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 2011
ÆÝÒÔ, 2011, òîì 140, âûï. 4 (10), ñòð. 18
CHARGE SEPARATION IN CO OXIDATION INVOLVING
SUPPORTED GOLD CLUSTERS
a
R. S. Berry , B. M. Smirnov
a Department
b*
of Chemistry, University of Chiago
60637 IL, Chiago, USA
b Joint
Institute for High Temperatures, Russian Aademy of Sienes
125412, Mosow, Russia
Reeived Marh 29, 2011
The harater of the atalyti oxidation of
CO by supported gold luster atalysts is analyzed with emphasis on
CO moleule
the unique harateristis of this proess. The sheme of this proess used here has the reagent
aptured in the interfae between the luster and support, with oxygen moleules or atoms loated on the support surfae to reat with the
CO.
(Other models have also been presented.) The experimental data indiate
that, together with ongurational transitions that lead to the
the
CO2
moleule, the harge separation due to apture of the
important. The proess of release of the
CO2
CO moleule joining
CO moleule by the
an oxygen atom to form
supported gold luster is
moleule results in harge exhange; the time for this proess is
relatively long beause of the large distane separating positive and negative harges, a distane exeeding the
luster radius. This provides a high eieny of the oxidation of
CO
with this atalyst despite the relatively
high ativation energy for the ongurational transition.
sure is the binding energy of luster atoms. Moreover,
1. INTRODUCTION
the melting points of gold lusters are anomalously low.
The gold luster is a partiularly interesting physi-
These properties of gold lusters make them espe-
al objet. Due to ompetition of interation between
5d and 6s shells of valene eletrons and relativisti
ially good atalysts.
eets, this luster admits an unusual variety of stru-
moleules so attahed may reat with a lower ativa-
tures [1℄. Clusters of small sizes exhibit linear, zigzag,
3D strutures; the transition between the
planar and 3D groundstate strutures of the negatively harged luster Aun ours for n = 12; 13; 14, as
tion energy than the unatalyzed substrate, whih of
planar, and
ourse leads to aeleration of the hemial proess. In
addition, reation of the attahed moleules may involve fewer intermediate stages than the unatalyzed
shown by both experimental studies [2, 3℄ and alula-
+
proess.
tions [4, 5℄. For positively harged gold lusters Aun ,
this transition ours at
n
= 7 (see [4, 5℄). Larger lus-
These general atalyti properties are har-
ateristi of almost any atalyst; the atalyti proess
involves transitions between dierent binding states of
ters, in addition to the iosahedral struture, an have
the atalyst with reating moleules.
tetrahedral, agelike, and tubular strutures [3, 6, 7℄.
Hene, several
lowest ongurational states of the ombined system of
Next, in ontrast to other metal lusters with the iosa-
the atalyst and reagent moleules must have energies
hedral struture, the gold luster onsisting of 55 atoms
similar enough, and barriers low enough, for eetive
does not have suh a struture [8℄. The same rih behavior appears in the melting of gold lusters.
To funtion, the atalyst must
form bonds with substrate reagent moleules, and the
transitions to our between these states in the ourse
The
of the hemial proess. Beause lowest ongurational
energy gap separating the solid and liquid aggregate
states of gold lusters are similar in energy, these forms
states is signiantly smaller for 13-atom gold lusters
an be expeted to play important roles in the bound
than for suh lusters of other metals [913℄, if we ex-
states of gold lusters with reagent moleules.
press these parameters in redued units where the mea-
A spei gold-based atalyti system that has at* E-mail: bmsmirnovgmail.om
trated attention onsists of lusters from 10 to 20 gold
1
R. S. Berry, B. M. Smirnov
ÆÝÒÔ,
òîì
140, âûï. 4 (10), 2011
atoms attahed to the surfae of a metal oxide semi-
guration.
ondutor.
