hydrogen adsorption kinetics on pd/ce0.8zr0.2o2

11
Hydrogen adsorption kinetics on Pd/Ce 0.8 Zr 0.2 O 2 F. C. Gennari, a C. Neyertz, a G. Meyer, a T. Montini b and P. Fornasiero* b Received 10th March 2006, Accepted 3rd April 2006 First published as an Advance Article on the web 20th April 2006 DOI: 10.1039/b603553a Hydrogen adsorption on Pd/Ce 0.8 Zr 0.2 O 2 was studied by temperature-programmed reduction, volumetric measurements and IR spectroscopy. Hydrogen uptake and reduction rate at 353 K are strongly dependent on the hydrogen pressure. At relatively high hydrogen partial pressure, reduction involves PdO, the surface and a significant fraction of the bulk of the ceria based oxide. Formation of oxygen vacancies even at low temperature (o373 K) is observed. The hydrogen adsorption process is mainly irreversible, as is shown by an increase in the 2 F 5/2 - 2 F 7/2 electronic transition of Ce 31 with hydrogen pressure and surface dehydroxylation. This ‘‘severe’’ reduction has a negative effect on the subsequent hydrogen adsorption capability. The decrease of hydrogen uptake capacity and rate during adsorption can be associated with the partial loss of superficial OH and the presence of Ce 31 , which deactivates Pd electronically. 1. Introduction Ceria (CeO 2 ) and ceria based oxides have been widely inves- tigated as promoters of activity, selectivity and thermal stabi- lity of many catalysts. 1 Due to its unique redox properties, CeO 2 favors hydrogenation reactions, conversion of CO and hydrocarbons, NO reduction, water gas shift and steam- reforming reactions. 2 Key properties of ceria that contribute to these applications are the ability to efficiently change cerium oxidation states (Ce 31 /Ce 41 ) and the participation of lattice oxygen species/anionic vacancies in the catalytic mechanism. The high oxygen mobility of ceria-based materials leads to an easy elimination of lattice oxygen and therefore to the creation of anionic vacancies. 3 Furthermore, CeO 2 is able to store oxygen and to release it under a reducing atmosphere, leading to CeO 2x compounds, the so-called oxygen storage capacity (OSC). Incorporation of zirconium into ceria lattice to form CeO 2 –ZrO 2 solid–solutions improves the OSC, reduces the reduction temperature of Ce 41 and increases the thermal stability of the solid–solution with respect to pure ceria. In addition, the reduction rates of ceria are significantly increased by supporting metals of group VIII 1,4 In this context, the interaction of H 2 with noble metal/ Ce x Zr 1x O 2 systems is of great interest due to its involvement in industrial catalysis, particularly for catalytic converters. 5–7 Among the various systems investigated, Pd based Ce x Zr 1x O 2 materials represent the most challenging and complex. In fact, Pd is able to adsorb hydrogen, forming various hydrides and promoting extensive hydrogen spillover onto the support, even at low temperature (above 183 K). 5 A great deal of research effort has been directed toward under- standing the reduction process over these oxides and their supported noble metal analogues. Interaction between the metal and the support has been shown to promote activation of hydrogen on the support surface. Spillover phenomenon has been used to explain the high reactivity of these materials, suggesting a direct participation of the bulk oxygen in catalytic reactions. 1 However, the mechanism of the reduction process remains a matter of debate. Considering the relevance of this field, it is interesting to note the lack of kinetic measurements on hydrogen adsorption at low temperature and for high surface area supports. In the present investigation, the kinetic of hydrogen uptake on a high surface area Pd/Ce 0.8 Zr 0.2 O 2 sample is investigated by means of temperature programmed reduction, FTIR, and volumetric measurements. The influence of the reduction conditions on the adsorption kinetics and evolution of superficial species during the reaction are discussed. 2. Experimental 2.1 Preparation of catalyst Ce 0.8 Zr 0.2 O 2 was prepared by a co-precipitation technique. A mixture of Ce(NO 3 ) 3 6H 2 O (Aldrich 99.99%) and ZrO (NO 3 ) 2 H 2 O (Aldrich, 99.99%) aqueous solutions was added drop wise to a NH 4 OH solution (Carlo Erba). The product was filtered, suspended in isopropanol and stirred under reflux for 6 h. 8 Finally, the sample was dried overnight at 383 K and then calcined in air for 5 h at 773 K. The obtained product is hereafter referred to as CZ80. Pd 0.53 wt% was loaded on Ce 0.8 Zr 0.2 O 2 by incipient wetness impregnation using Pd(NH 3 ) 2 (NO 2 ) 2 as a metal pre- cursor (concentration of the Pd(NH 3 ) 2 (NO 2 ) 2 water solution: 0.166 mol L 1 , quantity: 0.3 mL of solution per gramme of support). After drying at 383 K, the sample was calcined at 773 K for 5 h. Hereafter this sample is designated as Pd/CZ80. 2.2 Characterization techniques N 2 adsorption isotherms were measured at 77 K in a Micro- meritics ASAP 2000 analyzer, after degassing the sample at a Centro Ato ´mico Bariloche (CNEA) and Instituto Balseiro (UNCuyo), (8400) S.C. de Bariloche, A. Bustillo km 9.5, Rı´o Negro, Argentina. E-mail: [email protected]; Fax: þ54 02944 445190 b Chemistry Department, INSTM—Trieste Unit and Center of Excellence for Nanostructured Materials, University of Trieste, Via L. Giorgieri 1, 34127 Trieste, Italy. E-mail: [email protected]; Fax: þ39 040 5583903 This journal is c the Owner Societies 2006 Phys. Chem. Chem. Phys., 2006, 8, 2385–2395 | 2385 PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics Published on 20 April 2006. Downloaded by Iowa State University on 20/09/2013 21:26:26. View Article Online / Journal Homepage / Table of Contents for this issue

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Page 1: Hydrogen adsorption kinetics on Pd/Ce0.8Zr0.2O2

Hydrogen adsorption kinetics on Pd/Ce0.8Zr0.2O2

F. C. Gennari,aC. Neyertz,

aG. Meyer,

aT. Montini

band P. Fornasiero*

b

Received 10th March 2006, Accepted 3rd April 2006

First published as an Advance Article on the web 20th April 2006

DOI: 10.1039/b603553a

Hydrogen adsorption on Pd/Ce0.8Zr0.2O2 was studied by temperature-programmed reduction,

volumetric measurements and IR spectroscopy. Hydrogen uptake and reduction rate at 353 K are

strongly dependent on the hydrogen pressure. At relatively high hydrogen partial pressure,

reduction involves PdO, the surface and a significant fraction of the bulk of the ceria based oxide.

