New approach to the investigation of mechanisms and apparent activation energies for the reduction of metal oxides using constant reaction rate temperature-programmed reduction

Article abstract of DOI:10.1021/jp983233+

A new system has been developed for the study of both bulk and surface metal oxides by temperature programmed reduction (TPR) under both conventional linear heating and constant rate thermal analysis (CRTA) conditions. It is shown that constant rate temperature-programmed reduction (CR-TPR) is capable of producing higher resolution of overlapping events, provides more insight into reduction mechanisms, and allows easier quantification of reduction processes than conventional TPR. The CR-TPR curves for both bulk and supported copper oxides confirmed that reduction followed a nucleation or autocatalytic mechanism. Bulk nickel oxide was found to reduce via a similar mechanism. Advantages of the CR-TPR rate-jump technique to determine reaction energetics are illustrated by investigation of the apparent activation energy (E_a) of CuO reduction, and the results are compared with those obtained under linear heating conditions. Both approaches yield reasonable values of E_a under the appropriate experimental conditions employed. However, the CR-TPR rate-jump technique allows variations in E_a to be measured as a function of the extent of reduction, revealing changes in the reaction mechanism or kinetics. Our results suggest it is possible to estimate the apparent activation energy of both the nucleation and growth stages involved in reduction. The validity of the rate-jump technique employed is confirmed using the thermal decomposition of CaCO₃, a widely investigated process. The TPR system uses a hygrometer cell to monitor the production of H₂O as the sample is reduced. The sample temperature is controlled by a computer in such a way that the production of H₂O, i.e., the rate of reduction, can be maintained at a constant preselected value for CR-TPR experiments. Important instrumental features include a fast response furnace, direct temperature measurement, a sensitive specific detector, and control and data analysis software developed specifically for this work.

Full text of DOI:10.1021/jp983233+

338
J. Phys. Chem. B 1999, 103, 338-345
New Approach to the Investigation of Mechanisms and Apparent Activation Energies for
the Reduction of Metal Oxides Using Constant Reaction Rate Temperature-Programmed
Reduction
Michael J. Tiernan, Philip A. Barnes,* and Gareth M. B. Parkes
Centre for Applied Catalysis, Materials Research Group, UniVersity of Huddersfield, Queensgate,
Huddersfield, HD1 3DH, U.K.
ReceiVed: July 31, 1998; In Final Form: NoVember 9, 1998
A new system has been developed for the study of both bulk and surface metal oxides by temperature
programmed reduction (TPR) under both conventional linear heating and constant rate thermal analysis (CRTA)
conditions. It is shown that constant rate temperature-programmed reduction (CR-TPR) is capable of producing
higher resolution of overlapping events, provides more insight into reduction mechanisms, and allows easier
quantification of reduction processes than conventional TPR. The CR-TPR curves for both bulk and supported
copper oxides confirmed that reduction followed a nucleation or autocatalytic mechanism. Bulk nickel oxide
was found to reduce via a similar mechanism. Advantages of the CR-TPR “rate-jump” technique to determine
reaction energetics are illustrated by investigation of the apparent activation energy (E
and the results are compared with those obtained under linear heating conditions. Both approaches yield
reasonable values of E under the appropriate experimental conditions employed. However, the CR-TPR
rate-jump” technique allows variations in E to be measured as a function of the extent of reduction, revealing
a
) of CuO reduction,
a
“
a
changes in the reaction mechanism or kinetics. Our results suggest it is possible to estimate the apparent
activation energy of both the nucleation and growth stages involved in reduction. The validity of the “rate-
jump” technique employed is confirmed using the thermal decomposition of CaCO
process. The TPR system uses a hygrometer cell to monitor the production of H O as the sample is reduced.
The sample temperature is controlled by a computer in such a way that the production of H O, i.e., the rate
3
, a widely investigated
2
2
of reduction, can be maintained at a constant preselected value for CR-TPR experiments. Important instrumental
features include a fast response furnace, direct temperature measurement, a sensitive specific detector, and
control and data analysis software developed specifically for this work.
1. Introduction
1
.1 Conventional Temperature Programmed Reduction.
Temperature-programmed reduction (TPR) is a thermal analysis
method that is used for the qualitative study of metal oxides.
In particular, it has been widely applied in the study of catalyst
1
systems and their preparation procedures. Typically, the sample
is subjected to a predetermined linear heating rate and sample
reduction is followed by employing a katharometer to monitor
the uptake of H2 from a reducing gas mixture. The resulting
TPR profile contains information on the nature of the reducible
species present in the sample. Unfortunately, the use of linear
heating rates in thermal analysis techniques results in nonuni-
form reaction conditions throughout the sample leading to
relatively poor resolution and kinetic data.2,3 TPR studies are
further complicated by the fact that variations in sample mass,
heating rate, or gas flow rate lead to different H2 consumption
rates. Such changes in the concentration of H2 during sample
Figure 1. TPR profile of V
2 5 2
O in a 5% H in He atmosphere using a
sample weight of 3.0 ( 0.3 mg at linear heating rates of (a) 3, (b) 10,
-
1
and (c) 20 °C min
.
1
.2. Advantages of Constant Rate Thermal Analysis in
TPR. One solution to these problems is to apply the technique
of constant rate thermal analysis (CRTA) to TPR studies.
