Simulation of CO electrooxidation on nm-sized supported Pt particles: Stripping voltammetry

Article abstract of DOI:10.1016/S0009-2614(03)00980-1

The kinetics of CO electooxidation on nm-sized supported Pt crystallites exhibiting (111) and (100) facets were studied. The reaction kinetics for nm-size particles could be considerably different compared to these expected on the basis of simple superposition of the kinetics corresponding to the infinite faces. CO diffusion between facets of a nm-sized Pt particle might dramatically influence voltammograms observed by using CO stripping voltammetry. This effect might be important under steady-state reaction conditions as well. CO molecules might for example adsorb primarily on the (100) facets.

Full text of DOI:10.1016/S0009-2614(03)00980-1

Chemical Physics Letters 376 (2003) 220–225
www.elsevier.com/locate/cplett
Simulation of CO electrooxidation on nm-sized supported
Pt particles: stripping voltammetry
Vladimir P. Zhdanov a,b,*, Bengt Kasemo a
a
Department of Applied Physics, Chalmers University of Technology, G o€ teborg S-41296, Sweden
Boreskov Institute of Catalysis, Russian Academy of Sciences, Novosibirsk 630090, Russia
b
Received 7 February 2003; in final form 4 June 2003
Published online: 1 July 2003
Abstract
We analyze the kinetics of CO electrooxidation on nm-sized supported Pt crystallites exhibiting (1 1 1) and (1 0 0)
facets. Specifically, we show how the CO-diffusion-mediated communication between these facets may modify vol-
tammograms observed by using CO stripping voltammetry. The results obtained demonstrate that the reaction kinetics
for nm-sized particles can be remarkably different compared to those expected on the basis of simple superposition of
the kinetics corresponding to the infinite faces. These findings have implications for interpretation of experimental data
and for the design of real catalysts and also have important consequences for the efforts to bridge the so-called structure
gaps in electrocatalysis.
Ó 2003 Published by Elsevier B.V.
Electrochemistry is an old science [1]. The un-
derstanding of catalytic electrochemical reactions,
occurring under the influence of the strong electric
field near the electrode(s), is however, still limited,
because the common surface-science techniques
are often difficult to apply on the electrolyte–metal
interface, and have not by far provided the same
wealth of knowledge as gas–solid interfacial stud-
ies. Basic academic investigations of electrolyte–
metal interfaces are primarily focused on reactions
running on single-crystal electrodes [2]. In appli-
cations (e.g., in fuel cells [3]), however, electro-
chemical reactions often occur on very small (ꢀ10
nm) metal particles (e.g., Pt or Pt/Ru), deposited
on the walls of pores of a more or less inactive
conducting support (e.g., carbon). The specific
catalytic activity (i.e., the activity of an adsorption
site) of such particles may be quite different com-
pared to that of macroscopic samples. In analogy
with the conventional heterogeneous catalysis (on
the gas–metal interface), this structure gap can be
associated with several factors such as unique
electronic properties of nm-sized metal particles,
contribution of special sites (e.g., edges) to the
reaction rate, metal-support interaction [4] and/or
with purely kinetic effects, such as the interplay of
the reaction kinetics running on different commu-
nicating facets [5] (see also recent simulations
*
Corresponding author. Fax: +46-31-772-3134.
E-mail address: zhdanov@catalysis.nsk.su (V.P. Zhdanov).
0
009-2614/03/$ - see front matter Ó 2003 Published by Elsevier B.V.
doi:10.1016/S0009-2614(03)00980-1

