Analysis of the kinetics of N2O-CO reaction on Pd(1 1 0)

Article abstract of DOI:10.1016/j.susc.2005.03.020

Experimental studies indicate that the N₂O-CO reaction occurring on Pd(1 1 0) under UHV conditions exhibits a first-order kinetic phase transition in the steady-state case and also transient kinetics strongly dependent on the initial state of the system. We construct a mean-field kinetic model describing these phenomena. With a minimal number of the fitting parameters, the model reasonably reproduces the special features of the reaction kinetics.

Full text of DOI:10.1016/j.susc.2005.03.020

Surface Science 583 (2005) 36–45
www.elsevier.com/locate/susc
Analysis of the kinetics of N O–CO reaction on Pd(110)
2
a,b,
a
, Yunsheng Ma , Tatsuo Matsushima
a
*
Vladimir P. Zhdanov
a
Catalysis Research Center, Hokkaido University, Sapporo 001-0021, Japan
b
Boreskov Institute of Catalysis, Russian Academy of Sciences, Novosibirsk 630090, Russia
Received 17 December 2004; accepted for publication 14 March 2005
Available online 31 March 2005
Abstract
Experimental studies indicate that the N
2
O–CO reaction occurring on Pd(110) under UHV conditions exhibits a
first-order kinetic phase transition in the steady-state case and also transient kinetics strongly dependent on the initial
state of the system. We construct a mean-field kinetic model describing these phenomena. With a minimal number of
the fitting parameters, the model reasonably reproduces the special features of the reaction kinetics.
ꢀ
2005 Elsevier B.V. All rights reserved.
Keywords: Computer simulations; Reaction kinetics; Kinetic phase transitions; Low index single crystal surfaces; Pd(110); N
; Oxygen
2
O; CO;
N
2
1
. Introduction
to be also rapid. In particular, the steady-state
kinetics of the CO–O reaction is often controlled
2
During or after adsorption of N O on Pt-group
2
by reactant adsorption and/or blocking of adsorp-
tion sites by CO and accordingly exhibits a first-
order kinetic phase transition (see, e.g., the review
by Razon and Schmitz [6] and more recent experi-
mental data for Pt(111) [7], Pt(110) [8], Ir(111) [9],
and supported Pd [10]; for general theory of kinetic
phase transitions, see Refs. [11,12]). In analogy
with CO oxidation, this phenomenon is possible
metals, one can observe N O decomposition
2
accompanied by formation of adsorbed oxygen
and N desorption. The decomposition process is
2
rather rapid. Under temperature-programmed
conditions, it typically occurs below 200 K [1–5].
To run N O decomposition under steady-state con-
2
ditions, one can remove adsorbed oxygen by CO.
CO oxidation on Pt-group metals is well known
in the N O–CO reaction as well. In particular, it
2
was observed by Sadnankar et al. [14] on alu-
mina-supported Pt at atmospheric pressure. Recent
experimental studies performed in our group [15]
*
Corresponding author. Tel.: +7 3832 329513; fax: +7 3832
44687.
E-mail address: zhdanov@catalysis.nsk.su (V.P. Zhdanov).
3
0
indicate that the N O–CO reaction exhibits a
2
039-6028/$ - see front matter ꢀ 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.susc.2005.03.020

V.P. Zhdanov et al. / Surface Science 583 (2005) 36–45
37
first-order kinetic phase transition also on Pd(110)
under UHV conditions in the steady-state case. In
addition, the transient kinetics are found to be
strongly dependent on the initial state of the sys-
tem. In this paper, we present a mean-field kinetic
model of these phenomena. The results obtained
are of interest from the point of view of theory of
the kinetics of rapid catalytic reactions and also
from the view-point of applied environmental
3.5
3.0
520 K
5
00 K
2
2
1
.5
.0
.5
4
70 K
chemistry [13], because N O is one of the harmful
2
450 K
ingredients of motor vehicle gas.
-
7.4 -7.2 -7.0 -6.8 -6.6 -6.4 -6.2 -6.0 -5.8 -5.6
The paper is organized as follows. First, we out-
line the key experimentally observed features of the
reaction kinetics under consideration (Section 2).
Our kinetic model is described in Section 3. The
model parameters are validated in Section 4. The
results of the calculations are shown and discussed
in Section 5. Section 6 contains a brief summary.