Advantages of CRTA, in which the rate of reaction is regulated
to maintain a constant rate of reactant consumption or product
formation by controlling the temperature appropriately, have
been reported particularly for the study of thermal decomposition
4,5
reduction can lead to large distortions in the profiles obtained.
For these reasons, TPR profiles are known to be remarkably
dependent on the experimental conditions employed, which can
affect both the shape and resolution of reduction steps as well
as peak temperatures.1,2,4-7 A typical example of this is
illustrated in Figure 1, which shows reduction profiles for V2O5
obtained using different heating rates under a 5% H2 in He
atmosphere.
3,8
processes. Compared to conventional linear heating rate
techniques, CRTA reduces both temperature and pressure
gradients across the sample bed and allows the concentration
of reactant and product gases to be maintained at a constant
level throughout the whole process. CRTA can thereby enhance
resolution and provide better conditions for kinetic studies.2
*
Corresponding author. E-mail: P.A.Barnes2@hud.ac.uk. Fax: 00 44
,3,8
(
0)1484 472182.
1
0.1021/jp983233+ CCC: $18.00 © 1999 American Chemical Society
Published on Web 12/29/1998

Reduction of Metal Oxides
J. Phys. Chem. B, Vol. 103, No. 2, 1999 339
In addition, CRTA data can be used to distinguish between
reaction mechanisms and, in particular, to identify nucleation/
autocatalytic processes. The existence of a significant nucleation
step is revealed in CRTA experiments by an initial temperature
Stacey19 and ourselves,17 who both briefly mention the tech-
nique. The use of the CRTA “rate-jump” method to provide
kinetic information on the reduction of metal oxides has not
been reported.
“
overshoot” that is needed to initiate a reaction. This is followed
1.6. Experimental Considerations in CRTA-TPR. Con-
ventional TPR has proved to be a valuable technique for the
qualitative comparison of materials. However, the temperature
gradients throughout the system can cause the sample temper-
ature to differ from that of the thermocouple that is used to
estimate its temperature. This occurs in part because of the
differing heat capacities of the thermocouple, the sample holder,
and the sample. Thus, assuming a uniform supply of thermal
energy, it is not uncommon to have errors of several degrees.
The situation is further complicated by the differing emissivities
of these components and the difficulty in obtaining a completely
uniform hot zone in the furnace. In CRTA methods, time is
allowed for the system to reach a pseudothermal equilibrium
and so the measured temperature reflects the sample temperature
more accurately. In the present study, the sample holder is placed
directly on a plate-type thermocouple, thus ensuring better
temperature measurement in both linear heating and CRTA
experiments than is given by systems where the thermocouple
and sample pan are not in direct contact. The use of a
hygrometer to detect H2O production rather than H2 uptake
allows direct monitoring of the reduction process as a function
of temperature. The hygrometer response is directly proportional
to the reduction rate, and the highly sensitive nature of this
detector permits the use of small samples, which helps to further
reduce the effects of residual temperature or pressure gradients,
H2 concentration changes, and any possible influences of water
by a period where there is a fall in the temperature as the nuclei
grow and the reaction interface expands, before the temperature
rises again as the expanding regions of product overlap and the
reaction interface decreases. In the reduction of oxides, auto-
catalysis can occur in which adsorption of molecular hydrogen
on the metal may give rise to chemisorbed hydrogen atoms,
which further facilitate the reduction of adjacent oxide particles,
a process which produces a similar temperature profile to that
described above.
1
.3. Activation Energy in Solid-State Reactions. The
concept of activation energy in reactions involving solids is
somewhat different from the usual meaning of the term as
applied to homogeneous systems. In solid-state reactions, the
rate-controlling factors may not be simply chemical in origin
but may involve geometrical considerations, e.g., the nature and
size of the interface, the extent of lattice imperfections, which
can serve as the source of nuclei, or diffusion of either reactants
to the reaction interface or of products from it. For these reasons,
the term activation energy is referred to in this context as the
“
apparent” activation energy.
.4. Measurement of Activation Energy Using the CRTA
Rate Jump” Method. The basic CRTA approach can be
1
“
adapted to give the “rate-jump” method, which allows the
measurement of a model-free activation energy for the reaction
while still minimizing temperature and pressure gradients.
8
-11
1
,4-7,13
vapor on the profiles obtained.
This is achieved by causing the reaction rate to alternate between
two preselected values while monitoring the changes in sample
temperature required to ensure the desired rates are obtained.
Provided the reaction is allowed to reach equilibrium at the two
successive rates, the corresponding sample temperature mea-
surements can then be used to calculate an apparent activation
energy of the reaction. By making a number of “rate-jump”
measurements throughout the reaction, any variation in activa-
2
. Theoretical Background to the Measurement of Ea for
CuO Reduction
1
2
.1. Linear Heating Conditions. Hurst et al. proposed a
method for the calculation of activation energy from TPR
measurements. Equation 1 was used to express the rate of
reaction between a gas (H2) and a solid (S) at constant
temperature (T).
2
,8,9,12
tion energy throughout the process is readily observed.
Conventional methods used for the calculation of activation
energy under linear heating TPR conditions involve measuring
p
q
rate ) A[H ] [S] exp(-E /RT)
(1)
2
a
the temperature of maximum reduction, i.e., the peak temper-
ature, as a function of heating rate.1,13 This approach involves
where [S] represents the concentration of metal oxide, A is the
preexponential factor, and Ea is the apparent activation energy.