Formation of oxygen vacancies even at low temperature (o373 K) is observed. The hydrogen

adsorption process is mainly irreversible, as is shown by an increase in the 2F5/2 -2F7/2

electronic transition of Ce31 with hydrogen pressure and surface dehydroxylation. This ‘‘severe’’

reduction has a negative effect on the subsequent hydrogen adsorption capability. The decrease of

hydrogen uptake capacity and rate during adsorption can be associated with the partial loss of

superficial OH and the presence of Ce31, which deactivates Pd electronically.

1. Introduction

Ceria (CeO2) and ceria based oxides have been widely inves-

tigated as promoters of activity, selectivity and thermal stabi-

lity of many catalysts.1 Due to its unique redox properties,

CeO2 favors hydrogenation reactions, conversion of CO and

hydrocarbons, NO reduction, water gas shift and steam-

reforming reactions.2 Key properties of ceria that contribute

to these applications are the ability to efficiently change cerium

oxidation states (Ce31/Ce41) and the participation of lattice

oxygen species/anionic vacancies in the catalytic mechanism.

The high oxygen mobility of ceria-based materials leads to an

easy elimination of lattice oxygen and therefore to the creation

of anionic vacancies.3 Furthermore, CeO2 is able to store

oxygen and to release it under a reducing atmosphere, leading

to CeO2�x compounds, the so-called oxygen storage capacity

(OSC). Incorporation of zirconium into ceria lattice to form

CeO2–ZrO2 solid–solutions improves the OSC, reduces the

reduction temperature of Ce41 and increases the thermal

stability of the solid–solution with respect to pure ceria. In

addition, the reduction rates of ceria are significantly increased

by supporting metals of group VIII1,4

In this context, the interaction of H2 with noble metal/

CexZr1�xO2 systems is of great interest due to its involvement

in industrial catalysis, particularly for catalytic converters.5–7

Among the various systems investigated, Pd based

CexZr1�xO2 materials represent the most challenging and

complex. In fact, Pd is able to adsorb hydrogen, forming

various hydrides and promoting extensive hydrogen spillover

onto the support, even at low temperature (above 183 K).5 A

great deal of research effort has been directed toward under-

standing the reduction process over these oxides and their

supported noble metal analogues. Interaction between the

metal and the support has been shown to promote activation

of hydrogen on the support surface. Spillover phenomenon

has been used to explain the high reactivity of these materials,

suggesting a direct participation of the bulk oxygen in catalytic

reactions.1 However, the mechanism of the reduction process

remains a matter of debate.

Considering the relevance of this field, it is interesting to

note the lack of kinetic measurements on hydrogen adsorption

at low temperature and for high surface area supports. In the

present investigation, the kinetic of hydrogen uptake on a high

surface area Pd/Ce0.8Zr0.2O2 sample is investigated by means

of temperature programmed reduction, FTIR, and volumetric

measurements. The influence of the reduction conditions on

the adsorption kinetics and evolution of superficial species

during the reaction are discussed.

2. Experimental

2.1 Preparation of catalyst

Ce0.8Zr0.2O2 was prepared by a co-precipitation technique. A

mixture of Ce(NO3)3 � 6 H2O (Aldrich 99.99%) and ZrO

(NO3)2 �H2O (Aldrich, 99.99%) aqueous solutions was added

drop wise to a NH4OH solution (Carlo Erba). The product

was filtered, suspended in isopropanol and stirred under reflux

for 6 h.8 Finally, the sample was dried overnight at 383 K and

then calcined in air for 5 h at 773 K. The obtained product is

hereafter referred to as CZ80.

Pd 0.53 wt% was loaded on Ce0.8Zr0.2O2 by incipient

wetness impregnation using Pd(NH3)2(NO2)2 as a metal pre-

cursor (concentration of the Pd(NH3)2(NO2)2 water solution:

0.166 mol L�1, quantity: 0.3 mL of solution per gramme of

support). After drying at 383 K, the sample was calcined at

773 K for 5 h. Hereafter this sample is designated as Pd/CZ80.

2.2 Characterization techniques

N2 adsorption isotherms were measured at 77 K in a Micro-

meritics ASAP 2000 analyzer, after degassing the sample at

a Centro Atomico Bariloche (CNEA) and Instituto Balseiro(UNCuyo), (8400) S.C. de Bariloche, A. Bustillo km 9.5, RıoNegro, Argentina. E-mail: [email protected]; Fax: þ5402944 445190

bChemistry Department, INSTM—Trieste Unit and Center ofExcellence for Nanostructured Materials, University of Trieste, ViaL. Giorgieri 1, 34127 Trieste, Italy. E-mail: [email protected];Fax: þ39 040 5583903

This journal is �c the Owner Societies 2006 Phys. Chem. Chem. Phys., 2006, 8, 2385–2395 | 2385

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Page 2: Hydrogen adsorption kinetics on Pd/Ce0.8Zr0.2O2

623 K for 12 h. Powder X-ray diffraction patterns were

collected on a Philips PW 1710/01 instrument with CuKaradiation. In-situ FTIR spectra were collected at room tem-

perature (rt) on a Perkin Elmer 2000 FTIR spectrometer with

a MCT detector using a static quartz cell. The powdered

samples were pressed into self-supporting discs and activated

in-situ. A cleaning procedure, consisting of calcination with

oxygen at 773 K (pressure = 30 kPa, time = 0.5 h) followed

by evacuation at 773 K (0.5 h) repeated 3 times, was employed

as a standard first step in all investigations. The steps of

reduction–evacuation–adsorption were performed as follows.

(1) Reduction: heating for 10 min at the selected temperature

under D2 (pressure range from 1 kPa to 30 kPa), followed by

evacuation at the same temperature (0.5 h); (2) evacuation:

heating at 673 K (4 h); and (3) Adsorption: heating for 0.5 h

under 30 kPa of D2 at 373 K, followed by evacuation at the

same temperature. After each step, the sample was cooled to rt

for spectra recording. Methanol adsorption studies were con-

ducted by exposure of the cleaned samples to methanol vapor

(3 kPa, rt, 10 min) followed by evacuation. Afterwards, the

sample was heated for 1 h at 373 K under vacuum, and then

cooled to rt to collect the IR spectra.