Log10( PCO
)
Fig. 1. N
2
-desorption signal (arb. un.) as a function of CO
pressure, PCO (Torr), during N O–CO reaction on Pd(110)
2
ꢀ6
under steady-state conditions for PN2O = 3.3 · 10 Torr and
surface temperatures of 450, 470, 500 and 520 K. The N
2
-
desorption rate was measured at 43ꢁ off normal into the [001]
direction (at this angle, the rate is maximum). DAR means
‘
‘angular resolved’’ (D indicates that the background N
2
signal
has been subtracted).
2
. Experimental data
The kinetics of the N O–CO reaction was stud-
2
reaches a maximum, and afterwards monoto-
nously decreases. At lower temperatures, the N2-
desorption rate exhibits a stepwise behaviour
classified as a first-order kinetic phase transitions.
Such kinetic phase transitions are often associated
with a hysteresis if pressure is changed back and
forth (see e.g. experiments [7,9,10] and theory
[11,12]). The width of a hysteresis may however
be narrow or it can even be reduced to a single line
corresponding to the equistability criterion [12].
The latter seems to happen in the reaction under
consideration, because a hysteresis has not been
observed in this case.
ied on Pd(110) under UHV conditions by using the
technique [1–5] allowing measurement of the angu-
lar-resolved distribution of desorbing species. The
results focused on the temperature dependence of
the reaction rate have already been published in a
brief report [16]. More complete data including
the pressure dependence of the reaction rate will
be presented in detail elsewhere [15]. Here, we show
typical steady-state and transient kinetics which are
essential for our analysis and discussions below.
The specifics of the reaction under consider-
ation is that the yield is small and accordingly we
can hardly get an accurate angular-integrated sig-
nal. Fortunately, the angular-resolved signal is en-
hanced at around the collimation angle (43ꢁ off
normal into the [001] direction) because of the
sharp distribution, and can be used to follow the
reaction. In particular, Fig. 1 exhibits the N2-
desorption rate measured under steady-state con-
Fig. 2 shows the transient kinetics in the situa-
tion when first the reaction is run at steady state
and then, at t = 0, the CO pressure is switched
off. If under steady-state conditions the CO pres-
sure is lower than that corresponding to the
reaction-rate maximum (Fig. 2(a)), the N - and
2
CO -desorption rates drop at t > 0 relatively
2
ditions at fixed N O pressure as a function of
2
slowly and almost instantaneously, respectively.
If initially the CO pressure is higher than that asso-
ciated with the reaction-rate maximum (Fig. 2(b)),
the transient kinetics observed at t > 0 are some-
CO pressure at surface temperatures of 450, 470,
5
00 and 520 K. At T P 500 K, with increasing
s
CO pressure, the rate of N2 desorption first
monotonously increases (in this region, the reac-
tion rate is proportional to CO pressure), then
what more complex. Specifically, the N - and
2
CO -desorption rates first increase and than after
2

38
V.P. Zhdanov et al. / Surface Science 583 (2005) 36–45
5
4
3
2
1
00
00
00
00
00
0
desorption. Under TPD conditions [2], N desorp-
2
(
a)
tion dominates compared to N O desorption. Spe-
2
cifically, the N TPD spectra exhibit four peaks,
2
b –b , located at temperatures between 90 and
1
4
170 K, or more specifically at ’110 (b ), 125
4
N at 43°
2
(
bution of the flux of desorbing N molecules is
b ), 138 (b ), and 150 K (b ). The angular distri-
3 2 1
2
close to cosine for the b peak while in other cases
2
the flux is collimated either at ’43ꢁ (for the b and
1
CO at 0°
2
and b peaks) or at 50ꢁ (for the b peak) off normal
3
4
into the [001] direction. The cosine distribution is
suggestive of desorption of adsorbed N molecules
0
10
20
30
40
50
2
TIME (s)
formed after N O dissociation,
2
(
N
N
2
O)ad ! (N
2
)
ad + Oad
,
ð2Þ
ð3Þ
(
b)
8
6
4
2
00
00
00
00
0
(
2
)
ad ! (N
2 gas
) .
The inclined flux is related to N molecules desorb-
2
ing during N O dissociation,
2
N2 at 43°
(N O) ! (N ) + Oads
.
ð4Þ
In the latter case, the splitting of the N TPD sig-
2
ad
2 gas
2
nal seems to be primarily due to the N O–O lateral
2
CO at 0°
interactions (see e.g. interpretation [17] of similar
TPD spectra observed during N O decomposition
2
2
0
10
20
30
40
50
on Rh(110)).