Using this equation, it was shown that for a reduction process
that is first order with respect to H2 concentration (i.e., p ) 1)
and assumed to be first order in metal oxide concentration (i.e.,
q ) 1), the variation of the temperature of maximum reduction
rate (Tm) with linear heating rate (â) may be expressed as
a number of experiments and assumes that the kinetic model is
unaffected by the heating rates in the range employed.
1
.5. Previous Applications of CRTA. The number and
diversity of thermal analysis techniques in which the heating
regime is modified, in some manner, by the rate at which the
sample reacts is ever increasing.2
,3,14-17
In the present work,
we focus on one of these techniques, i.e., constant rate thermal
analysis (CRTA). Although originally developed for applications
under vacuum conditions,18 CRTA has also been applied by
2
ln T - ln â + ln [H ] ) E /RT + constant (2)
m 2 m a m
1
where [H2]m is the hydrogen concentration at Tm. The reduction
of CuO has been reported to be first order with respect to H2
concentration, and hence, a plot of the left-hand side of eq 2
versus 1/Tm should give a straight line with slope Ea/R. The
pre-exponential factor (A) from the Arrhenius equation is
included in the constant part of eq 2.
An alternative method proposed by Wimmers et al. is based
on the following form of the general kinetic equation for solid-
state reactions
several workers under flowing gases to study thermal decom-
position reactions.3
,14,19
A detailed review of the technique was
1
8
given by Rouquerol in 1989 who pointed out the similar nature
of CRTA to the technique of “quasi-isothermal and quasi-
2
0
isobaric” thermal analysis developed by F. and J. Paulik,
which, in essence, relies on the same basic principle, i.e., control
13
3
of the rate of reaction. In a previous paper, we have demon-
strated the usefulness of CRTA as an analytical tool for the
study of decomposition reactions. The application of CRTA to
temperature-programmed oxidation (TPO) studies has also been
d∝ /dt ) Af(∝ ) exp(-E /RT)
(3)
a
1
4
documented. To the best of our knowledge, the only previous
reports of TPR performed under CRTA conditions were by
where R is the fraction of sample reacted at time t and f(R) is

340 J. Phys. Chem. B, Vol. 103, No. 2, 1999
Tiernan et al.
a function depending on the reaction mechanism. It was
proposed that the activation energy for reduction of a metal
oxide under linear heating conditions can be determined without
knowledge of the specific reduction mechanism using the
following equation:
(16 channel, 16 bit) analog-to-digital convertor (ADC) and a
Eurotherm 818P temperature programmer using a 486DX PC
computer. The software, developed by the authors, controls the
temperature programmer, acquires the data, and processes the
results. The program was written in ANSI C using a C++
compiler (Borland) and provides the option to perform either
linear heating or various SCTA experiments including CRTA.
2
ln(â/T ) ) -E /RT + ln(AR/E ) + C
(4)
m
a
m
a
The ceramic sample holder is placed on a plate-type
thermocouple (type R) in a water-cooled furnace (Stanton
Redcroft model 761, swept volume <7.5 cm ). This allows both
2
When ln(â/Tm ) is plotted versus 1/Tm a straight line is expected
with a slope of -Ea/R. The authors13 noted that eq 4 is generally
applicable for the determination of activation energy from
conventional TPR measurements. This method assumes that any
changes in the reduction model (f(R)) and the extent of reduction
3
accurate temperature measurement and the fast furnace response,
including cooling regimes, required for CRTA experiments. An
accurate constant flow of reducing gas over the sample is
maintained using an electronic Bronkhorst Hi-Tec mass-flow
controller. Gases evolved from the sample are analyzed using
an electrolytic hygrometer detector cell (Mark 2) supplied by
Salford Electrical Instruments that is capable of a full-scale
(
R) at Tm, caused by the changes in heating rate employed, are
negligible.
Equations 2 and 4 are essentially the same (since -ln(â/Tm2)
2 ln Tm - ln â), except that eq 2 takes into account the
)
3
-1
possible effects of the change in [H2]m as a function of heating
rate. In the present work, both equations are employed to
indicate any effects of H2 concentration changes during linear
heating experiments on the Ea measured. The method derived
by Wimmers et al.13 in eq 4 has the advantage that it is not
necessary to assume first-order kinetics with respect to the metal
oxide and knowledge of the order in H2 is also unnecessary.
Gas-solid reactions such as reductions are typified by complex
kinetics that cannot be described by a single nth order expression
over the entire reaction.1
response of 10 ppm at a flow rate of 100 cm min . In this
application, it is used on the least sensitive settings to avoid
overloading the detector. The response is flow rate dependent
and a calibration factor is used to correct for the actual flow
rate used and convert the output directly into the rate of
evolution of water expressed in milligrams per minute. The
hygrometer is mounted immediately above the furnace and is
connected by 10 cm of 3 mm o.d. stainless steel tubing to
minimize the swept volume and time delay between H O
2
,13
production and detection. The connecting tubing is held at 120
2.2. CRTA “Rate-Jump” Method. Kinetic analysis of “rate-
°C to eliminate the risk of condensation and adsorption effects.
jump” experiments in solid-state reactions is based on the
general kinetic eq 3 above.
