Experimental Microkinetic Approach of the Catalytic Oxidation of

Aug 9, 2010 - Energy Fuels , 2010, 24 (9), pp 4781–4792. DOI: 10.1021/ef100582w .... N.V. Vernikovskaya , T.L. Pavlova , V.V. Mokrinskii , D.Yu. Mur...
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Energy Fuels 2010, 24, 4781–4792 Published on Web 08/09/2010

: DOI:10.1021/ef100582w

Experimental Microkinetic Approach of the Catalytic Oxidation of Diesel Soot by Ceria Using Temperature-Programmed Experiments. Part 2: Kinetic Modeling of the Impact of the Ceria/Soot Contacts on the Rate of Oxidation Badr Bassou,† Nolven Guilhaume,† Karine Lombaert,‡ Claude Mirodatos,† and Daniel Bianchi*,† † Institut de Recherche sur la Catalyse et l’Environnement de Lyon (IRCELYON), UMR 5256 CNRS, Universit e Claude Bernard Lyon I, Bat. Chevreul, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne, France, and ‡Renault, Diesel Innovative Catalytic Materials, Direction de l’Ing enierie Mat eriaux, 1 All ee Cornuel, 91510 Lardy, France

Received May 8, 2010. Revised Manuscript Received July 19, 2010

An experimental microkinetic approach of the catalytic oxidation of diesel soots is developed considering mechanical mixtures of ceria and soot (ceria/soot weight ratio R) to mimic the situation of a catalyst-coated filter. Three ceria/soot mixtures denoted as TC-R = 10, TC-R = 1, and LC-R = 10 have been prepared according to the tight and loose contacts, respectively. Temperature-programmed experiments (without O2) performed on stabilized ceria/soot mixtures provide the rate of the CO2 production, RCO2(T), via the reaction between carbon defect sites Cf of the soot and oxygen species transferred by the ceria particles. The RCO2(T) curves present two peaks at low and high temperatures. The study is dedicated to the kinetic modeling of the RCO2(T) curves at low temperatures. According to the experimental microkinetic approach, two plausible kinetic models of the reaction have been selected on the basis of literature data; they differ from the implication or not of oxygen diffusion on the ceria surface. The mathematical kinetic formalisms, associated with the models, consider that the ceria/soot contacts constitute key kinetic parameters of the soot oxidation and their properties, such as the average number of contacts Nc between a ceria particle and the soot particles and the average surface sc of a contact, included in the kinetic equations. Different kinetic parameters have been obtained using experimental procedures, such as the activation energy of oxidation of the carbon defect sites (187 kJ/mol) and the Nc values for the different ceria/soot mixtures (i.e., Nc = 4.3 for TC-R = 10). It is shown that the microkinetic approach permits obtaining theoretical RCO2(T) curves consistent with the experimental data for the three mixtures, considering similar values of the kinetic parameters, except the Nc and R values. Moreover, the kinetic models have been extended to catalytic soot oxidation in the presence of O2 by including its adsorption on ceria. This study confirms the interest of the experimental microkinetic approach for the understanding of the key kinetic parameters controlling the catalytic soot oxidation. Moreover, it provides a mathematical formalism for the comparison of the performances of different solid catalysts, in particular for the development of new formulations.

concepts of the microkinetics,1 has been applied in our group to different catalytic systems, such as the oxidation of CO on Pt-supported particles,2-5 the photocatalytic oxidation of 2-propanol (IPA) on TiO2,6,7 the reconstruction of gold particles in the presence of CO,8 and the catalytic oxidation of diesel soots according to the fuel-borne catalytic process (denoted as FBC).9,10 In this last case, the experimental microkinetic approach has oriented the modification of the catalyst to decrease the light-off temperature of the soot.11

1. Introduction The experimental microkinetic approach consists of, determining by appropriated experimental procedures, the kinetic parameters of the surface elementary steps of a plausible kinetic model of a catalytic reaction. This allows for the evaluation a priori of the catalytic activity of the solid (for instance, expressed as the turnover frequency, TOF, in s-1) for different experimental conditions (i.e., temperature of the reaction and partial pressures of the reactants). The comparison between these theoretical values and the experimental measurements of the reaction rate validates the microkinetic approach, whereas a significant difference leads to the reconsideration of some elementary steps of the kinetic model. It must be noted that the different rates (global reaction and elementary steps) must be performed in the absence of physical processes (i.e., diffusion); this fixes the window validity of the experimental microkinetics. This approach, in line with the