In principle, the gas-phase N O may react with
adsorbed oxygen [18],
TIME (s)
2
Fig. 2. N
function of time at respectively 43ꢁ and 0ꢁ off normal into the
001] direction (at these angles, the rates are maximum) in the
situation when, after reaching a steady state at T = 470 K,
(a) and 0.5 ·
Torr (b), the CO pressure was switched off (at t = 0).
and CO signals have not been subtracted.
The time scale corresponding to the drop of the CO signal in
2 2
- and CO -desorption signals (arb. un.) measured as a
(
N O) + O ! (N ) + (O )
,
2
gas
ad
2 gas
2 gas
[
s
but on Pd(110) this step does not seem to occur.
In addition to steps (1)–(4), we have reversible
CO adsorption,
ꢀ
6
ꢀ6
P
1
N O = 3.3 · 10 Torr, and PCO = 0.1 · 10
6
2
ꢀ
0
The background N
2
2
2
ðCOÞgas ꢀ ðCOÞad;
ð5Þ
case (a) characterizes the switching-off procedure. Variation of
the other signals is related to the reaction kinetics.
and the Langmuir–Hinshelwood (LH) reaction be-
tween adsorbed CO and oxygen,
reaching a maximum decrease, respectively, rela-
tively slowly and almost instantaneously.
(CO) + O ! (CO )
ad
ad
2 gas
.
ð6Þ
In applied environmental chemistry, the N O–
2
3
. Kinetic model
CO reaction is usually considered to be a subreac-
tion of the NO–CO reaction [13]. Specifically, the
N O formation is believed to occur as
N O–CO reaction running on Pd(110) includes
2
2
reversible adsorption on N O,
2
(
NO) + N ! (N O)ads,
ad
ad
2
ðN OÞ ꢀ ðN OÞ .
ð1Þ
Dissociation of adsorbed N O molecules results
2
gas
2
ad
or
2
(NO)ad + (NO)ad ! (N
2
O)ads + Oads.
in the formation of adsorbed oxygen and N2

V.P. Zhdanov et al. / Surface Science 583 (2005) 36–45
39
For our present discussion, these steps are how-
ever irrelevant.
Thus, the reaction scheme we use includes steps
we discuss these steps in detail. In particular, we
take into account the effect of oxygen-induced sur-
face restructuring on the rate of N O adsorption.
2
(
1)–(6). Basically, this scheme is close to those pro-
The LH step is discussed briefly. The influence of
surface restructuring on the latter step is neglected,
because the step is rapid anyway and its specific
does not matter. In addition, the reaction kinetics
can under certain conditions be complicated by
surface-oxide formation. In our present model,
the latter process is neglected, because at present
its role is open for debate.
posed by Sadnankar et al. [14] and McCabe and
Wong [19] for interpretation of the steady-state
kinetics of the N O–CO reaction on alumina-sup-
ported Pt and Rh, respectively.
To simplify the treatment of the reaction kinet-
2
ics, we take into account that N O dissociation
2
and desorption and N2 desorption are rapid.
Under TPD conditions, as already mentioned,
these steps occur at temperatures between 90 and
4.1. N O adsorption and dissociation
2
170 K. This means that the corresponding activa-
tion energies are in the range from 5 to 12 kcal/
After adsorption, N O molecules may dissoci-
2
mol (for the DFT calculations of the N O binding
2
ate via channels (2) and (4). The activation energy
for channel (2) is slightly lower than that for chan-
nel (4), because at low temperatures under TPD
conditions the intensity of the corresponding N2
energies on Pd(110), see Ref. [20]) and accordingly
under steady-state or transient conditions at rela-
tively high temperatures (e.g., between 450 and
5
N O and N coverages are very low. For these rea-
20 K as in the cases shown in Figs. 1 and 2) the
TPD peak (b , with a cosine angular distribution)
2
is comparable or higher than those of the other N2
peaks [2]. At temperatures about 500 K, the N2
flux is however collimated at ’43ꢁ [16,15] like in
the case of the b and b N TPD peaks. This indi-
2
2
sons, we may always use the steady-state approxi-
mation in order to describe N O dissociation and
2
desorption and N desorption. More specifically,
2
1
3
2
we replace steps (1)–(3) by a N O adsorption step
2
cates that at these temperatures channel (4) is more
important due to the entropic factor or, more spe-
cifically, due to a higher value of the pre-exponen-
tial factor of the corresponding rate constant
(according to the transition state theory, the pre-
exponential factor is proportional to the partition
function of an activated complex, and this func-
tion is expected to be larger for channel (4)). In
accompanied by dissociation resulting in instanta-
neous N desorption (for details, see Section 4.1
2
below). The surface is considered to be covered
only by CO or O. The equations for coverages of
these species are as follows
ad
dh =dt ¼ k PN2O ꢀ kLHhOhCO;
ð7Þ
ð8Þ
O
N O
2
our treatment, N O dissociation is accordingly as-
2
ad
CO
des
CO
dhCO=dt ¼ k PCO ꢀ k hCO ꢀ kLHhOhCO;
sumed to occur via channel (4).
