Local reaction rates and surface diffusion on nanolithographically prepared model catalysts: Experiments and simulations

Article abstract of DOI:10.1063/1.1854622

Combining molecular beam methods and angular resolved mass spectrometry, we have studied the angular distribution of desorbing products during CO oxidation on a planar Pd/silica supported model catalyst. The model catalyst was prepared by means of electron beam lithography, allowing individual control of particle size, position, and aspect ratio, and was characterized by atomic force microscopy and scanning electron microscopy before and after reaction. In the experiment, both oxygen and CO rich regimes were investigated using separate molecular beams for the two reactants. This allows exploration of diffusion effects of reactants on the particles and of shadowing and backscattering phenomena. A reaction-diffusion model was developed in order to extract information about local reaction rates on the surface of the catalyst nanoparticles. The model takes into account the structural parameters of the catalyst as well as the backscattering of the reactants and products from the support. It allows a quantitative description of the experimental data and provides a detailed understanding of temperature and reactant flux dependent effects. Moreover, information on the surface mobility of oxygen under steady-state reaction conditions could be obtained by comparison with the experimental results.

Full text of DOI:10.1063/1.1854622

Local reaction rates and surface diffusion on nanolithographically prepared model
catalysts: Experiments and simulations
M. Laurin, V. Johánek, A. W. Grant, B. Kasemo, J. Libuda, and H.-J. Freund
Citation: The Journal of Chemical Physics 122, 084713 (2005); doi: 10.1063/1.1854622
View online: http://dx.doi.org/10.1063/1.1854622
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/122/8?ver=pdfcov
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THE JOURNAL OF CHEMICAL PHYSICS 122, 084713 ͑2005͒
Local reaction rates and surface diffusion on nanolithographically prepared
model catalysts: Experiments and simulations
M. Laurin and V. Johánek
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
A. W. Grant and B. Kasemo
Department of Applied Physics, Chalmers University of Technology, S-412 96 Göteborg, Sweden
J. Libudaa͒ and H.-J. Freund
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
͑Received 2 September 2004; accepted 9 December 2004; published online 18 February 2005͒
Combining molecular beam methods and angular resolved mass spectrometry, we have studied the
angular distribution of desorbing products during CO oxidation on a planar Pd/silica supported
model catalyst. The model catalyst was prepared by means of electron beam lithography, allowing
individual control of particle size, position, and aspect ratio, and was characterized by atomic force
microscopy and scanning electron microscopy before and after reaction. In the experiment, both
oxygen and CO rich regimes were investigated using separate molecular beams for the two
reactants. This allows exploration of diffusion effects of reactants on the particles and of shadowing
and backscattering phenomena. A reaction-diffusion model was developed in order to extract
information about local reaction rates on the surface of the catalyst nanoparticles. The model takes
into account the structural parameters of the catalyst as well as the backscattering of the reactants
and products from the support. It allows a quantitative description of the experimental data and
provides a detailed understanding of temperature and reactant flux dependent effects. Moreover,
information on the surface mobility of oxygen under steady-state reaction conditions could be
obtained by comparison with the experimental results. © 2005 American Institute of Physics.
͓DOI: 10.1063/1.1854622͔
I. INTRODUCTION
level ͑see, e.g., Refs. 10–12͒. For example, a distribution of
particle sizes or shapes may result in some average output,
disguising phenomena occurring on individual particles. Sec-
ond, only few experimental techniques can provide suffi-
ciently detailed experimental data on the surface kinetics and
on surface transport phenomena under reaction conditions. In
order to overcome these problems, our group and others have
recently started to apply molecular beam techniques to
model catalysts ͑see Refs. 13–18 and references therein͒ that
aim at revealing microscopic and molecular level effects.
The model catalysts reduce the complexity of the surfaces to
a controllable level. Simultaneously, the application of mo-
lecular beam methods allows the extraction of detailed ki-
netic data under most well defined conditions.
In this work we employ a supported model catalyst,
which was prepared by electron beam lithography19–23
͑EBL͒. This preparation method has been used only recently
in ultrahigh vacuum ͑UHV͒ reactivity studies.6,24 It provides
the advantage of the highest level of control over structural
parameters, including homogeneous particle sizes, exactly
controllable particle distances and positions, and variable as-
pect ratios.
Many heterogeneous catalysts are based on nanometer-
sized metal particles, finely dispersed on oxide supports.1,2
Reaction kinetics on such supported particle systems can dif-
fer strongly from the kinetics on single crystal surfaces.
There are many effects which can contribute to these modi-
fied kinetics, including, e.g., geometric and electronic prop-
erties or interactions with the support, which lead to changes
in the adsorption and reaction properties of a catalyst par-
ticle. In addition, there are pure nanoscale effects related to
kinetics, which simply arise from the limited size of the par-
ticles, i.e., even without a change of their electronic and ad-
sorption properties. Examples for such phenomena are so-
called communication effects resulting from the coupling of
surface areas with different adsorption or reaction behavior
via surface diffusion3–5 or coverage fluctuations in confined
surface regions.6–9 Both are intimately related to the surface
mobility of the reactants.
There are very little experimental data available on such
phenomena. This lack of knowledge is a result of experimen-
tal challenges associated with studies of such kinetic effects
on real catalysts. First, the enormous complexity of the sur-
faces of real heterogeneous catalysts often precludes detailed
insights into the kinetics at the molecular and single particle
Returning to the communication effects discussed above,
these phenomena arise from the coupling of regions with
locally different adsorption or reaction properties via surface
diffusion ͑for example, facets with different crystallographic
orientation on a single particle͒. This potentially gives rise to
locally different reaction rates. The direct experimental veri-
a͒
Author to whom correspondence should be addressed. Fax: ϩ49-30-
84134139. Electronic mail: libuda@fhi-berlin.mpg.de
0021-9606/2005/122͑8͒/084713/12/$22.50
122, 084713-1
© 2005 American Institute of Physics
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084713-2
Laurin et al.
J. Chem. Phys. 122, 084713 ͑2005͒
fication of such phenomena, however, would require mea-
surements of local reaction rates on individual parts of a
catalyst particle, e.g., on the different microfacets. The de-
velopment of methods, which allow local kinetic experi-
ments, is a major challenge. As a possible alternative ap-
proach, we have recently suggested the application of
angular resolved measurements of the desorbing products
from a planar model catalyst with arrays of identical or
nearly identical particles.24,25 The basic idea is that the angu-
lar distribution may contain information on the local reaction
rates on differently oriented facets of the particles.
We have chosen the CO oxidation on Pd particles as
model reaction. The mechanism and kinetics of CO oxida-
tion on platinum metals are well understood.26,27 In general,
oxygen adsorbs dissociatively and CO molecularly, with CO
having a strongly inhibiting effect on the oxygen adsorption.
From the two adsorbed species, CO2 is formed in a
Langmuir–Hinshelwood ͑LH͒ reaction step. The surface mo-
bilities of both reactants are rather different. The diffusion
barriers are low for adsorbed CO on platinum metal surfaces,
leading to high mobility, even at low sample
temperature.28,29 The diffusion activation energies for the ad-
sorbed oxygen are significantly higher ͑see, e.g., Ref. 28͒. As
a result, CO diffusion is expected to be fast as compared to
reaction. For oxygen, on the other hand, surface diffusion
and surface reaction may occur on the same time scale, or
reaction may even be fast as compared to diffusion.