A standard cleaning procedure was always applied as a first

step before Temperature-Programmed Reduction (TPR) or

OSC measurements, to ensure a clean sample surface and

reproducible experimental conditions. It consisted of heating

the sample in 5% O2/Ar (25 mL min�1) from rt to 773 K at a

heating rate of 10 K min�1, holding at that temperature for

1 h, and then cooling, first in 5% O2/Ar to 423 K and finally to

rt in Ar. TPR experiments were performed in a conventional

system equipped with a thermal conductivity detector,9 under

5% H2/Ar (flow rate of 25 ml min�1) and different heating

rates (6–16 K min�1). The selection of experimental conditions

was in agreement with the criteria developed by Monti and

Backer.10 After TPR up to 1273 K, the sample was held at this

temperature for 15 min, then the gas was switched to Ar and

the sample cooled to 700 K, whereupon it was re-oxidised by

pulsing pure O2 (100 ml) every 30 s for 1 h. O2 uptake (total

OSC) was measured by detecting the breakthrough point.11

Hydrogen pre-reduction and adsorption kinetics were mea-

sured using a volumetric equipment-type Sievert, previously

reported.12 It consists mainly of an adsorption reactor, data

acquisition-control facilities, the high-pressure and the vacuum

lines, a mass flow controller, and temperature and pressure

transducers. The use of a mass flow controller allows data

acquisition under isobaric conditions. The sample was pre-

treated in O2 at 673 K for 1 h as a standard cleaning procedure.

The sample was then cooled to the selected reduction tempera-

ture (298–353 K) and kept for 0.5 h at this temperature. After

reduction, the sample was evacuated first at the reduction

temperature and then at 673 K for 4 h, cooled to the adsorption

temperature and held at that temperature for 0.5 h.

3. Results and discussion

3.1 Surface and structural characterization

Nitrogen adsorption at 77 K showed that CZ80 is a mesopor-

ous material with a BET surface area of 135 m2 g�1, a BJH

average pore diameter of 7.5 nm (calculated from the de-

sorption isotherm) and total pore volume of 0.25 mL g�1. The

material presents a typical diffraction pattern of a cubic single

phase Ce0.8Zr0.2O2 solid–solution (a = 0.5374 nm), with poor

crystallinity after calcination at 773 K (Fig. 1(a)) but with

good crystallinity after calcination at 1273 K (Fig. 1(b)).

The surface composition of CZ80 was determined by FTIR,

using information from the dissociation of methanol into

methoxy species over a Ce0.8Zr0.2O2 surface (Fig. 2). Bands

at 2914 cm�1 and 2806 cm�1 are assigned to [nas(CH3)] and

[ns(CH3)] of on-top OCH3 (I) modes, respectively. The bands

at 1152 and 1103 cm�1 correspond to on-top methoxy species

on Zr41 and Ce41, respectively. The band at about 1055 cm�1

includes adsorption due to methoxy species bridged over cus

Ce41 and over cus Zr41.13,14 The presence of a noticeable

shoulder at 1038 cm�1 in the IR spectrum confirms the

formation of a solid–solution.14 Using the same set of samples

as in ref. 14, we obtained a similar and linear calibration curve

for on-top methoxy (I) species Zr41. From this information,

we determined that the surface composition of the CZ80 was

80% cerium-rich. Therefore, CZ80 is a homogenous solid–so-

lution of composition Ce0.8Zr0.2O2 in the bulk (XRD) and

surface (FTIR).

3.2 TPR measurements

The reactivity of CZ80 and Pd/CZ80 toward hydrogen was

analyzed by TPR from rt to 1273 K. Fig. 3 shows representa-

tive TPR profiles obtained at 10 K min�1. The profile of CZ80

(Fig. 3(a)) presents a wide reduction peak centered near 800 K

and a weak, broad peak at about 1000 K. In the case of Pd/

CZ80 (Fig. 3(b)), an intense and sharp reduction peak is

observed at 352 K with a shoulder at 390 K and a weak, high

temperature peak similar to that observed for CZ80. Notably,

TPR profiles of single phase CexZr1�xO2 mixed oxides gen-

erally present a single reduction peak due to concomitant

surface and bulk reduction.15,16 On the basis of the homo-

geneity of the present sample, this broad H2 consumption can

be mainly associated with the presence of some kind of buoy-

ancy effect, i.e. baseline-derived due to the sample sintering/

compacting. This effect is certainly present during the TPR

and can give rise to this apparent H2 uptake. The higher

Fig. 1 XRD patterns of Ce0.8Zr0.2O2 after calcination at 773 K (a)

and 1273 K (b).

2386 | Phys. Chem. Chem. Phys., 2006, 8, 2385–2395 This journal is �c the Owner Societies 2006

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Page 3: Hydrogen adsorption kinetics on Pd/Ce0.8Zr0.2O2

chemical reactivity of the Pd/CZ80 with hydrogen corrobo-

rates catalysis of hydrogen dissociation and spillover by noble

metals, promoting support reduction at lower temperatures.1

After TPR, CZ80 and Pd/CZ80 show oxygen uptake at

700 K of 826 and 898 mmol O2 g�1, respectively. Assuming

that only Ce31 is reoxidized, the degree of cerium reduction

would be 67% and 73%, respectively. Notably, however, in

the case of Pd/CZ80 some Pd reoxidation can occur.17 Com-

plete reoxidation of Pd to PdO would require 23 mmol O2 g�1.

These results confirm the observation that the main role of Pd

is to decrease the reduction temperature but not to increase

significantly the extent of CZ reduction.4,18 The degree of

reduction reached in both samples indicates that the dominant

peak in TPR runs is associated with the simultaneous surface

and bulk reduction of the support, as theoretically predicted.15

Whereas in the case of pure ceria only the surface is available

for low temperature reduction, the role of Zr is to enhance the

migration of oxygen vacancies into the bulk and to allow

cerium reduction at lower temperatures.3,11,18 Furthermore,

despite the initial high surface area of the samples, these

processes cannot be distinguished by the traditional TPR

technique.

A series of TPR experiments were performed varying the

heating rate for CZ80 and Pd/CZ80. Using eqn (4) derived

from the Kissinger method (see Appendix), apparent activa-

tion energies of 160 kJ mol�1 (�6 kJ mol�1) and 42 kJ mol�1

(�4 kJ mol�1) were calculated for CZ80 and Pd/CZ80,

respectively, with a correlation coefficient >0.99 (see inset in

Fig. 3(a) and 3(b)). These values provide evidence that the

rate-determining step of the reduction reaction is different for

processes taking place in the presence or absence of Pd. An

apparent activation energy of about 50 kJ mol�1 was reported

for CO oxidation over NM/CeO2 catalysts under conditions

where oxygen migration from the support is believed to be rate

limiting.19 TPR measurements on aged low surface area

Ce0.5Zr0.5O2 give two distinct reduction peaks, which were

associated with different controlling regimes.20 The absence of

an isotopic effect on the low temperature reduction suggested

that oxygen migration from the bulk was the limiting factor

for the low temperature reduction (Eapp = 39 kJ mol�1),

whereas at high temperature the rate-determining step was

associated with the formation/desorption of adsorbed water

molecules (Eapp = 90–120 kJ mol�1).20 The low temperature

ceria–zirconia reduction can be associated with the catalytic

effect of a pyrochloric-related phase, which is able to activate

the hydrogen in a similar way to a noble metal.21–24 The

ordered pyrochloric-related phase is generated by redox

aging.21–24 The occurrence of scrambling at temperatures

Fig. 2 FTIR difference spectra of methoxy species formed by methanol dissociative adsorption over fresh Ce0.8Zr0.2O2 at room temperature

followed by outgassing at 373 K: (A) C–H stretching region; (B) O–C stretching region. The difference spectra result from subtracting the spectra

before and after adsorption.