(2) Bourane, A.; Bianchi, D. J. Catal. 2001, 202, 34–44. (3) Bourane, A.; Bianchi, D. J. Catal. 2002, 209, 126–134. (4) Bourane, A.; Bianchi, D. J. Catal. 2004, 222, 499–510. (5) Bourane, A.; Derrouiche, S.; Bianchi, D. J. Catal. 2004, 228, 288– 297. (6) Arsac, F.; Bianchi, D.; Chovelon, J. M.; Ferronato, C.; Herrmann, J. M. J. Phys. Chem. A 2006, 110 (2), 4202–4012. (7) Arsac, F.; Bianchi, D.; Chovelon, J. M.; Ferronato, C.; Herrmann, J. M. J. Phys. Chem. A 2006, 110 (2), 4213–4222. (8) Roze, E.; Quinet, E.; Caps, V.; Bianchi, D. J. Phys. Chem. C 2009, 113, 8194–8200. (9) Retailleau, L.; Vonarb, R.; Perrichon, V.; Jean, E.; Bianchi, D. Energy Fuels 2004, 18, 872–882. (10) Vonarb, R.; Hachimi, A.; Jean, E.; Bianchi, D. Energy Fuels 2005, 19, 35–48. (11) Bianchi, D.; Jean, E.; Ristori, A.; Vonarb, R. Energy Fuels 2005, 19, 1453–1461.

*To whom correspondence should be addressed. Telephone: 0033472431419. Fax: 0033472448114. E-mail: daniel.bianchi@ircelyon. univ-lyon1.fr. (1) Dumesic, J. A.; Rudd, D. F.; Aparicio, L. M.; Rekoske, J. E.; Trevi~ no, A. A. The Microkinetics of Heterogeneous Catalysis; American Chemical Society: Washington, D.C., 1993. r 2010 American Chemical Society

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standardized at 873 K for 3 h to remove NOx impurities.14 This was associated with a decrease in its surface area (156 m2/g) because of the limited stability of unpromoted CeO2.16 The experimental microkinetic approach of the impacts of CeO2 on the oxidation of the soots in the CCF process has been performed according to the “tight” and “loose” contacts defined by Neeft et al.12,13 Known amounts of soot and ceria were mixed either firmly in an agate mortar to obtain the tight contact (denoted as TC) or with a spatula until an “apparent” homogenization (on the basis of the color of the mixture) to obtain the loose contact (denoted as LC). Two ceria/soot weight ratios (denoted as R) have been studied, 10 and 1, leading to three mixtures denoted as TCR = 10, LC-R = 10, and TC-R = 1. The R values were of the order of magnitude of the effective ratios used by Neeft et al. in their TGA analysis, in the range of 2.5-35.13 According to Neeft et al.,12,13 the loose contact was representative of coated filters. However, Raman spectra have shown that the tight contact leads to a better homogeneity of the mixture14 that is favorable for the experimental microkinetic approach. 2.2. Analytical System for Transient Experiments. The analytic system and the experimental procedure have been described in detail in part 1 (10.1021/ef100581z).14 Briefly, various valves allowed us to perform controlled switches between regulated gas flows in the range of 100-1000 cm3/min (at the atmospheric pressure), which passed through a quartz microreactor (volume of ≈2 cm3) filled by the C-containing sample. The gas composition (molar fractions) at the outlet of the reactor was determined using a quadrupole mass spectrometer (with an analysis frequency of 0.66 Hz) after a calibration procedure with gas mixtures of known compositions (the accuracy was dependent upon the complexity of the gas mixture in the range of 2-10%). The temperature of the solid sample was simultaneously recorded, using a small K-type thermocouple (diameter Φ = 0.5 mm). This analytical system allowed us to perform TPEs (helium gas flow; heating rate, R) and isothermal adsorption of O2 using x% O2/y% Ar/He gas mixtures (Ar was a tracer showing the beginning of the consumption of O2).14 The main experiments performed to study the soot oxidation were as follows: a CeO2/soot mixture (weight in the range of 0.1-0.3 g) was introduced into the microreactor and heated in helium (100 cm3/min) to T = 473 K for 2 h to remove weakly adsorbed carbonate species on ceria.14 Then, the sample was cooled to 300 K in helium, and the temperature was progressively increased (R = 50 K/min), performing a first TPE in the temperature range of 300-1100 K. Then, the sample was cooled to 300 K, and after the adsorption of 1% O2/1% Ar/He, to quantify the total amount of oxygen provided by ceria to the soot, a new TPE was performed. These experiments (denoted as TPE/O2 adsorption cycles) are repeated, and the successive TPEs were denoted as TPE-i, with i being the rank in the series. During the different experiments, the evolutions of the molar fractions of the gases were determined using mass spectrometry (MS); they provided the rates of chemical processes as a function of the temperature for TPE-i. The successive TPE-i led to the progressive oxidation of the soot, establishing a correlation between the amount of oxygen transferred from ceria to soot and the soot conversion.14 TPEs in the presence of O2 (denoted as O2-TPO) have also been performed using similar experimental conditions with x% O2/y% Ar/He gas mixtures, with x and y in the range of 1-5. They provided the rates of CO2 and CO productions and O2 consumption as a function of the temperature.