A critical point for the present experiment is that the
CO2 product interacts only weakly with the metal surface,
leading to nearly instant desorption after formation. More-
over, desorption is typically found to be preferentially di-
rected along the surface normal for close-packed surfaces
͑the exact distribution may depend on the local surface and
adsorbate structure͒.26,30 Consequently, the angular distribu-
tion of CO2 can be assumed to directly reflect the distribu-
tion of local reaction rates on the particles.
FIG. 1. Electron beam lithographic ͑EBL͒ preparation of a model catalyst:
͑a͒ cleaning of the Si͑100͒ substrate with a 0.4 ␮m thick oxide layer; ͑b͒
spin coating of a photoresist layer; ͑c͒ exposure to a predesigned pattern
with an electron beam; ͑d͒ development, i.e., dissolution of the photoresist;
͑e͒ Pd evaporation; ͑f͒ lift-off, i.e., dissolution of the remaining resist.
schematic diagram of the EBL procedure is shown in Fig. 1.
In this work, we used a 0.4 ␮m thick thermal oxide layer
grown on Si͑100͒ as the substrate. The Pd towers were fab-
ricated with a double layer resist system, consisting of a
bottom layer of PMGI-SF7 ͑polyimide͒ and top layer of 1:2
diluted ZEP520 in anisole. The pattern was exposed with a
dose of 160 ␮C cm−2 in an EBL system ͑JEOL JBX9300FS͒.
After dissolving the exposed polymer, a 500 nm thick film of
Pd ͑99.95% purity, K.A. Rasmussen, AB͒ was vapor depos-
ited at ϳ3ϫ10−6 mbar at a flux of ϳ8 Å s−1 as measured by
a quartz crystal microbalance in an electron beam deposition
system ͑AVAC HVC-600͒. The remaining resist was “lifted-
off” in Shipley 1165 ͑N-methyl-2-pyrrolidone͒ leaving the
Pd towers in the prescribed pattern ͑Fig. 1͒. After resist re-
moval, the sample was cleaned for 1 h at 770 K in 5% O2 in
Ar, followed by 1 h at 820 K in 2% H2 in Ar at a flow rate of
ϳ500 ml min−1 in a flow reactor, and cooled in Ar, which
removed ϳ70% of the contaminants according to XPS.
The EBL sample was fabricated at the Chalmers Univer-
sity of Technology and transported to the FHI, where the
molecular beam experiments were performed. The sample
was further cleaned in the molecular beam UHV apparatus
͑described in Sec. II B͒ by exposure to ϳ4ϫ10−4 mbar O2
from a gas doser for 2 h at a sample temperature of 650 K
and subsequent oxygen removal by CO exposure. Finally, the
cleanliness of the Pd particles was checked by means of CO
titration. For this purpose, the sample was exposed to a mo-
lecular beam of O2 ͑ϳ3ϫ1014 molecules cm−2 s−1, 30 s͒ at
room temperature, followed by titration at 440 K with a mo-
lecular beam of CO ͑ϳ2.9ϫ1014 molecules cm−2 s−1, 30 s͒.
The amount of CO2 produced was compared to the value
expected on the basis of the Pd surface area calculated from
the structural parameters of the sample and the O saturation
coverage.31,32
In a recent work, we have demonstrated qualitatively
that this method can indeed provide the desired
information.24 It was shown that pronounced dependences of
the angular distribution of the desorbing CO2 can be ob-
served for sufficiently large Pd particles. Previous analysis of
the angular distributions, however, was limited to a simple
and qualitative model. In this work, we present details on the
preparation method and on the experimental approach. We
further develop a microkinetic model, which is capable of a
quantitative description of the experimental results.
II. EXPERIMENT
A. Electron beam lithography
The fabrication of nanoparticles by EBL has recently
been used successfully in surface science and catalysis ͑e.g.,
Refs. 19–23͒. The advantage of the method is that it provides
ultimate control over structural parameters such as particle
size, shape, and separation, as compared to more traditional
preparation methods, such as physical vapor deposition. It is
a serial technique in which an electron beam is rastered
across the surface of an electron sensitive polymeric film
͑resist͒, creating a computer generated pattern in this film. A
The sample fabricated by EBL consists of ϳ450 nm
high Pd towers with ϳ500 nm diameter. The particles are
arranged in a hexagonal array with 1500 nm particle separa-
tion ͑center to center͒ covering 1 cm2 area ͑Fig. 2͒. The mor-
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084713-3
Reactions on nanolithographically prepared catalyst
J. Chem. Phys. 122, 084713 ͑2005͒
FIG. 2. SEM images of the Pd/silica model catalyst
prepared by EBL ͑a͒ before and ͑b͒ after reaction, note
the faceting and the ring of small Pd particles surround-
ing every big particle ͑see text for discussion͒; ͑c͒ AFM
image and ͑d͒ AFM height measurement of the
particles.
phology of the particles was investigated by SEM ͑scanning
electron microscopy͒ and AFM ͑atomic force microscopy͒
prior and by SEM after the experiments to verify that no
major morphological changes occurred ͑as has been ob-
served, e.g., in Ref. 19 under more drastic reaction condi-
tions͒.
Briefly, the molecular beam of CO was generated by an ef-
fusive beam source ͑EB͒ ͑incidence angle ␾=0°, ␥=35°, see
Fig. 3 for details of the experimental setup͒. Isotopically
marked 13CO ͑min 99% 13CO, Isotec Inc.͒ was used in order
to reduce the background level. It was further purified by a
Waferpure MiniXL WPMV200CO, Mykrolis GmbH filter.
The O2 ͑99.9995%, Linde AG͒ beam was provided by a su-
personic source ͑SSB͒ at large incidence angle ͑␾=60° from
the surface normal, ␥=0°, Fig. 3͒. This experimental setup
ensures that one side of the particles is completely shaded
from a direct O2 flux. The 13CO2 ͑we drop the superscript in
the following͒ signal was recorded simultaneously by a line-
of-sight angular resolved quadrupole mass spectrometer
͑QMS͒ ͑doubly differentially pumped͒, and in an angular
integrated fashion by a non-line-of-sight QMS ͑Fig. 3͒. The
angle ␾ is measured between the surface normal and the
angular resolved QMS with positive ␾ directed toward the
O2 beam and negative ␾ toward the shaded side. Angles
+35° to +90° are not accessible experimentally because in
this range the SSB is shadowed by the angular resolved
QMS.
A close inspection reveals a ring of small Pd islands
surrounding every Pd tower. This effect is likely due to re-
shaping of the polycrystalline particles toward the Wulff
shape in the annealing and cleaning sequences during which
the small aggregates may split off the central particle.19,20,33
Similar effects have been observed previously for Pt model
catalysts prepared by EBL. From SEM images ͓Fig. 2͑b͔͒,
the surface ratio of primary EBL particles to the split-off
particles can be estimated as ϳ5. As a result, the CO oxida-
tion should under all conditions be dominated by the primary
particles. In particular as the CO oxidation shows a weak
structure dependence, so that no enhanced activity of smaller
particles is expected. Furthermore, small split-off particles
may only give rise to an additional symmetric contribution to
the CO2 signal, which should not critically affect the angular
resolved results discussed in the following.
III. MOLECULAR BEAM EXPERIMENTS
A. Experimental procedure
B. Molecular beam apparatus
The experiments were performed in the UHV molecular
beam apparatus at the FHI already described in Ref. 34.
