Modelling study of single walled carbon nanotube formation in a premixed flame

Abstract

In this study the formation processes of catalyst nanoparticles and single walled carbon nanotubes (SWCNTs) in a premixed flame doped with Fe(CO) 5 were first modelled using a three-step SWCNT growth model including a detailed surface chemistry model. The growth of SWCNTs was experimentally studied by the length measurement of the SWCNT using Raman radial breathing mode (RBM) and size measurements of the iron oxide catalyst particles using XRD and TEM. The flame chemistry and the formation of the catalyst particles were modelled in detail by means of a sectional model. In a post-processing step the SWCNT population balance growth model was numerically solved using a multivariate stochastic population balance solver. The model was able to capture the growth characteristics and revealed the role of the monolayer. The computational study on the adsorption, dissociation, and reactions of CO, H 2 and H 2 O on iron nanoparticles showed that carbon, hydrogen and oxygen atoms form at the surface of the catalyst. Their ratio, which is controlled by the surface reaction pathways, affects the growth of SWCNTs, the formation of monolayers and the phase transformation of catalyst particles.

Full text

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Modelling study of single walled carbon nanotube formation in
a premixed flame†
John Z. Wen,aMatthew Celnik,bHenning Richter,cMeri Treska,a
John B. Vander Sandeaand Markus Kraft*b
Received 7th November 2007, Accepted 25th January 2008
First published as an Advance Article on the web 7th February 2008
DOI: 10.1039/b717256g
In this study the formation processes of catalyst nanoparticles and single walled carbon nanotubes
(SWCNTs) in a premixed flame doped with Fe(CO)5were first modelled using a three-step SWCNT
growth model including a detailed surface chemistry model. The growth of SWCNTs was
experimentally studied by the length measurement of the SWCNT using Raman radial breathing mode
(RBM) and size measurements of the iron oxide catalyst particles using XRD and TEM. The flame
chemistry and the formation of the catalyst particles were modelled in detail by means of a sectional
model. In a post-processing step the SWCNT population balance growth model was numerically
solved using a multivariate stochastic population balance solver. The model was able to capture the
growth characteristics and revealed the role of the monolayer. The computational study on the
adsorption, dissociation, and reactions of CO, H2and H2O on iron nanoparticles showed that carbon,
hydrogen and oxygen atoms form at the surface of the catalyst. Their ratio, which is controlled by
the surface reaction pathways, affects the growth of SWCNTs, the formation of monolayers and the
phase transformation of catalyst particles.
Introduction
There has been increasing research interest in the application and
production of carbon nanotubes (CNTs) over the last two
decades.1This is due to their unique electrical, mechanical and
chemical properties.2CNTs have potential applications in multi-
disciplinary areas such as sensors, polymer composites, electron-
ics, mechanical actuators, hydrogen storage in fuel cells, and
catalysis. The exploration and investigation of applications in
such fields require well characterized structure and greater
production yield, which only become achievable when the
synthesis process can be precisely controlled. Since the discovery
of single walled carbon nanotubes (SWCNTs) in a plasma
discharge process in the presence of an iron catalyst,1a variety
of methods including arc-discharge, laser ablation, chemical
vapor deposition (CVD) and aerosol reactor techniques have
been investigated.2The energy supplies are quite different for
these methods: while an aerosol synthesis method, such as
a HiPCO reactor,3requires an external energy source, flame
synthesis can produce SWCNT carbon precursors, heat, and
catalyst simultaneously in a continuous reacting flow.4Synthesis
of SWCNTs in pyrolysis flames has been studied extensively by
Vander Wal and co-workers.5,6In their approaches catalyst
particles were generated, for example, by nebulizing iron salt
solutions. The reactive mixture was then introduced into
a fuel-rich acetylene flame. Variation of mixture composition
and flow rates allowed for the optimization of SWCNT forma-
tion. The same author also observed the formation of SWCNTs
in diffusion flames when a floating catalyst was formed from
a metallocene.7The alternative flame synthesis approach was
based on the addition of a catalyst precursor, such as iron
pentacarbonyl (Fe(CO)5), to the inflow gas mixture prior to
the stabilization of a premixed flat flame, as reported in the
work of Height et al.4,8,9Those authors identified a nanotube
formation window of fuel-to-oxygen ratios. They found that
while, relative to stoichiometric conditions, an excess of the
carbon supply is necessary to enable inception of nanotubes,
soot-like structures are formed at too high fuel-to-oxygen ratios.