The number of suitable metal oxides for
disussions of dieletri lusters beause of the large
this purpose is restrited and inludes Fe O , MgO,
energy gap that separates the ground and rst exited
2
2 3
2
TiO , and CeO ; other ompounds as supports show
The seond hannel is irrelevant for most
state of suh systems. In ontrast, for metal systems
only weak atalyti eets. These supports may be in
and metal lusters, the seond type of transition is often
the form of miron-size partiles, marosopi solids, or
favorable. Nevertheless, in spite of this basi dierene
lms. It is interesting that bulk gold is an ineetive
between dieletri and metal systems, our experiene
atalyst, and it was perhaps surprising that only gold
in the analysis of dieletri lusters is useful for metal
lusters (and some gold lusters with a foreign metal
lusters beause dieletri lusters are simpler [2426℄.
atom) indue oxidation of CO in atmospheri air at
An important property of the PESs for dieletri lus-
room temperature and moderate temperatures.
This
ters is the large number of loal energy minima; these
eet was disovered in 1987 by Japanese sientists [14
are separated by energy barriers [2730℄. This is impor-
16℄, who extrated gold lusters or partiles from solu-
tant for the phase transitions in lusters [25, 26℄. Eah
tions of their ompounds on surfaes.
loal minimum of a PES orresponds to a loally stable
This atalyti
eet is strong for gold partiles 1 nm in diameter (the
luster state beause the ongurational and osillatory
WignerSeitz radius of gold is 0.17 nm); for a gold par-
degrees of freedom are separable [31℄.
tile 5 nm in diameter or larger, the atalyti eet
From the standpoint of the properties of the PES,
disappears. Moreover, the optimal size of gold lusters
the dierene between a metal luster and a dieletri
for CO oxidation is believed to be 10 atoms [1720℄;
one lies in the larger number of isomers for metal lus-
the 8-atom luster is also quite eetive [21℄.
ters, eah isomer orresponding to a spei loally sta-
As we indiated, the atalyti eetiveness of sup-
ble atomi onguration. Correspondingly, the liquid
ported gold lusters is sensitive to the type of the sup-
state of a metal luster diers from that of a typial
port and to the luster size; it is also sensitive to other
dieletri luster by its muh larger number of loally
onditions, for example, to the degree of overing of the
stable ongurations. This number of ourse inreases
support by oxygen moleules [22, 23℄. This testies to
with inreasing luster exitation [32℄. Suessive ou-
the seletive harater of the hemial proess. Conse-
pation of many luster ongurations leads, in eet, to
quently, we annot expet to nd universal interpreta-
their mixing as a result of eetive transitions between
tions of the nature of this proess, and our analysis of
them. Hene, as we onsider the hemial reation of
the harater of the oxidation proess of CO in air is
a bound system onsisting of a metal luster and re-
therefore guided largely by experimental results.
atant moleules and interpret it as a ongurational
transition on a single PES or between PESs of dierent eletroni states, we nd the atalyti proess to be
a sort of an analog of the phase transition in a metal
2. USING THE POTENTIAL ENERGY
luster.
SURFACE FOR ANALYSIS OF
Indeed, in both ases the transition inludes
several or many ongurational states that may orre-
CONFIGURATIONAL TRANSITIONS
spond to dierent PESs.
We now turn to the potential energy surfae (PES)
One more important property in the phase tran-
of the ombined system, whih is a onvenient tool for
sitions of small lusters is the dynami oexistene of
the interpretation and analysis of ongurational tran-
phases near the melting point [3338℄. This means, in
sitions. For this, we onstrut the potential energy of
the simplest ases, that part of the time the luster is
a system of bound atoms at eah xed position of the
found in the solid state that orresponds to the global
nulei, in aord with the BornOppenheimer approxi-
minimum of the PES, and rest of the time, it is loated
mation, and vary the onguration of the nulei. In this
3N 6-dimen-
in the liquid aggregate state
atoms with the
leads to many transitions between dierent PESs or be-
oordinates of the enter of mass and the orientation
tween dierent loal minima of the same luster PES.
eliminated. The internal energy is the dependent vari-
Beause the gold lusters under onsideration here on-
way, we obtain PES of this system in a
sional spae of atomi oordinates for
N
1)
.
This property marks
the fat that near the melting point, luster evolution
able. Then a ongurational transition an our either
1) The real situation may be more omplex. For example, there
as evolution of this atom system from one loal mini-
may be a temperature regime in whih the luster moves among a
mum to another on one PES or to a transition from one
small number of solid-like isomers. Alternatively, there may even
PES to another, orresponding to a different eletroni
be more than two phases oexisting in dynami, thermodynami
state, with an assoiated hange of the atomi on-
equilibrium.