For decomposition experiments on CaCO , used to investigate
the validity of “rate-jump” activation energy measurements, a
3
Ea at each jump is calculated using
katharometer was used to detect the CO evolved.
2
3
.2. Materials. CuO (99.9999%, Aldrich) and “green” NiO
T2
(
99.99%, Aldrich) were used. An equal mass mixture of the
two oxides was made by grinding the two components together
Ea ) RT1
ln((d∝ /dt) /(d∝ /dt) )
1
2
T1 - T2
and sieving through a 180 µm mesh.
T2
A supported Cu/Al2O3 sample, containing a nominal con-
centration of 10 wt % Cu, was prepared by a wet impregnation
technique using an aqueous solution of cupric acetate (Aldrich).
The γ-Al2O3 (Alfa Chemicals) used was preheated at 800 °C
in air for 15 min. After impregnation and removal of excess
H2O by rotary evaporation, the sample was dried at 100 °C for
8 h. Calcination was then achieved in air at 400 °C for 30 min.
The sample was ground and sieved to less than 180 µm prior
to reduction. X-ray diffraction (XRD) data, obtained using Cu
KR (λ ) 1.5418 Å) radiation, indicated that copper was present
as CuO in the calcined sample with the main CuO peak evident
at a 2θ angle of 35.5 °. Analysis of the line breadth indicated
a mean particle diameter of 14 nm.
or E ) RT1
ln(C /C )
(5)
a
1
2
T1 - T2
where T1 and T2 are the temperature measurements correspond-
1
0
ing to the two preset target reaction rates C1 and C2. No
knowledge of the reduction model is required. For this method
to be successful, the time taken to execute each rate jump should
be as small as possible in comparison to the total duration of
the reduction process since it is assumed that the changes in R
and f(R) at each rate jump are negligible. This arises because
the rate of solid-state processes, such as reduction, is controlled
by the interfacial area between reactant and product and the
object in the “rate-jump” method is to measure the temperatures
required for two specified rates for a negligible change in
interfacial area. For this reason, the magnitude of the rate jumps
is kept as small as possible which also serves to minimize
changes in reactant and/or product concentrations. Furthermore,
by using a large number of rate jumps, which can be achieved
with low reaction rates and/or high sample masses, it is possible
to explore the reduction process in detail.
CaCO (Analar grade) was supplied by BDH and used as
3
received.
3
.3. TPR Conditions. For all reduction experiments, the
reduction atmosphere consisted of 5% hydrogen in helium at a
3
-1
flow rate of 52 cm min .
.3.1. Linear Heating Conditions. Apart from experiments
3
performed at various heating rates for the calculation of the
activation energy of CuO reduction, all conventional TPR
3
. Experimental Section
.1. Equipment. The apparatus has been previously described
and used to study decomposition reactions under both linear
heating and a variety of sample-controlled heating techniques
-
1
experiments used a linear heating rate of 5 °C min . For the
reduction of individual bulk metal oxides, a sample weight of
1.5 ( 0.1 mg was employed. The reduction of the mixture of
both oxides was carried out using a sample mass of 3.0 ( 0.1
mg to maintain a constant mass of each oxide and thereby allow
direct comparisons to be made. For supported CuO/Al2O3, a
sample mass of 11.5 ( 0.1 mg was used. To measure the
apparent activation energy of bulk CuO reduction, a series of
3
3
including CRTA. The essence of the system is that it involves
computer control of the sample temperature to regulate the
reaction rate via a feedback loop. The sample furnace and
hygrometer detector cell are interfaced via a Comark Compuface

Reduction of Metal Oxides
J. Phys. Chem. B, Vol. 103, No. 2, 1999 341
TABLE 1: Experimental Conditions Employed for CRTA
“
Rate-Jump” Experiments for the Reduction of CuO
sample
no. of
rate
jumps
a
b
Oc
d
mass
C1 (mg
C2 (mg
R (mg H2O
H2O min-1) H2O min
-1
)
(%) min mg
-1
-1
)
run (mg)
-
-
-
-
2
2
3
3
-2
-2
-2
-3
-3
-3
-3
-3
a
b
c
d
40.0
20.0
10.3
4.7
1.04 × 10
1.04 × 10
8.10 × 10
5.85 × 10
1.26 × 10
1.26 × 10
1.04 × 10
8.10 × 10
0.2 0.26 × 10
4.3 0.52 × 10
8.8 0.79 × 10
15.0 1.24 × 10
78
31
21
10
a
b
C
1
) lower water evolution rate target.
C
2
) higher water
c
evolution rate target. O ) percentage of the total reduction process
which occurred in the initial “overshoot” of the target reduction rates
d
in each run. R ) rate of water evolution per unit mass of sample.
Figure 3. TPR profile of NiO under linear heating rate conditions.
Figure 2. TPR profile of CuO under linear heating rate conditions.
linear heating experiments was performed using 1.5 mg of CuO
-
1
Figure 4. TPR profile of an equal mass mixture of CuO and NiO
under linear heating rate conditions.
at heating rates of 2, 5, 10 and 20 °C min . Equations 2 and
were then used to yield values for the apparent activation
energy of the reduction.