The present study is dedicated to the microkinetic approach of the catalytic oxidation of diesel soots in the situation of a coated filter (denoted as catalyst-coated filter or CCF). The difference with the FBC process is that the ceria/soot contacts are obtained mechanically, and this may modify a priori the kinetic parameters controlling the soot oxidation. Classically, to prevent experimental difficulties, the CCF process is studied using the tight and loose contact concepts proposed by Neeft et al.12,13 This consists of mimicking different situations encountered in a coated filter by (i) mixing soot and ceria either mechanically in an agate mortar (tight contact) or with a spatula (loose contact) and (ii) using different ceria/soot weight ratios, R (with R > 1). In part 1 (10.1021/ef100581z),14 we have shown how temperature-programmed experiments (denoted as TPEs) in the presence and absence of O2 provide data on the impacts of the ceria/soot mixtures on the soot oxidation. In particular, successive TPEs of the ceria/soot mixtures, similar to the classical temperature-programmed reduction (TPR) of ceria by either H2 or CO, followed by O2 adsorption at 300 K, have shown that, after a decrease during the first three TPE/O2 adsorption cycles, the amount of oxygen transferred from ceria to the soot remains constant with the progressive oxidation of the soot, regardless of the ceria/soot mixture. However, the amount of oxygen available for the soot oxidation (in μmol of O/g of soot) is dependent upon the ceria/soot mixture; it is favored by a tight contact and a high R value. Moreover, we have shown that this amount appears correlated to the catalytic performances of ceria to decrease the temperature of the soot oxidation by O2.14 The present experimental microkinetic approach is mainly dedicated to the kinetic modeling of TPE experiments (in the absence of O2) for three ceria/soot mixtures with an extension to experiments in the presence of O2. This allows us to reveal that the main impact of the type of ceria/soot mixture on the rate of the soot oxidation is linked to differences in the properties of the ceria/soot contacts (described as kinetic parameters) and not to a significant modification of the activation energies of the surface elementary steps. To our knowledge, it is the first time that the ceria/soot contacts are considered at this level of description of the kinetic of the catalytic oxidation of the soot by a metal oxide catalyst. 2. Experimental Section 2.1. Material and Pretreatment Procedures. In part 1 (10.1021/ ef100581z),14 we have shown that, after a standardization for 8 h in air at 673 K, diesel soots collected on SiC filters and a commercial model soot, Printex U from Degussa, have similar surface properties, considering the amount of surface-oxygenated complexes in μmol of SOCs/g of soot. For Printex U, this treatment led to its oxidation (24% of the soot), associated with an increase in the surface area from 110 to 510 m2/g, in agreement with the literature data.15 In the present study, only standardized Printex U has been used, to prevent considering that the observations were associated with the homemade diesel soots. Ceria used for the catalytic oxidation of the soots was provided by Rhodia (HSA; surface area, 325 m2/g). It was

3. Results (12) Neeft, J. P. A.; Makkee, M.; Moulijn, J. A. Chem. Eng. J. 1996, 64, 295–302. (13) Neeft, J. P. A.; van Pruissen, O. P.; Makkee, M.; Moulijn, J. A. Appl. Catal., B 1997, 12, 21–31. (14) Bassou, B.; Guilhaume, N.; Lombaert, K.; Mirodatos, C.; Bianchi, D. Energy Fuels 2010, 24, DOI: 10.1021/ef100581z. (15) Yezerets, A.; Currier, N. W.; Kim, D. H.; Eadler, H. A.; Epling, W. S.; Peden, C. H. F. Appl. Catal., B 2005, 61, 120–129.

The experimental microkinetic approach of a heterogeneous gas/solid catalytic reaction is based on a plausible kinetic model that fixes the surface elementary steps that must (16) Perrichon, V.; Laachir, A.; Abouarnadasse, S.; Touret, O.; Blanchard, G. Appl. Catal., A 1995, 129, 69–82.