2
ÆÝÒÔ,
òîì
140, âûï. 4 (10), 2011
Charge separation in CO oxidation : : :
tain only a few atoms, this property is important for
is that the CO moleules being oxidized are aptured
atalyti proesses involving these lusters.
either in the boundary between a luster and the support on top of a suiently small gold luster [21℄.
Meanwhile, oxygen moleules are fastened to the sup-
3. CO OXIDATION WITH SUPPORTED GOLD
port surfae or oxygen atoms are taken for CO oxida-
CLUSTERS AS A CATALYST
tion from the support [17, 44, 45℄. (Clusters as small
4
as Au
We now onsider oxidation of the CO moleule in
2
reation with the oxygen moleule O
that proeeds
on top of the luster [46℄.) We
the subsequent analysis.
aording to the sheme
2CO + O2 ! 2CO2 :
2
may bind O
use these peuliarities of gold lusters as atalysts in
(3.1)
4. PECULIARITIES IN THE STUDY OF
Beause the energy to break the COO bond is 5.45 eV
CATALYSIS BY CLUSTERS
and the binding energy of the OO bond is 5.12 eV,
In the simplest version of a model of the atalyti
even the hemial reation
CO
+ O2 ! CO2 + O
proess, the rate is determined by the Arrhenius for(3.2)
mula [47℄
is energetially favorable and orresponds to an energy
kh
release of 0.33 eV if moleules before and after the pro-
= A exp
ess are in their ground vibrational states. Therefore,
from the standpoint of the PES, a low rate for the to-
where the temperature
tal proess in (3.1) at low temperatures may be the
and
Ea
T
Ea
T
;
(4.1)
is expressed in energy units
is the ativation energy of this proess. In this
result of energeti or entropi barriers on the PES in
ase, we an assume that the atalyst dereases the a-
the ourse of this hemial proess in the gaseous phase.
tivation energy
Catalysts may redue or even remove these barriers.
does not suitably desribe proess (3.1) under onsider-
Ea
of the proess. We see that this ase
ation here. Indeed, in this ase, the rate of the atalyti
Aording to the general priniple of heterogeneous
atalysis [3942℄, a atalyti hemial proess involving
proess as a funtion of temperature has the so-alled
two moleules proeeds on a surfae with whih the
volano form [39, 41, 42, 48℄, i. e., it has a maximum
moleules are bonded and whih in our ase is a luster
at a denite temperature that reets the ompetition
If bound moleules are in rapid equilibrium
between the attahment proess of moleules to the at-
with free gaseous moleules, the proess proeeds in a
alyst surfae and the hemial proess. Indeed, at low
manner similar to that in the gaseous phase. But the
temperatures, the rate of the atalyti proess is low
parameters of individual stages of the hemial pro-
beause of the low rate of the hemial proess, but
ess are dierent, depending on whether it proeeds
the overall rate beomes low again at high tempera-
with free or bound moleules. The objet of our anal-
tures beause the probability of moleular attahment
ysis is proess (3.1) with supported gold lusters as a
to the atalyst surfae is small. Hene, the rate of the
atalyst.
atalyti proess has a maximum at midrange temper-
surfae.
As shown in [14
16; 43℄, gold lusters sup-
ported by ertain semiondutors, metal oxides, pro-
atures. The simple Arrhenius version is not adequate
vide a high rate of this proess. Moreover, a subsequent
to desribe proess (3.1) with supported gold lusters
study of proess (3.1) with supported gold lusters as
as a atalyst, as indiated by the experimental rate of
atalysts demonstrated that the number of metal ox-
this proess given in Fig. 1.
