The kinetics of low-temperature oxidation of cobalt nanoparticles in porous media

Article abstract of DOI:10.1134/S0036024411020257

The kinetics of oxidation of Co nanoparticles used in heterogeneous catalysis in silica gels and alumina with various porous structures was studied at room temperature. A mathematical model describing processes in the system was suggested. The experimental observations were qualitatively explained.

Full text of DOI:10.1134/S0036024411020257

ISSN 0036ꢀ0244, Russian Journal of Physical Chemistry A, 2011, Vol. 85, No. 2, pp. 217–224. © Pleiades Publishing, Ltd., 2011.
Original Russian Text © A.V. Mugtasimov, N.V. Peskov, G.V. Pankina, P.A. Chernavskii, V.V. Lunin, 2011, published in Zhurnal Fizicheskoi Khimii, 2011, Vol. 85, No. 2, pp. 266–274.
CHEMICAL KINETICS
AND CATALYSIS
The Kinetics of LowꢀTemperature Oxidation of Cobalt Nanoparticles
in Porous Media
A. V. Mugtasimova, N. V. Peskovb, G. V. Pankinaa, P. A. Chernavskiia, and V. V. Lunina
a Faculty of Chemistry, Moscow State University, Moscow, Russia
b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia
eꢀmail: chern@kge.msu.ru
Received February 25, 2010
Abstract—The kinetics of oxidation of Co nanoparticles used in heterogeneous catalysis in silica gels and aluꢀ
mina with various porous structures was studied at room temperature. A mathematical model describing proꢀ
cesses in the system was suggested. The experimental observations were qualitatively explained.
Keywords: kinetics, lowꢀtemperature oxidation, cobalt nanoparticles, porous media.
DOI: 10.1134/S0036024411020257
INTRODUCTION
diffusion coefficients in a binary system and, with
metal oxidation, manifests itself as the difference of
the diffusion coefficients of oxygen and metal ions.
Because of the difference of the diffusion coefficients
Studies of the kinetics and mechanism of lowꢀtemꢀ
perature oxidation of metal nanoparticles acquire
practical importance in view of rapidly developing
nanotechnologies. Lowꢀtemperature oxidation (temꢀ
perature range from ~280 to ~400 K) is substantially
different from highꢀtemperature processes, which are
well described by the Wagner theory [1], in which a key
role is played by diffusion.
of metal and oxygen ions (for Co, Doxygen < Dmetal), the
accumulation and subsequent condensation of vacanꢀ
cies occurs at the metal–oxide boundary, which results
in the formation of cavities [5, 6, 7]. Characteristically,
the condensation of vacancies causes the formation of
“bridges” at the initial oxidation stage. These bridges
connect the oxide shell with the metallic nucleus, and
the diffusion of metal ions and electron tunneling
occur through them [8].
The theory of lowꢀtemperature oxidation or oxidaꢀ
tion in thin films was for the first time formulated by
Caberra and Mott (C–M theory) [2]. It involves the
appearance of an electric potential (Mott potential)
between oxide–adsorbed oxygen and oxide–metal
boundaries at the initial time moment. The correꢀ
sponding electric field can pull out metal atoms and
move them toward the outside oxide surface, where an
oxide film grows. The theory qualitatively correctly
describes the formation of planar thin oxide films, but
ignores potential gradients in films and assumes that
the diffusion coefficients of metal ions, oxygen ions,
electrons, and vacancies are constant. The picture is
considerably complicated in spherical particles comꢀ
pared with planar films, where the presence of size
effects is obvious. In part, these effects are caused by
the dependence of the Mott potential on the radius of
particles. Considering this circumstance, it can be
shown [3] that the rate of oxidation increases as the
radius of particles decreases.
The formation of cavities at the metal–oxide
boundary should likely cause a more substantial
decrease in the rate of oxidation than is predicted by
the C–M theory, because, as vacancies are accumuꢀ
lated and condensed, the real metal–oxide separation
surface through which metal ions diffuse decreases.
Earlier, in works concerned with the formation of
spherical cavities in the oxidation of metal nanopartiꢀ
cles, most attention was given to systems in which
nanoparticles were dispersed in a liquid inert medium
[5] or were obtained by ionic sputtering in a high vacꢀ
uum and subsequently deposited on a carbon substrate
[6]. Studies were performed by highꢀresolution transꢀ
mission electron microscopy. As concerns the kinetics
of oxidation of metal nanoparticles, the corresponding
information is exceedingly scarce.