V.P. Zhdanov, B. Kasemo / Chemical Physics Letters 376 (2003) 220–225
221
[
6,7]). In the case of electrochemical reactions, the
difference in the reaction kinetics on single-crystal
surfaces and supported particles may in addition
be connected with differences in the electric field
strength near a nm catalyst particle and on a flat
surface [8].
Experimentally, the structure-gap problem in
electrochemistry can be tackled by employing
model planar supported catalysts [9,10]. In paral-
lel, this problem can be treated theoretically. At
present, the corresponding theoretical studies are
in fact lacking. To demonstrate what may happen
in this case, we analyze in this Letter the kinetics of
CO electrooxidation on nm-sized supported Pt
particles. Specifically, we show how the interplay
of reactions on different facets may modify vol-
tammograms obtained by using CO stripping
voltammetry. This subject is of interest from the
points of view of general theory and methodology
of experimental studies of electrochemical reac-
tions, because the stripping voltammetry is widely
used in electrochemistry. In addition, the results
obtained may also be useful for the design of
strategies of improving practically important sup-
ported catalysts (note that poisoning by CO is one
Fig. 1. CO stripping voltammetry kinetics for a nm-sized Pt
particle, containing (1 1 1) and (1 0 0) facets, in the case when
there is no CO diffusion between the facets. The upper panel
shows CO coverages of the (1 0 0) and (1 1 1) facets as a function
of the electrode potential. The two peaks on the lower panel
exhibit, respectively, the contributions of these facets to the
total reaction rate (the partial and total reaction rates are di-
vided by v, because in the calculations the integration over time
was replaced by integration over potential). The insert into the
lower panel demonstrates the particle shape (with a top (1 0 0)
facet, side (1 1 1) facets and with the largest (1 0 0) facet attached
to the support).
of the problems in applications of H
2 2
–O and
CH OH–O fuel cells [3]; for recent simulations of
3
2
CO oxidation in fuel cells, see [11]).
At equilibrium, the shape of nm catalyst parti-
cles is determined by the Wulff rule, minimizing
the total surface free energy. Practically, this
means that catalyst particles of fcc metals contain
primarily the (1 1 1) facets and partly the (1 0 0)
facets (see, e.g., the insert in Fig. 1). In reality,
catalyst particles often do not reach equilibrium
and accordingly the relative area of the (1 0 0)
facets may be larger than that corresponding to
equilibrium. In our treatment, CO oxidation is
assumed to occur primarily on the (1 1 1) and
Under electrochemical conditions, oxidation of
CO molecules adsorbed on single-crystal Pt sur-
faces is usually assumed (see, e.g., simulations
[
(
15,16]) to run via the Langmuir–Hinshelwood
LH) mechanism with participation of adsorbed
hydroxyl
þ
À
COads þ OHads ! CO
2
þ H þ e þ 2 Ã
ð1Þ
where à denotes a free surface site. Adsorbed hy-
droxyl is formed via water dissociation
þ
À
H
2
O þ Ã ꢀ OHads þ H þ e
ð2Þ
(
1 0 0) facets of a Pt crystallite. CO formation on
2
edges is neglected [12]. Specifically, CO is first
adsorbed almost up to saturation and then the
Adopting this mechanism for CO oxidation on a
Pt crystallite, we should take into account that the
values of the rate constants of the corresponding
elementary steps may be different on different
facets. In addition, adsorbate diffusion on and
between the facets should be included into the
model. Details of the realization of these pre-
scriptions depend on the technique used for
2
CO formation is observed during linear increase
of the electrode potential, u ¼ vt, where v is the
scan rate. The corresponding experimental data
for CO oxidation on single-crystal and supported
Pt catalysts can be found, e.g., in [2,13,14],
respectively.