At temperatures about 500 K, the LH step is ra-
where PN O and PCO are the reactant pressures,
2
ad
N2O
k
panied by dissociation resulting in N desorption,
k
is the rate constant of N O adsorption accom-
pid and accordingly during the N
in analogy with the CO–O reaction the Pd surface
O–CO reaction
2
2
2
2
ad
CO
des
CO
and k are the rate constants for CO adsorp-
is primarily covered either by O or CO. Under
steady-state conditions, these two regimes take
place respectively to the left and right from the
reaction-rate maximum (Fig. 2(a)). The distribu-
tions of O and CO on the Pd(110) surface are dif-
tion and desorption, kLH is the rate constant of the
LH step. The coverage dependence of these rate
constants is discussed in the next section.
ferent and accordingly the corresponding coverage
ad
4
. Specification of the reaction steps
dependences of k
well.
are expected to be different as
N2O
The kinetics of rapid catalytic reactions are sen-
sitive to the coverage dependence of the rates of
reactant adsorption and desorption [12]. Below,
In particular, oxygen adsorption typically re-
sults in surface restructuring with the formation
of anisotropic (1 · 2) ‘‘missing-row’’ islands

40
V.P. Zhdanov et al. / Surface Science 583 (2005) 36–45
[
21,22]. The corresponding LEED patterns are of
Eq. (9) predicts that the rate of N O adsorption
2
the c(2 · 4) symmetry. During CO oxidation by
accompanied by dissociation linearly decreases
with increasing oxygen coverage and that the satu-
oxygen and N O, the LEED patterns are also
indicative of the formation of the (1 · 2) or
2
ration of the overlayer takes place at h = 0.5.
O
(
1 · 3) ‘‘missing-row’’ islands (see Refs. [23,15],
Both these predictions are in good agreement with
measurements [25] of the apparent sticking coeffi-
respectively) provided that the CO pressure is suf-
ficiently low (to the left from the reaction-rate
maximum in Fig. 1). This means that oxygen and
Pd diffusion is rapid compared to the LH step
and oxygen is able to migrate and to induce the is-
land formation. To be specific, we assume in our
calculations that the islands are of the (1 · 2) type.
In this case, the local oxygen coverage inside such
islands is 0.5 and accordingly the fraction of the
cient for N O adsorption and dissociation at
2
T ’ 500 K (at much lower temperatures, the oxy-
s
gen diffusion is slow and the saturation oxygen
coverage may be higher than 0.5 ML). At these
temperatures, the dissociation probability pdis is
appreciably lower than unity [25]. This means that
jdis ꢁ jdes and accordingly Eq. (10) can be rewrit-
ten as
surface covered by islands is 2h . (For the (1 · 3)
O
pdis ¼ j =jdes;
dis
ð11Þ
islands, the corresponding fraction, 3h , is some-
O
what higher. This difference is however insignifi-
cant for our presentation below.)
or
N O molecules may adsorb both inside and out-
2
pdis ¼ p expðDE=k TÞ;
ð12Þ
0
B
side the ‘‘missing-row’’ islands. Inside the islands,
N O dissociation seems to be suppressed due to
where p0 and DE are respectively the ratio of
the pre-exponential factors and the difference of
the activation energies for dissociation and des-
orption.
2
spatial constraints. Diffusion of N O molecules
2
from these islands to the (1 · 1) area is expected
to be suppressed as well due to rapid desorption
Adsorbed CO may also induce ‘‘missing-row’’
restructuring of the Pd(110) surface [28]. Under
(
the activation energy for N O desorption is some-
2
what higher than for diffusion, but this can be com-
pensated by a higher pre-exponential factor [24]).