.3.2. CRTA Conditions. CRTA runs were performed using
4
unsupported CuO have reported a wide variety of peak tem-
3
2
2
23
24
peratures including 187, 320, and 333 °C when using a
katharometer to monitor H2 uptake under linear heating condi-
tions. Comparison of peak temperatures is difficult because of
different experimental and pretreatment conditions employed
-
1
maximum heating and cooling rates of 5 and 10 °C min ,
respectively. The heating rate was varied between these limits
in order to maintain a constant target water evolution rate (i.e.,
-
3
-1
reduction rate) of ca. 1 × 10 mg min . A sample mass of
1
23
by the various workers. Boyce et al. showed that the
temperature at which the maximum rate of copper reduction
occurred varied considerably with the experimental conditions
such as heating rate and sample size, even when there was no
major depletion of H2. It was also found that different samples
of CuO exhibited different reduction characteristics.23
1
.5 ( 0.1 mg of each bulk oxide was employed. A CRTA
experiment was also performed using 3.2 ( 0.1 mg of the CuO/
NiO mixture. For the supported CuO/Al2O3 sample, a sample
mass of 12.5 ( 0.1 mg was employed.
For the measurement of Ea, CRTA “rate-jump” experiments
were performed on CuO as outlined in Table 1. Maximum
A similar reduction profile was obtained for the CuO/Al2O3
sample under linear heating conditions with a single peak
covering a temperature range of 155-265 °C and peak
maximum at 205 °C. The lower peak temperature for the
supported sample agrees with previous findings that supported
-
1
heating and cooling rates of 5 and 10 °C min , respectively,
were again used in order to alternate between the target water
evolution rates, C1 and C2. Equation 5 was used to calculate
the activation energy for each jump.
3
.4. Decomposition of CaCO3. To demonstrate the validity
1
CuO reduces more easily than bulk CuO.
of the “rate-jump” method, the activation energy for the
decomposition of CaCO3 (in He at 25 cm3 min ) was
investigated. Maximum heating and cooling rates of 5 and 10
Figure 3 shows the profile obtained for NiO. As expected, a
single peak is observed over a temperature range of 300-420
-1
°
C with a maximum at 346 °C. The maximum rate of H2O
-
1
°
C min , respectively, were used in order to maintain target
-2
-1
25
production is 2 × 10 mg min . Mile et al. studied the TPR
-
2
carbon dioxide evolution rates of 5.1 × 10 (C1) and 6.5 ×
mg min (C2) throughout 10 rate jumps with 15.8 ( 0.1
mg of sample.
of NiO using a 5% H2/N2 reducing gas mixture, a heating rate
-
2
-1
1
0
-1
of 12 °C min , and a sample size of 60 mg. A peak temperature
of 400 °C for unsupported NiO was reported. Again, comparison
with the present study is difficult because of the different
experimental conditions employed. The higher peak temperature
they reported may be due to the higher heating rate and/or larger
sample mass used. Differences in the purity of the oxide
employed may also have contributed; they also reported the
presence of a small peak, attributable to traces of black Ni2O3,
in some of their profiles.
4
. Results and Discussion
.1. Comparison of CRTA and Linear Heating Tech-
4
niques. Figures 2-4 illustrate the TPR results obtained under
-
1
linear heating conditions of 5 °C min . Figure 2 shows the
hygrometer profile produced for the reduction of CuO. A single
peak is seen over a temperature range of 245-335 °C with a
maximum at 280 °C. The maximum rate of H2O production
The profile obtained for the reduction of the equal mass
mixture of the two oxides is shown in Figure 4. Two strongly
-
2
-1
was ca. 3.3 × 10 mg min . Previous TPR studies of

342 J. Phys. Chem. B, Vol. 103, No. 2, 1999
Tiernan et al.
Figure 7. TPR profile of an equal mass mixture of CuO and NiO
under CRTA conditions.
Figure 5. TPR profile of CuO under CRTA conditions.
Figure 8. Extent of reaction (R) versus temperature plot for the TPR
of an equal mass mixture of CuO and NiO under (a) linear heating
and (b) CRTA conditions.
Figure 6. TPR profile of NiO under CRTA conditions.
overlapping peaks are seen covering a temperature range of
a nucleation or autocatalytic reduction mechanism, which is
followed by a long period where the rate is maintained at a
constant level. During this stage, the temperature covers a range
of between 180 and 230 °C, again much lower than would
appear to be possible from the linear heating profile (Figure 3).
245-410 °C with maxima at 303 and 341 °C for the CuO and
NiO, respectively. The increase in peak temperature for CuO
compared with 280 °C in Figure 2 appears to be due to overlap
of the two reduction peaks. Doping with NiO has been
previously reported to lower the reduction temperature of pure
CuO in TPR experiments due to modification of the CuO lattice
Figure 7 shows the reduction of the equal mass mixture of
CuO and NiO under CRTA conditions. The overall profile
mirrors those for the individual oxides with CuO reduction
proceeding at a constant rate over a temperature range of 110-
24
by the dopant producing extra nucleation sites. However, such
a phenomenon would not be expected in the present study when
using a physical, rather than chemical, mixture of the two oxides.
Figure 5 shows the reduction of CuO under CRTA conditions.
The temperature trace shows how the computer system controls
the sample temperature in attempting to maintain a constant
rate of reaction. It can be seen that apart from the initial
1
50 °C, while NiO is reduced at a constant rate between 170
and 230 °C.