Fig. 3 Temperature-programmed reduction profiles of Ce0.8Zr0.2O2

(a) and Pd/Ce0.8Zr0.2O2 (b). The heating rate is 10 K min�1. The inset

plots show the application of the Kissinger method.

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Page 4: Hydrogen adsorption kinetics on Pd/Ce0.8Zr0.2O2

lower than that of the corresponding reduction peaks sug-

gested that, on bare ceria–zirconia mixed oxides, water for-

mation/desorption was the rate determining step for the high

temperature reduction.20,25 However, the scrambling process

could be of a different type from the hydrogen activation

required for the reduction. Notably, the severe oxidation pre-

treatment, which leads to high temperature reduction, destroys

the ordered pyrochloric related structure. Therefore, the ab-

sence of an active phase (pyrochlore or noble metal) able to

efficiently split hydrogen suggests that H2 activation could be

the rate-determining step for the high temperature reduction.

The same hypothesis is valid for the present fresh high surface

area sample. The decrease of the surface area of CZ80 leads

to a shift to higher temperature of the reduction peak (data

not shown), in agreement with that already reported for

Ce0.5Zr0.5O2, both fresh and after the first TPR-mild oxida-

tion.20 The decrease of surface area, with concomitant de-

crease of the hydroxyl population, reduces the centres for

hydrogen activation and favours water desorption. Further-

more, keeping Monti and Baiker’s K-factor constant10 but

increasing the total flow rate on fresh CZ80 has no effect on

water evolution during the TPR (mass spectrometer). Notably,

we can not exclude some chromatographic effect or water

adsorption, even on the trace heated transfer lines. All these

observations are consistent with hydrogen activation as the

rate-determining step for the high temperature, unpromoted

reduction of ceria–zirconia. Accordingly, we associate the

limiting step during non-isothermal reduction of high surface

area CZ80 and Pd/CZ80 with hydrogen activation and oxygen

migration from the bulk, respectively.

3.3 Isothermal measurements: volumetric adsorption of

hydrogen

The effect of hydrogen pressure on H2 uptake was studied at

353 K (Fig. 4), temperature at which PdO is reduced and bulk

palladium hydrides are decomposed.26 Although H2 does not

appreciably dissociate on oxide surfaces, such as ceria–zirco-

nia solutions, under the experimental conditions employed

(Fig. 4 (c)), it dissociates on Pd readily at low temperature

(Fig. 4 (a) and (b)). The H2 uptake is dependent on the

hydrogen pressure and saturates at a value of about 705 and

85 mmol g�1 for 133 kPa and 6.6 kPa, respectively. In the first

case, similar H2 uptake was obtained after dynamic OSC at

temperatures from 303 to 363 K and was associated with total

surface reduction and partial bulk reduction of ceria.27 In the

last case, the hydrogen consumption can mainly be associated

with PdO reduction (45 mmol g�1), and only marginally with

surface palladium hydride formation or spillover.

It has been shown that hydrogen induces ceria reduction in

two ways: hydrogen activation at the surface to form hydroxyl

groups; and the creation of oxygen vacancies. In the first

process, the so called ‘‘reversible reduction’’, Ce31 can be

reoxidized by pumping off the sample in the absence of an

oxidizing agent.28,29 In contrast, in the so-called ‘‘irreversible

reduction’’, the ceria redox state would remain unmodified

upon evacuation. From Faraday magnetic balance studies, it

has been demonstrated that the reversible reduction is very

important for samples reduced at o673 K, and that evacua-

tion treatment at 773 K eliminates most of the hydrogen

chemisorbed on ceria. Additional magnetic susceptibility mea-

surements clearly showed that the interaction of hydrogen

with Pd/CeO2 leads to complete ceria surface reduction at

room temperature.28 A large amount of hydrogen is adsorbed

on ceria, leading to the formation of surface hydroxyls via a

spillover process from palladium. Evacuation at 373 K induces

the reverse migration of hydrogen (back spillover), which leads

to the reoxidation of Ce31 ions.28 Furthermore, it has been

demonstrated that H2, which is adsorbed and spilled over Pd/

CexZr1�xO2 during reduction up to 573 K, can be desorbed

upon heating in vacuum at 673 K, leading to about 90%

reoxidation.18

A preliminary kinetic study suggests that the hydrogen

adsorption rate after evacuation is dependent on the hydrogen

pressure used during the reduction.27 To further elucidate this

influence and also to determine the effect of temperature,

hydrogen uptake measurements on Pd/CZ80 were performed

in the temperature range 298–373 K and at 6.6 and 133 kPa of

hydrogen pressure. Fig. 5 shows representative curves of Pd/

CZ80. Hydrogen adsorptions are indeed higher for the weakly

pre-reduced sample. In addition, hydrogen uptakes also de-

pend on the pre-reduction pressure, being of 585 and 355 mmol

g�1 for the sample pre-reduced under 6.6 kPa of H2 and 133

kPa, respectively (Fig. 5). Considering these values of hydro-

gen uptake (m) as maximum values (m100%), the conversion ais defined as

a ¼ mðtÞm100%

ð1Þ

and the experimental data given in Fig. 5 can be transformed

into a degree of conversion. Hydrogen uptake curves display

three distinct regions: an initial, rapid increase, particularly

Fig. 4 Hydrogen uptake at 353 K: Pd/Ce0.8Zr0.2O2 with P(H2) =

133 kPa (a), Pd/Ce0.8Zr0.2O2 with P(H2) = 6.6 kPa (b) and bare

Ce0.8Zr0.2O2 with P(H2) = 133 kPa (c).