They also investigated the effect of Fe(CO)5concentration on
theparticlesizedistributionandtheshapeofthemetalliccatalyst.
In their work the quantity of condensed material increased
dramatically withtheFe(CO)5concentration,whereasnanotubes
appeared to be cleaner at lower concentrations. The afore-
mentioned experimental studies under a variety of synthesis
conditionssuggestthattheremaybemorethanonesetofphysical
and chemical processes by which the catalyst exhibits its function
during the formation and growth of SWCNTs, though the
fundamental catalytic step is the same.10
In order to increase the production yield and further achieve
structure-selective production of SWCNTs (for example with
desired diameters and chiralities), experimental and numerical
investigations of the formation mechanism of SWCNTs are
essential. Recently several in situ electron microscopy studies
of carbon nanofibre growth have been reported at the atomic
aMaterial Science and Engineering, Massachusetts Institute of Technology,
77 Massachusetts Ave, Cambridge, MA, 02139, USA. E-mail: zywen@
mit.edu; Fax: +1 617-253-6933; Tel: +(01) 617-258-6118
bChemical Engineering, University of Cambridge, Pembroke Street,
Cambridge, UK, CB2 3RA. E-mail: mk306@cam.ac.uk; Fax: +44 (0)
1223 334796; Tel: +44 (0) 1223 762784
cNano-C, Inc., 33 Southwest Park, Westwood, MA, 02090, USA. E-mail:
HRichter@nano-c.com; Fax: +1 781-407-9419; Tel: +1 781-407-9417
† This paper is part of a Journal of Materials Chemistry theme issue on
carbon nanostructures.
1582 | J. Mater. Chem., 2008, 18, 1582–1591 This journal is ª The Royal Society of Chemistry 2008
PAPERwww.rsc.org/materials | Journal of Materials Chemistry
This is the Computational Modelling Group’s latest version of the paper.
For the published version please refer to doi: 10.1039/b717256g

Page 2

scale for CVD processes using gaseous hydrocarbons as carbon
feedstocks.11–13Some experimental evidence showed that the
catalytic particles remained crystalline during the growth of
carbon nanostructures. When carbon atoms became available
at the surface of the catalyst, the growth process was initiated
at edges (or steps) on the crystalline metal surface and retained
by the carbon supply through surface diffusion. Recently,
Rodriguez et al.14reported their observation on the inception
and early growth of SWCNTs in an entirely condensed-phase
process which was arranged in host multi-walled carbon nano-
tubes (MWCNTs) filled with metal particles. The injection of
carbon atoms into metal particles was achieved through the
electron irradiation of the host tubes. They found that when
MWCNTs containing metal particle cores were irradiated with
an electron beam, carbon from graphitic shells surrounding the
metal particles was ingested into the body of the particle, and
subsequently grew SWCNTs inside the host nanotubes. Based
on this observation, they proposed that bulk diffusion, rather
than surface diffusion, was responsible for the growth of
SWCNTs from the solid-state catalyst. The solid state of the
catalyst, which was found in these experimental studies,
however, did not agree with the widely accepted vapor–liquid–
solid (VLS) model for SWCNT growth.15In the VLS model,
the carbon feedstock is in the vapor phase before it dissolves
into the catalyst to form a liquid metal carbide particle. When
this particle becomes carbon saturated, the solid-phase CNTs
begin to grow. The VLS model has been implemented in mole-
cular dynamic studies of SWCNT growth mechanisms, and
helped to explain the roles of the metal catalyst.16–18Although
the VLS model does not offer a detailed description of the
surface chemistry on the catalyst, or the CNT inception process,
it provides a convenient approach to study the growth process
of CNTs which should be modelled through multi-scale
approaches.19In addition, the VLS model assumes bulk diffu-
sion through a liquid catalyst. Upon improvement, a similar
model should, therefore, be able to describe the major processes
of CNT formation if the properties of the liquid catalyst in the
VLS model are replaced by those of the solid catalyst.