The experimental data obtained comparatively
The kinetics and mechanism of oxidation of metal
recently make us take a different view of the oxidation nanoparticles in pores of an inert carrier, as, for
of nanoparticles of certain metals and introduce addiꢀ instance, in heterogeneous metal deposited catalysts,
tional limitations into the C–M theory. For spherical are often of interest for applications. In such systems,
particles, the Kirkendall effect [4] is of special imporꢀ in addition to the oxidation of nanoparticles, oxygen
tance. This effect is a consequence of the difference of mass transfer in carrier pores can occur. In this work,
217

218
MUGTASIMOV et al.
Properties of Co/porous carrier samples
200 kV accelerating voltage. A sample in the form of a
suspension in ethanol was deposited on a carbon film
situated on a copper micronet. Electron microscopic
images for the determination of Co particleꢀsize disꢀ
tribution functions were processed using a program
specially designed for this purpose.
Ssp
,
s
,
xCo
%
,
d
,
nm
D ,
nm
2
Sample
σ
m2/g
m2/g
Co/SiO2
380
6
5%Со/Qꢀ6
20%Co/Qꢀ6
5%Co/Qꢀ10
6
6
5
8
6.7
9.7
4.9
4.9
3.7
7.2
4.1
9.1
14.5 10
5.2 6.9
15
7.5
A Method for Studying the Kinetics of Oxidation
320 10
180 15
100 30
3
Immediately before measurements, samples were
reduced in a flow of hydrogen. The reactor was a meaꢀ
suring cell of a vibratingꢀcoil magnetometer, which
was a flow microreactor with volume 0.5 ml. The
20%Co/Qꢀ10 11
26
3
5%Co/Qꢀ15
3.9
20%Co/Qꢀ15 14
13
8
15
5
weight of samples was 26
10–3 g. Magnetization was
×
5%Co/Qꢀ30
20%Co/Qꢀ30 15
Co/Al2O3
4.9
assumed to be proportional to the cobalt metal weight.
Reduction was performed under the conditions of linꢀ
11
9
ear heating at a rate of 9 K/min to
Т = 973 K at a
380
8
5%Со/Eꢀ380
20%Со/Eꢀ380 13
5%Со/Eꢀ200
20%Со/Eꢀ200 13.6
5%Со/Eꢀ90 4.2
20%Со/Eꢀ90 11.3
2
7
7
8
7
6
8
3
4
4
9
4
9
2
hydrogen flow rate of 60 cm3/min. The completeness
of reduction was controlled by measuring magnetizaꢀ
tion. After a constant magnetization was reached,
samples were cooled to 283 K in a flow of specialꢀ
purity argon.
12
200 10
90 20
3
2.5
13
4.7
9.4
Oxidation was performed in an О2 + N2 mixture at
atmospheric pressure and 283 K. Saturation magnetiꢀ
zation σs was determined by extrapolation to an infiꢀ
Note: s is the specific surface area of the carrier, d is the mean diamꢀ
nite field in the 1/
Н
– s coordinates. A maximum field
σ
eter of pores, x is the content of Co metal after reduction,
Co
2
strength was 6.3 kOe. Magnetic field strength was
determined using an RSh1ꢀ10 magnetic induction
meter.
DCo is the mean size of Co particles, σ is the variance of the
Co particle size distribution, S is the specific surface area
sp
calculated from the content of the metal after reduction and
the mean size of particles; the mean size and variance were
determined from magnetic measurements.
The Determination of the Size of Co Particles
Co particleꢀsize distribution was determined using
the method described in [9]. To check the applicability
of this method, we studied several samples by transꢀ
mission electron microscopy. The selection of samples
for transmission microscopy studies was determined
by the degree of “transparence” of substrates to elecꢀ
tron beams. Samples with a low content of Co deposꢀ
ited on silica gel were most suitable. The table contains
the mean particle sizes and distribution variances
we study the kinetics of oxidation of Co nanoparticles
at room temperature in inert carriers with various
chemical natures and porous structures often used in
heterogeneous catalysis.
EXPERIMENTAL
The objects of study were prepared by the tradiꢀ
tional method of the impregnation of carriers by a
solution of Co nitrate with the required concentraꢀ
tion. Carriers were Qꢀ3, Qꢀ6, Qꢀ10, Qꢀ15, and Qꢀ30
CARIACT silica gels (Fujisilysia chemical ltd.) with
narrow pore size distributions and alumina (Engelꢀ
hard) with pore diameters 8, 10, and 20 nm. The pore
size distributions and specific surface areas of silica
gels were determined by lowꢀtemperature nitrogen
adsorption on an ASAB 2010 adsorbtometer. Before
calcining, catalysts were dried at 90°С for 10 h. Calꢀ
cining was performed in a flow of air at 400°С. The
volume flow rate of air was 480 h–1. The 0.2% Pt/5%
Co/Qꢀ6 sample was prepared from a calcined 5%
Co/Qꢀ6 sample by impregnating it with a solution of
determined this way for catalysts reduced at 600°С
.