2388 | Phys. Chem. Chem. Phys., 2006, 8, 2385–2395 This journal is �c the Owner Societies 2006

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Page 5: Hydrogen adsorption kinetics on Pd/Ce0.8Zr0.2O2

evident at 313 and 298 K (a o 0.3%); a more gradual increase

(0.3 o a o 0.8%); and a third region with a continuously

decreasing rate of uptake at long times (a > 0.8). In general,

adsorption profiles were similar for the samples reduced at

different pressures, with some differences in the second region.

The first region in the isothermal adsorption curve lasts from

less than 100 s (T > 333 K) to 1800 s (298 and 313 K),

depending on the hydrogen adsorption temperature. This

behavior is evident for temperatures lower than 333 K but is

less marked for higher temperatures. Following the first step, a

period of stable adsorption rate was observed that ranged

from 100 s to 1 h, with longer periods occurring at lower

temperatures. The second region is followed by a period in

which the rate of hydrogen uptake continually decreases with

increasing time. Note that all the hydrogen uptakes in Fig. 5

overlap after a sufficiently long time, that time being strongly

dependant on the temperature.

In the case of homogeneous ceria–zirconia, surface and bulk

reductions are expected to occur almost concurrently,15 how-

ever, an inflexion point in the slope of hydrogen uptake at 298

and 313 K (Fig. 5) is observed for the Pd/CZ80 pre-reduced at

6.6 kPa of H2. As already discussed, this sample is less reduced

with respect to the sample that was pre-reduced at 133 kPa of

H2. Accordingly, with Perrichon et al.30 421 mmol of H2 g�1

are extracted for the reduction of the surface of the present

CZ80. The inflexion point in Fig. 5 is observed at approxi-

mately 200 mmol g�1. The total hydrogen uptake, obtained

from the pre-reduction plus adsorption before the inflexion

point, is less then expected for surface reduction according to

Perrichon et al.30 Assuming that the change in the slope is

associated with the end of surface reduction, the linear corre-

lation hydrogen uptake-surface area seems to overestimate the

hydrogen contribution for the present high surface area sam-

ple. By increasing the adsorption temperature, the difference

between surface and bulk reduction could be eliminated. Since

pre-reducing the sample at 133 kPa of H2 has already reduced

the surface, no such contribution is observed (Fig. 5B). An

alternative, and more reasonable, explanation for the presence

of this inflexion point involves a progressive rehydroxylation

of the surface during reduction. Water produced during the

first stage of the reduction could partially reoxidize the sample,

consequently the surface has additional hydrogen near the

surface that can increase the reduction rate. In fact, it is known

that the interaction with hydrogen leads to the formation of

OH, which favors hydrogen spillover and therefore supports

reduction. By increasing the temperature, the rehydroxylation

and spillover processes are accelerated, limiting the presence of

the inflexion point. Notably, the samples that were more

‘‘reversibly’’ pre-reduced should have a significantly higher

hydroxyl population, which strongly promotes hydrogen spil-

lover and chemisorption onto the support. Finally, although

less probable, we cannot exclude the alternative explanation

that the inflexion point is based on subtle differences between

the surface in proximity to Pd particles, the rest of the surface

and the bulk of ceria zirconia.

Kinetic modelling of the hydrogen uptake curves (Fig. 5)

was performed with non-linear regression analysis. As a first

step, it was assumed that the dominant reaction mechanism

does not change for conversions below 0.8, then typical

reduction models (Table 1) were tested according to eqn (2).

The fitting showed that these models are inadequate for

describing the experimental data up to about a = 0.8.

Furthermore, an attempt to develop the kinetic model for

the curves in the first region (up to a = 0.3) was performed.

Conversion data for the first region were calculated (eqn (1))

(Fig. 6) from hydrogen uptake curves after pre-reduction at

different pressures presented in Fig. 5. Applying the regression

method (eqn (8)), the n and K parameters were obtained

(Tables 2 and 3) and the fitting quality was evaluated using

the mean square deviation (MSD). The average values of n

Fig. 5 The effect of pre-reduction conditions on the hydrogen adsorption on Pd/Ce0.8Zr0.2O2 at different temperatures. P(H2) = 133 kPa. Pre-

reduction conditions: P(H2) = 6.6 kPa at 353 K (A) and P(H2) = 133 kPa at 353 K (B).

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Page 6: Hydrogen adsorption kinetics on Pd/Ce0.8Zr0.2O2

were 0.56 and 0.55 for samples pre-reduced at 6.6 kPa and 133

kPa, respectively, suggesting a diffusion-controlled reaction.

The plot of [ln(1 � a)]1/n versus time (not shown) presents a

good least-squares fit with a linearity constant R > 0.99,

confirming the predicted model. As summarized in Table 1

(see also Appendix), different theoretical equations adequately

describe diffusion-controlled mechanism. The best fit was

obtained using two-dimensional diffusion by plotting [(1 � a)ln(1 � a) þ a] versus time (Fig. 7). These plots demonstrate the

high quality least squares fits with a linearity constant of

R > 0.99. Activation energies, calculated from Arrhenius

plots, are 58 (�4) kJ mol�1 and 60 (�4) kJ mol�1 for Pd/

CZ80 pre-reduced at 6.6 kPa and 133 kPa, respectively.

Considering the impossibility of obtaining a model for the

complete a range, additional analyses were performed in order

to examine the temperature dependence in the second region.

The evaluation of the apparent activation energy (Eapp) was

performed using the Arrhenius plot—eqn (7) of Appendix.

The aim of eqn (7) is to provide a fitting that is independent of

the form of the functions F(P) and G(a) (see Appendix). Fig.

8A and 8B show the ln t versus T�1 plot for the runs shown in

Fig. 5 at constant conversions (0.2 o a o 0.8, i.e. mainly in

the second region). The curves are virtually parallel, which

means that there are no clear changes in the reaction path as

the reaction progresses. Therefore, despite the complexity of

the curves shown in Fig. 5 (including the presence of an

inflexion point), Eapp is independent of the reduction degree.

Activation energy values of 50 kJ mol�1 (�3 kJ mol�1) and 60

kJ mol�1 (�3 kJ mol�1) (with correlation coefficients >0.99)

were obtained for hydrogen adsorptions after reduction at 6.6

kPa (Fig. 8A) and 133 kPa (Fig. 8B), respectively. The Eapp

values increase slightly upon increasing the hydrogen pressure

during pre-reduction and, in agreement with this, the value of

Eapp under hydrogen flow (the lowest hydrogen pressure used,

approximately 5 kPa) is 42 kJ mol�1. These values are

comparable with those obtained under isothermal experiments

by El Fallah et al.31 (67 kJ mol�1) and Sadi et al.32 (63 kJ

mol�1), for CeO2 initial reduction and for reduction of Rh/

CeO2 catalysts, respectively. The variation in sample composi-

tion may explain the differences.