The description of SWCNT related chemical and physical
processes in a premixed flame is very challenging since the in situ
monitoring of inception and growth of SWCNTs in a chemically
dynamic and energy intensive process is almost impossible with
current experimental techniques. The lack of experimental
studies hinders the development of detailed kinetic models for
the growth of SWCNTs in flames. Additional complexities arise
from the presence of a number of carbon feedstocks from
combustion products and subsequent complex surface chemistry
on the catalyst. The description of SWCNT growth in flames
should at least include: the gas-phase reaction kinetics of
hydrocarbon combustion, the chemical pathway for the thermo-
decomposition of the catalyst precursor (e.g., Fe(CO)5), the
inception, growth and coagulation of metal nanoparticles, the
surface adsorption and catalytic disproportionation reactions of
carbon feedstocks at active metal surfaces, the inception and
growth of SWCNTs from the metal surface, and the deactivation
ofthecatalyst.8Ithasbeenfoundthatthesizeandstructureofthe
CNTs formed in aerosol processes directly correlate to the struc-
ture and surface morphology of the metal catalyst particles.20
Therefore, to model the formation of CNTs in a premixed flame,
which produces catalyst nanoparticles and SWCNTs simulta-
neously, an accurate prediction of the size and structure of
catalyst particles is essential. Wen et al.21recently investigated
the electronic structure and thermodynamic properties of major
Fe/C/O intermediates during the thermal decomposition of
Fe(CO)5. In that work a kinetic model was developed which
describes the thermal decomposition pathways of Fe(CO)5and
subsequent formation and growth mechanisms of iron nano-
particles. The model successfully predicted the size and yield of
iron nanoparticles formed in shock tubes at a variety of reaction
temperatures and pressures, similar to flame conditions.
The kinetic modeling of SWCNT formation in flame synthesis
has been scarce. Recently Puri et al.22proposed a CNT/CNF
(carbon nanofibre) growth model to predict the formation of
carbon nanostructures on a substrate which was placed in
ethylene/air flames. Their model considered a complex hydro-
carbon mixture and described a 1D bulk diffusion model from
the leading edge (where combustion products deposit on the
surface of particles) to the trail edge (where the particle connects
to the substrate). The model showed that with the onset of incep-
tion and growth of nanostructures, bulk diffusion dominates as
the major driving potential for carbon atom transport through
the nanoparticle. Another finding in their work was the contribu-
tion of CO to CNT formation in flame synthesis. Since the
concentration of hydrocarbons in the vicinity of the CNT growth
zone is negligible, they suggested that CO is the major contri-
butor to carbon deposition on the catalyst.
The objective of this work was to numerically investigate the
possible mechanisms of SWCNT growth and catalyst nano-
particle formation in flames, and to study the roles of gas-phase
species during the growth of SWCNTs. A simplified three-step
(carbon deposition, bulk diffusion and growth of monolayers
or SWCNTs) model was first implemented in the flame simula-
tion by coupling with a recently developed stochastic population
balance solver for nanoparticle/SWCNT formation.23The
measured particle size and the yield and length of SWCNTs
were compared with the model prediction. Secondly a detailed
surface chemistry model was proposed to describe the surface
adsorption, dissociation and reaction of CO, water and hydro-
gen on catalyst nanoparticles. The roles of carbon, hydrogen
and oxygen surface atoms during the phase transformation of
catalyst nanoparticles and the formation of SWCNTs were
investigated numerically.