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be studied by experimental procedures, for the evaluation of their kinetic parameters (i.e., coverage of the adsorbed species, rate constants, and activation energies), to determine those controlling the global rate of the reaction in the absence of contributions of physical processes.2-10 For the CO2 and CO productions during TPE, this model is based on the plausible elementary steps considered for the non-catalytic and catalytic oxidation of carbon material.9,10,17,18 3.1. Plausible Kinetic Model for the Catalytic Oxidation of the Soot. In previous studies dedicated to the FBC process using ceria,9-11 the plausible kinetic model for TPE was based on the unified mechanism for the non-catalytic and catalytic oxidation of C-containing materials proposed by the Moulijn group.17,18 A similar model is used in the present study, and we summarize briefly the literature data supporting the proposal. It is well-known that different SOCs are present on the surface of carbon materials (carboxylic, lactones, carbonyl, ketone, ester, carboxylic anhydric, quinone, semiquinone, and pyrone) in amounts depending upon the solid preparation and pretreatment procedures. The stabilities of these SOCs and their amounts on the soot surface (μmol of SOCs/ m2) have been studied by temperature-programmed desorption (TPD) procedures; strongly overlapped CO2 and CO peaks are observed in the temperature range of 400-900 and 400-1100 K, respectively.19-28 It is considered that the desorption of a SOC produces either CO or CO2, except for the anhydride.28 The TPD spectra provide the activation energies of desorption/decomposition of the different SOCs, forming CO2 and CO that are in the range of 117-322 kJ/ mol (seven species) and 142-376 kJ/mol (eight species), respectively,25 indicating that the less stable SOCs desorb as CO2 and the more stable SOCs desorb as CO. In part 1 (10.1021/ef100581z),14 it has been shown that TPD of the standardized Printex U leads to the desorption of CO2 for Td > 600 K and CO for Td > 700 K according to broad peaks, indicating that several SOCs are involved, in agreement with the literature data.19-28 CO and CO2 productions from the standardized Printex U were 4010 and 944 μmol/g, respectively, indicating that the total amount of SOCs desorbed, 4954 μmol of SOCs/g, represents roughly a coverage of 0.55 of the soot surface (assuming 1019 SOCs/m2 at full coverage). This means that the first TPE experiment of a ceria/soot mixture is dominated by the properties (desorption and oxidation) of the SOCs, preventing the evaluation of the oxygen transfer from ceria to soot from the CO2 and CO productions. According to the microkinetic approach of the

soot oxidation, the desorption of a SOC appears as the last step of the plausible kinetic model. For the non-catalytic oxidation of the carbon material, the desorption of the SOCs creates surface-defect sites (denoted as Cf, CCf, or CnCCf, where Cn is the bulk of the soot), which may react with O2 to form SOCs of different stabilities according to two elementary steps17,18 S1 : Cn CCf þ 1=2O2 f Cn CCf ðOÞ ðSOC of high stability; desorbing as COÞ

ð1Þ

S2 : Cn CCf ðOÞ þ 1=2O2 f Cn CðOÞCf ðOÞ ðSOC of limited stability; desorbing as CO2 Þ

ð2Þ

Steps S1 and S2 do not consider the nature of the SOCs. The desorption/decomposition of the SOCs contribute to the soot oxidation via the production of CO and CO2 according to17,18 S3 : Cn CðOÞCf ðOÞ f Cn - 1 CCf ðOÞ þ CO ð3Þ S4 : Cn CCf ðOÞ f Cn - 1 CCf þ CO

ð4Þ

S5 : Cn CðOÞCf ðOÞ f Cn - 1 CCf þ CO2

ð5Þ

Steps S1 and S2 can be slightly modified in the presence of O2 by introducing an adsorption step, such as17,18 S0 : 2Cf þ O2 f 2Cf ðOads Þ ð6Þ S1a : Cn CCf þ Cf ðOads Þ f Cn CCf ðOÞ þ Cf S2a : Cn CCf ðOÞ þ Cf ðOads Þ f Cn CðOÞCf ðOÞ þ Cf

ð7Þ ð8Þ

Step S0 allows for the differentiation of the non-catalytic and catalytic oxidation of the soot. It can be considered that the role of a solid catalyst, such as CeO2, is to provide oxygen species to the soot at a lower temperature than with pure soot according to ð9Þ S1b : Osce þ Cn CCf f Cn CCf ðOÞ S2b : Osce þ Cn CCf ðOÞ f Cn CðOÞCf ðOÞ

ð10Þ

where Osce is an oxygen of the ceria surface. In the absence of O2, a TPE of a ceria/soot mixture leads to the reduction of the catalyst (CeO2-x) via steps S1b and S2b. These surface elementary steps assume that there is a close contact between ceria and Cf sites, i.e., reaction at the ceria/soot interface. However, it can be considered that diffusion processes are involved in the oxygen transfer according to S1c : ðOsce Þ þ soot f sootðOss Þ