3.4 IR investigations

3.4.1 H/D spillover and reduction. In situ IR spectroscopy

was used to further investigate the hydrogen activation/ad-

sorption processes on Pd/Ce0.8Zr0.2O2. D2 was used as a

reducing agent in order to also follow H/D scrambling.

Although the conditions used for the in situ reduction of the

Pd/Ce0.8Zr0.2O2 samples in the IR cell are similar to those used

for volumetric measurements, only a qualitative comparison is

possible.

Table 1 Rate equations for the various gas–solid and solid–solidreaction models

Kinetic modelsEquationG(a) n

Unimolecular decay (first order) �ln (1 � a) 1Phase boundary controlledreaction (contracting area)

(1 � (1 � a))1/2 1.11

Phase boundary controlledreaction (controlled volume)

(1 � (1 � a))1/3 1.07

Zero order a 1.24Two-dimensional growth of nuclei(Avrami–Erofeev)

(�ln(1 � a))1/2 2

Three-dimensional growth ofnuclei (Avrami–Erofeev)

(�ln(1 � a))1/3 3

Power law (n = 2) a2 0.62Two-dimensional diffusion (1 � a)ln(1 � a) þ a 0.57Jander [1 � (1 � a)1/3]2 0.54Ginstling 1 � 2/3a � (1 � a)2/3 0.57

Fig. 6 A comparison of the conversion degree (a) obtained from Fig. 5 (symbols) with the reaction model according to eqn (8). The parameters K

and n are calculated from the fitting of these data (solid line). Pre-reduction conditions: P(H2) = 6.6 kPa (A) and P(H2) = 133 kPa (B).

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Page 7: Hydrogen adsorption kinetics on Pd/Ce0.8Zr0.2O2

Fig. 9A presents the n(OD) bands resulting from D2 ad-

sorption at 1 kPa (curve (b)) and 30 kPa (curve (c)) on Pd/

CZ80 (353 K, 10 min), after evacuation at the same tempera-

ture. Analogous experiments were performed for 3 kPa (not

shown) and the general behavior is similar to 30 kPa. For

reference, curve (a) represents the OH bands after the cleaning

procedure (Fig. 9A) and after evacuation (Fig. 9B). The fresh

Pd/CZ80 sample is characterized by the OH bands at 3780,

3665 and 3500 cm�1, associated with OH(I) on Zr41, OH(IIA)

on Ce41 and oxyhydroxide impurities in the pore, respec-

tively.14,33 After D2 reduction, occurrence of H–D exchange is

evident at 353 K and is independent of the D2 pressure, and

bands due to OD(I) on Ce41 (2740 cm�1) and OD(IIA) on

Ce41 or Zr41 (2700 cm�1) are observed.34 The intensities of

these bands increase with D2 pressure, as can be seen by

comparing curves (b) and (c) (Fig. 9A). Interestingly, the

sample reduced at 30 kPa (curve c) shows an additional band

at 2120 cm�1. This band is associated with the forbidden 2F5/2

- 2F7/2 electronic transition of Ce31 and it is indicative of

oxygen vacancy formation.35,36 After evacuation at 673 K

(4 h), the superficial species are modified. In particular, the

H–D exchange continues and the intensity of the 2120 cm�1

band increases for curve (c) (Table 4). Considering that

evacuation without previous reduction does not introduce

modifications in the bands (from a comparison of curve (a)

in Fig. 9A with Fig 9B), the changes observed provide

evidence of D2 interaction under vacuum. On the other hand,

a comparison of the changes observed for OH species reveals

that H–D exchange occurs first for (OH) species on Ce41

before exchange of (OH) species on Zr41. Thus, there is a

difference in the activity of the various (OH) groups. Further-

more, adsorption at 373 K increases both H–D exchange and

Fig. 7 Plots of [(1 � a)ln(1 � a) þ a] versus time for Pd/Ce0.8Zr0.2O2 after pre-reduction at P(H2) = 6.6 kPa (A) and P(H2) = 133 kPa (B).

Symbols: experimental data; solid line: mathematical fitting.

Table 2 Parameters K and n for adsorption curves in the first region(pre-reduced at 6.6 kPa)

Temperature/K K n MSD

298 0.00814 0.51 7 � 10�6

313 0.00120 0.51 1 � 10�5

333 0.02129 0.55 2 � 10�5

353 0.02363 0.62 4 � 10�5

373 0.04211 0.62 7 � 10�4

Table 3 Parameters K and n for adsorption curves in the first region(pre-reduced at 133 kPa)

Temperature/K K n MSD

298 0.01060 0.48 1 � 10�4

313 0.01401 0.51 4 � 10�5

333 0.02012 0.54 2 � 10�5

353 0.003496 0.62 1 � 10�5

373 0.06248 0.62 2 � 10�4

Fig. 8 Arrhenius plots at constant conversions for the hydrogen

adsorption of Pd/Ce0.8Zr0.2O2 at 133 kPa. Data obtained from

Fig. 5. Pre-reduction conditions: P(H2) = 133 kPa at 353 K (A) and

P(H2) = 6.6 kPa at 353 K (B).

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Page 8: Hydrogen adsorption kinetics on Pd/Ce0.8Zr0.2O2

Ce31 formation. The Ce41 - Ce31 reduction is evidenced

both by the appearance of OD (IIB) species on Ce or Ce–Zr at

2685 cm�1 and by the higher intensity of the 2120 cm�1 band

with respect to the evacuation step (Table 4).

Comparison of FTIR measurements performed under high

and low pressure reveals that the differences observed could be

interpreted by ceria reduction with creation of oxygen vacan-

cies. As already discussed in several investigations,20,28,31,37 the

interaction of hydrogen with ceria may lead either to water

formation, i.e. irreversible reduction of ceria, or to chemisorp-

tion of hydrogen as hydroxyls, which can be further desorbed

as hydrogen under vacuum, inducing a reversible reduction of

the oxide. Clearly, the sample reduced under high pressure (3

and 30 kPa) showed the occurrence of irreversible reduction,

with a similar final degree of ceria reduction (Table 4). In

contrast, during the reduction at 1 kPa there is no evidence of

irreversible reduction, and the final ceria reduction degree is

lower. In both cases, the final surface sample looks without

hydroxyls with similar intensity of OD bands. Subtracted

spectra show that OD intensity increases with the reduction

degree.