Experimental
The formation processes of iron catalyst and SWCNTs during
premixed flame synthesis have been experimentally investigated
using in-chamber probe sampling and advanced material charac-
terization techniques (Raman spectroscopy, X-ray diffraction
(XRD), scanning electron microscopy (SEM), scanning trans-
mission electron microscopy (STEM) and transmission electron
microscopy (TEM)).24The schematic diagram of the flame
burner and associated apparatus can be found in a previous
study of a premixed acetylene–oxygen–argon flame.4The experi-
mental system investigated in this work consisted of a premixed
methane–oxygen–argon flame with a fuel-to-oxygen ratio (F) of
2.1. The flame was supplied with an argon dilution of 15 molar
percent, a cold gas feeding velocity of 22.5 cm s?1, and a burner
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pressure of 26.7 kPa (200 Torr). Fe(CO)5 was used as the
precursor of the metal catalyst. Its vapor in argon carrier gas
was supplied to the premixed feeding gases via a temperature-
controlled bubbler (6.0 ? 0.2
Fe(CO)5 (150 ppm) was controlled by adjusting the feeding
rate of an argon stream, which was channeled through the
bubbler and then added to the methane–oxygen mixture
upstream of the burner. Additional argon was fed into the
chamber in order to reach the desired inert concentration in
the cold gas mixture. Condensed material was extracted from
the flame by means of a quartz probe with an inner diameter
of 1.5 mm. For each sampling the location of the probe was
adjustedatvariousheightsaboveburner(HAB)overacontrolled
time. The time (or height) dependent nanoparticle sizes were
determined using XRD and TEM24(the XRD data are shown
later in Fig. 4). The composition of those nanoparticles was
identified using TEM as either iron particles coated with
carbonaceous layers or iron oxide particles without the coating
material.24The time (or height) dependent SWCNT structures
were analyzed using Raman, SEM, STEM, and TEM. At the
smaller HAB, the individual SWCNTs started to grow from
nanoparticles, while at the larger HAB, the SWCNT bundles
formed. The diameter of individual SWCNTs was around
1 nm. The Raman spectra showed three characteristic zones
for the growth of SWCNTs (an induction zone, a stable growth
zone, and a non-growth zone).
In order to further investigate the structure of SWCNTs, the
lengths of SWCNTs produced in this flame which were estimated
using the SEM imaging technique are reported here. The proce-
dure for the assessment of SWCNT length has been detailed in
a previous study.25The as-produced SWCNTs were dispersed
in ethanol and sonicated (tip mode, 30 W, 20 kHz). Prior to
deposition on holey carbon grids, the dispersion was diluted
with additional ethanol. During SEM imaging at magnifications
of typically 10000 to 20000, SWCNT bundles were identified and
lengths measured manually using a feature of the instrument’s
control software. As shown in Fig. 1, the length evolution of
SWCNTs with increasing HAB had a similar shape to the
measured Raman spectra. With increasing HAB, the SWCNTs
consistently grew up to 200 mm HAB after the inception was
initiated.
?C). The molar fraction of
Numerical models
The kinetic model used in this work includes the gas-phase
reaction kinetics of methane–oxygen–argon combustion, the
chemical pathway of the thermo-decomposition of Fe(CO)5,
the models for inception, growth and coagulation of iron nano-
particles, and a simplified three-step model which describes the
carbon deposition, bulk diffusion, and growth of SWCNTs
and monolayers. We adopted GRI-Mech26to describe the gas-
phase hydrocarbon reactions in the premixed flame. To model
the formation of iron nanoparticles, a recently developed
reaction mechanism for the decomposition of Fe(CO)5 and
subsequent formation of small iron clusters (i.e., Fen, n # 8)21
was added in GRI-Mech. To describe the growth of iron
nanoparticles (i.e., Fen, n > 8), two numerical approaches were
employed. When the flame structure (the flow velocity, tempera-
ture and species concentrations) was computed using the detailed
combustion chemistry using CHEMKIN,27a sectional method21
for the growth of iron nanoparticles was adopted. The effect of
the formation of iron nanoparticles on the flame structure was
addressed by taking into account the radiation heat transfer
from the iron particles (as defined later). When the growth of
SWCNTs was modeled using the stochastic population balance
solver23which was run as a post-processor, the aforementioned
chemical pathways of iron nanoparticle growth were converted
into a reaction mechanism and coupled with the SWCNT growth
model (as described later). The CHEMKIN calculated flame
temperature profile and gas-phase species concentrations
(including ones for iron clusters, Fen, n # 8) were used as inputs
for post-processing.