RESULTS AND DISCUSSION
The Influence of CO Preadsorption and the Presence
of H2O Vapor on the Rate of Oxidation
At room temperature, a comparatively well ordered
oxide film with a crystal structure close to the CoO
cubic (FCC) phase [10] is formed on the surface of
Co. CoO is an antiferromagnet, and a decrease in
magnetization is therefore observed during oxidation.
Two time stages with different cobalt oxidation rates
are observed. The first fast stage ends at approximately
the tenth second, and the process is then sharply
[
Pt(NH3)4]Cl2.
Electron microscopic studies were performed on a decelerated. Such a dynamics is quite correctly qualiꢀ
JEOL 2010 transmission electron microscope at a tatively described by the C–M theory [2]. The first fast
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THE KINETICS OF LOWꢀTEMPERATURE OXIDATION
219
stage is characterized by the formation of a thin oxide
layer under the action of the Mott potential.
α
Co
→
CoO
0.8
0.6
0.4
0.2
It was suggested in [11] that the initial rate of oxiꢀ
dation was proportional to the degree of metal surface
coverage by atomic oxygen; that is, dissociative
adsorption of oxygen occurred on the surface. To subꢀ
stantiate this hypothesis, we performed an experiment
in which carbon monoxide was adsorbed on the surꢀ
face of Co immediately before oxidation. The adsorpꢀ
tion of CO was performed under pulsed conditions in
a flow of Ar, and the amount of adsorbed CO was
recorded using an IR detector situated at the exit of the
reactor. During subsequent oxidation with a 23% О2 +
N2 mixture, CO desorption was observed at the initial
time moment probably because of the displacement of
CO by adsorbed oxygen. The formation of СО2 was
not observed, but the amount of desorbed CO was
smaller than that of CO initially adsorbed. It was menꢀ
tioned in [12] that, during the adsorption of CO on Co
at room temperature, partial disproportionation of
CO with the subsequent formation of surface Co carꢀ
bide was possible. Nevertheless, as mentioned, we did
not observe the formation of noticeable amounts of
СО2. Experiments showed that the preadsorption of
CO noticeably decreased the rate of subsequent Co
oxidation no matter what the nature of the carrier. It
follows that the result obtained substantiates the earꢀ
lier suggestion that the limiting process of the initial
oxidation stage is the adsorption of oxygen.
4
3
2
1
Oxidation
with air
0
800
1600
τ
, s
Fig. 1. Dependences of the degree of transformation on the
concentration of oxygen at the passivation stage and durꢀ
ing subsequent oxidation in a flow of air: (
) 2.5% O + N , ( ) 5% O + N , and (4) 10% O + N .
2 2
1) 0.2% O + N ,
2 2
(
2
3
2
2
2
2
Vertical lines mark the moments of the replacement of
oxygen mixtures with a flow of air.
after preliminary passivation in gas mixtures with varꢀ
ious oxygen concentrations. It was found that the rate
of oxidation in air noticeably depended on the conꢀ
centration of oxygen during passivation.
The presence of Pt in samples has the opposite
influence on the oxidation of cobalt nanoparticles. We
then observe a substantial increase in the rate of oxidaꢀ
tion. We believe that this is caused by the ability of
platinum to dissociatively adsorb oxygen with subseꢀ
quent spillover of atomic oxygen to cobalt oxide.
Characteristically, an increase in the rate of oxidation
is observed at both the first rapid and subsequent slow
stage of the reaction.
The results of the passivation of a 5% Co/Qꢀ6 catꢀ
alyst are shown in Fig. 1. During the first 15 min, the
catalyst was exposed to a flow of mixtures of oxygen
with nitrogen, and mixtures were then replaced by a
flow of air. This time moment is marked by a vertical
line in the figure. Characteristically, at the stage of pasꢀ
sivation, the degree of transformation is independent
of oxygen concentration, as is typical Knudsen diffuꢀ
sion controlled processes. The rate of oxidation in an
air flow increases in parallel with an increase in the
concentration of О2 at the passivation stage.