The greater resolution of the two reduction processes obtained
under constant rate conditions becomes more apparent when
the R (extent of reaction) versus temperature profile for the linear
heating experiment (Figure 8a) is compared to that for the CRTA
experiment (Figure 8b). This form of presentation is extremely
valuable for quantitative comparison of the effects of the two
TPR methods.
“
overshoot” of the target reaction rate, the rate of H2O
production is maintained at a constant level (corresponding to
-
3
-1
a reduction rate of ca. 1 × 10 mg of H2O min ) over the
majority of the reduction process. The reduction proceeds at a
constant rate over a temperature range of 120-160 °C. This
shows that the reduction of CuO can be achieved at a much
lower temperature than that indicated in Figure 2 under
conventional linear heating conditions. It should be noted that
the transient overheating or “overshoot” at the initial stage of
the reduction does not arise from poor temperature control but
indicates that the reduction process involves either a nucleation
reaction mechanism21 or autocatalysis. This “overshoot” effect
is not found in systems that do not exhibit a significant
The unusual shape of the alpha (R) versus temperature profile
in Figure 8b can be explained as follows. As mentioned above,
a transitional overheating in the initial stages of a CRTA curve
has been previously attributed to a significant nucleation
3
,20
stage.
Both CuO and NiO have been reported to exhibit
sigmoidal reduction isotherms characteristic of a nucleation or
3
1,26,27
autocatalytic reduction mechanism.
In terms of the reduc-
tion of metal oxides, the nucleation step involves the initial
removal of oxygen atoms from the lattice. Once the concentra-
tion of vacancies reaches a critical value, they are then
annihilated by lattice rearrangement with the formation of metal
nuclei. The nuclei then grow and, as they expand, the area of
the sample-product interface, i.e., the interface between the
metal oxide and the metal nuclei, increases causing the reduction
process to accelerate. In addition, the reaction interface increases
3
,20
nucleation stage.
The results illustrate the ability of CRTA
experiments to reveal kinetic and mechanistic information that
is not apparent from conventional TPR curves (Figure 2) and
are discussed in greater detail below.
The reduction of NiO under CRTA conditions is shown in
Figure 6. The profile obtained is broadly similar to that of CuO
in Figure 5. Again, there is a brief initial “overshoot”, indicating

Reduction of Metal Oxides
J. Phys. Chem. B, Vol. 103, No. 2, 1999 343
TABLE 2: Variation of T with Linear Heating Rate (â) for
m
CuO Reduction
â (°C min-1)
T
(°C)
m
2
5
0
0
245
280
297
340
1
2
addition, comparison of parts a and b of Figures 8a and 8b
clearly shows the enhanced resolution obtainable using CRTA.
4
.2. Measurement of Ea for CuO Reduction. 4.2.1. Linear
Heating Conditions. The variation of Tm for CuO reduction with
â is shown in Table 2. A plot of 2 ln Tm - ln â + ln [H2]m
versus 1/Tm was found to be a straight line described by the
equation Y ) 6677.3X - 10.2 (correlation coefficient ) 1.000).
Using eq 2, the apparent activation energy for CuO reduction
Figure 9. Extent of reaction (R) versus temperature plot for the TPR
2 3
of a CuO/Al O sample under CRTA conditions.
-
1
by H2 was therefore calculated to be 55.5 kJ mol . Similarly,
due to the appearance of new nuclei. In a CRTA experiment,
this means that, as reduction proceeds, the temperature must
drop in order to maintain a constant rate of reaction as the
2
a plot of ln(â/Tm ) versus 1/Tm was also found to be a straight
line (Y ) -6576.9X + 0.9 (correlation coefficient ) 1.000),
-1
which, from eq 4, produces a value for Ea of 54.7 kJ mol .
1
reaction interface increases. In some cases, e.g. NiO, the metal
The correlation between the values obtained using eqs 2 and 4
indicates that changes in H2 concentration during reduction are
nuclei formed are thought to dissociate and activate dihydrogen
molecules leading to autocatalysis. As the reduction proceeds,
the expanding metal nuclei continue to grow and eventually
merge. This merging causes the area of the sample-product
interface to decrease, and the temperature has to rise again to
prevent deceleration of the reaction. It is this rise, fall, and then
rise again of the temperature that causes the R versus temper-
ature profile to curve back on itself during both reduction
processes in Figure 8b.
-1
negligible even at a heating rate of 20 °C min when the
-2
maximum rate of H2O evolution was as high as ca. 6.76 × 10
-1
-1
mg min . An apparent activation energy of ca. 55 kJ mol is
in reasonable agreement with previous literature values deter-
mined using eq 2. Gentry et al. reported an activation energy
of 67 ( 10 kJ mol using a reducing mixture of 10% H2 in
N2, while Boyce et al. reported values of between 67 and 82
24
-1
23
-1
kJ mol using 6% H2 in N2. The activation energy of 52 kJ
As mentioned above, isothermal studies have also indicated
the existence of a nucleation/autocatalytic mechanism for the
-1
28
mol , found by Hayden et al. in an experiment which
measured the rate of production of H2O from the reaction of a
supersonic molecular beam of H2 at fixed energy with an
oxygen-covered Cu{110} surface at temperatures between 377
and 527 °C, also agrees well with our result.