Since the growth model for iron nanoparticles was originally
developed for the thermo-decomposition of Fe(CO)5in argon,
no pathways have been developed for the formation of iron
oxide nanoparticles. In this study we made the following
assumptions to take into account the formation mechanism of
iron oxide nanoparticles. First, the iron nanoparticles form
upstream in the flame through the combination of their precur-
sors (gas-phase iron clusters). Secondly, the oxidation of iron
nanoparticles occurs at the surface of iron particles. This oxida-
tion process could eventually convert iron nanoparticles into
iron oxide nanoparticles in the presence of sufficient oxidation
agents (e.g., O2and H2O). Since a reduction agent, H2, is also
abundant in the flame, the final composition of nanoparticles
is determined by the competition between oxidation and reduc-
tion mechanisms. In this work it was further assumed that
both oxidation and reduction processes have little effect on the
size of nanoparticles.
In the simplified SWCNT growth model, a numerical
approach proposed in a previous study23for the SWCNT/nano-
particle formation in a flow reactor was employed. That model,
which was based on previous studies on stochastic modelling of
soot particle formation in combustion,28–34has been modified to
describe the following processes at three steps: carbon deposition
at the iron particle surface, carbon diffusion in iron particles, the
growth of SWCNTs and the formation of graphitic monolayers
at particle surfaces. The latter two processes were viewed as a
single step since both were supplied with the same flow of carbon
supply (see below). Here the model principles which describe the
major physical and chemical processes of SWCNT growth are
Fig. 1
RamanRBMintensities.Thedashedlineshowsthetrendofbothdatasets.
The comparison of measured SWCNT length (squares) and
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Page 4

repeated. Please refer to the original work for detailed informa-
tion. The mathematical model on the stochastic particle
approach can be found from the literature.29,35–37
Carbon deposition model
The model describes two carbon deposition processes which
occur at the surface of iron catalyst, CO disproportionation
(or Boudouard reaction) and CO hydrogenation, as shown in
eqn (1) and (2). These processes have been identified as major
carbon transfer channels from gaseous CO to catalyst particles
in a CO rich environment:3
2CO / Cs+ CO2
r ¼ kSact[CO][CO](1)
2CO + H2/ Cs+ H2Or ¼ kSact[CO][H2] (2)
Sact¼ S0? Sml
(3)
where Sactis the exposed metal surface area of catalyst particles
and is calculated using eqn (3). S0is the total particle surface area
and Smlis the surface area of the carbon monolayer. r is the
reaction rate (atoms cm?3s?1) and k is the rate constant
(cm atoms?1s?1). [CO] and [H2] are the gas-phase concentrations
of CO and H2, respectively. Cs denotes solid phase carbon
deposited at the surface. Similar to the approach proposed in
the previous study,23a temperature-independent rate constant
was employed for both processes whereby the reaction rate
depends on the available surface area and the concentration of
gas-phase reactants.
Carbon diffusion model
Once a carbon atom has become available at the catalyst surface,
it was assumed that the carbon diffuses into the iron particle
before growing SWCNTs and monolayers. Since it was found
that the bulk diffusion of carbon atoms in the catalyst was
hindered by a higher energy barrier which corresponds to the
carbon diffusion through the surface and sub-surface catalyst
atoms,38a single energy barrier, as shown in eqn (4), was used
to account for the transport of carbon in iron particles. The
diffusivity of this transport process was assumed to be large.
To account for the carbon atoms which can be accommodated
in the particle, their maximum number was calculated by the
saturation limit of carbon in iron. If the carbon supply to the
surface continues beyond the accommodation limit, carbon
atoms either form a monolayer at the surface or grow into
SWCNTs. Eqn (4) was used to calculate the concentration of
carbon atoms accommodated in an iron nanoparticle:
½C?sat
½Fe?¼?0:062305 þ 1:176 ? 10?4T?exp
where T is the temperature, s ¼ 0.0172 N cm?1 39is the surface
tension, v is the particle volume, kBis the Boltzmann constant
and R is the particle radius.