Considerable progress in understanding atalyti
ides eetive as a support is restrited and inludes
2 3
2
2
only Fe O , MgO, TiO , and CeO . Furthermore, gold
hemial proesses with supported lusters as atalysts
lusters funtion eetively as atalysts only if their
has been ahieved by omputer simulations based on
size does not exeed 1 nm, approximately six times
the density funtional theory (DFT). However, it may
the WignerSeitz radius for gold.
be dangerous to overestimate the power of omputer
If the diameter of
the gold partile exeeds 5 nm, the atalyti eet for
simulations for this problem.
supported gold partiles disappears entirely.
simulation is meant to desribe omplex atomi sys-
For this
Beause this omputer
reason, less than 1 % of the deposited gold ontributes
tems, its auray is restrited.
to the atalyti oxidation proess if gold partiles and
the auray indiated in alulations [49℄ is 1 % for
lusters are prepared by traditional hemial methods
the bond lengths, the auray of the barrier heights
[20℄. One more onlusion from experimental researh
is estimated as only 2530 %. Although these auray
3
In partiular, while
R. S. Berry, B. M. Smirnov
P;
100
ÆÝÒÔ,
%
òîì
140, âûï. 4 (10), 2011
of atoms). The omputer simulation of this luster by
moleular dynamis with fous on separation of its aggregate states in the ourse of luster evolution [33, 34℄
80
allows desribing luster dynamis. These simulations
demonstrate that the ontribution to the entropy of
60
the phase transition due to thermal motion of atoms is
3040 % near the melting point [26, 56℄.
This means
40
that the transition from the stati desription to the
20
mal motion (osillations and large-amplitude displae-
dynami one in this ase orresponds to taking therments) of atoms in the luster into aount. This leads
0
80
60
40
20
0
20
40Æ
T;
to a derease of the alulated melting point for this
luster by 3040 %. This analysis shows that omputer
C
simulation of omplex atomi systems based only on
evaluation of the PES parameters with the assumption
Fig. 1.
P
of motionless atoms, i. e., stati alulations, are unre-
The temperature dependene of the fration
of the
CO
moleules
that are oxidized to
moleules in an air ow with an admixture
atalyst
Au/TiO2
CO2
alisti, may be misleading, and must be ombined with
CO and the
experimental results to determine the extent of their
[17, 45℄
validity.
Therefore, in the analysis of proess (3.1), we are
guided primarily by experimental measurements, al-
estimates seem optimisti, the auray of these param-
though omputer simulation by the DFT method gives
eters of the PES may be gauged by omparing dierent
us some understanding of the harater of this proess.
alulations. But there is one more reason why we an
There are many measurements of the rate of the hem-
onsider evaluation of parameters of the stati PES as
ial proess, summarized in [45℄. These measurements
only indiative model alulations.
The fat is that
are based on a reator with a atalyst through whih
thermal motion and rearrangements of atoms in this
a ow of air goes, with an admixture of CO (usually
omplex atomi system may hange the parameters of
about 1%).
the barriers to transition, beause the alulations de-
transformed in CO
sribe only the stati system, whereas we have to deal
dierent experiments are made under dierent ondi-
here with a dynami one.
tions; these may be redued to orrespond to identi-
The fration of CO moleules that are
2
is measured. Measurements from
Therefore, the prinipal unique quality of the at-
al onditions for dierent air pressures, CO onentra-
alyti proess by lusters lies in its dynamis, rather
tions, and the time of residene inside the reator, but
than simply in the strutures formed in intermediate
the results annot be ompared if the atalyst proper-
stages of the proess. This has been alled dynamial
ties are varied [45℄. Nevertheless, if we restrit ourselves
utionality [5, 50℄), a property that haraterizes the
to ertain onditions as is done in Fig. 1, we an ob-
adaptability of a omplex atomi system to nd an op-
tain a qualitative understanding of the harater of this
timal onguration or suession of ongurations for
proess if we invoke also some results of DFT omputer
eetive transitions at eah intermediate stage. Sine a
alulations.
metal luster may hange the onguration of its atoms
far more readily than an a marosopi metal surfae,
lusters may be better atalysts in priniple [51℄. This
5. CHARACTER OF CO OXIDATION WITH
possibility is espeially important for metal lusters
SUPPORTED GOLD CLUSTERS
that have a large number of ongurational states with
low exitation energies [5255℄. One treatment of gold
We now base our disussion on the rate of pro-
nanolusters did take rearrangements into aount [46℄;
ess (3.1) aording to Fig. 1 and infer the parameters
2 moleules to
of the main stages of this proess when supported gold
this work addresses the attahment of O
the supported lusters, but does not onsider binding or
lusters are used as the atalyst.