The presence of water vapor in the oxidizing gas
mixture strongly accelerates oxidation. One of the
possible explanations of the acceleration of oxidation
of cobalt nanoparticles by oxygen in the presence of
water vapor is the predominant adsorption of H2O
,
We also observe an increase in the rate of oxidation
as the duration of passivation grows.
which has a lone electron pair and is a donor of elecꢀ
trons, on Co2+ ions (which are Lewis acid centers), as
distinct from O2 molecules. Electron density transfer
from water molecules to metal cations occurs. An
increase in electron density on the surface of oxide
accelerates the diffusion of metal cations from the
metallic nucleus outward, which accelerates oxidaꢀ
tion [13].
According to Fig. 1, in the oxidation of a 5%
Co/Qꢀ6 sample with a low content of cobalt, there is
no dependence of the degree of Co
→
CoO transforꢀ
mation on the partial pressure of oxygen. Nevertheꢀ
less, when moist air is subsequently introduced, the
rate of oxidation is the higher the higher the concenꢀ
tration of oxygen in a passivating mixture. We believe
that the higher the concentration of oxygen in a passiꢀ
vating mixture, the more imperfect is the oxide layer
formed. It contains more cationic vacancies and voids
Passivation Effects
The processes that occur in passivation of metal
deposited catalysts are of interest for practical applicaꢀ at the metal–oxide boundary, which, accordingly,
tions. We therefore made an attempts to study the increases the rate of oxidation when air in subseꢀ
kinetics of oxidation of Co nanoparticles in air directly quently introduced.
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MUGTASIMOV et al.
The duration of oxidative treatment has a similar lower oxygen concentration. As a result, the oxidation
effect. As exposure to passivating mixtures increases, of these particles occurs at a lower rate.
the rate of subsequent oxidation in a flow of moist air
The oxidation of metals is accompanied by an exoꢀ
grows.
thermic effect and, in reality, the oxidation of Co
nanoparticles is not an isothermal process. This in turn
results in a dependence of the degree of transformaꢀ
tion on the concentration of Co particles in a granule.
At low concentrations, heat released in the oxidation
of one Co particle does not influence the oxidation of
neighboring Co particles because of a low heat conꢀ
ductivity of the porous medium. We then do not
observe noticeable heating of the system as a whole.
Note that a substantial increase in the degree of
transformation after the introduction of air is caused
by the accelerating action of water vapor. The lower
the partial pressure of oxygen and the shorter the time
of passivation, the less imperfect oxide layer is formed
under mild oxidation conditions and the more effecꢀ
tive is passivation. It is likely that, in the limit, the pasꢀ
sivating oxide layer must have a minimum number of
defects and must be formed at the earliest stages of oxiꢀ
dation, when the oxide film is formed only because of
the Mott potential.
The dependence of the degree of transformation of
Co into CoO for a series of Со/Al2O3 samples with
various mean diameters of carrier pores and low Co
contents (5 wt %) is shown in Fig. 2. The observed
increase in the rate of oxidation as the diameter of
pores grows is evidence of the inside diffusion mechaꢀ
nism of the process. In addition, taking into account
the size of pores and the free path of О2 molecules at
room temperature, the conclusion can be drawn that
we observe Knudsen diffusion. Therefore, the diffuꢀ
sion coefficient is independent of the partial pressure
of oxygen. Indeed, we found that the rate of oxidation
was independent of the concentration of oxygen to
within measurement errors at oxygen concentration
less than 10% for samples with equal Co concentraꢀ
tions and equal diameters of pores.
The Influence of Diffusion in Carrier Pores
on the Kinetics of Oxidation of Co Particles
The objects studied have developed pore structures,
and it was reasonable to study the influence of diffuꢀ
sion on the oxidation of Co nanoparticles situated in
carrier pores. A fairly large number of papers were
concerned with the influence of the porous structure
of carriers on the kinetics of heterogeneous including
catalytic reactions under stationary conditions. The
formalism developed earlier is, however, almost inapꢀ
plicable to the oxidation of Co particles in porous
media, because the oxidation of Co nanoparticles
occurs under nonstationary conditions. The rate of
oxidation of Co particles depends not only on the parꢀ
tial pressure of oxygen (is limited by diffusion at the
initial oxidation stage) but also on the mechanism of
oxidation of nanoparticles. As the reaction proceeds,
the mechanism of oxidation changes. After the formaꢀ
tion of a thin oxide film (the Cabrerra–Mott mechaꢀ
nism, in which the rate is limited by electric field
strength between a metallic nucleus and a negatively
charges external oxide surface), a fairly sharp transiꢀ
tion to the diffusion mechanism occurs (the rate is
limited by thermally activated diffusion of cobalt catꢀ
ions through the oxide layer). It follows that two diffuꢀ
sion processes with various physical natures occur
simultaneously in the reaction system, diffusion of
oxygen in carrier pores and diffusion of cobalt ions in
the solid cobalt oxide phase. A consideration of the
kinetics of oxidation of Co nanoparticles in porous
media requires taking into account factors specified
above.