In order to extract the angular distribution of the desorb-
ing CO2, we apply a method which has already been briefly
FIG. 3. Molecular beam apparatus used for the experi-
ments: two molecular beams ͓one generated by an EB
and one generated by a supersonic source ͑SSB͔͒ are
superimposed on the sample surface, the reaction rate is
measured by means of a line-of-sight rotatable mass
spectrometer ͑QMS͒ and a non-line-of-sight mass spec-
trometer ͑QMS͒.
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084713-4
Laurin et al.
J. Chem. Phys. 122, 084713 ͑2005͒
described in the literature34 ͑see Fig. 4͒. After steady state is
established for a given set of reaction conditions, the CO2
signal is measured on the front side of the sample from ␾
=−90° to ␾= +90° by the angular resolved QMS ͓Fig. 4͑a͔͒.
The diffuse background of CO2 is determined on the back-
side of the sample at ␾=−95° and ␾= +95° and linearly
subtracted from the signal. For comparison, the data are then
normalized with respect to few points around ␾=0° ͓Figs.
4͑a͒ and 4͑b͔͒.
The acceptance area of the angular resolved detector
changes as a function of the detection angle.35 We determine
the detector function by using a well defined angular distri-
bution, i.e., the one of Ar scattered from a flat sample cov-
ered by a thick ice ͑H2O͒ layer at a surface temperature of
T=100 K. As Ar trapping is complete under these
conditions,36 detailed balance requires that the angular re-
solved distribution of the desorbing Ar is cosine ͓Fig. 4͑c͔͒.
Consequently, the CO2 signal is normalized to the ratio of
the Ar signal and a cosine distribution. The angular distribu-
tion of the desorbing CO2 flux obtained in this fashion is
plotted in Fig. 4͑d͒.
B. Experimental results and discussion
A summary of the experimental results obtained via the
procedure described in Sec. III A is provided in Fig. 5. Here,
we focus on the most essential observations. For more de-
tailed results and discussions we refer to the previous
publications.24,25
The global reaction kinetics is illustrated in Fig. 5͑a͒.
The steady-state reaction rates were measured in an angular
integrated fashion by the non-line-of-sight QMS as a func-
tion of the fraction of CO in the incident flux xCO
=FCO/͑FCO+FO2͒. Here, FCO and FO2 are the fluxes of CO
and O2 at the sample position. The total flux in this experi-
ment was kept constant and is equivalent to a pressure of
ϳ10−4 Pa.
Up to xCOϷ0.5, the CO2 production rate increases lin-
early with xCO. This regime, denoted in the following as the
O-rich regime, is characterized by a low ⌰CO ͑CO coverage;
⌰
denotes the oxygen coverage͒ on particle surface.37 At
O
higher xCO, the kinetics switches to the so-called CO-rich
regime characterized by a higher ⌰CO and a lower ⌰O. At
lower surface temperatures, the transition to the CO-rich re-
gime is connected to a substantial decrease in the reaction
rate. This effect is due to inhibition of oxygen adsorption by
preadsorbed CO. At higher temperatures, the CO desorption
rate increases and the CO inhibition vanishes ͓Fig. 5͑a͔͒.
In the following, we investigate the angular distribution
of the desorbing CO2 in both regimes, O rich and CO rich.
The experiments were performed at a constant O2 flux of
F
O2=5.6ϫ1014 cm−2 s−1 and CO fluxes of FCO=2.9
ϫ1014 cm−2 s−1 ͑O-rich regime, xCO=0.34͒ and FCO=11.6
ϫ1014 cm−2 s−1 ͑CO-rich regime, xCO=0.67͒. The resulting
total gas fluxes are equivalent to pressures in the range
10−4–10−3 Pa.
FIG. 4. Experimental data analysis: ͑a͒ Signal measured by the angular
resolved QMS from −95° to +95°; ͑b͒ normalized signal after background
subtraction ͑inset on a polar plot͒; ͑c͒ Ar signal backscattered from an ice
covered sample at 100 K and theoretical cosine distribution ͑see text͒; ͑d͒
angular distribution of the CO2 desorption rate after correction for the ex-
perimentally derived detector function ͑inset on a polar plot͒. In the gray
zone, the O2 beam is shaded by the angular resolved QMS.
The angular distributions of CO2 are displayed in Fig.
5͑c͒. Under O-rich conditions, the distribution is symmetric.
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084713-5
Reactions on nanolithographically prepared catalyst
J. Chem. Phys. 122, 084713 ͑2005͒
FIG. 6. Geometric model used in the microkinetic simulations: the Pd par-
ticle is represented by a half prolate spheroid ͑polar radius c=450 nm, equa-
torial radius a=250 nm͒ sitting on a support disk of rϷ25 ␮m diameter.
The CO flux is incident from ␾=0° and the O2 flux from ␾=60°, ␪=0° thus
creating an area around ␪=180° where the particle and the support receive
no direct flux from the O2 beam. The backscattering of the reactants and
products from the support is also included in the model.
FIG. 5. Experimental data on the angular distribution of desorbing CO2: ͑a͒
global production rate as a function of xCO for temperatures T=440, 450,
465, and 490 K; ͑b͒ angular dependence of the CO2 production rate as a
function of xCO ͑see text͒; plain line, O-rich regime; dotted line, CO-rich
regime; ͑c͒ dependence on surface temperature.
In contrast, a strong asymmetry is observed under CO-rich
conditions, with a higher CO2 production rate on the particle
side facing the O2 beam.
Under O-rich conditions, the missing temperature depen-
dence points to the fact that the O diffusion length exceeds
the particle size. The weak temperature dependence under
CO-rich conditions is more difficult to understand and is
partly the result of a compensation effect, discussed in Sec.
IV D.
The critical quantities, which explain these results, are
the diffusion lengths of CO and oxygen on the time scale of
the residence times of the adsorbates on the surface. In the
O-rich regime under steady-state conditions, the large ⌰O
leads to large oxygen residence times and thus to large dif-
fusion lengths ͑before reaction occurs͒. Thus, ⌰O is equili-
brated over the whole particle surface. Under CO-rich con-
ditions, however, ⌰O is significantly smaller. This leads to
drastically reduced residence times and diffusion lengths.
Under these conditions there is no equilibration of ⌰O on the
particle. Consequently, ⌰O and CO2 production are enhanced
on the particle side directly exposed to the O2 beam ͑see Ref.
24 for details͒. In contrast, CO diffusion is much faster and
the diffusion length is expected to exceed the particle size,
both under CO- and O-rich conditions.
The surface temperature dependence of the angular dis-
tributions of CO is shown in Fig. 5͑c͒. ͑Note that a slightly
different experimental geometry was used, for details see
Ref. 24.͒ Only weak temperature dependent effects are ob-
served in the angular distribution, in contrast to the strong
dependence on xCO. The symmetric distribution under O-rich
conditions is nearly independent of temperature. The asym-
metry observed under CO-rich conditions is found to become
slightly less pronounced with increasing surface temperature.
IV. MICROKINETIC SIMULATIONS
A. Description of the model
In order to model the experimental data, we start from a
mean field approach38 and add scattering and surface diffu-
sion processes. The reaction-diffusion model is illustrated in
Fig. 6. The catalyst particle ͑diameter 500 nm, height
450 nm͒ is represented by a half prolate spheroid ͑polar ra-
dius c=450 nm, equatorial radius a=250 nm͒. The support is
described by a disk of radius ϳ25 ␮m. For the numerical
treatment, the system is discretized using spherical coordi-
nates in a ͑r,␪,␾͒ system where r is the radius, 0ഛ␪Ͻ2␲
the azimuth, and 0ഛ␾ഛ␲ the colatitude ͑Fig. 6͒. The par-
ticle is divided into 400 surface elements ͑␪ϫ␾=20ϫ20͒
and the support into 20 000 surface elements ͑rϫ␪=1 000
ϫ20͒.