222
V.P. Zhdanov, B. Kasemo / Chemical Physics Letters 376 (2003) 220–225
calculations. For nm-sized catalyst particles, the
Monte Carlo (MC) technique is the most relevant
Application of the MF equations implies that
adsorbate diffusion is rapid. In the case of con-
ventional CO oxidation on Pt (at the interface
between the gas phase and metal), CO diffusion is
known [19] to be very fast (the activation barrier
for this process is about 0.3 eV). Under electro-
chemical conditions, CO diffusion is expected to
be slower due to CO interaction with the solution.
Accurate data for the latter regime of CO diffu-
sion are still lacking. There are only estimates [20]
indicating that at room temperature the CO dif-
[
5]. If, however, the reaction behaviour is not too
complex, as in the case under consideration, the
mean-field (MF) approximation is somewhat more
instructive, because it allows straightforward il-
lustration of the main points.
To introduce the MF kinetic equations for re-
action on a Pt crystallite, it makes sense first to
recall the corresponding equations for single-
crystal surfaces. In the latter case, the LH step (1)
is described as
À13
2
fusion coefficient is about or above 5 Â 10
cm
À1
s . This means that during the typical time in-
terval, ’10 s, corresponding to CO stripping, the
CO diffusion length is about or longer than 20
nm. This value is comparable to or slightly larger
than typical facet sizes. Under such circum-
stances, we may use the MF approximation for
describing CO oxidation on the facets of a nm-
sized Pt particle. The time characterizing CO
diffusion between the facets may, however, be
comparable to or longer than the reaction time
scale (especially if the potential barriers for CO
jumps over the facet edges are higher than those
on the facets). Thus, the MF equations for reac-
tion on the facets should be complemented by
terms, taking into account interfacet CO diffusion
(to be specific, we analyze reaction on a pyrami-
dal Pt particle with the top (1 0 0) facet (Fig. 1)),
i.e., we have:
dhCO=dt / ÀhCO
h
OH
;
ð3Þ
where hCO and hOH are the reactant coverages.
(
Here and below the coverages are defined as the
ratio of the absolute coverage to the absolute
saturation coverage. For CO adsorption on
Pt(1 1 1) and Pt(1 0 0), the absolute saturation
coverage is in the range between 0.6 and 0.8 [2,17].
The relative coverage used in calculations can,
however, be close to unity.)
In the reaction under consideration, the OH
coverage is usually low, hOH ꢁ 1, steps (2) are rapid
and accordingly close to adsorption–desorption
equilibrium. This means that the OH coverage is
proportional to the fraction of vacant sites, i.e.,
h
OH / 1 À hCO (the fraction of vacant sites is con-
sidered to be equal to 1 À hCO, because hOH ꢁ 1).
Substituting this expression into Eq. (3) (cf. [18])
and incorporating in addition the effect of the elec-
trode potential on the reaction rate (in analogy with
the Butler–Volmer law [1]), we obtain
dh
dh
1
2
=dt ¼ k
=dt ¼ k
1
expðae
expðae
0
0
u=k
u=k
B
B
TÞh
TÞh
1
2
ð1 À h
ð1 À h
1
2
Þ À J12
Þ À J21
;
;
ð5Þ
ð6Þ
2
dhCO=dt ¼ ÀkLH expðae
0
u=k
B
T ÞhCOð1 À hCOÞ; ð4Þ
where h
1
, h
2
, k
1
2
and k are the CO coverages and
where kLH is the potential-independent factor, a the
reaction rate constants on the (1 1 1) and (1 0 0)
facets, and J12 and J21 are the net rate (per site) of
CO jumps between the (1 1 1) and (1 0 0) facets.
Using these equations, we assume that the depen-
dence of the reaction rate on the electrode poten-
tial is the same for both types of the facets (in
principle, this dependence might be slightly dif-
ferent on different facets, but in our present
treatment this effect is neglected). The activation
barriers for reaction on the (1 1 1) and (1 0 0) facets
are, however, considered to be different. Specifi-
cally, the reaction is assumed to be somewhat
faster on the (1 0 0) facet (see below).
effective transfer coefficient, e the absolute value of
0
the electron charge, and k the Boltzmann constant.
B
The term ÔeffectiveÕ means that a takes into account
the true transfer coefficient for step (1) and also the
fact that at quasi-equilibrium the OH coverage ex-
ponentially depends on u. The exact value of a is not
known. To be specific, we use a ¼ 0:5. (In reality, a
may be higher than 0.5 or, in principle, even higher
than one. The increase in a may change the position
and width of the voltammetry peaks. The shift of the
peaks may, however, be compensated by the cor-
responding change in kLH.)