For these reasons, N O decomposition seems to
occur primarily due to adsorption and dissociation
on the (1 · 1) patches. This explains why during the
reactive conditions with surface restructuring the
reactive conditions at T ’ 500 K, it does not seem
s
to occur, because the surface exhibits the (1 · 1)
LEED pattern [15,23]. Practically, this means that
2
dissociation of N O molecules occurs among CO
2
molecules, and accordingly in analogy with NO
dissociation e.g. on Rh(111) [26] the N O dissoci-
2
N angular distribution is collimated at ’43ꢁ like
2
ation rate may rapidly drop with increasing CO
coverage due to N O–CO lateral interactions.
in the TPD case on the (1 · 1) surface.
Thus, in the situation when the surface is pri-
2
For this reason, in the situation when the surface
is primarily covered by CO, the rate constant
marily covered by oxygen, the rate constant of
N O adsorption accompanied by dissociation
2
ad
N2O
k
can be represented as [27]
and N desorption can be represented as
2
ad
N2O
n
ad
ad
N2O
ad
dis N2O
k
¼ ð1 ꢀ hCOÞ p j
;
dis N O
2
ð13Þ
k
¼ ð1 ꢀ 2h Þp j
;
ð9Þ
O
where pdis is the dissociation probability at low
coverages (Eq. (12)), and n P 2 is the exponent
used below as a fitting parameter (the fact that n
may be above 2 means that due to lateral interac-
tions the dissociation becomes more probable
where (1 ꢀ 2h ) is the fraction of the surface
O
ad
N2O
remaining in the (1 · 1) state, j
is the N O
2
impingement rate constant, and p is the dissoci-
ation probability given by
dis
when a N O molecule has more nearest-neighbour
2
p
dis = jdis/(jdis + jdes),
ð10Þ
vacant sites but it does not necessarily mean that
the dissociation is possible only if a molecule has
several vacant sites [27]).
where jdis and jdes are the N O dissociation and
desorption rate constants.
2

V.P. Zhdanov et al. / Surface Science 583 (2005) 36–45
41
ad
Expressions (9) and (13) for kN2O are applicable
when the surface is covered either by O or CO. In
Table 1
Kinetic parameters used in the calculations
calculations, it is convenient to use a single expres-
ad
Parameter
Value
Dimension
Ref.
ad
N2O
sion for k , given by combination of Eqs. (9) and
k
Eq. (14)
AM [25]
AM [25]
Fitting
KT
N2O
ꢀ3
(
13),
p
0
2 · 10
4
–
DE
kcal/mol
–
ad
N2O
n
ad
dis N2O
n
4
k
¼ ð1 ꢀ 2h Þð1 ꢀ h Þ p j
.
ð14Þ
O
CO
ad
N2O
5
5
ꢀ1
ꢀ1
j
3.38 · 10
s
Torr
ad
CO
k
Eq. (15)
AM [28]
KT
4
.2. CO adsorption and desorption
p
0.3
–
ad
CO
ꢀ1
ꢀ1
j
4.09 · 10
s
Torr
CO adsorption on Pt-group metals usually oc-
des
CO
k
Eq. (16)
TST [24]
TPD [28]
TPD [28]
1
6
ꢀ1
curs via precursor states and the effect of oxygen
on the adsorption rate is weak. Neglecting this
effect, we use the following simplest expression
for the rate constant of precursor-mediated CO
adsorption
mdes
10
38
7
s
E
des
kcal/mol
kcal/mol
A
kLH
Eq. (17)
TST [24]
DFT [29]
12
ꢀ1
m
LH
10
22
s
kcal/mol
E
LH
ad
CO
ad
CO
k
¼ ½ð1 ꢀ hCOÞ=ð1 ꢀ hCO þ phCOÞꢂj
ad
CO
;
ð15Þ
All the values (except n) were obtained either from general
theory or on the basis of independent experimental data pre-
sented in the corresponding references.
where j is the CO impingement rate constant,
and p < 1 is the parameter related to the precursor
states. In agreement with experiment [28], Eq. (15)
implies that the CO sticking coefficient is close to
unity at low coverages.
