height profile along the growth window.
4. RESULTS AND DISCUSSION 4.1. Experiments. Parts a and b of Figure 3 show the axial profiles of temperature and CNT array heights, respectively, on the quartz rod at the center of the reactor. In the course of synthesis of CNTs by the floating catalyst, there is a consensus about growth localization in a so-called growth window.27,28 The region along the reactor, where the array heights are longer than 0.5 mm, is considered to be the growth window. Of course, there exist CNTs before this zone, but their height is less than 0.5 mm and their properties were not measured in this study. Figure 3a demonstrates that the temperature in this region increases from 825 to 850 °C and then decreases to 835 °C. According to Figure 3b, the growth window is about 15 cm long. A series of numbers were assigned to the local points along the growth window. This figure shows that the height of CNTs increases to about 2.5 mm at point 4 (47 cm from the entrance of the reactor) and then decreases. The CNT growth rate after point 4 decreases, while the temperature increases to a maximum 850 °C at 46 cm. Parts a, b, c, and d of Figure 4 present FESEM images of points 2, 4, 5, and 7, respectively, at the middle of the CNT array heights. It can be seen in Figure 4 that the average diameter of CNTs covered by amorphous carbon increases along the growth window up to 51 cm from the entrance of the reactor, beyond which it slightly decreases. Figure 5 shows FESEM micrographs of CNT arrays of point 4 before and after the thermogravimetric analysis (TGA) experiment up to 505 °C. The FESEM micrographs show that the average diameter of the CNTs has reduced from 110 to 75 nm by TGA up to 505 °C, which suggests that an overlayer of amorphous carbon covers the CNTs. This layer can be mostly removed by oxidation in air during a gentle TGA experiment up to around 500 °C.20 Therefore, throughout the simulations, it was assumed that the base diameter of the CNTs is equal to the nanoparticle diameter while along the arrays is 1.5 times the base diameter due to formation of amorphous carbon on the outer surface of the CNTs. This situation is shown in Figure 6. 1145
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Figure 4. FESEM images of midpoint of CNT arrays at (a) point 2, (b) point 4, (c) point 5, and (d) point 7.
Figure 6. Figure of CNTs used in this paper, where Dp is the diameter of a CNT and is the same as the diameter of an iron nanoparticle.
Table 2. Number Density of Carbon Nanotubes along the Growth Window longitudinal position (cm) 43 number of CNTs (m2)
Figure 5. FESEM micrographs of a CNT array at point 4, before (a) and after (b) partial oxidation in a TGA experiment up to 505 °C.
The number of CNTs per unit surface of the reactor is reported in Table 2. These values were calculated from the FESEM images is shown in Figure 4 . As can be seen in Table 2,
47
49
53
3.7 1012 2.5 1012 2.28 1012 1.7 1012
the number density of CNTs decreases along the reactor length. This trend is caused by the decreasing number of nanoparticles due to consumption of ferrocene along the reactor. 4.2. Modeling. 4.2.1. Concentrations and CNT Height Profiles. Figure 7 presents ferrocene and iron particle concentration profiles along the reactor. The actual temperature profile, shown in Figure 4a, was applied in the model. It can be seen in Figure 7 that ferrocene is consumed mainly at the beginning of the reactor. The concentration of iron nanoparticles increases sharply at the beginning along the reactor due to the decomposition of ferrocene. At the maximum point, all the ferrocene is decomposed. The concentration of iron nanoparticles then decreases slightly due to the mass transfer of iron particles from the bulk to the surface of the substrate. 1146
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Figure 7. Concentrations of ferrocene and iron particles along the reactor. Figure 9. Comparison between experiment and calculated height of carbon nanotubes with coefficient parameter.
Figure 8. Concentration of xylene along the reactor.
Figure 8 illustrates the concentration profiles of xylene along the reactor at various reaction times (up to 30 min). At the early time of the reaction, xylene is converted to CNTs. Later on and when the CNTs are formed, xylene is converted to both CNTs and amorphous carbon on the surface of CNTs. This is the reason for increasing the conversion against time. Figure 8 also shows that the conversion of xylene is less than 7%. Therefore, it is reasonable to assume constant xylene bulk concentration, if necessary. The array heights can be regarded as the average growth rate of CNTs along the reactor. Figure 9 presents a comparison between experimental and model CNT heights along the growth window. It can be observed in Figure 9 that the model follows the experimental height properly. However, the model overpredicts the experimental value by 20%. The reason for this error is that deactivation of catalyst, caused by amorphous carbon formation, is not taken into account in the model. Therefore, a simple deactivation coefficient was considered for the xylene decomposition reaction (carbon source) as follows: k00CNT ¼ k0CNT
4ðDout þ Din Þ j expð αtÞ Dout 2 Din 2
ð18Þ
The deactivation coefficient α was evaluated by fitting eq 18 to the experimental data shown in Figure 9. This value was found to be 1.04 104 s1. Figure 9 demonstrates that considering deactivation leads to a better fitting of the model to the experimental data and the calculation error is reduced to 5%. Kuwana et al.11 also investigated the effect of deactivation of catalyst on the rate of CNT formation and reported a deactivation coefficient of the same order of magnitude. 4.2.2. Effect of Temperature. Increasing the temperature leads to an increase in the xylene decomposition rate which has a
Figure 10. Variation of CNT average height at different temperatures.