(17) Moulijn, J. A.; Kapteijn, F. Carbon 1995, 33, 1155–1165. (18) Chen, S. G.; Yang, R. T.; Kapteijn, F.; Moulijn, J. A. Ind. Eng. Chem. Res. 1993, 32, 2835–2840. (19) Kyotani, T.; Zhang-Guo, Z.; Hayashi, S.; Tomota, A. Energy Fuels 1988, 2, 136–141. (20) Du, Z.; Sarafin, A. F.; Longwell, J. P. Energy Fuels 1990, 4, 296– 302. (21) Huttinger, K. J.; Nill, J. S. Carbon 1990, 28, 457–465. (22) Brown, T. C.; Haynes, B. S. Energy Fuels 1992, 6, 154–159. (23) Pan, Z.; Yang, R. T. Ind. Eng. Chem. Res. 1992, 31, 2675–2680. (24) Marchon, B.; Tysoe, W. T.; Carrazza, J.; Heinemann, H.; Somorjai, G. A. J. Phys. Chem. 1988, 92, 5744–5749. (25) Haydar, S.; Moreno-Castilla, C.; Ferro-Garcia, M. A.; CarrascoMarin, F.; Rivera-Utrilla, J.; Perrard, A.; Joly, J. P. Carbon 2000, 38, 1297–1308. (26) Szymanski, G. S.; Karpinski, Z.; Biniak, S.; Swiatkowski, A. Carbon 2002, 40, 2627–2639. (27) Domingo-Garcia, M.; Lopez Garzon, F. J.; Perez-Mendoza, M. J. J. Colloid Interface Sci. 2002, 248, 116–122. (28) Figueiredo, J. L.; Pereira, M. F. R.; Freitas, M. M. A.; Orfao, J. J. M. Carbon 1999, 37, 1379–1389.

ðsurface diffusion at the contact ceria=sootÞ

ð11Þ

S2c : Oss þ Cn CCf f Cn CCf ðOÞ

ð12Þ

S3c : Oss þ Cn CCf ðOÞ f Cn CðOÞCf ðOÞ

ð13Þ

For the FBC process, calculations have indicated that the Os diffusion is limited to a short distance from its source,10 signifying that it is difficult to discriminate between steps S1b and S2b and steps S1c, S2c and S3c. In the absence of O2, the diffusion of oxygen from the bulk to the surface of the catalyst particles can also be considered, such as ð14Þ S4 : Obce f Osce This leads to the view that two oxygen reservoirs are available in ceria (the surface and the bulk oxygen species). In the 4783

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presence of O2, the oxygen reservoirs of the catalyst are maintained via the adsorption step S0b : O2 f 2Osce

ð15Þ

Finally, the plausible kinetic model supporting the experimental microkinetic approach of the catalytic oxidation of the soot is constituted by the following elementary steps S0a or S0b, followed by either S1b and S2b or S1c, S2c, and S3c, and the mechanism is ended by steps S3, S4, and S5 for the CO2 and CO productions. Whatever the choice of the elementary steps, the ceria/soot contacts are key parameters in the kinetic model of the catalytic soot oxidation; their dependence upon the type of ceria/soot mixture must be formalized in the kinetic equations. For the FBC process, the contacts were assumed permanent during the soot oxidation,9,10 because of ceria particles, formed simultaneously with the soot, were well-dispersed on the soot. In part 1 (10.1021/ ef100581z),14 we have shown that this is also true for the mechanical mixtures, except for TPE-i, with i < 3, where different processes occur in parallel to the soot oxidation, such as the accumulation of strongly adsorbed carbonate on ceria and the sintering of the ceria particles that decreases its capacity to provide oxygen.14 For the study of the FBC process,9,10 we have not formalized the ceria/soot contacts as a kinetic parameter because a single ceria/soot mixture was used; the contacts were assumed constant. In the present study, mainly in dedication to the kinetic modeling of the rate of the CO2 production [denoted as RCO2(T)] during TPE of CeO2/soot mixtures because of the oxidation of the soot by the oxygen species of ceria, the experimental conditions simplify the description of the plausible kinetic model. 3.2. TPE/O2 Adsorption Cycles of the Ceria/Soot Mixtures. These data have been described in detail in part 1 (10.1021/ef100581z.14 However, they are briefly summarized to facilitate the presentation and to fix the main aims of the microkinetic approach of the present study. For the three ceria/soot mixtures, the rates of the CO2 and CO productions during the first TPE14 are due to the overlap of different processes, such as (i) the desorption of the SOCs of the standardized soot, (ii) the oxidation of the soot by oxygen species provided by ceria, (iii) the oxidation of CO by ceria, and (iv) the formation of strongly adsorbed carbonate species on ceria. After this first TPE, the main part of the SOCs has been removed from the soot-forming carbon surface-defect sites Cf (eqs 3-5), whereas ceria has been saturated by strongly adsorbed carbonates.14 This indicates that, after the adsorption of O2 at 300 K, the following TPEs are dominated by the oxidation of the Cf sites by the oxygen species provided by ceria (eqs 9 and 10). However, three successive TPE/O2 cycles must be performed to obtain reproducible data, such as the evolution of the rate of the CO2 production with the temperature [denoted as RCO2(T )] and the adsorption of O2 at 300 K (i.e., the ceria/soot interface is stabilized after three cycles). For the three ceria/soot mixtures, the experimental data exploited in the present study are obtained for TPE-i, with i > 3. This allows for the development of the microkinetic approach of the RCO2(T) curves via the oxygen species of ceria and the Cf sites of the soot. However, TPD of the pure standardized Printex U has shown that the CO production is not ending at 1100 K,14 indicating that a small fraction of SOCs may remain on the soot surface and their oxidation may contribute slightly to RCO2(T).