The microkinetic model used to describe the reaction is
based on the experimental information available on the CO
oxidation on Pt group metals ͑see the Introduction͒. The
simple mean field description was previously developed to
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084713-6
Laurin et al.
J. Chem. Phys. 122, 084713 ͑2005͒
FIG. 7. ͑a͒ Model for the incoming
reactant fluxes: ͑b͒ CO flux at the
surface of the particle ͑direct and
backscattered, see text͒ and ͑c͒ O2
flux ͑direct and backscattered͒. ͑d͒
Model for the outgoing CO2 flux: the
CO2 flux emitted from the particle
over the unit sphere surrounding the
particle ͑dotted line͒; ͑e͒ 2D cut
through the particle containing the xz
plane; values at the top side consti-
tute the direct flux; values at the bot-
tom side are integrated and reemitted
with a cosine distribution toward ␾
=0, constituting the backscattered
flux; the direct and backscattered
fluxes are summed ͑line͒ and yield
the total angular CO2 distribution.
describe the CO oxidation kinetics on a Pd catalyst as a
function of reactant flux and surface temperature.38,39 This
model is capable of quantitatively reproducing both the
steady-state and the transient kinetics. In future work, an
extension of the microkinetic description to kinetic effects
beyond the mean field approximation would be possible on
the basis of Monte Carlo models.25,40,41 In some cases, such
effects have been shown to play an important role ͑see, e.g.,
Ref. 42͒.
port. FCO is incident from ␾=0°, leading to a symmetric flux
distribution. FO2 is incident from ␪=0°, ␾=60°. The latter
results in the shading of parts of the particle on the side
opposite to the beam, i.e., some surface elements do not
receive any direct flux of O2. In addition to the direct flux,
molecules can impinge on the support. As the interaction of
both reactants with SiO2 is weak, CO and O2 might either be
trapped for a short time in a physisorbed state on the support
and subsequently desorb ͑trapping/desorption channel͒ or
might be directly backscattered into the vacuum ͑direct in-
elastic scattering channel͒. We do not distinguish between
these processes and we refer to the sum of both channels as
the backscattering component from the support. Moreover,
there is no explicit incorporation of molecules trapped on the
support and diffusing to the particles ͑see below͒. A fraction
of this backscattered flux collides with the Pd particles and
leads to an additional CO and O2 flux. This is particularly
relevant on the parts of the catalyst particle which receive no
or little direct flux. The backscattering contribution is mod-
eled assuming a cosine distribution from the support for both
CO and O2. This assumption is justified by the fact that the
SiO2 support is rough on the atomic scale and both trapping-
desorption and direct scattering channels are expected to be
rather diffuse. It should be noted that the backscattered fluxes
onto the particle are different for O2 and CO, due to the
shadow of the particle on the support, which has to be taken
into account for O2 ͑see Figs. 6 and 7͒. The role of support
backscattering for the present type of experiments is investi-
gated in detail in Sec. IV E. After establishing the local re-
actant fluxes, the nonspatial part of
For the present model catalyst, some kinetic parameters
were adjusted to quantitatively reproduce the angular inte-
grated kinetics. Briefly, the steps are as follows ͑see Ref. 39
for details͒: ͑i͒ CO adsorbs on the metal with a sticking co-
efficient SCO, modeled by a Langmuir molecular adsorption
term ͑a weak dependence of SCO on ⌰O is taken into ac-
count͒; ͑ii͒ O2 adsorbs dissociatively with a sticking coeffi-
cient SO2, modeled by a Langmuir dissociative adsorption
term; ͑iii͒ the LH reaction step between the adsorbed species
proceeds with a reaction rate kLH with an Arrhenius-type
temperature dependence ͑activation energy ELH, preexponen-
tial factor ALH͒; ͑iv͒ CO can desorb from the metal with a
rate constant kdes ͓Arrhenius-type temperature dependence,
activation energy Edes, preexponential factor Ades; a factor
͑␣CO͒ describing the coverage dependence of Edes is used͔;
͑v͒ O2 desorption can be neglected in the temperature range
considered; and ͑vi͒ CO2 interacts weakly with the metal
surface, resulting in desorption immediately after
formation.26
⌰CO and ⌰O are defined with respect to an atom
density of NPd=1.53ϫ1015 cm−2 as in Ref. 39, correspond-
ing to the surface atom density of Pd͑111͒. A fitting of the
model with respect to the global steady-state rates as a func-
tion of the surface temperature and xCO leads to the follow-
ing parameters: Edes=142 kJ mol−1, Ades=4ϫ1014 s−1, ␣CO
=0.12; ELH=53 kJ mol−1; Ades=5ϫ107 s−1; initial sticking
coefficients SC0 O=0.7 and SO0 2=1–͓7.4ϫ10−4ϫT ͑K͔͒ ͑the
latter includes a dependence on the surface temperature͒;
other parameters as in Ref. 38.
d⌰CO FCO
=
SCO − kdes⌰CO − kLH⌰CO⌰O,
dt
NPd
͑1͒
d⌰O
FO2
NPd
= 2
SO2 − kLH⌰CO⌰O + ١ ͑D ١ ⌰O͒
dt
In a first step, the reactant fluxes ͑FCO,FO2͒ are calcu-
lated at each surface element of the particle and of the sup-
can be integrated for any initial ͑⌰CO,⌰O͒ distribution. In a
second step, the spatial part of Eq. ͑1͒ is integrated using the
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084713-7
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J. Chem. Phys. 122, 084713 ͑2005͒
FIG. 8. Simulated data: ͑a͒ steady-state reaction rate as
a function of xCO ͑T=440, 450, 465, and 490 K, Ediff
=55 kJ mol−1͒; ͑b͒ angular distribution of desorbing
CO2 in the O-rich regime ͑xCO Ͻ0.5͒, the angular dis-
tribution is symmetric, switching to an asymmetric dis-
tribution under CO-rich condition ͑xCOϾ0.6͒ ͑xCO
,
from 0.05 to 0.95 in steps of 0.05; see text͒; ͑c͒ example
of oxygen coverage distribution on the surface of the
particle ͑top view, CO-rich regime; black, low O cov-
erage; white, high O coverage͒; ͑d͒ oxygen concentra-
tion profiles as a function of xCO; ͑b–d͒ T=465 K,
E
diff=55 kJ mol−1
.
finite element method with periodic boundary conditions on
␪ and no flux across ␾=90°, ␪. The physical meaning of
the latter is that we do not take surface diffusion from the
oxide to the particle or vice versa into account. This simpli-
fication is justified by the large particle size and by the weak
interaction of the reactants with the support. Estimates of the
size of adsorbate capture zones on similar systems under
reaction conditions are typically in the range of a few
nanometers.43,44 Thus, we expect that the adsorbate flux via
surface diffusion over the particle/support interface is negli-
gible as compared to the direct flux.
limit of low adsorbate coverages.26 However, more highly
directed distributions are possible at higher coverages.30 In
Sec. IV F we investigate the effect of the local CO2 distribu-
tion on the type of angular resolved experiments discussed in
this work. In general, n=1 is in good agreement with our
experimental results.