positive effect on the growth of CNTs. However, increasing the temperature can cause an increase in the diameter of iron nanoparticles13 and a decrease in the number density of CNTs. According to eq 16, these two phenomena can affect the height of CNTs in an opposite manner. Therefore, it is not easy to make a direct conclusion about the effect of temperature on the height of CNTs. At a constant temperature, the diameter of iron nanoparticles increased. The diameter of nanoparticles increases along the axial direction (z) as a result of nanoparticle coalescence. When nanoparticles are nucleated, a primary nucleation particle of less than 1 nm is produced. After production of a certain number of particles, the frequency of biparticle collision increases, resulting in enlargement of the particles (1120 nm).13 The CNT number density (the number of CNTs per surface area) decreased along the reactor length due to the decreased frequency of collision caused by the decreased number of nanoparticles. The average height of nanotubes vs temperature as predicted based on the model of this work is shown in Figure 10. It is worth noting that the temperature of the reactor was kept constant along the reactor (no temperature profile considered) in this simulation. Figure 10 shows that the maximum height takes place at 870 °C. At temperatures higher than 900 °C, further increase in the temperature leads to reduction of average height due to increase in the formation of amorphous carbon and accumulation of iron nanoparticles. These two factors act as obstacles in the mass transfer rate and prevent the growth of CNT height. 4.2.3. Effect of Concentration. Variations of nanotube height with concentration of ferrocene and xylene in the feed, calculated 1147
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’ AUTHOR INFORMATION Corresponding Author
*Tel.: (98-21) 6696-7797. Fax: (98-21) 6646-1024. E-mail: mostoufi@ut.ac.ir.
Figure 11. Effect of (a) concentration of xylene and (b) amount of Fe deposited on average height of carbon nanotubes.
at the optimum temperature of 870 °C, are illustrated in parts a and b, respectively, of Figure 11 . Increase in ferrocene and xylene concentrations lead to increases in catalyst particles and carbon source, respectively. This directly affects the height of CNT arrays. Increasing the concentration of xylene results in an increase of carbon atoms deposited in the growth window and affects the concentration gradient in each section of substrate. According to eq 16, this directly affects the height of nanotubes, as shown in Figure 11 a. The effect of ferrocene concentration on nanotube length is more significant compared to that of xylene since it directly affects j and kCNT. In fact, an increase in ferrocene concentration leads to an increase in the amount of iron deposited on the growth window (j) and an increase in xylene decomposition rate acceleration (kCNT) according to eq 10.
5. CONCLUSIONS An advanced model of xylene decomposition for the multiwall carbon nanotube (MWCNT) arrays in a floating catalyst (FC) reactor with xylene and ferrocene as the carbon source and catalyst precursor, respectively, was developed. It was found that the reactor yields the maximum average height of CNTs in the temperature range 825875 °C. Increase in the concentration of xylene and ferrocene in the feed can increase the formation of carbon atoms and catalyst particles that lead to an increase in the height of CNTs. Experimental values 20% lower than computational values in terms of the height of carbon nanotubes were observed. The model predicts MWCNT array heights 20% higher than the experimental values. Incorporation of a catalyst deactivation rate into the model results in a very close prediction of MWCNT array heights.
’ NOMENCLATURE A = entrance surface of reactor (m2) As = surface of every section in substrate (m2) DavCNTs = average diameter of carbon nanotubes (m) Dp = diameter of iron nanoparticle (m) Ci = molar concentration of component i (mol/m3) Din = diameter of substrate (m) Dout = diameter of quartz reactor (m) Dim = diffusion coefficient of xylene in the gas mixture (m2/s) k0A = pre-exponential factor of reaction amorphous carbon formation (m/s) k0CNTs = pre-exponential factor of reaction graphitic carbon formation (m3/g of Fe 3 s) 0 k A = rate constant of reaction amorphous carbon formation in surface in reactor volume (1/s) k0 CNTs = rate constant of reaction carbon nanotube formation in reactor volume (1/s) lavCNTs = average height of carbon nanotubes (m) MC = molecular weight of carbon (12 kg/kmol) MFe = molecular weight of iron (56 kg/kmol) n = number of nanotubes per unit surface (m2) t = time (s) Ur = velocity of feedstock in the reactor (m/s) x = mole fraction xg = mole fraction of graphite phase xA = mole fraction of amorphous phase z = Cartesian coordinate (m) Greek Symbols
α = deactivation coefficient (1/s) j = amount of Fe per surface of growth window (g/m2) F = density (g/cm3) FCNTs = density of carbon nanotubes (g/cm3)
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