Figure 1. Rate of CO2 productions as a function of the temperature [RCO2(T)] during TPE-i (i > 3) for T < 970 K for three ceria/soot mixtures: (a) TC-R = 10, (b) LC-R = 10, and (c) TC-R = 1. (Inset) Evolution of the molar fractions of CO2, CO, and O2 during TPE of TC-R = 10.

The total amount of oxygen provided by ceria during a TPE is quantified by the oxygen consumption during the adsorption of 1% O2/1% Ar/He at 300 K.14 For the three ceria/soot mixtures, it has been shown that this amount decreases progressively for TPE-i/O2 cycles (i < 3) and then remains roughly constant (taking into account the accuracy of the analytical procedure). The decrease in the amount of oxygen available for the soot oxidation is due to different processes on ceria, such as the sintering of the particles and the formation of strongly adsorbed carbonates. The inset in Figure 1 shows CO2, CO, and O2 productions during TPE-4 for TC-R = 10; O2 (10 μmol of O2/g of ceria) and CO (113 μmol of CO/g of soot) are detected at T < 440 K and T > 980 K, respectively, whereas two CO2 peaks are observed in the temperature range of 440-1100 K (total amount of 508 μmol/g). These data are reproducible for the following TPE-i (9 g i > 4). Similar results are obtained with the other ceria/ soot mixtures, and Figure 1 provides the RCO2(T) curves at low temperatures (first CO2 peak) for TC-R = 10, TC-R = 1, and LC-R = 10. After TPE-i (9 g i g 4), the amounts of O2 adsorption at 300 K on the three ceria/soot mixtures are reproducible, 64, 94, and 46 μmol of O2/g of ceria for TCR = 10, TC-R = 1, and LC-R = 10, respectively. In the inset of Figure 1, the broad O2 peak at T < 473 K (also observed with different intensities for TC-R = 1 and LC-R = 10) is ascribed to the desorption of peroxide or superoxide species, O2δ- (δ = 1 or 2), formed on surface-defect cerium sites of the reduced ceria, during the adsorption of O2 at 300 K.14 However, it can be observed (inset of Figure 1) that these O2δspecies desorb before the appearance of CO2, suggesting that they are not involved in the elementary steps of the soot oxidation.14 Taking into account that, for TPE-i/O2 cycles (i > 3), (i) the RCO2(T) and (ii) the amount of oxygen adsorbed at 300 K are reproducible for the three ceria/soot mixtures, it can be considered that the ceria/soot contacts are maintained during the progressive oxidation of the soot,14 in agreement with the environmental transmission electron microscopy (TEM) study by Simonsen et al.29 The inset in Figure 1 shows that, for TC-R = 10, RCO2(T) presents two main peaks at Tm ≈ 810 K and Tm > 1100 K. This is also the situation for TC-R = 1 and LC-R=10.14 This indicates that there are two reservoirs of reactants (either oxygen species or Cf sites) with different kinetic parameters. (29) Simonsen, S. B.; Dahl, S.; Johnson, E.; Helveg, S. J. Catal. 2008, 255, 1–5.