V.P. Zhdanov, B. Kasemo / Chemical Physics Letters 376 (2003) 220–225
223
The total net rate of CO jumps between the
1 1 1) and (1 0 0) facets is equal to the difference of
(1 0 0) facet and the reaction is faster on this facet.
The former is in line with the conventional surface-
science data [22], and the latter is in agreement
with the results of CO potentiodynamic measure-
ments on the (1 1 1) and (1 0 0) faces [2]. On the
(1 1 1) face at T ¼ 300 K, the maximum reaction
rate during CO stripping voltammetry is usually
observed at u ’ 0:7 eV [23]. To reproduce this
(
the jump rates in the two directions. In the MF
approximation, the rate of jumps from a given
facet to another facet is proportional to CO cov-
erage of the former facet, the fraction of vacant
sites on the latter facet, and the number of sites,
N , on the boundary between the facets. Thus, the
b
À4
À1
total net jump rate is given by
result, we employ k
1
=v ¼ 10 eV (to measure
potential, we use eV; the dimensionality of v is
accordingly eV/s). With this choice, the only free
kinetic parameter we have is k12=v. The latter pa-
rameter was changed over a wide range in order to
illustrate the effect of CO-diffusion-mediated
communication between the facets on the stripping
kinetics. The calculations were performed for
T ¼ 300 K. The fraction of sites belonging to the
J ¼ N
b
½j12
h
1
ð1 À h
2
Þ À j21
h
2
ð1 À h
1
ފ;
ð7Þ
where j12 and j21 are the corresponding jump rate
constants [21]. The net CO fluxes per site are de-
fined by J12 ¼ J=N and J ¼ ÀJ=N , where N
1
21
2
1
and N are the numbers of sites on the corre-
2
sponding facets. These numbers can be represented
as N
1
ꢂ pN
t
and N
2
ꢂ qN
t
t
, where N is the total
number of sites on the catalyst particle, and p and
q ꢂ 1 À p are the fractions of the sites belonging to
the (1 1 1) and (1 0 0) facets, respectively. Thus, we
get:
(
1 1 1) facets was taken to be 0.8 (i.e., p ¼ 0:8 and
q ¼ 0:2). The initial conditions (at t ¼ 0) were
u ¼ 0, ¼ 0:99 ML and ¼ 0:99 ML
h
1
h
2
(
ML ꢂ monolayer). The reaction kinetics obtained
with this specification are presented in Figs. 1–5
exhibiting the (1 1 1) and (1 0 0) facet coverages,
J12 ¼ ½k h ð1 À h Þ À k h ð1 À h ފ=p;
ð8Þ
ð9Þ
12
1
2
21
2
1
the average reaction rate per site, hW i ¼ pW þ
1
J
21 ¼ À½k12
h
1
ð1 À h
2
Þ À k21
h
2
ð1 À h ފ=q;
1
qW
2
, where W
1
¼ k
1
expðae
0
u=k
B
TÞh
1
ð1Àh
1
Þ, W ¼
2
where k12 ꢂ j12
N
b
=N
t
and k21 ꢂ j21
N
b
=N
t
. (Note
that k12 ¼ k21 expðDEad=k T Þ, where DEad is the
B
difference of the adsorption energies on the (1 0 0)
and (1 1 1) faces. In addition, we have k exp
¼ k
ðDE =k T Þ, where DE is the difference of the ac-
tivation energies of reaction on the (1 1 1) and
2
1
r
B
r
(
1 0 0) faces.)
To integrate the equations above, we replace
the derivatives dh
i
=dt by vdh =du and then divide
i
both sides of the equations by v. This procedure is
convenient because it explicitly shows that in order
to obtain the results there is no need in separate
values of the potential-independent rate factors
and v (one rather needs the ratios of these factors
and v).
At present, the exact values of the parameters
DEad and DE
conventional CO adsorption and oxidation on Pt
22], the scale of these parameters is expected to be
a few kcal/mol. In our calculations, we use
r
are not known. In analogy with
Fig. 2. Voltammetry kinetics in the case of slow CO diffusion
À1
[
(
with k12=v ¼ 1 eV ) between the (1 1 1) and (1 0 0) facets. The
upper panel shows CO coverages of the (1 0 0) and (1 1 1) facets.
The lower panel exhibits the contributions of these facets (the
dashed and thin solid lines, respectively) to the total reaction
rate (the thick solid line).
DEad ¼ DE ¼ 0:1 eV as probable values. The fact
r
that both parameters are positive means that the
CO binding energy is somewhat higher on the