?2sv
kBTR
?
(4)
SWCNT growth and monolayer formation model
Following the diffusion of carbon atoms in an iron particle,
carbon atoms accumulate from some specific location at the
surface, for example an edge. Subsequently the carbon starts to
form a monolayer or to grow a SWCNT. In this work, a coeffi-
cient, fcnt, which specifies the percentage of carbon atoms to
grow SWCNTs, was used to account for the competition for
carbon atoms between the formation of monolayers and the
growth of SWCNTs. This assumption gives the diameter of
SWCNTs which is consistent with the diameter of catalyst parti-
cles that initialize the growth process. The carbon addition rate
to a SWCNT is therefore calculated using eqn (5):
dncnt
dt
¼ kSactfcnt
?
½CO?2þ½CO?½H2?
?
(5)
where ncntis the number of carbon atoms of a SWCNT. The
SWCNTs were assumed to have a constant graphitic density of
1.8gcm?3andagraphenethicknessof0.34nm.23Thisassumption
gives the rate of length growth of SWCNTs as shown in eqn (6):
?
dLcnt
dt
¼
mc
prcdgphdcnt
?dncnt
dt
(6)
where Lcntis the length of a SWCNT, mcis the mass of a carbon
atom and dcntis the diameter of a SWCNT. The carbon addition
rate to a monolayer is calculated using eqn (7):
dnml
dt
¼ kSactð1 ? fcntÞ
?
½CO?2þ½CO?½H2?
?
(7)
The diameter of particles with monolayers was calculated from
the total number of carbon and iron atoms in the particle and
the number of carbon atoms in the monolayer.
Detailed surface chemistry model
Since the simplified model cannot provide detailed information
about the surface chemistry of catalysts, which controls the
carbon supply rate from the gas-phase carbon source to growth
processes of SWCNTs, a surface chemistry model is necessary to
describe the adsorption of these gas-phase species, dissociation
of the adsorbate, and reactions between surface species. In
addition, this detailed model is expected to take into account
the temperature effect on the surface reaction kinetics, which
has been unavailable in the simplified model. In a CO–H2–
H2O rich combustion environment, as in the premixed methane–
oxygen–argon flame, the chemical and physical processes are
complexdueto the simultaneously
reactions, interfacial phenomena, and bulk molecular diffusion
processes (e.g. the diffusion of C and O atoms) in catalyst nano-
particles. As will be discussed later, the bulk diffusion of C and O
atoms in the catalyst can bring about a possible phase transfor-
mation of the nanoparticle material. Here it was assumed that
those catalyst particles are in the solid phase though it is difficult
to exclude the formation and function of liquid-phase particles.
Three major combustion products, CO, H2 and H2O, are
assumed to be gas-phase molecular suppliers to the surface
reactions. Since surface chemistry on iron nanoparticles is
unavailable in the literature, the reaction rates were taken mostly
from the literature data for the Fe(111) crystalline surface (with
7.1 ? 1014iron atoms cm?2).40The chemical pathways for three
types of surface reactions and the calculation of temperature
dependent rates are presented in the following section and are
occurringgas-phase
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Page 5

summarized in Table 1. The equations for the rate calculation are
listed in the footnotes of Table 1.
To describe the surface chemistry related to CO, a four-step
model was employed. The adsorption of CO molecules on the
catalyst surface belongs to the scope of chemisorption, because
the C–metal bond forms between a CO molecule and a surface.41
Following the chemisorption process, upon increasing the
temperature of the catalyst surface, the CO molecules can either
desorb to form gaseous molecules or dissociate into C and O
atoms on the surface. The adsorbed CO molecules can diffuse
on the surface and combine with O atoms to form gaseous
CO2, whereas the associated C and O atoms can diffuse into
the bulk material. To describe these processes the following
reactions were included in the model:
CO adsorption
COg+ * / COad
(R1)
CO dissociation
COad+ * / Cad+ Oad
(R2)
CO desorption
Cad+ Oad/ COg+ *(R3)
CO2combination
COad+ Oad/ CO2,g+ 2* (R4)
where the subscripts g and ad represent the gas-phase species and
adsorbate, respectively. The symbol * represents a surface site.