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In the relationship with the catalytic oxidation of the soot by ceria, it must be noted that the oxygen species of ceria that may decrease the light-off temperature of the soot oxidation is providing the first broad CO2 peak (for T > 980 K, the soot surface may activate O2). For TC-R = 10, an approximate deconvolution of the peak at Tm = 810 K indicates that the amount of CO2 production is 154 μmol of CO2/g of soot because of the reaction of 154 μmol of C/g of soot with 30.8 μmol of O/g of ceria (ceria/soot weight ratio R = 10). This amount can be compared to the adsorption of O2 at 300 K, 64 μmol of O2/g of ceria. However, the amount of O2 desorbing as Oδ- is of 10 μmol/g of ceria, indicating that 54 μmol of O2/g of ceria (or 108 μmol of O/g of ceria or 1080 μmol of O/g of soot) is involved in the soot oxidation. This amount is consistent (considering the accuracy to the analytical procedure) with the total amount of CO2 and CO productions during TPE, (508  2 þ 113) = 1129 μmol of O/g of soot. Finally, only ≈28% of the oxygen provided by ceria is involved in the first CO2 peak, which is of interest to the catalytic soot oxidation. From these calculations and in the relationship with the catalytic oxidation of the soot, it appears that the kinetic modeling of the first peak of CO2 (Figure 1) must reveal the key kinetic parameters, allowing for the decrease in the oxidation temperature of the soot. This justifies that the aim of the experimental microkinetic approach of the present study is to provide, for the three ceria/soot mixtures, a kinetic modeling of the evolution of the rate of the CO2 production RCO2(T) during a TPE (for TPE-i, i > 3) at T < 950 K. 3.3. Plausible Kinetic Model for the TP Experiments and Associated Kinetic Formalism. 3.3.1. Plausible Kinetic Model. In comparison to the oxidation of the soot in the presence of O2, TPE-i (i > 3) experiments implicate only the oxygen species of the ceria catalyst and the carbon defect sites of the soot formed by the removal of the SOCs. This significantly simplifies the plausible kinetic model for the modeling of the RCO2(T) curves during TPE. Two kinetic models M1 and M2 have been considered by selecting surface elementary steps from eqs 1-15 and slightly modifying the notation. The surface elementary steps of M1 are Oasce þ Cn - Caf f Cn Caf ðOÞ rate constant kra , activation energy Era

The location of the Oasce and Caf species for the ceria soot mixtures involved in model M1 must be clearly specified. In a previous work dedicated to a microkinetic approach of the FBC process, it was considered that the active oxygen species of ceria were provided to the soot by a diffusion step before their reaction with a Cf site. However, calculations have indicated that the diffusion is limited to a very short distance from the source, signifying that the active oxygen and Cf are in close contact. This facilitates the mathematical formalism to implicate the ceria/soot contact as a kinetic parameter of the soot oxidation; the Oasce and Caf species involved in eq 16 are the oxygen species of ceria (Osce) and the Cf species of the soot, respectively, which are situated on the interface between the two solids. The first RCO2(T) peak in Figure 1 indicates that one of the two reactants Oasce or Caf is progressively consumed in parallel to the CO2 production. It seems excluded that this reactant is Caf because (i) the ceria/soot contact is maintained during the soot oxidation14 and (ii) a large amount of soot remains after TPE-i (i < 9). The fact that the Oasce species are progressively consumed seems at first contradictory to the increase of RCO2(T) at high temperatures, forming the second RCO2(T) peak (inset of Figure 1). However, this can be explained considering that ceria has two oxygen reservoirs that are involved within different temperature ranges during TPE. The first reservoir is constituted by the Oasce species, and the second reservoir is constituted by oxygen species of ceria that are not in contact with the soot surface, surface (Osce) and bulk (Obce) oxygen species. The size of this second reservoir must be significantly larger than that of the Oasce species. The Osce and Obce species may diffuse on the surface of ceria at the contact with the soot, forming new Oasce at temperatures depending upon their activation energy of diffusion (a priori, the diffusion of Osce must precede that of Obce). This means that the amount of Oasce species must decrease during the soot oxidation until a temperature is obtained allowing for the diffusion of the Osce species according to Osce f Oasce

ð19Þ

ð16Þ

A similar reaction can be considered for Obce possibly via the intermediate formation of Osce according to eq 14. The surface elementary steps of model M1 (eqs 16-18) and eq 19 constitute the plausible kinetic model M2 involved in the TPE at high temperatures. 3.3.2. Mathematical Formalism Associated with the Plausible Kinetic Models. Equations 16-18 lead to different kinetic equations, allowing for the modeling of the rate of the CO2 production during TPE. Considering that a TPE experiment consists of the reduction of ceria by the soot, we adopt the view that the kinetic formalism must be similar to that of the reduction of ceria by a gaseous reactant, such as CO (via the formation of active adsorbed CO species); the Cf sites in contact with ceria behave like the adsorbed CO species. This leads us to reference the surface concentrations of the different adsorbed species (Oasce, Caf, and intermediate adsorbed species) to ceria, i.e., μmol of Oasce (or active Caf)/ m2 of ceria, and the rate of CO2 production RCO2(T) is provided with the unit of molecules of CO2 m-2 of CeO2 s-1. This unit can be converted to CO2 g-1 of soot s-1 considering the surface area of the stabilized ceria and the ceria/soot weight ratio.