224
V.P. Zhdanov, B. Kasemo / Chemical Physics Letters 376 (2003) 220–225
3
Fig. 5. As in Fig. 2 for very rapid CO diffusion (k12=v ¼ 10
Fig. 3. As in Fig. 2 for the case of comparable rates of CO-
interfacet diffusion (k12=v ¼ 10 eVÀ1) and reaction.
À1
eV ).
rated. The integral contribution of the (1 1 1) facets
to the reaction rate is higher than that of the (1 0 0)
facet, because the area of the (1 1 1) facets is larger.
(In reality, the splitting of the peaks corresponding
to the (1 1 1) and (1 0 0) facets may be weaker [17].
We treat the case of an appreciable splitting in order
to exemplify the main point of the Letter.)
For relatively slow interfacet diffusion with
À1
k =v ¼ 1 eV , the reaction peaks are overlapping
12
but only slightly (Fig. 2). This means that the role
of interfacet diffusion is minor. The integral con-
tribution of the (1 1 1) facets to the reaction rate is
also in this case higher than that of the (1 0 0) facet.
If during CO stripping the rates of interfacet
diffusion and reaction are comparable, the vol-
tammetry spectrum contains (see Fig. 3 for
2
À1
Fig. 4. As in Fig. 2 for rapid CO diffusion (k12=v ¼ 10 eV ).
À1
k =v ¼ 10 eV ) two peaks with considerable
12
overlap. The shape of this spectrum is quite dif-
ferent compared to those shown earlier (Figs. 1
and 2). In particular, the first and second peaks are
observed at somewhat higher and lower potentials,
respectively. In addition, the integral intensity of
the first peak is now larger than that of the second
peak. All these features are directly related to CO
interfacet diffusion. In particular, the shift of the
first peak to higher potential is explained by the
fact that just before the stripping the CO coverage
of the (1 0 0) facet is higher than that (0.99 ML) in
k
2
expðae
0
u=k
B
T Þh
2
ð1 À h
2
Þ, and also the corre-
and qW , of the facets
sponding contributions, pW
to this rate.
If there is no communication between the facets
1
2
(
i.e., k12 ¼ 0), the reaction kinetics is given by simple
superposition of the kinetics corresponding to the
infinitefaces. Specifically, themodelpredicts(Fig. 1)
stripping of the (1 0 0) and (1 1 1) facets at u ’ 0:5
and 0.7 eV, respectively. In this case, the reaction
peaks representing different facets are well sepa-

V.P. Zhdanov, B. Kasemo / Chemical Physics Letters 376 (2003) 220–225
225
the case of non-communicating facets, because CO
diffusion from the (1 1 1) facets to this facet is en-
ergetically favourable. Due to a smaller number of
vacant sites on the (1 0 0) facet, the onset of reac-
tion on this facet is accordingly shifted to higher
potential. The integral intensity of the first peak is
larger because the CO molecules located initially
on the (1 1 1) facets may diffuse to the (1 0 0) facet
and react there. This reaction channel is preferable
compared to reaction on the (1 1 1) facets, because
the (1 0 0) facet is catalytically more active.
on the nm scale. This makes it a demanding ex-
perimental task to unambiguously identify one re-
sponsible factor, or the relative contributions of
several cooperatively acting factors. Under such
circumstances, of course, we cannot exclude that
our model will be refined when more experimental
data are available.
Acknowledgements
This work was supported by the Swedish En-
ergy Agency (Grant No. P12554-1) and MISTRA
(Grant No. 95014).
If CO diffusion is fast, the stripping of both
facets occurs nearly simultaneously as shown in
2
À1
Fig. 4 for k12=v ¼ 10 eV . In this case, CO oxi-
dation runs almost exclusively on the (1 0 0) facet
and the voltammetry spectrum contains a single
narrow peak. Scrutinizing the upper panel in
Fig. 4, one can notice that, despite fast diffusion,
the coverage of the (1 0 0) facet during reaction is
somewhat lower than that of the (1 1 1) facets.
According to thermodynamics, one could expect
the opposite. This means that equilibrium between
the facets is still lacking. With further increase of
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