26
reduction of CuO. For example, Pease and Taylor noted that
CuO reduction occurs most readily at the copper-copper oxide
interface with the rate of water production being proportional
to the interface area, which increases after formation of the first
metal nuclei. A similar conclusion was reached by Hayden et
4
.2.2. CRTA “Rate-Jump” Method. The activation energy of
CuO reduction was also investigated by the CRTA “rate-jump”
method. In selecting the values for the reaction rates, two
different considerations apply. First, the underlying “constant”
rate (i.e., the lower level) is chosen to provide enough time to
achieve a reasonable number of “rate jumps”, typically 20-
28
al. who measured the rate of H2O production from an adsorbed
monolayer of oxygen on a Cu{110} single crystal surface
exposed to a supersonic molecular beam of hydrogen molecules
under ultrahigh vacuum conditions. At a constant molecular
beam energy and surface temperature, the rate of reaction was
found to be slow at the start, increase rapidly, and then gradually
decrease. This behavior was explained by a model in which H
atoms (formed by dissociation of H2 on the surface) could only
3
0, during the experiment. The upper reaction rate has to be
sufficiently different from the lower rate to ensure the corre-
sponding change in temperature can be measured accurately.
However, it is important that the difference in the two rates is
not so great as to risk a change in mechanism or a significant
alteration in the extent of the nature of the reaction interface.
The validity of the CRTA “rate-jump” method employed was
first confirmed using the decomposition of CaCO3 as a model
reaction. The activation energy appeared to remain constant
throughout the decomposition with an average value of 205 (
29
react with oxygen atoms at the edges of oxygen islands. Thus,
one of the important factors in the reaction rate was the size of
the interface between the clean and oxygen-covered copper
surface.
Criado et al.15,21 have illustrated the usefulness of CRTA in
determining the kinetics of solid-state decomposition reactions
from an analysis of the shape of the R versus temperature profile.
From this work, the shapes of the profiles for each process
shown in Figure 8b appear characteristic of a formation and
growth of nuclei/autocatalytic kinetic model.21
-
1
15 kJ mol . Activation energies for this reaction have been
11,30
reviewed in detail by Reading et al.
who noted that, although
there is a wide variation in reported values, measurements made
under appropriate experimental conditions and using “sensible”
methods to calculate Ea yielded values of between 190 and 227
The R versus temperature curve obtained for the reduction
of CuO/Al2O3 is shown in Figure 9 and is again characteristic
of a nucleation or autocatalytic reduction mechanism. Supported
CuO has been previously reported to show a sigmoidal reduction
-
1
kJ mol . Such values were believed to be in reasonable
agreement with the reported value for the enthalpy of formation
-
1 11
of CaCO3 of about 177 kJ mol .
1
,27
isotherm characteristic of this type of reduction mechanism.
A typical “rate-jump” experiment for CuO reduction is shown
in Figure 10. Again there is a brief initial “overshoot”, followed
by a longer period where the reaction rate swings between the
Determination of the reduction mechanism of metal oxides using
linear heating TPR has also been attempted based on the analysis
1
3
-2
-2
of TPR patterns measured at several heating rates. This
approach requires several experiments to yield similar informa-
tion that would be obtained from a single CRTA curve. In
two preset target levels of 1.04 × 10 (C1) and 1.26 × 10
-
1
(C2) mg H2O min . These rates were selected in accordance
with the criteria mentioned above. For each of the 31 rate jumps,

344 J. Phys. Chem. B, Vol. 103, No. 2, 1999
Tiernan et al.
the acceleratory growth stage before the rate jumps, and the
activation energy measurements, begin. In this case, the
measured value of Ea reflects the growth stage rather than the
nucleation stage. The initial differences in Ea, found over the
6
-fold range of reaction rates used (Table 1, column “R”),
decrease as the reaction proceeds with the values converging
once the initial influence of nucleation diminishes.
We believe that the activation energy measurement of 55 kJ
mol- made under linear heating experiments is similar to that
obtained for the initial value for run a because the Tm value is
mainly determined by the reduction rates on the low-temperature
1
1
3
side of the TPR peak where the effect of nucleation will
predominate.
Figure 10. TPR profile of CuO under CRTA “rate-jump” conditions.
The second trend seen in Figure 11, namely the decrease in
the activation energy over of course of the reduction, possibly
arises due to autocatalytic effects as described in the Introduc-
2
7
tion. Voge and Atkins reported similar findings for the
decrease in the activation energy of the isothermal reduction of
supported CuO. A similar decrease in the activation energy was
also reported by Hayden et al. in their molecular beam
28
experiment. While no conclusive explanation was given, they
suggested that lateral interactions between adsorbed oxygen
atoms or adsorbate-induced surface reconstructions might influ-
ence the barrier height.
The Ea values determined in the last few rate jumps in each
experiment were deemed unreliable because the reaction rate
did not quite reach the set target levels as the reduction neared
completion. Thus, Figure 11 only shows Ea values as a function
of R until ca. 90% of the reduction is complete. The discrepancy
between curves a-c and curve d in Figure 11 may indicate that
the small number of rate jumps in the latter experiment did not
satisfy the assumption that R remain constant in each jump.