oxidation of CO. We an estimate the transition from
Fig. 1 an be obtained from the volano urve by ut-
a statistial desription of the system to the dynami
ting o the upper part of the urve, as it is shown in
The dependene in
one for the phase transition in the 13-atom Lennard
Fig. 2. This means that the time of residene of CO
Jones luster (i. e., with the LennardJones interation
moleules inside the reator exeeds the time required
4
ÆÝÒÔ,
òîì
140, âûï. 4 (10), 2011
Charge separation in CO oxidation : : :
hange or the barrier energy height for a given ongu-
P
rational transition, and
v
is a typial veloity of atoms
in this transition. If the Massey riterion is small for
all the ongurational transitions of this proess, an
eetive equilibrium is established in this system, and
the populations of the initial and nal states are determined by the statistis. Correspondingly, in this ase,
an equilibrium between ongurational and vibrational
1
states, for both free and bound reagent moleules, is
subjeted to the thermodynami laws, rather than the
dynamis of evolution of this system.
In this ase, we have the ompetition of two over-
0
all proesses; in the rst, the state of CO bound with
T
the atalyst results in release of the unreated CO
2
moleule. The other hannel is the formation of CO .
The temperature dependene of the fration
Fig. 2.
The probability of CO
of transformed moleules as follows from the volano
form for the rate of a atalyti proess
P
where
1
1
and
2
2
formation is given by
= 1 +1 2 ;
(5.2)
are typial times orresponded to evo-
lution of the system in a given hannel. Assuming the
transition in a given ongurational state to be deter-
0
2
mined by the barrier energies
"1
and
"2 ,
we have the
typial times of realization of a given hannel
1
A sheme of proess (3.1) as transitions be-
Fig. 3.
= a exp
tween ongurational states of a omplex system on-
"1 T
2
;
= b exp
"2 T
:
sisting of a atalyst and reatant moleules. The ross
From this, we nd the temperature dependene of the
setion is taken for eah transition along a line that
probability
joins loal minima of the PES for this transition. The
the yield for the nal produt of the hemial proess
CO
moleule from the initial free state
in state
1
0
is aptured
P1
of a given hannel of the proess. Hene,
may depend strongly on the temperature.
in whih DFT alulations [21℄ indiate that
This sheme of the atalyti proess as a result of
it beomes positively harged, and hene the reversible
sequential transitions between ongurational states of
transition with release of the
Co
moleule requires a
tunnelling eletron transition to neutralize the
Subsequent ongurational transitions in diretion
lead to formation of the
CO2
this system allows understanding some features of this
CO.
proess. In partiular, on a suiently long time sale,
2
this proess is reversible, and the rates of the diret
moleule
and inverse proesses are onneted by the priniple
of detailed balane. But the dynamis of this proess
for the hemial proess under the given onditions; un-
are important for shorter time sales, and the rate of
der these onditions, the probability of attahment of
a atalyti proess is determined mostly by the slow-
the CO moleule to the atalyst surfae is one.
est stage, whose rate is expressed through the barrier
height separating the orresponding loal minima of the
We analyze the harater of the proess under onsideration.
PES.
In the framework of the PES onept,
Then the probability
the transition is a sum of transitions between dierent
PESs, as shown in Fig. 3. We note that the transition
between neighboring PESs is eient if the Massey pa-
P
rameter [57℄ for this transition is small:
Here,
a
= a~vE 1:
of realization of hannel 1
(5.1)
1
= 1 + A exp(
;
E =T )
a
where the temperature
T
E is the energy
Ea
5
= "1
(5.3)
is expressed in energy units,
the ativation energy is
is a typial distane that haraterizes a reog-
nizable hange of the system energy,
P
is given by
"2
= 0:50 eV;
R. S. Berry, B. M. Smirnov
and
A
ÆÝÒÔ,
= ab = 6:4 10
;
1:4
1:2
1:0
0:8
0:6
0:4
0:2
0
0:2
0:4
0:6
0:8
11
under standard onditions of the experiment given in
Fig. 1.
Based on these data, we an ompose the following
piture of the proess (3.1), represented in Fig. 3. The
ongurational transitions inlude both variation of the
PES as a result of hanges of the atomi onguration
and a hange of the harge distribution in this system.