4.4. Kinetic parameters
The CO-desorption rate constant is represented
as
The values of the kinetic parameters used in
Eqs. (12) and (14)–(17) were obtained (Table 1)
by employing the results of independent adsorp-
tion measurements (AM), TPD experiments, ele-
mentary kinetic theory (KT), transition-state
theory (TST), and results of calculations based
on the density-functional theory (DFT). The only
fitting parameter is the exponent n in Eq. (14).
des
CO
k
¼ mdes exp½ꢀðEdes ꢀ AhCOÞ=k
B
Tꢂ;
ð16Þ
where mdes is the pre-exponential factor, Edes is the
activation energy at low coverages, and A > 0 is
the parameter related to repulsive lateral CO–CO
interactions.
4
.3. Reaction between adsorbed CO and O
5. Results of calculations
The rate constant for the LH reaction between
Our model is based on Eqs. (7) and (8) com-
adsorbed CO and O usually depend on adsor-
bate-adsorbate lateral interactions. The effect of
this dependence on the reaction kinetics is however
minor, because anyway the LH step is fast com-
bined with expressions (14)–(17) for the rate con-
stants for the elementary reaction steps. To use
the model, we should specify the exponent n in
the rate constant (14) describing N O adsorption
2
pared to N O and CO adsorption and CO desorp-
2
and dissociation. If the probabilities of adsorption
and dissociation on the surface covered by CO
were proportional to (1 ꢀ hCO), one would have
n = 2. With this exponent, the model predicts a ki-
netic phase transition but its shift to lower CO
pressures with decreasing temperature is much
weaker compared to that observed in the
tion. For this reason, we employ the simplest
expression for the LH-reaction rate constant,
k
LH ¼ mLH expðꢀELH=k
B
TÞ;
ð17Þ
where mLH and ELH are the coverage-independent
Arrhenius parameters.

42
V.P. Zhdanov et al. / Surface Science 583 (2005) 36–45
-
-
-
-
-
-
-
-
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
-
-
-
-
1.0
1.2
1.4
1.6
0
.6
.4
.2
0
0
0
.2
.1
.0
0
0
0
.0
.4
0
0
0
0
0
.3
.2
.1
.0
0
0
.3
.2
0.1
(
a)
(b)
0
.0
-7.2
-7.0
-6.8
-6.6
-6.4
-6.2
-6.0
-5.8
-7.2
-7.0
-6.8
Log10( PCO
-6.6
)
-6.4
-6.2
Log10( PCO
)
Fig. 3. Rate of N
2
2
or CO formation, W (ML/s), and CO and O coverages as a function of CO pressure, PCO (Torr), calculated under
6
s
steady-state conditions for PN O = 3.3 · 10 Torr and T = 520 (a) and 470 K (b). In the latter case, the model predicts a first-order
2
kinetic phase transition or, more specifically, bistablity. The stable and unstable solutions are indicated by the thick and dashed lines,
respectively. The thin solid lines marked by arrows show hysteresis. The thin solid line located between the latter lines corresponds to
the equistability condition (the exact location of this line slightly depends on the details of the interplay between reaction kinetics and
diffusion of adsorbed species [12]).
experiment (Fig. 1). To reproduce the experimen-
tally observed shift, we use n = 4. The fact that
dict in analogy with CO oxidation and in agree-
ment with the experiment that the reaction rate is
proportional to CO pressure, because in this case
it is determined by the rate of CO adsorption on
the surface covered primarily by oxygen (CO
desorption here is nearly negligible). For higher
CO pressures, also in analogy with CO oxidation,
the surface is mainly covered by CO, CO is typi-
cally close to the adsorption–desorption equilib-
rium, and accordingly the reaction rate drops
with increasing CO pressure, because it is deter-
n > 2 physically means that the N O dissociation
2
rate rapidly decreases with increasing CO coverage
due to N O–CO lateral interactions in the acti-
2
vated state for N O dissociation [27].
2
Typical steady-state reaction kinetics calculated
above and below the critical temperature are
shown in Fig. 3(a) and (b), respectively. If CO
pressure is lower than that corresponding to the
reaction-rate maximum, the model is seen to pre-

V.P. Zhdanov et al. / Surface Science 583 (2005) 36–45
43
mined by N O adsorption and dissociation on the
2
-
-
-
1.0
1.5
2.0
CO-covered surface.
Below the critical temperature, the model or
more specifically Eqs. (7) and (8) predict a well-
developed hysteresis as shown in Fig. 3(b). Note
that the corresponding stable and unstable solu-
tions, indicated respectively by the thick and
dashed lines, are stable and unstable with respect
to temporal perturbations. Spatio-temporal pertur-
bations and/or fluctuations may reduce the width
of the hysteresis or, as already mentioned in Sec-
tion 2, may result in the stepwise transition along
the equistability line with no hysteresis. Whether
it happens in reality depends on the details of
nucleation and propagation of kinetic phases or,
in other words, of chemical waves [12].