The CRTA “rate-jump” method possesses the same advan-
tages as ordinary CRTA experiments. The uniform reaction
a
Figure 11. Apparent activation energy (E ) for CuO reduction as a
function of the extent of reduction (R), measured from CRTA “rate-
jump” experiments.
a value for Ea was obtained using eq 5 thereby allowing any
variation in Ea with extent of reduction (R) to be determined.
Obviously, the rate of H2 consumption is not constant throughout
the reduction process in Figure 10 due to the small changes in
rate at each jump. However, as discussed above, changes in H2
concentration during reduction under linear heating conditions,
when the maximum rate of H2O evolution varied from 6.76 ×
11
conditions allow more reliable kinetic data to be obtained than
-
2
-1
-1
-2
-1
1
°
0
mg min at 20 °C min to 1.65 × 10 mg min at 2
8-10
under conventional linear heating conditions.
The correlation
-
1
C min , did not affect the measured activation energy.
between the Ea measurements from “rate-jump” and linear
heating experiments in the present study would appear to
indicate that linear heating experiments can provide an accept-
able measurement of an “overall” value of Ea, at least under
Therefore, it would seem reasonable that the small change in
H2 concentration at each rate jump can be considered to be
negligible under the conditions used for the rate jump experi-
ments (see Table 1).
30
the experimental conditions employed. Reading et al. reported
Laureiro et al.12 studied the variation of Ea with extent of
reaction using the CRTA “rate-jump” method to investigate the
dehydration kinetics of Wyoming montmorillonite. It was found
that the apparent activation energy increased during the course
of the dehydration process indicating increasing difficulty in
the progress of the reaction. The authors noted that this behavior
was not exceptional and as such the measurement of mean
that rising temperature experiments also yielded reasonable
results for the activation energy of CaCO3 decomposition
provided reasonable care was taken with the experimental
conditions and calculation methods used. In the present study,
it can be seen that, because the “rate-jump” method employed
measures the variation of Ea with extent of reaction, it gives a
greater insight into the reduction process. It also casts doubt on
the validity of measuring a single activation energy for many
solid-gas reactions. Further work is necessary to fully explore
the potential of the “rate-jump” technique in providing important
information that may be correlated with the mechanism of
reactions.
values of kinetic parameters using conventional thermal methods
must be questioned.12 Other studies
9,11
have also reported the
use of the “rate-jump” method to investigate variations in Ea in
thermal decomposition reactions.
Figure 11 illustrates the variation of Ea as a function of R
after the initial “overshoot”) for the various rate-jump experi-
(
ments performed on CuO reduction. Two trends are apparent.
First, there is a decrease in the initial apparent activation energies
5
. Conclusions
-
1
measured for runs a-d from 55 to 35 kJ mol . This trend is
accompanied by a marked increase in the percentage of reaction
occurring in the “overshoot” stage from 0.2% to 15% (Table 1,
column “O”). This observation can be explained in the terms
of a nucleation and growth model of reduction in which the
activation energy required during nucleation is higher than that
needed in the growth stage. Thus, when a large percentage of
the reaction occurs in the “overshoot” (nucleation) part of the
CRTA curve, the reduction will have progressed further into
The use of CRTA for the study of the reduction of metal
oxides has been shown to have several advantages over
conventional linear heating TPR. Reduction under CRTA
conditions provides a greater insight into the nature of the
reduction mechanism, improves resolution of overlapping
processes, and reveals that reduction can be achieved at
considerably lower temperatures than indicated in linear heating
experiments. The CRTA curves for the reduction of CuO and
NiO clearly confirmed that both reactions followed a nucleation/

Reduction of Metal Oxides
J. Phys. Chem. B, Vol. 103, No. 2, 1999 345
autocatalytic mechanism. A supported CuO sample was found
to be reduced by a similar mechanism. The CRTA “rate-jump”
method allowed the measurement of the apparent activation
energy of CuO reduction without any prior knowledge of the
specific reduction model. Ea was measured as a function of the
extent of reaction by employing a number of rate-jumps that
thereby provided further insight into the nature of the reduction
model by allowing separate values to be obtained for the
nucleation and growth stages of the process. It is believed that
the experimental apparatus developed in this work has consider-
able potential for application in the study of supported catalyst
systems and in corrosion studies where the properties of surface
oxide films are of great importance.
(8) Rouquerol, J. Thermochim. Acta 1989, 144, 209.
9) Ortega, A.; Akhouayri, S.; Rouquerol, F.; Rouquerol, J. Thermo-
chim. Acta 1994, 247, 321.
10) Ortega, A.; Akhouayri, S.; Rouquerol, F.; Rouquerol, J. Thermo-
chim. Acta 1994, 235, 197.
11) Reading, M.; Dollimore, D.; Rouquerol, J.; Rouquerol, F. J. Therm.
Anal. 1984, 29, 775.
12) Laureiro, Y.; Jerez, A.; Rouquerol, F.; Rouquerol, J. Thermochim.
(
(
(
(
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7
1
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(
(
Acknowledgment. This work is funded by an Engineering
and Physical Sciences Research Council (EPSRC) grant. The
authors also gratefully acknowledge the assistance of Dr. C. L.
A. Lamont for helpful discussions.
(
(
(
18) Rouquerol, J. Bull. Soc. Chim. Fr. 1964, 31.
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1