To study the degree to which the oxidation of Co
nanoparticles was nonisothermal, we performed
experiments in which both the concentration of oxyꢀ
gen and the concentration of Co in porous matrices
were varied. In catalyst samples with a low content of
Co, we did not observe a dependence of the degree of
transformation on the partial pressure of oxygen. Conꢀ
versely, for samples with a high content of Co, the
dependence of the degree of transformation on the
concentration of О2 was strong. Since the thickness of
the oxide layer (the degree of Co transformation into
CoO in our experiments) depended on temperature,
an increase in the degree of transformation as the conꢀ
centration of oxygen grew could be explained by exoꢀ
thermic effects. When the sample was diluted with an
inert carrier, the effect decreased, which substantiated
the hypothesis of the influence of exothermicity on the
degree of transformation.
The time dependence of the degree of transformaꢀ
tion of Co into oxide is shown in Fig. 3 for a 20%
Co/Qꢀ30 catalyst for two oxygen concentrations (0.2
and 10%). The catalyst was diluted with an inert carꢀ
rier in Fig. 3a and was used in the pure form in Fig. 3b.
To obtain an objective picture of the process, we
must take into account the presence of a gradient of
oxygen concentration in the volume of a porous carꢀ
rier granule, as a result of which Co particles near the
surface of the granule and in its center have different
To more completely understand the oxidation of
degrees of transformation into oxide at each time Co nanoparticles, it is reasonable to use a mathematiꢀ
moment. With taking into account the passivation cal model, which clarifies the roles played by various
effect, this results in passivation of Co particles situꢀ factors and their significance in the mechanism of the
ated close to the center of the granule because of a reaction.
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THE KINETICS OF LOWꢀTEMPERATURE OXIDATION
221
α
Co
→
CoO
1
2
0.6
0.4
0.2
3
0
1
2
3
4
log [s]
τ
Fig. 2. Dependences of the degree of transformation of Co into CoO for a series of Со/Al O samples with various diameters of
2
av
3
pores during oxidation with 1% O + N :
(1) 5% Co/E90 (mean diameter of pores is
d
= 20 nm), (
2
) 5% Co/E200 (d =
2
2
av
10 nm), and (3) 5% Co/E380 (d = 8 nm).
av
A Mathematical Model of the Oxidation
of Metal Nanoparticles in a Porous Carrier
portional to the concentration c0 of oxygen in the gas
phase and the square of the concentration of free
adsorption centers on the surface of the particle, is
the rate constant for the adsorption of O2. It is
assumed that the number of adsorption centers
ka
A model of the oxidation of a nanoparticle. It is
known that the oxidation of metals includes electroꢀ
chemical processes, which are currently difficult to
model in detail because of the complexity of processes
and deficiency of information about model parameter
values. For this reason, we suggest a simple phenomeꢀ
nological model capable of describing the observed
kinetics of oxidation at a qualitative level.
(adsorption layer capacity) and the
constant are
ka
independent of the degree of oxidation
term is the rate of a decrease in the
α
. The
K x = kx(1 − α)θ
concentration of oxygen during metal oxidation. The
rate of an increase in the degree of oxidation is
,
k K x
v
In our model of oxidation of a metallic nanoparticle,
we consider an abstract reaction consisting of two
stages: dissociative adsorption of О2 molecules from the
gas phase onto the surface of the particle, О2 (g) + 2* =
2O, where the asterisk means an adsorption center on
the surface of the particle, and the oxidation of the
metal in the form M + O = MO. We can then write
equations for the evolution of the mean concentration
where the coefficient is the ratio between the numꢀ
ber of adsorption centers and the number of metal
atoms in the particle. This ratio can be estimated using
the equation
k
v
k = r3 − (r − l )3 rp3
,
(2)
(
)
c
v
p
p
which is the ratio between the volume of the surface
layer of atoms and the volume of the particle. Here,
of oxygen atoms on the surface of the particle and the
degree of particle oxidation ,
θ
α
is the radius of the particle and is the metal lattice
lc
rp
constant.