520 K
5
00 K
4
70 K
-2.5
4
50 K
-3.0
-
7.4 -7.2 -7.0 -6.8 -6.6 -6.4 -6.2 -6.0 -5.8 -5.6
Log10( PCO
)
Fig. 4. Rate of N or CO formation, W (ML/s), and CO and O
2
2
coverages as a function of CO pressure, PCO (Torr), calculated
6
under steady-state conditions for PN O = 3.3 · 10 Torr and
2
s
T = 450, 470, 500, and 520 K. The dashed lines indicating a
The equistability condition corresponds to the
case when the rate of a chemical wave describing
the interplay of two kinetic phase (one is e.g. on
one side of the surface and another one on the
other side) is equal zero. Usually, the equistability
line is located near the middle of the bistability
window. To get the equistability condition, one
should analyze the propagation of a chemical
wave, i.e., to solve the diffusion-reaction equa-
tions. For the conventional models of CO oxida-
tion, this can be easily done (see, e.g., Ref. [12])
and one can obtain explicit expression for the equi-
stability condition. In our case, the propagation of
chemical waves depends not only on reaction steps
and adsorbate diffusion, but also on the details of
adsorbate-induced surface restructuring, and the
corresponding analysis is far from trivial.
first-order kinetic phase transition correspond to the equi-
stability condition.
be located at the middle of the bistability window,
we have constructed Fig. 4, which can be directly
compared with the experimental data shown in
Fig. 1. The agreement between the experiment
and calculations is seen to be good.
The transient reaction kinetics predicted by the
model are in good agreement with the experiment
as well (cf. Figs. 2 and 5). In particular, the model
reasonably reproduces all the special features of
the reaction kinetics measured after switching off
CO pressure.
Finally, it is appropriate to articulate that the
reaction under consideration is rapid and accord-
ingly the reaction rate (or more specifically the rate
From the theoretical point of view, the situation
with the formation of critical nuclei is far from
trivial as well not only for the NO –CO reaction
of N desorption) can be identified with that of
2
N O dissociative adsorption both under steady-
2
2
but also for CO oxidation. For the latter reaction
on Pt(111) [7], Pt(110) [8], Ir(111) [9], and sup-
ported Pd [10], one can observe hysteresis. In our
case, the measured reaction kinetics does not how-
ever show hysteresis. One of the probable reasons
of this finding is that the nucleation of kinetic
phases on Pd(110) might be related to oxygen-in-
duced surface restructuring and accordingly it
might be facilitated due to thermodynamic driving
forces.
state and transient conditions (this identification
is exact in the former case and very accurate in
the latter case). In our simulations, the value of
the rate constant for the latter step was chosen
by using the data reported in Ref. [25]. The mea-
surements performed in our group are in agree-
ment with those presented in Ref. [25]. Thus, we
can conclude that our measurements (Figs. 1 and
2) and calculations (Figs. 4 and 5) are in reason-
able quantitative agreement despite the fact that
that the measured reaction rates are presented in
arbitrary units.
Assuming the kinetic phase transition to occur
at the equistability point and that this point to

44
V.P. Zhdanov et al. / Surface Science 583 (2005) 36–45
0
0
0
.15
.10
.05
0
0
0
0
0
.04
.03
.02
.01
.00
N2
N2
CO2
CO2
0.00
.6
0
0
0
0
0
0
0
.5
.4
.3
.2
.1
.0
O
0.5
O
0
0
0
0
.4
.3
.2
.1
(
a)
(b)
CO
CO
0.0
0
10
20
30
40
50
0
10
20
30
40
50
TIME (s)
TIME (s)
Fig. 5. Rate of N
2
2
or CO formation and CO and O coverages as a function of time calculated for the situation (as in Fig. 2) when,
ꢀ6
ꢀ6
ꢀ6
after reaching a steady state at T
is switched off (at t = 0).
s
= 470 K, PN O = 3.3 · 10 Torr, and PCO = 0.1 · 10 (a) and 0.5 · 10 Torr (b), the CO pressure
2
6
. Conclusion
We have constructed a mean-field kinetic model
of the N O–CO reaction on Pd(110). With a
[2] H. Horino, S.W. Liu, A. Hiratsuka, Y. Ohno, T. Matsu-
shima, Chem. Phys. Lett. 341 (2001) 419.