In analogy to the reactants, CO2 can be emitted into the
vacuum or collide with the support upon desorption ͑see
Figs. 6 and 7͒. In latter case trapping/desorption is also taken
into account. The product backscattering depends on both the
CO2 distribution and the particle shape. The total CO2 flux
towards the support is calculated by integration over the
lower half unit sphere. Afterwards, the flux is reemitted into
the vacuum assuming a cosine distribution. The direct and
the backscattered product channels are added and constitute
the full CO2 angular distribution.
An Arrhenius temperature dependence of the oxygen dif-
fusion coefficient D is assumed,
Ediff
D = D exp
,
ͩ ͪ
0
RT
with Ediff representing the diffusion activation energy. Little
experimental data are available on the diffusion coefficient
for oxygen on Pd͑111͒. We thus assume a “normal” prefactor
of D0=10−7 m2 s−1.28 The effect of Ediff on the angular dis-
tribution of CO2 is investigated in Sec. IV C. It is found that
a value of Ediff=͑55±10͒ kJ mol−1 is in good agreement with
our experimental results. This value is also consistent with
previous estimates24,25 and with theoretical investigations.45
This value is used for the simulations unless otherwise
stated. For simplicity, we neglect coverage dependences of
the diffusion coefficient D.
B. Influence of the CO/O2 ratio
We validate the kinetic model by simulating the global
steady-state reaction rates as a function of xCO and surface
temperature ͑by integration over the full particle surface͒
͓Fig. 8͑a͔͒. A comparison with the experimental data is plot-
ted in Fig. 5͑a͒. It shows a good agreement under all condi-
tions. Both the temperature dependence and the transition
point between the two regimes are well reproduced.
Next, we investigate the local variation of ⌰O and the
reaction rates. The steady-state oxygen coverage on the sur-
face of the catalyst particle at T=465 K and xCO=0.7 ͑CO
rich conditions͒ is displayed in Fig. 8͑c͒ ͑white: high ⌰O,
black: low ⌰O͒. ⌰O is significantly higher on the side facing
the O2 beam. This indicates that ⌰O is not equilibrated over
the surface under these conditions. ⌰O profiles along the x
axis ͑y=0͒ are displayed in Fig. 8͑b͒ for various xCO values.
Under O-rich conditions ͑xCOϽ0.4͒, the ⌰O profiles are al-
most flat. With decreasing xCO they approach saturation cov-
erage ͑⌰mOax=0.25͒. With increasing xCO, ⌰O decreases and a
gradient in ⌰O appears. Once we approach the transition
As pointed out before, the diffusion barrier for CO on
close packed noble metal surfaces is in general small.28 This
leads to a high CO mobility, even at low surface temperature.
For CO/Pd͑111͒ a value of 175 meV was found by Snabl et
al.29
⌰
is therefore averaged to ⌰CO over the surface of
CO
the particle. After every integration step, we obtain a couple
͑⌰O,⌰CO͒ from which the CO2 production for each surface
element of the particle is calculated as rCO2=kLH⌰CO⌰O.
The angular distribution of the desorbing CO2 from a Pd
area element is modeled by a cosn␾ distribution. n=1 was
found experimentally for CO oxidation on Pd͑111͒ in the
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084713-8
Laurin et al.
J. Chem. Phys. 122, 084713 ͑2005͒
FIG. 9. The role of oxygen surface diffusion investi-
gated at T=465 K; Ediff=35 kJ mol−1 ͑a͒, 45 kJ mol−1
͑b͒, 55 kJ mol−1 ͑c͒, 65 kJ mol−1 ͑d͒, and without oxy-
gen diffusion ͑e͒; the two regimes O-rich ͑xCO =0.34͒
and CO-rich ͑xCO=0.67͒ are compared. Left to right:
Angular distribution of CO2, ⌰O along the x axis of the
particle and top view of ⌰O distribution on the particle
surface ͑white, high ⌰O; black, low ⌰O͒.
between the O-rich and the CO-rich regimes ͑0.4ϽxCO
Ͻ0.6͒, the ⌰O profiles change rapidly and the ⌰O ratio be-
tween the shaded side and the beam side becomes very large.
Within the CO-rich regime ͑xCOϾ0.6͒, the gradient in ln ⌰O
͑d ln ⌰O/dx͒ is nearly constant while ln ⌰O decreases rap-
idly ͓Fig. 8͑c͔͒.
Here, the angular distributions rapidly change towards an
asymmetric shape, with a strongly enhanced CO2 production
on the particle side facing the O2 beam. After switching to
the CO-rich regime, a further increase in xCO only leads to
minor changes in the angular distributions. In terms of the
⌰
profiles discussed above, this is a result of the constant
O
As discussed in our previous work,24 this behavior can
be easily understood qualitatively: On both sides of the tran-
sition point between the CO-rich and the O-rich regimes, the
reaction rates are comparable. Simultaneously, ⌰O changes
by approximately two orders of magnitude between xCO
=0.3 and xCO=0.7. A similar change follows for the oxygen
residence time. As a result, the diffusion length of the ad-
sorbed oxygen decreases dramatically. Consequently, no
complete equilibration occurs and a switching from a sym-
metric to an asymmetric angular distribution is observed.
As ⌰CO is assumed to be constant over the particle, the
differences in ⌰O directly reflect the changes in local reac-
tion rate. In order to compare these results with the experi-
ments, the resulting CO2 angular distributions have to be
calculated ͑taking into account the local angular CO2 distri-
bution and possible support backscattering of the products͒.
The corresponding simulations are displayed in Fig.
8͑d͒. As expected, we obtain broad symmetric CO2 distribu-
tions in the limit of small xCO values ͑O rich͒. With increas-
ing xCO, nearly no changes in the angular distributions are
observed until the transition to the CO-rich regime occurs.
gradient in ln ⌰O with increasing xCO. Comparison of the
simulations to the experiments displayed in Fig. 5͑b͒ shows
that the angular distributions and their behavior as a function
of xCO is well reproduced.
C. Influence of the surface diffusion rate
In our previous work, we have given an estimate of the
diffusion activation energy for oxygen Ediff based on resi-
dence times and diffusion lengths from a simple mean field
model.24 The present reaction-diffusion model allows us to
refine this analysis by a direct comparison to the experimen-
tal angular distributions. We simulate CO2 angular distribu-
tions for diffusion activation energies ranging from
35 kJ mol−1 to the case of “immobile” oxygen ͑see Fig. 9͒
under the conditions applied in the experiments ͑i.e., xCO
=0.34; xCO=0.67; T=465 K͒. Focusing on the ⌰O profiles
first, it is seen that for diffusion activation barriers of
35 kJ mol−1 and below, the oxygen distribution is homoge-
neous, both under CO- and O-rich conditions. This indicates
an equilibration of ⌰O over the particle surface independent
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084713-9
Reactions on nanolithographically prepared catalyst
J. Chem. Phys. 122, 084713 ͑2005͒
of the reaction conditions. As a consequence, the CO2 distri-
butions are symmetric and independent of xCO. For Ediff
=45 kJ mol−1 a weak gradient is found in the ⌰O profile
under CO-rich conditions ͑xCO=0.67͒, leading to a slight
asymmetry in the CO2 distribution. Under O-rich conditions
on the contrary, the distribution remains symmetric. As dis-
cussed in the preceding section, this is a result of the oxygen
residence time being typically one to three orders of magni-
tude larger under O-rich conditions ͑xCO=0.34͒, thus allow-
ing for the equilibration of ⌰O at higher Ediff. At Ediff
=55 kJ mol−1 a larger ⌰O gradient is established, giving rise
to a strongly asymmetric CO2 distribution under CO-rich
conditions. Conversely, the distribution still remains sym-
metric under O-rich conditions. For larger Ediff ͑65 kJ mol−1
and above͒, the ⌰O profiles finally show pronounced gradi-
ents both under CO-rich and O-rich conditions, leading to
asymmetric distributions in both cases. In the case of immo-
bile oxygen ͑no diffusion͒, it is noteworthy that a dip appears
in the ⌰O profiles on the shaded side of the particle. This dip
is the result of a minimum in the local O2 flux impinging on
the particle. The total local flux is the sum of the direct beam
flux and the backscattering of reactants from the support. As
a result of the particle geometry, latter contribution is en-
hanced in the vicinity of the particle support boundaries. This
effect is discussed in detail in Sec. IV E.