The experimental data were analyzed to select the
parameter in the form of the Arrhenius
θ = kac0(1 − θ)2 − kx(1 − α)θ,
(1)
ꢀ
α = k kx(1 − α)θ,
v
kx = kx(α, rp)
where c0 is the volume concentration of oxygen in the
exponential function with additional parameters takꢀ
ing into account the special features of the kinetics of
the reaction,
gas phase.
In the rightꢀhand side of the first equation, the Ka
=
2 term is the rate of an increase in the surface
kac0(1 − θ)
⎡
⎤
Ex kv
kx(α, rp) = kx0 exp −
concentration of oxygen because of dissociative
adsorption. It is as a rule assumed that this rate is proꢀ
,
(3)
⎢
⎣
⎥
RT(1 − α)
⎦
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MUGTASIMOV et al.
α
α
Co
→
CoO
Co
→
CoO
(a)
(b)
0.4
0.3
0.2
0.1
0
0.8
10% O2 + N2
0.6
0.4
0.2
0
10% O2 + N2
0.2% O2 + N2
0.2% O2 + N2
−
1
0
1
2
3
τ [s]
−
1
0
1
2
3
τ
log
log [s]
Fig. 3. Dependences of the degree of transformation on time for a 20% Co/Qꢀ30 catalyst at two oxygen concentrations (0.2 and
10%); (a) catalyst diluted by an inert carrier and (b) pure catalyst.
degree of oxidation qualitatively corresponds to the
experimental data.
where
is the “effective” activation energy of oxidaꢀ
Ex
is the universal gas constant, and T is the temꢀ
tion,
R
perature. It is known that, at least at the initial process
stage, the rate of oxidation increases as the size of the
particle decreases. In addition, at the slow state, the
degree of oxidation of small particles is higher comꢀ
A Model of the Oxidation of Nanoparticles
in a Porous Granule
Metal nanoparticles are situated in inert carrier
pores in metal deposited catalysts. It follows that a catꢀ
alyst consists of porous grains or granules containing
nanoparticles. For simplicity, let a granule be a sphere
with radius Rg. Its volume and mass are then
pared with large particles. The parameter takes into
account the influence of the size of particles on the
rate of oxidation at the initial (fast) reaction stage. At
the slow stage, the rate of oxidation tends to zero as
k
v
. This is taken into account in (3) by the
α → 1
V = 4/3 πR3
(1 − α)−1
and Mg
g
= ρgVg, respectively, where ρg is
(
)
g
multiplier in the exponent.
the specific gravity of the material of granules. The
mass of a metal in a granule is determined through its
The time dependences of the degree of oxidation
of particles with various diameters (m) are shown in percent content in the catalyst, pm, by the equation
Fig. 4. The dependences were obtained using the
parameters = 300 K; 0 = 1.71
10–4 g/cm3, which
corresponds to a 10 torr partial pressure of oxygen;
= 2.06
105 cm3/(g s), = 1015 s–1
. Suppose that metal partiꢀ
100 − p
m
M m = p M
(
)
)
(
m
g
T
c
×
cles are equally sized balls with radius rp. The volume
of such a ball is
p3, and its mass is ρp
v
.
v = 4 3 πr
(
)
p
p
×
,
=
Ex
ka
kx0
It follows that, if all particles are equally sized, the
granule contains Np m/(ρp metal particles. We
10 kJ/mol. The influence of the size of particles on the
=
M
v
)
p
assume for simplicity that metal particles are uniꢀ
formly distributed over the volume of the granule.
The number of particles in a spherical granule layer
α
0.6
r
, r + dr is then calculated by the equation
1
2
.
dN p(r) = (N p/Vg)4πr dr
2
0.4
During time dt
,
=
dNO (r,t) (1/2)NadN pKa(r,t)dt
2
3
oxygen molecules are adsorbed on the surface of
nanoparticles in the dr granule spherical
layer. The volume concentration of oxygen in pores
in a spherical layer therefore changes by
(
r
,
r
+
)
0.2
dc(r, t) =
is the number of
, where
mO dNO (r,t) dV (r)
Na
adsorption centers on the surface of a nanoparticle,
is the mass of the oxygen molecule,
γ
2
2
0
100
200
300
400
500
, s
τ
=
dV (r)
mO
γ
2
2
is the volume of pores in a spherical layer, and
γ4πr dr
Fig. 4. Influence of diffusion on the kinetics of oxidation of
–2
2
Co: (1) D = 10 cm /s, (2) D = D /2, and (3) D = D /4.