We assume, as alulations have indiated, that apture of the CO moleule by the supported gold luster
proeeds through formation of the CO
+
ion, in whih
the valene eletron eventually transfers to an oxygen
atom loated at some distane from this ion.
Then
òîì
140, âûï. 4 (10), 2011
nm2
1111
0000
0000
1111
0000
1111
0000
1111
+
0000
1111
0000
1111
00000 5 000
1111
10
15
111
000
111
nm
000
111
000
111
000 111
111
000
000
111
a
:
Fig. 4.
b
:
:
r;
The shemati harge density distribution after
CO
the reversible proess of release of the CO moleule
the apture of the
onsists in a tunnelling eletron transition that reneu-
provides the probability
tralizes the CO, while formation of the moleule CO
nelling eletron transition for separated harges of the
results in transport of O
of their joining.
2
+ up to the point
to the barrier height
That may inlude many subsequent
Ea
for the tun-
eV, and version b relates
"=2
eV
of all these transitions.
sults and some results of alulations.
where
In partiular,
and
"
the support surfae, and this opens additional possibilities for a hemial proess, adding harge exhange
me
1; 5860℄, whih supports our on-
is the eletron mass. Taking typial values for
distribution and also assume that the positive harge
positively harged [
is distributed uniformly over the luster surfae.
lusion. But we must also note that atomi gold has a
We
see that a typial distane between the positive and
very large eletron anity, omparable to that of halo-
10 luster
negative harges exeeds the radius of the Au
gen atoms, and hene we might presume that small
for both examples.
Nevertheless, a
We onsider this proess from another standpoint.
onlusion that the bilayer luster struture leads to
If the harges of CO
its optimal eieny as a atalyst [17, 20, 44℄ annot
+
and O
are separated in aor-
2
dane with Fig. 4 and formation of CO
be inferred from this onsideration.
from them
proeeds in the optimal way, we nd the optimal rate
We now base our disussion on the sheme given in
onstant for a typial time of this proess for bound
Fig. 3, with parameters of the experiment in Fig. 1. In
partiles at room temperature as
this ase, there is ompetition between the proesses
If
we assume that the harge exhange proess is without
11
is the length of this barrier,
these onditions if we assume axial symmetry of this
port surfae of the type under onsideration may be
= 6:4 10
l
Figure 4 gives the surfae harge distribution under
proesses to it. Indeed, a small gold luster on a sup-
of harge exhange and the ativation transition.
is the barrier height that orresponds to the
= 2 eV and " = 4 eV, we obtain the respetive distanes l = 1:6 nm and l = 1:1 nm between harges.
than a free gold luster beause it beomes harged on
gold lusters would behave similarly.
"
eletron binding energy,
a supported gold luster may be better as a atalyst
A
"=4
to the ase
Our analysis is based on the ited experimental re-
barrier, we obtain
A = 6:4 10 11
positive and negative harges. Version a orresponds
toward CO
transitions between neighboring PESs with the total
ativation energy
moleule in proess (3.1) that
for the probability
= v exp
l
Ea
T
2 10
5 s;
tane between an eletron and ion that provides this
106 m/s is a typial veloity of a bound oxygen ion on the surfae, l 1 nm is a typial distane
probability. Assuming the potential energy to be on-
between harges,
where
of the tunnelling transition. We alulate a typial dis-
stant, we obtain the probability
eletron transition as [61℄
A
= exp( 2S );
S
=
A
~
e
Ea
in this ase we have
for the tunnelling
p2m " l
v
= 0:5 eV is the barrier height, and
exp(Ea =T ) 19. A typial life-
time of the bound CO moleule on the surfae has the
same order of magnitude. We note that this is a rough
;
estimate and gives only a sale of times.
(5.4)
Here these
times are short ompared with a typial residene time
6
ÆÝÒÔ,
òîì
140, âûï. 4 (10), 2011
Charge separation in CO oxidation : : :
of free moleules inside the reator for these measure-
of this atalyti proess, and presumably of others in-
ments, but in reality the lifetime of a bound moleule
volving metal lusters.
may exeed the residene time for free moleules.
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