3.5 General discussion

The identification of the rate-determining step for the reduc-

tion of ceria-based materials is still controversial, although

there is some agreement that bulk reduction is the limiting step

of the overall process. El Fallah et al.31 and Bernal et al.29 have

discussed the reduction of CeO2 on the basis of a four-step

model, where the first three steps are surface processes (for-

mation of hydroxyl groups, anionic vacancies and water) and

only the fourth is a bulk process (diffusion of surface vacan-

cies). Since on bare CeO2 hydrogen dissociation could be the

limiting step of the surface process, the presence of a noble

metal enhances H2 dissociation and hydrogen spillover on the

surface. In this case, water formation (or water desorption) or

bulk diffusion of surface vacancies can be rate controlling.

Bruce et al.38 have proposed two contributions to the hydro-

gen uptake on ceria: one due to hydroxylation of the surface

oxide; and a second due to incorporation of hydrogen into the

ceria lattice. Using ab initio calculations, Sholberg et al.39

concluded that the uptake of small amounts of hydrogen by

ceria is spontaneous below 763 K. They also predicted that

hydrogen atoms within the bulk form hydroxyl groups and

produce a slight expansion of the lattice (1.5%). Another

mechanism, established by Fierro et al.40 and Cunningham

et al., is the incorporation of H2 in the CeO2 to form ceria

bronzes, CeO2Hx; a hypothesis supported by Lamonier et al.41

who analysed the ceria cell lattice expansion observed by in

situ X-ray diffraction with both ceria reduction and insertion

of hydrogen into the lattice.

Non-isothermal measurements (mainly TPR) have been

used to obtain information on the steps involved during the

reduction of ceria or ceria-based solid–solutions. Typically,

the reduction of ceria shows two peaks: a low-temperature

peak, assigned to the reduction of the most easily reducible

species on the surface; and a high-temperature peak, asso-

ciated with the removal of the bulk oxygen.42 In contrast,

reduction of the CeO2–ZrO2 mixed oxides shows a main broad

reduction feature, in agreement with the promotion of the

reduction in the bulk of CeO2 upon doping with ZrO2.15,16,43

As inferred from Fig. 3, in the latter case, surface and bulk

reduction cannot be distinguished since both processes occur

almost simultaneously during the TPR experiment. When a

noble metal is present, Ce41 to Ce31 reduction is possible at

lower temperature, due to the ability of the metal to dissociate

hydrogen.4,18,44 We have calculated apparent activation

Fig. 9 Room temperature IR spectra of Pd/Ce0.8Zr0.2O2 after various

treatments: reduction with D2 at 353 K, 10 min, evacuation at the

same temperature 0.5 h (A); samples from (A) after further evacuation

at 673 K, 4 h (B); and samples from (B) after further D2 adsorption at

373 K for 0.5 h and evacuation at the same temperature 0.5 h (C). (a)

Reference spectra after cleaning standard procedure (A) and further

evacuation (B). (b) 1 kPa of D2. (c) 30 kPa of D2. The spectra have

been normalized by the sample weight.

Table 4 Relative intensity of the IR band at 2120 cm�1 of Pd/Ce0.8Zr0.2O2 after treatment with D2 under different pressures (Fig.9): Pre-reduction at 353 K, 10 min (A); evacuation at 673 K, 4 h (B);and adsorption at 373 K, 0.5 h (C)

Fig. 90 kPa(curve a)

1 kPa(curve b) 3 kPaa

30 kPa(curve c)

A 0 0 1.1 2.3B 0 0 2.3 4.6C 0 3.8 5.1 5.1

a Not shown in Fig. 9.

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Page 9: Hydrogen adsorption kinetics on Pd/Ce0.8Zr0.2O2

energies of 160 kJ mol�1 (�6 kJ mol�1) and 42 kJ mol�1 (�4kJ mol�1) for CZ80 and Pd/CZ80, respectively (Fig. 3, inset).

The higher apparent activation energy obtained for CZ80 is

typical of an activated process, whereas the value for Pd/CZ80

reduction was associated with a bulk diffusion process. These

values are in good agreement with those reported under

similar experimental conditions for bare ceria after thermal

pretreatments.20

Isothermal hydrogen adsorption measurements for Pd/

CZ80 after pre-reduction at different pressures exhibit con-

siderable similarities with the overall kinetics, i.e. similar

temperature dependencies of the reduction rate throughout

the adsorption process and similar values of the apparent

activation energy, with higher values for the samples reduced

at higher pressure. All these features suggest a correlation

between the adsorption processes for the samples reduced at

6.6 and at 133 kPa. However, minor differences exist in the

quantitative aspects of the adsorption after reduction under

different H2 pressures. The hydrogen uptake during adsorp-

tion is higher for the sample reduced at 6.6 kPa with respect to

that reduced at 133 kPa. The occurrence of the irreversible

reduction in the last case is apparent from volumetric and

FTIR measurements (Fig. 9 and Table 4). Moreover, the total

hydrogen uptake during pre-reduction plus adsorption pro-

cesses is lower for the sample reduced at the lower pressure.

Although one possibility is that Pd21 was not completely

converted to Pd0 during reduction at 6.6 kPa, we believe that

irreversible reduction also occurs to a minor extent for the

sample reduced at 6.6 kPa. Moreover, the irreversible reduc-

tion observed in our experiments might be associated with the

presence of residual deuterium after desorption at 673 K. The

formation of bronze-like phases, which are stable at 373 K,

cannot be excluded.

From the previous discussion and also based on FTIR

information, it is clear that the adsorption rate after pre-

reduction at low pressure is much more rapid than the

corresponding adsorption rate at high pressure. In addition,

hydrogen adsorption after high reduction pressures proceeded

with a higher apparent activation energy (60 kJ mol�1)

than those reduced at low pressure in both static conditions

(50 kJ mol�1, Fig. 8) and flow conditions (40 kJ mol�1).

These results show a correlation between the extension of

irreversible reduction and the apparent activation energy.

The negative influence of Ce31 on the ability of noble metals

to activate/adsorb hydrogen was clearly demonstrated by a

combination of TEM and chemisorption experiments.45

Therefore, the observed difference in the kinetic behavior

can be attributed to a stronger electronic deactivation of the

metal during the reduction at high pressure. In fact, stronger

pre-reduction conditions leads to a higher degree of reduction/

presence of Ce31.

4 Conclusions

The present work shows that the hydrogen adsorption kinetics

of a high surface area Pd/CZ80 solid–solution is strongly

affected by hydrogen pressure used during the pre-reduction

step. The combined use of TPR measurements, IR spectro-

scopy and a protocol based on hydrogen reduction–desorption

–adsorption cycles has identified experimental conditions that

induce irreversible reduction. The use of high hydrogen pres-

sure during pre-reduction showed a negative effect on both

hydrogen uptake and adsorption rate. IR measurements de-

monstrated that during desorption, elimination of water oc-

curs with the simultaneous formation of oxygen vacancies.