[
3] H. Horino, I. Rzeznicka, A. Kokalj, I. Kobal, A.
Hiratsuka, Y. Ohno, T. Matsushima, J. Vac. Sci. Technol.
A 20 (2002) 1592.
2
minimum number of the fitting parameters, it rea-
sonably describes the first-order kinetic phase
transition, observed in this reaction under stea-
dy-state conditions, and also the transient kinetics.
In addition, we have discussed why the steady-
state kinetics do not exhibit hysteresis. The latter
aspect of the problem remains however open for
further theoretical analysis.
[4] K. Imamura, H. Horino, I. Rzenicka, I. Kobal, A. Kokalj,
Y. Ohno, B.E. Nieuwenhuys, A. Hiratsuka, T. Matsu-
shima, Surf. Sci. 566 (2004) 1076.
[
[
5] T. Matsushima, Surf. Sci. Rep. 52 (2003) 1.
6] L.F. Razon, R.A. Schmitz, Catal. Rev. Sci. Eng. 28 (1986)
8
9.
[7] M. Berdau, G.G. Yelenin, A. Karpowicz, M. Ehsasi, K.
Christmann, J.H. Block, J. Chem. Phys. 110 (1999) 11551.
[
8] B.L.M. Hendriksen, J.W.M. Frenken, Phys. Rev. Lett. 89
2002) 046101.
9] S. Wehner, F. Baumann, J. Kuppers, Chem. Phys. Lett.
70 (2003) 126.
(
[
3
Acknowledgement
[
10] V. Johanek, M. Laurin, A.W. Grant, B. Kasemo, C.R.
Henry, J. Libuda, Science 304 (2004) 1639.
[11] J.W. Evans, Langmuir 7 (1991) 2514.
One of the authors (V.P. Zh.) is grateful for the
Guest Professorship at the Catalysis Research
Center, Hokkaido University.
[
[
[
12] V.P. Zhdanov, B. Kasemo, Surf. Sci. Rep. 20 (1994) 111.
13] V.P. Zhdanov, B. Kasemo, Surf. Sci. Rep. 29 (1997) 31.
14] R.R. Sadnankar, J. Ye, D.T. Lynch, J. Catal. 146 (1994)
5
15] Y. Ma, T. Matsushima, Langmuir, submitted.
11.
[
[
References
16] Y. Ma, I. Kobal, T. Matsushima, J. Phys. Chem. 109
(
2005) 689.
[17] V.P. Zhdanov, T. Matsushima, Surf. Sci., in press,
doi:10.1016/j.susc.2005.03.043.
[
1] Y. Ohno, K. Kimura, M. Bi, T. Matsushima, J. Chem.
Phys. 110 (1999) 8221.

V.P. Zhdanov et al. / Surface Science 583 (2005) 36–45
45
[
18] R. Burch, S.T. Daniells, J.P. Breen, P. Hu, J. Catal. 224
2004) 252.
19] R.W. McCabe, C. Wong, J. Catal. 121 (1990) 422.
[24] V.P. Zhdanov, Elementary Physicochemical Processes on
Solid Surfaces, Plenum, New York, 1991.
(
[
[
[25] S. Haq, A. Hodgson, Surf. Sci. 463 (2000) 1.
[26] H.J. Borg, J.F.C.-J.M. Reijerse, R.A. van Santen, J.W.
Niemantsverdriet, J. Chem. Phys. 101 (1994) 10052.
[27] V.P. Zhdanov, B. Kasemo, J. Chem. Phys. 104 (1996)
2446.
20] A. Kokalj, I. Kobal, T. Matsushima, J. Phys. Chem. B 107
(2003) 2741.
[
[
[
21] H. Tanaka, J. Yoshinobu, M. Kawai, Surf. Sci. 327 (1995)
L505.
22] R.A. Bennett, S. Poulston, I.Z. Jones, M. Bowker, Surf.
Sci. 401 (1998) 72.
23] I. Rezeznicka, T. Matsushima, Chem. Phys. Lett. 377
[28] K. Yagi-Watanabe, H. Fukutani, J. Chem. Phys. 112
(2000) 7652.
[29] Z.P. Liu, P. Hu, Topics Catal. 28 (2004) 71.
(2003) 279.