To calculate the reaction rates of R1–R4, the following equa-
tions (eqn (8)–(12)) were employed. The reaction parameters
for R1–R3 were adopted from the literature.42The reaction
rate for R4 was calculated using the parameters determined in
a recent experimental work.43In this study,
radðQÞ ¼
P
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2pmkBT
p
s0exp
?
?DEad
RT
?
fðQÞNA
(8)
where rad(Q) is the surface adsorption rate, Q is the surface
coverage of adsorbate which is calculated from the ratio of the
number of adsorbates over the maximum number of surface
sites, P and T are the pressure and temperature of gas-phase
species respectively, m is the mass of adsorbate, s0¼ 0.7744is
the sticking probability under the initial conditions (the effect
of temperature on the initial sticking probability was neglected
in the present study), DEadis the activation barrier for adsorp-
tion, and f(Q) is a function which accounts for the effects of
increasing coverage of all adsorbate on the sticking probability.
It has an expression42of
fðQÞ ¼
1
1 þ 0:15 ?
SQ
1?SQ
(9)
In eqn (8), NA¼ 7.1 ? 1014atoms cm?2is the maximum number
of surface sites per unit area.42
rdesðQÞ ¼ kdesexp
?
?DEdes
RT
?
Q
(10)
where rdes(Q) is the surface desorption rate, kdes is the rate
constant (as shown in Table 1), and DEdes is the activation
barrier for desorption.
rdissðQÞ ¼ ?kdissexp
?
?DEdiss
RT
?
(11)
where rdiss(Q) is the surface dissociation rate, kdissis the rate
constant (as shown in Table 1), and DEdiss is the activation
barrier for surface dissociation.
rCO2ðQÞ ¼ ?kCO2exp
?
?DECO2
RT
?
? qa
O
(12)
where rCO2s(Q) is the rate for CO2formation, kCO2is the rate
constant (as shown in Table 1), and DECO2is the activation
barrier for the combination reaction (R4).
The adsorption of H2 and H2O molecules on the catalyst
surfaces often accompanies instantaneous dissociation.45,46For
this dissociative adsorption process, the following equation
was used to calculate the adsorption rate:
Table 1Parameters of the adsorption and subsequent surface reactions of CO, H2and H2O on iron nanoparticles
Reaction
Saturation
coverage/atoms cm?2
Initial sticking
probability
Activation barrier
Ea/kcal mol?1
Rate constants k/kdes/kdiss/kCO2
References
COg/ COad
1.05 ? 1015
0.580.02.4 ? 1030s?1cm?2calculated
using eqn (8) and (9)b
1 ? 1017s?1b
1 ? 1011s?1b
4.7 ? 106s?1a
1.0 ? 1030s?1cm?2calculated
by eqn (8) and (10)b
3.7 ? 1012s?1b
1.73 ? 1010s?1b
1.4 ? 1011s?1b
3.2 ? 1010s?1b
9.4 ? 1010 s?1b
2.3 ? 1030s?1cm?2calculated
using eqn (8) and (10)b
42,44,50
COad/ COg
COad/ Cad+ Oad
COad+ Oad/ CO2,g
H2,g/ 2 Had
32.0
20.0
12.2
0.0
42
42
43
1.38 ? 1015
0.24
40,45,51
2 Had/ H2,g
Oad+ Had/ OHad
OHad/ Oad+ Had
2OHad/ H2Og+ Oad
OHad+ Had/ H2,g+ Oad
H2Og/ Had+ OHad
21.0
14.2
24.2
23.6
17.3
0.0
45,52
53
53
53
53
1.42 ? 1015
1.0
48,54
aThe reaction rate was calculated using k ? exp(?Ea/RT) ? Qa0, a ¼ 0.63.bThe reaction rate was calculated using k ? expð?Ea=RTÞ ?Q
i
Hi, where
i is the index of a reactant.
1586 | J. Mater. Chem., 2008, 18, 1582–1591This journal is ª The Royal Society of Chemistry 2008