FIG. 10. Simulated data: Temperature dependence of ͑a͒ the angular distri-
bution of CO2 and ͑b͒ the
⌰
profiles ͓T=440,465,495 K, Ediff
O
As shown in Sec. III B and Ref. 24, the experimental
CO2 distributions exhibit a fully symmetric distribution for
=55 kJ mol−1, CO-rich ͑xCO =0.67͒, and O-rich ͑xCO =0.34͒ regimes͔.
x
CO=0.34 ͑O-rich͒ and a pronounced asymmetry for xCO
As discussed before, the ⌰O profiles and consequently
the CO2 angular distributions are controlled by the oxygen
diffusion length. The latter depends on two factors:24 ͑i͒ the
oxygen residence time, which depends on the O steady-state
coverage and on the reaction rate, and ͑ii͒ the oxygen diffu-
sion coefficient. Under O-rich conditions, ⌰O is high and the
reaction rate is nearly independent of the surface temperature
͑CO adsorption is the rate determining step, Figs. 5 and 8͒.
Therefore, the oxygen residence time is nearly independent
of the surface temperature. In contrast, the diffusion coeffi-
cient D increases with increasing temperature ͑for Ediff
=55 kJ mol−1, D490 K/D440 K=4.6͒. However, the increase
only has a moderate effect on the ⌰O profiles since the dif-
fusion length is already larger than the particle size. As a
result, the changes in the CO2 angular distributions are weak.
The situation is more complicated in the CO-rich re-
gime. Figures 8͑a͒ and 10͑b͒ show that both the reaction rate
and ⌰O increase with increasing temperature. Oxygen disso-
ciative adsorption is the rate determining step. The oxygen
adsorption rate increases as ⌰CO decreases with increasing
temperature. The changes in reaction rate and ⌰O compen-
sate and lead to a weak temperature dependence of the resi-
dence time. The temperature dependence of the diffusion
length is therefore mainly due to the diffusion coefficient.
With the diffusion length ͑which is below the particle size͒
increasing with increasing temperature, the oxygen gradient
decreases slightly and the asymmetry of the angular distribu-
tion becomes less pronounced. As a last point it should be
noted that in the temperature interval considered the changes
in ⌰O due to the temperature dependence of the diffusion
length are considerably weaker than the changes which occur
=0.67 ͑CO-rich͒. A comparison between the experiments and
the simulations allows us to obtain an estimate of the activa-
tion energy for the oxygen diffusion under reaction condi-
tions of ͑55±10͒ kJ mol−1. The lack of experimental data for
the present system precludes a direct verification of this re-
sult by comparison to other experiments. However, the value
is fully consistent with recent density functional theory cal-
culations by Honkala and Laasonen, who derived an activa-
tion barrier of 54 kJ mol−1 on Pd ͑111͒.45
D. Influence of the surface temperature
In the next step, we investigate the surface temperature
dependence of the angular distributions of CO2, both under
CO-rich and under O-rich conditions. The simulated angular
distributions of CO2 and the ⌰O profiles are displayed in Fig.
10. The model yields a weak dependence in the temperature
range 440ഛTഛ490 K for both O-rich and CO-rich condi-
tions. In the first case ͑xCO=0.34͒ the angular distribution of
CO2 is almost symmetric at 490 K. There is a very slight
decrease in the rate on the shaded particle side with decreas-
ing surface temperature. Under CO-rich conditions ͑xCO
=0.67͒, the CO2 distributions are asymmetric with an en-
hanced reaction rate on the particle side facing the O2 beam.
Under both sets of flux conditions, the asymmetry increases
only weakly with decreasing temperature.
A comparison with the experimental data ͑Fig. 5͒ shows
that the temperature dependence is well reproduced by the
simulations. We can now obtain a deeper insight into the
kinetic origin of the temperature dependence on the basis of
the simulations.
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084713-10
Laurin et al.
J. Chem. Phys. 122, 084713 ͑2005͒
upon switching between the reaction regimes ͑CO rich and O
rich͒. Therefore, the CO2 angular distributions are more sen-
sitive to changes of xCO than of the surface temperature.
E. Influence of backscattering effects
from the support
The desired experimental information in the angular re-
solved experiments is carried primarily by those molecules
which undergo no additional scattering processes with the
surface. In practice, two additional channels have to be taken
into account. First, the incident molecules can be diffusely
backscattered from the support and subsequently collide with
the metal particles. This leads to a diffuse flux of reactants
towards the particles. Second, the reaction products desorb-
ing from the side facets of the particles can collide with the
support and can be backscattered into the vacuum. It is im-
portant to determine how these contributions affect the ex-
perimental results discussed in this work and to what extent
they might complicate the extraction of information on local
reaction rates.
In order to study the relevance of support backscattering
contributions, we analyze these effects in detail in terms of
the present kinetic model. We first investigate the effect of
support backscattering in the incident reactant flux. In Figs.
7͑b͒ and 7͑c͒ the total CO and O2 fluxes toward the particle
surface are plotted for section of the particle along the x axis.
The total flux contains two components, the direct beam con-
tribution and the backscattering contribution. Whereas the
direct flux is maximal at those parts of the particle directly
facing the beams, the backscattering channel is most promi-
nent at the particle edges. It is noteworthy that there are
substantial differences in the backscattered fluxes of CO and
O2. For CO, the backscattered flux approaches a value of
50% of the maximum direct flux at the edge of the particle
and vanishes on top. For O2, a large fraction of the particle is
shaded from a direct flux. The backscattered contribution
from the support is also asymmetric due to the shadow on the
support on the shaded side of the particle. As a result, the
total O2 flux on the shaded side is relatively low in spite of
the support backscattering contribution. It is also noteworthy
that support backscattering creates a zone at xϷ−100 nm
where the flux has a local minimum.
In addition, the backscattering of the products is taken
into account as described in Sec. IV A. Product backscatter-
ing simply adds a symmetric component to the angular dis-
tribution of CO2. Thus, it only qualitatively affects the re-
sults ͓Fig. 7͑e͔͒.
It is now interesting to investigate the effects of both
backscattering contributions on the total angular distribution.
In Fig. 11, a comparison of the ⌰O profiles and CO2 angular
distributions is shown for a hypothetical case, in which sup-
port backscattering is completely neglected and for a case in
which the effect is fully taken into account ͑T=465 K, Ediff
=55 kJ mol−1͒. Focusing on the ⌰O profiles first, the differ-
ences between the models are weak under O-rich conditions.