1 2 1 3 2
is the porosity coefficient.
can be estimated using
Na
γ
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A
Vol. 85
No. 2
2011

THE KINETICS OF LOWꢀTEMPERATURE OXIDATION
223
2
The rate of temperature changes in the oxidation
the equation
2, where
l is the metal latꢀ
Na ≈ 4πrp πl
qρm
∂α
tice constant. We eventually obtain that the rate of
changes in the concentration of oxygen in granule
pores caused by adsorption onto the surface of nanoꢀ
reaction is
, where q is the heat effect of the
Q =
ρgcg ∂t
reaction. The boundary conditions for temperature
have the same form as the boundary conditions for
oxygen concentration; that is, zero flux in the center of
a granule and condition of the third kind at the exterꢀ
nal boundary.
particles is
a, where a = mO NaNp/Vg.
a 2γ K
(
)
2
On the assumption that the diffusion flux of oxygen
in granule pores is proportional to the gradient of conꢀ
centration (the Fick law), we obtain a system of equaꢀ
Numerical modeling shows that the rate of the
reaction increases as the partial pressure of oxygen
grows. Note that, in model (1)–(3) of the oxidation of
one particle without taking oxygen diffusion in pores
into account, the rate of oxidation was almost indeꢀ
pendent of oxygen pressure. The pressure dependence
of the rate is caused by diffusion deceleration and the
nonisothermal character of the reaction. Taking only
diffusion deceleration into account leads to a kinetics
that qualitatively differs from the experimental data.
The inclusion of temperature effects remedies this
shortcoming of the model.
tions for the concentration of oxygen in pores
,
c(r,t)
surface concentration of oxygen
, and the degree
θ(r,t)
of oxidation
,
α(r, t)
2
∂c 1 ∂
2 ∂c
∂r 2γ
a
=
γDr
−
k c 1 − θ ,
(
)
a
(
)
r2
∂t
∂r
2
∂x
∂t
(4)
= kac(1 − θ) − kx(1 − α)θ,
∂α
= k kx(1 − α)θ.
v
∂t
Calculations are performed with augmenting Eqs. (4)
∂c
∂r
In model (5), the degrees of oxidation at the slow
reaction stage (at long times) depend on pressure, and
the higher the pressure of oxygen the larger the degree
of oxidation at the slow reaction stage. This difference
increases as the mass of a metal grows. It follows from
the plot of temperature changes (Fig. 5) that a subꢀ
stantial increase in the mean temperature of a granule
is observed at the fast reaction stage, which determines
the degree of oxidation at the slow stage. The higher
the pressure of oxygen the higher the temperature at
the fast stage and, accordingly, the higher the degree of
oxidation. The amount of heat released during the
reaction increases as the mass of a metal grows. For
this reason, for the sample with pm = 20%, the temperꢀ
ature at the fast stage is much higher than for the samꢀ
ple with pm = 5%. Therefore, the difference between
the degrees of oxidation at the slow stage is larger.
by the boundary conditions
and
hc(c0 − c)
=
r = Rg
∂c
r →0 ∂r
= 0 and zero initial conditions.
lim r
(
)
Equations (4) were solved numerically with the
parameters Rg = 1 mm, ρg = 3.3 g/cm3
m = 10%, rp
3 nm, and = 0.25 nm. Oxidation model parameter
,
p
=
l
values are the same as in Fig. 4.
It follows from calculations that the rate of oxidaꢀ
tion decreases as the rate of oxygen diffusion in granꢀ
ule pores lowers. This result is in qualitative agreement
with the experimental data on the oxidation in carriers
with different pore sizes. Note that, as distinct from
the experimental data, the degrees of oxidation in varꢀ
ious carriers calculated by (4) tend to one value with
time. This likely means that model (4) ignores certain
important factors (for instance, cobalt passivation,
temperature changes, etc.). Also note that we assumed
To summarize, we showed that the limiting stage of
the reaction was the dissociative adsorption of oxygen
molecules resulting in the oxidation of surface cobalt
atoms. After the formation of a continuous cobalt
oxide layer on the surface of particles, the Mott potenꢀ
tial value becomes the rate limiting factor. This value is
independent of the partial pressure of oxygen in the
oxidation of Co particles. The Mott potential
increases the mobility of cobalt cations through the
oxide layer and contributes to tunneling of electrons
from the metallic nucleus to oxygen molecules
adsorbed on the outside oxide surface.
in calculations that
γ
= 1 because of the absence of
data on the porosity of carriers.