The apparent activation energy calculated in the temperature

range 293–373 K increases with the hydrogen pressure from 50

kJ mol�1 (6.6 kPa) to 60 kJ mol�1 (133 kPa), showing a

correlation with the extension of irreversible reduction. The

difference in the kinetic behavior can be attributed to a

stronger electronic deactivation of the metal during reduction

at high pressure, due to the gradual deactivation with pressure

increase. The present results suggest that the observed deacti-

vation of the hydrogen chemisorptions capacity of

Pd/CexZr1�xO2 could be related both to the presence of

Ce31 and to dehydroxylation of the support surface.

Appendix: Kinetics information from non-isothermal

and isothermal measurements

Gas–solid reactions such as reductions are characterized by

complex kinetics, which frequently cannot be described by a

single nth-order expression over the complete reaction range. A

common feature of a reduction of a solid by hydrogen is that

the overall process may involve several intermediate steps:

adsorption, desorption, diffusion, chemical reaction, etc. In

addition, a great number of factors influence the reaction, such

as temperature, gas flow rate, size and shape of the particles,

surface characteristics, etc. Therefore, the identification of

rate-controlling steps is strongly dependent on the type of

sample and experimental conditions.

When the rate process occurs as a single well-defined

process, the reduction rate R may be expressed by means of

the following rate equation:46

R ¼ @a@t¼ KðTÞ � GðaÞ � FðPÞ ð2Þ

The overall reduction rate R is a function of the temperature,

T, the reduction degree, a, and the gas phase composition, P,

(hydrogen and water). The term K(T) is a function that

contains the Arrhenius equation, i.e. K(T) = A exp (�Eapp/

RT). The F(P) and G(a) functions depend on the gas composi-

tion and the structural evolution of the reacting solid, respec-

tively. The F(P) function is considered constant when the

experiments are carried out with only one feed composition

and differential conditions prevail in the reactor. In the case of

G(a), different mechanistic assumptions can be tested and a list

of reduction rate laws is available in Table 1.47,49 Eqn (2) was

written assuming separable variables, which is the case for

most common systems.

Under differential conditions, the gas phase composition

dependent term F(P) is approximately a constant. In this case,

eqn (2) can be expressed as

@a@t¼ KðTÞ � GðaÞ ð3Þ

For non-isothermal experiments, taking into account a

constant heating rate, b, and assuming an Arrhenius

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Page 10: Hydrogen adsorption kinetics on Pd/Ce0.8Zr0.2O2

dependence of the rate constant with the temperature, eqn (3)

can be rewritten as

@a@T¼ A

b� exp�Eapp=RT �GðaÞ ð4Þ

Kissinger has established a single method to estimate the

apparent activation energy without complete non-isothermal

curve fitting, which is based on the shift of the temperature,

Tm, of the rate maximum as a function of heating rate, b.37

Assuming that the conversion at rate maximum and the G(a)function are independent of the heating rate, and using

eqn (4), the following expression can be deduced:

lnbT2m

� �¼ � Eapp

RTmþ ln

AR

Eapp

� �þ C ð5Þ

Plotting ln (T2mb�1) versus T�1 gives a straight line with a

slope equal to Eapp/R, where R is the gas constant. No prior

knowledge of the kinetic model describing the reduction

mechanism is required in order to calculate Eapp. Wimmers

et al.47 have developed the same expression as eqn (5) and

showed that it is generally applicable for the determination of

the activation energy from conventional TPR measurements.

Using different approaches, the equations developed by

Gentry et al.48 and Monti and Backer10 are similar.

In the case of isothermal measurements, an alternative

procedure to evaluate the apparent activation energy can be

used.46 By substitution of the K(T) function by an Arrhenius

expression in eqn (2), rearranging and integrating, we obtain:

gðaÞ ¼Za

0

@aGðaÞ ¼ A� exp�Eapp=RT �FðPÞ � t ð6Þ

Taking the logarithm of both sides we obtain the following

expression:

lnðtÞ ¼ lngðaÞ

A� FðPÞ

� �þ Eapp

RTð7Þ

At a given reaction-degree, a, and at a constant gas phase

composition (F(P) = cte), the reaction mechanism does not

change with temperature. Based on this hypothesis, plotting ln

t as a function of the inverse of the temperature at conversion

constant, the slope gives the value of the apparent activation

energy (Eapp). No assumption about the controlling mechan-

ism step is required.

An alternative procedure for obtaining kinetic parameters

involves non-linear regression. In these complete model-fitting

techniques, a dynamic model for the gas–solid reaction is

proposed and its solution (by numerical computer codes) is

compared with experimental data. Generally, a single mechan-

ism will dominate and the rate-controlling step can be deter-

mined from experiments. In this case, from eqn (2) different

mechanistic assumptions for G(a) can be tested, including

models that describe diffusion-controlled processes, random

nucleation and growth processes and boundary-controlled

processes. A summary of the rate laws is listed in Table 1.

Typical analysis methods produce a lineal function (plotting

G(a) versus t) in which the slope reveals information regarding

the reaction mechanism. For isothermal reactions the conver-

sion can be expressed by the general equation describing

nucleation and growth processes

a = 1 � exp(�K tn) (8)

where a is the fraction reacted by time t, K is a constant

depending both on nucleation frequency and on the rate of

grain growth, and n is a constant associated with the geometry

of the system. Eqn (8) can be used in a more useful form,

known as the Avrami–Erofeev equation for n = 2, 3, and the

first-order kinetics for n = 1 (see Table 1):

[�ln(1 � a]1/n = k t (9)

in which k = K1/n. However, Hancock and Sharp49 have

demonstrated that eqn (8) provides an almost universal rela-

tion and it is the basis of a method of comparing kinetic data

for solid-state reactions, where different n values are possible.

Since integral values of n are typical of Avrami–Erofeev (or

Johnson–Mehl) equations, n values between 0.54 and 0.62 are

associated with diffusion-controlled reactions. Then, the rate-

limiting mechanism and the adequate kinetic expression are

ascertained from the value of n.

Acknowledgements

We wish to thank Prof. Mauro Graziani, University of Trieste,

for his support and helpful discussions. We also acknowledge

the University of Trieste and Centre of Excellence for Nano-

structured Material, INSTM, FISR2002 ‘‘Nanosistemi in-

organici ed ibridi per lo sviluppo e l’innovazione di celle a

combustibile’’, FIRB2001—contract no. RBNE0155X7,

CONICET (Consejo Nacional de Investigaciones Cientıficas

y Tecnicas) and ANPCyT (Agencia Nacional de Promocion

Cientıfica y Tecnologica) for partial financial support.

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