This is the result of the rapid equilibration of ⌰O. Under
CO-rich conditions however, the ⌰O gradient is significantly
reduced by the support backscattering, because the back-
FIG. 11. Simulated data: ͑a͒ Effect of the backscattering on the angular
distributions of desorbing CO2 and ͑b͒ on the ⌰O profiles under O-rich
͑xCO=0.34͒ and CO-rich ͑xCO =0.67͒ conditions. The backscattering is either
fully “switched on” or “off” for both the incident beams and the desorbing
products.
scattering of oxygen gives rise to a strong relative enhance-
ment of the O2 flux on the shaded side of the particle.
In Fig. 11͑a͒ the corresponding CO2 angular distribu-
tions are displayed. Under both CO- and O-rich conditions,
support backscattering results in a drastic modification of the
angular distributions. Taking the previous discussion into ac-
count, it is apparent that under O-rich conditions the differ-
ences almost exclusively arise from product backscattering.
The latter leads to a reduced width of the CO2 distributions.
For the CO-rich case, on the other hand, the differences re-
sult from both reactant and product backscattering. The ef-
fect is particularly strong on the O-shaded side, where back-
scattering tremendously enhances CO2 production and thus
effectively reduces the asymmetry of the distributions.
We now compare the calculated distributions and the
experimental results from Fig. 5. It is found that the experi-
mental data are well reproduced by the model including sup-
port backscattering. Conversely, the model neglecting the
backscattering channel predicts artificially broad angular dis-
tributions and strongly overestimates the asymmetry of the
angular distributions.
F. Influence of the local angular distribution of CO2
A key point in the simulation of the angular distribution
of CO2 from a supported nanoparticle system is the angular
distribution of CO2 from a local surface element. From
single crystal studies it is well known that such distributions
may sensitively depend on many factors such as the local
surface structure or the adsorbate coverages.46 For the
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084713-11
Reactions on nanolithographically prepared catalyst
J. Chem. Phys. 122, 084713 ͑2005͒
gular dependent effects can be easily detected even in the
case of very diffuse local distributions of desorbing products
͑n=1͒. Indeed, a comparison with the experimental distribu-
tions ͑Fig. 5͒ shows the best agreement for nϷ1. Therefore
we conclude that under the experimental conditions applied
in this work, the local CO2 distribution is well described by
diffuse CO2 desorption. With respect to the applicability of
the method, this result demonstrates that angular dependent
measurements of the type performed in this work should be
feasible for many reaction systems, and do not require par-
ticularly narrow local angular distributions of desorbing
products.
V. CONCLUSIONS
We have studied the angular distribution of desorbing
CO2 during CO oxidation on a supported palladium model
catalyst using a combination of molecular beam methods and
angular resolved mass spectrometry.
͑1͒ The Pd model catalyst was prepared by electron
beam lithography on a SiO2 film on Si͑100͒. Pd particles
with ϳ500 nm diameter and an aspect ratio of nearly 1 were
prepared on a perfect hexagonal lattice with a particle den-
sity of 5.1ϫ107 cm−2. A cleaning procedure was developed
in order to remove contaminations from the particle surface.
͑2͒ Molecular beam experiments were performed using a
combination of CO and O2 beams, establishing different lo-
cal reactant fluxes on different parts of the particles. The two
reaction regimes of the CO oxidation ͑CO rich and O rich͒
are characterized by specific angular CO2 distributions. Un-
der CO rich reaction conditions, the CO2 distribution
strongly depends on the local fluxes, whereas nearly sym-
metric distributions are observed under O-rich conditions.
The angular distributions show a weak temperature depen-
dence in the range between 440 and 490 K.
FIG. 12. Simulated data: Effect of the local angular distribution of CO2
͑modeled by a cosn ␾ distribution͒ on the total angular distribution of prod-
ucts desorbing from the particle ͑N.B.: the backscattered fluxes always fol-
low a cos1 ␾ distribution͒ at T=465 K, Ediff=55 kJ mol−1. Values of n=1
͑a͒, n=4 ͑b͒, and n=16 ͑c͒ are investigated under O-rich ͑full lines, xCO
=0.34͒ and CO-rich ͑dotted lines, xCO =0.67͒ conditions. The figures on the
right show the total angular distributions, assuming local cos ␾, cos4 ␾, and
cos16 ␾ ͑top to bottom͒ CO2 distributions.
present model catalyst, the prolonged heat treatment after
preparation leads to reshaping of the particles, preferentially
exposing low-index facets. Some experimental information
is available for the angular distribution of CO2 desorbing
from such surfaces. On Pd͑111͒, for example, it was found
that in the limit of low coverage the CO2 distribution is
broad and well described by a cosine distribution.26 In the
limit of high ⌰O, however, much stronger peaking along the
surface normal was observed.30
͑3͒ The experimental results were quantitatively repro-
duced by a diffusion-reaction model, taking into account the
geometry of the model catalyst and reactant and product
backscattering effects from the support.
In the following, we investigate the role of the width of
the local angular distribution on the total CO2 distribution
emitted by the supported catalyst. In the simulations, the
local distribution of desorbing CO2 is described by a func-
tion cosn ␾. Some representative results are given in Fig. 12,
ranging from diffuse desorption ͑n=1͒ to highly directed de-
sorption along the particle surface normal ͑n=16͒. It is found
that the total CO2 distribution becomes increasingly broad
with increasing n. In spite of the strong dependence on the
width of the local distribution, the qualitative picture remains
unchanged, however: Under O-rich conditions the CO2 dis-
tributions are symmetric, whereas they become strongly
asymmetric in the CO-rich regime. Although the asymmetry
shows the expected decrease with decreasing n, the effect
remains clearly visible down to n=1.
͑a͒ The different angular distributions of CO2 in the two
reaction regimes were related to pronounced differences in
the oxygen residence time. As a result, equilibration of ⌰O
occurs under O-rich conditions only, and pronounced gradi-
ents in ⌰O are established under CO-rich conditions.
͑b͒ By comparison of the experimental angular distribu-
tions with the simulations as function of the CO/O2 ratio, we
obtain an estimate for the activation energy for oxygen dif-
fusion on the particle surface of ͑55±10͒ kJ mol−1.
͑c͒ The model reproduces the weak temperature depen-
dence of the angular distributions, which can be related to a
partial compensation of the temperature dependences of the
diffusion coefficient, the reaction rate and the steady-state
coverages.
Several conclusions follow from these results. First of
all, it is apparent that a highly directed product desorption
leads to a stronger asymmetry of the total CO2 distribution.
Therefore, a highly peaked local desorption is advantageous
for the type of experiment discussed here. However, the an-
͑d͒ By comparison with the experimental results it was
shown that a quantitative description of the experiment re-
quires trapping-desorption and direct scattering processes
from the support to be taken into account, both for the in-
coming reactants and for the desorbing products. Support
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Laurin et al.
J. Chem. Phys. 122, 084713 ͑2005͒
10H.-J. Freund, M. Bäumer, J. Libuda, T. Risse, G. Rupprechter, and S.
Shaikhutdinov, J. Catal. 216, 223 ͑2003͒.
backscattering is found to significantly broaden the angular
distribution of desorbing products. In spite of this effect,
strong angular dependences remain, which can be easily de-
tected experimentally.
͑e͒ Finally, the effect of the local angular distribution of
CO2 desorbing from a single particle facet on the total angu-
lar CO2 distribution was investigated. The experimental data
are consistent with a broad local distribution ͑cosn ␾ with
nϷ1͒. Other systems, with a more peaked product distribu-
tion, are expected to create even more pronounced angular
dependent effects than observed in the present case.