The experimental kinetics of oxidation depends on
oxygen pressure (see Fig. 3b). This dependence can be
explained by the influence of temperature on the rate
of oxidation. To check this possibility, we constructed
the following nonisothermal model of oxidation (5),
in which the heat conductivity equation at temperaꢀ
ture
Т was added to the model (4) equations,
∂c 1 ∂
2 ∂c
∂r
=
γDr
− F(c, x),
+ Q(x, y),
(
)
)
r 2
∂t
∂r
The partial pressure of oxygen substantially influꢀ
ences the imperfection of the oxide layer in lowꢀtemꢀ
perature oxidation. On the other hand, this results in a
dependence of the effective passivation of Co nanoꢀ
particles on the time of passivation and the partial
pressure of oxygen. On the other hand, this causes the
passivation of cobalt particles in “narrow” carrier
pores and a dependence of the rate of oxidation and
∂T 1 ∂
2 ∂T
∂r
2
=
λr
(
r 2
∂t
∂x
∂t
∂r
(5)
= kac(1 − x) − kx(1 − α)x,
∂α
= k kx(1 − α)x.
v
∂t
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A
Vol. 85
No. 2
2011

224
MUGTASIMOV et al.
Tav/T0
2.0
1% O2
10% O2
50% O2
1.8
1.4
1.0
1.8
1.6
1.4
1.2
1.0
0
10 20 30 40 50
0
100
200
300
400
500
, s
τ
Fig. 5. Relative changes in the mean temperature of a granule,
T /T .
av 0
the degree of Co
diameter of carrier pores.
CoO transformation on the gives a qualitatively correct explanation of experimenꢀ
tal observations.
After the end of the fast stage, process develops in
the diffusion mode, the rate of oxidation of metal
nanoparticles is limited by the diffusion of metal ions
REFERENCES
1. C. Wagner, Z. Phys. Chem. Abt. B 21, 25 (1933).
2. N. F. Caberra and N. Mott, Rep. Prog. Phys. 12, 163
and oxygen through the oxide layer. For cobalt, DCo ӷ
DO, and the rate determining stage is therefore the difꢀ
fusion of cobalt cations through the oxide layer. The
diffusion coefficient of cobalt cations in the reaction
under elevated temperature conditions increases as
the partial pressure of oxygen at the oxide/gas boundꢀ
ary grows. The rate of oxidation and the final degree of
(1948–1949).
3. V. P. Zhdanov and Bengt Kasemo, Chem. Phys. Lett.
452, 285 (2008).
4. A. D. Smigelskas and E. O. Kirkendall, Trans. AIME
171, 130 (1947).
5. Y. Yin, R. M. Riou, C. K. Erdonmez, et al., Science
304, 711 (2004).
6. C. M. Wang, D. R. Baer, L. E. Thomas, et al., J. Appl.
Co
CoO transformation therefore increase as the
partial pressure of oxygen grows.
Phys. 98, 094308 (2005).
7. P. A. Chernavskii, G. V. Pankina, V. I. Zaikovskii, et al.,
For samples with high cobalt contents (11–20 wt %),
local heat release begins to substantially influence the
reaction. The reaction passes from the kinetic oxidaꢀ
tion mode to the diffusion mode characterized by a
dependence of the degree of transformation on the
partial pressure of oxygen and the absence of such a
dependence on the size of cobalt crystallites. An
increase in the concentration of cobalt increases the
amount of heat released in the reaction and local temꢀ
perature and, in the absence of diffusion limitations
and at high oxygen partial pressures, results in an
increase in the rate of the reaction and the final degree
J. Phys. Chem. C 112, 9573 (2008).
8. H. J. Fan, M. Knez, R. Scholz, et al., Nano Lett.
(2007).
9. P. A. Chernavskii, Vei Chu, A. Yu. Khodakov, et al., Zh.
Fiz. Khim. 82, 83 (2008) [Russ. J. Phys. Chem. A 82
951 (2008)].
10. S. W. Charles and S. Linderoth, J. Magn. Magn. Mater.
196–197, 18 (1999).
11. P. A. Chernavskii, G. V. Pankina, A. P. Chernavskii,
7, 993
,
et al., J. Phys. Chem. C 111, 5576 (2007).
12. Rao K. Mohana, D. Scarano, G. Spoto, and
of Co
CoO transformation.
A. Zecchina, Surf. Sci. 204, 319 (1988).
The suggested mathematical model quite correctly
describes the processes that occur in the system and
13. S. R. J. Saunders, M. Monteiro, and F. Rizzo, Progress
Mater. Sci. 53, 775 (2008).
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A
Vol. 85
No. 2
2011