11H.-J. Freund, Surf. Sci. 500, 271 ͑2002͒.
12H.-J. Freund, H. Kuhlenbeck, J. Libuda, G. Rupprechter, M. Bäumer, and
H. Hamann, Top. Catal. 15, 201 ͑2001͒.
13J. Libuda and H.-J. Freund, J. Phys. Chem. B 106, 4901 ͑2002͒.
14C. R. Henry, Surf. Sci. Rep. 31, 231 ͑1998͒.
15C. C. Chusuei, X. Lai, K. Luo, and D. W. Goodman, Top. Catal. 14, 71
͑2001͒.
16T. Hrncir, V. Matolin, and V. Nehasil, Surf. Sci. 482-485, 260 ͑2001͒.
17K. Judai, S. Abbet, A. S. Worz, U. Heiz, and C. R. Henry, J. Am. Chem.
Soc. 126, 2732 ͑2004͒.
18M. Bowker, P. Stone, R. Bennett, and N. Perkins, Surf. Sci. 497, 155
͑2002͒.
19S. Johansson, L. Österlund, and B. Kasemo, J. Catal. 201, 275 ͑2001͒.
20K. Wong, S. Johansson, and B. Kasemo, Faraday Discuss. 105, 237
͑1996͒.
The results suggest that angular resolved experiments of
the type presented in this work can be quantitatively under-
stood on the basis of a microkinetic diffusion-reaction
model. The information on the distribution of reaction rates
on the particle surface survives in spite of support scattering
effects and diffuse local angular distributions of the desorb-
ing products. As a result, information on kinetic parameters
such as surface diffusion rates as well as on local reaction
rates on supported nanoparticles can be extracted from a
comparison of experiment and simulation.
21J. Grunes, J. F. Zhu, E. A. Anderson, and G. A. Somorjai, J. Phys. Chem.
B 106, 11463 ͑2002͒.
22A. S. Eppler, G. Rupprechter, L. Guczi, and G. A. Somorjai, J. Phys.
Chem. B 101, 9973 ͑1997͒.
23A. S. Eppler, J. Zhu, E. A. Anderson, and G. A. Somorjai, Top. Catal. 13,
33 ͑2000͒.
24V. Johanek, M. Laurin, J. Hoffmann, S. Schauermann, A. W. Grant, B.
Kasemo, J. Libuda, and H.-J. Freund, Surf. Sci. Lett. 561, L218 ͑2004͒.
25J. Hoffmann, S. Schauermann, J. Hartmann, V. P. Zhdanov, B. Kasemo, J.
Libuda, and H.-J. Freund, Chem. Phys. Lett. 354, 403 ͑2002͒.
26T. Engel and G. Ertl, J. Chem. Phys. 69, 1267 ͑1978͒.
27T. Engel and G. Ertl, in The Chemical Physics of Solid Surfaces and
Heterogeneous Catalysis, edited by D. A. King and D. P. Woodruff
͑Elsevier, New York, 1982͒, Vol. 4, p. 73.
ACKNOWLEDGMENTS
28E. G. Seebauer and C. E. Allen, Prog. Surf. Sci. 49, 265 ͑1995͒.
29M. Snabl, O. Borusik, V. Chab, M. Ondrejcek, W. Stenzel, H. Conrad, and
A. M. Bradshaw, Surf. Sci. Lett. 385, L1016 ͑1997͒.
30T. Matsushima and H. Asada, J. Chem. Phys. 85, 1658 ͑1986͒.
31X. Guo, A. Hoffman, and J. T. Yates, Jr., J. Chem. Phys. 90, 5787 ͑1989͒.
32F. P. Leisenberger, G. Koller, M. Sock, S. Surnev, M. G. Ramsey, F. P.
Netzer, B. Klötzer, and K. Hayek, Surf. Sci. 445, 380 ͑2000͒.
33S. Johansson, K. Wong, V. P. Zhdanov, and B. Kasemo, J. Vac. Sci. Tech-
nol. A 17, 297 ͑1999͒.
The authors acknowledge the support of the Deutsche
Forschungsgemeinschaft and of the Competence Center for
Catalysis at Chalmers, supported by the Swedish Energy Ad-
ministration, Chalmers, and its member companies: AB
Volvo, Johnson Matthey CSD, Saab Automobile Powertrain
AB, Persorp AB, MTC AB, Eka Chemicals, and the Swedish
Space Administration. M.L. thanks C. Beta ͑FHI Berlin͒ for
helpful discussions. The authors thank G. Weinberg ͑FHI
Berlin͒ for the SEM images of the lithographically prepared
model catalyst.
34J. Libuda, I. Meusel, J. Hartmann, and H.-J. Freund, Rev. Sci. Instrum. 71,
4395 ͑2000͒.
35G. Comsa and R. David, Surf. Sci. Rep. 5, 145 ͑1985͒.
36P. U. Andersson, M. B. Nagard, K. Bolton, M. Svanberg, and J. B. C.
Pettersson, J. Phys. Chem. A 104, 2681 ͑2000͒.
37J. Libuda, I. Meusel, J. Hoffmann, J. Hartmann, L. Piccolo, C. R. Henry,
and H.-J. Freund, J. Chem. Phys. 114, 4669 ͑2001͒.
38J. Hoffmann, I. Meusel, J. Hartmann, J. Libuda, and H.-J. Freund, J. Catal.
204, 378 ͑2001͒.
1Handbook of Heterogeneous Catalysis, edited by G. Ertl, H. Knoezinger,
and J. Weitkamp ͑VCH, Weinheim, 1997͒.
2J. M. Thomas and W. J. Thomas, Principle and Practice of Heterogeneous
Catalysis ͑VCH, Weinheim, 1997͒.
39J. Hoffmann, S. Schauermann, V. Johánek, J. Hartmann, and J. Libuda, J.
Catal. 213, 176 ͑2003͒.
3V. P. Zhdanov and B. Kasemo, J. Catal. 170, 377 ͑1997͒.
4V. P. Zhdanov and B. Kasemo, Phys. Rev. B 55, 4105 ͑1997͒.
5V. P. Zhadanov and B. Kasemo, Surf. Sci. 405, 27 ͑1998͒.
6V. Johánek, M. Laurin, A. W. Grant, B. Kasemo, C. R. Henry, and J.
Libuda, Science 304, 5677 ͑2004͒.
40V. P. Zhdanov, Surf. Sci. Rep. 45, 233 ͑2002͒.
41V. P. Zhdanov and B. Kasemo, Surf. Sci. Rep. 39, 25 ͑2000͒.
42S. Völkening and J. Wintterlin, J. Chem. Phys. 114, 6382 ͑2001͒.
43V. Nehasil, T. Hrncir, S. Zafeiratos, S. Ladas, and V. Matolin, Surf. Sci.
454, 289 ͑2000͒.
7V. P. Zhdanov and B. Kasemo, Surf. Sci. 496, 251 ͑2002͒.
8K. A. Fichthorn, E. Gulari, and R. M. Ziff, Phys. Rev. Lett. 63, 1527
͑1989͒.
44V. Matolin and I. Stara, Surf. Sci. 398, 117 ͑1998͒.
45K. Honkala and K. Laasonen, J. Chem. Phys. 115, 2297 ͑2001͒.
46T. Matsushima, Surf. Sci. Rep. 52, 1 ͑2003͒.
9Y. Suchorski, J. Beben, E. W. James, J. Evans, and R. Imbihl, Phys. Rev.
Lett. 82, 1907 ͑1999͒.
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