Oasce þ Cn Caf ðOÞ f Cn OCaf ðOÞ rate constant krb , activation energy Erb ð17Þ Cn OCaf ðOÞ f CO2 þ Cn - 1 - Caf desorption of the SOC as CO2

rate constant kdif , activation energy Edif

ð18Þ

In eqs 16 and 17, Oasce and Caf represent an active surface oxygen species of ceria and an active carbon defect site on the soot, respectively. Note that, after three successive TPEs, (i) the carbon defect sites represent the main reactants on the soot surface (the contribution of the remaining SOCs to the CO2 production must be very limited), justifying that only eq 16 is involved in the first stage of the kinetic modeling, and (ii) the absence of CO desorption during TPE for T < 950 K (Figure 1 and ref 14) prevents considering in model M1 an elementary step, such as S4 (eq 4). The rate of desorption of the CnCaf(O) species formed in eq 16 must be very low, as compared to that of oxidation (eq 17), because of high activation energies of desorption in agreement with literature data for SOCs desorbing as CO.25 4785

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In line with the mean field approximation, the RCO2(T) curve from the kinetic model M1 (eqs 16-18) is obtained according to the following set of kinetic equations. Rate of consumption of the active oxygen species:@ -

d½Oasce  ¼ kra ½Oasce ½Caf  þ krb ½Oasce ½Caf ðOÞ dt

The elementary step of eq 27 controls the diffusion process, according to a rate similar to that of a desorption of a first kinetic order. The contribution of diffusion of Osce species leads to the modification of eq 20 for model M2 - d½Oasce  ¼ kra ½Oasce ½Caf  þ krb ½Oasce ½Caf ðOÞ - kdf ½Osce  dt ð29Þ

ð20Þ

Rate of production of the first intermediate SOC species: d½Caf ðOÞ ¼ kra ½Oasce ½Caf  - krb ½Oasce ½Caf ðOÞ ð21Þ dt

The kinetic modeling of the RCO2(T) curves during a TPE can be performed using eqs 19-27. However, in line with the experimental microkinetics approach of catalytic processes,2-8 different kinetic parameters must be evaluated by specific experimental procedures. This has been performed using the TC-R = 10 ceria/soot mixture. 3.4. Measurement of Kinetic Parameters of the Plausible Kinetic Model of TPE for TC-R = 10. These measurements constitute a crucial step of the procedure because they limit the number of variables used to compare the experimental and theoretical RCO2(T) curves. 3.4.1. Activation Energy Era of the Elementary Step eq 16. According to eq 16, the rate constant kra (or its activation energy) can be obtained via the measurement of either the rate of the oxygen consumption or the rate of oxidation of the Caf species at the beginning of the soot oxidation, when [Oasce] and [Caf] can be considered as constant [low amount of Caf(O) species]. The mesurement of the rate of Oasce consumption during TPE is very difficult; for instance, it can be suggested to follow the rate of appearance of Ce3þ formed by the reduction of ceria by the soot, using magnetic susceptibility measurements.9 However, there is an overlap with the production of Ce3þ by the desorption of the O2δspecies. The activation energy of the rate constant kra has been measured according to the following experiment. After TPE-6, the adsorption of O2 is performed at 300 K according to the switch He f 1% O2/1% Ar/He and then the temperature is increased (50 K/min) in the presence of O2 (1% O2TPO). Figure 2 shows the evolution of the molar fractions of O2, Ar, and CO2 (there is no CO production). For T < 490 K, it can be observed that the molar fraction of O2 increases according to a broad peak because of the desorption of the O2δ- species; this confirms that they are not significantly involved in the soot oxidation.14 For T > 490 K, the molar fraction of oxygen decreases before the apperance of CO2 in the gas phase. This is consistent with eqs 19-21; the CO2 production may start after the formation of an amount of Caf(O) and OCaf(O). We have previously shown, in agreement with literature data, that the rate of adsorption of oxygen on a reduced ceria is very high, at 300 K.9,11,14 This allows for the consideration that (i) the rate of oxygen consumption in Figure 2, RO2(T), provides the rate of oxidation of the Caf species, RCaf(T)=1/2RO2(T), and (ii) the amount of Oasce species remains constant in the presence of O2. At the beginning of the O2 consumption, the amounts of Caf and Caf(O) can be considered as constant and negligible, respectively, indicating that RO2(T) at low oxygen conversion is only due to eq 16. Figure 3 provides ln[RO2(T)] = f(1/T) at low O2 conversion (symbols b), and the straight line leads to an activation energy of Era=184 ( 5 kJ/mol. This activation energy corresponds to a full coverage of the Oasce species. Considering that ceria cannot be reduced deeper than CeO2-x, with x in the range 0.18-0.20 according to the specific surface area of the solid,32

Rate of production of the second intermediate SOC species desorbing as CO2: d½OCaf ðOÞ ¼ krb ½Oasce ½Caf ðOÞ - kd ½OCaf ðOÞ ð22Þ dt Rate of the CO2 production [RCO2(T)]: dCO2 ¼ kd ½OCaf ðOÞ dt

ð23Þ

where [Oasce] and [Caf] denote the surface concentration of the active species (units of molecules/m2 of CeO2). Similarly, [Cf(O)] and [OCf(O)] represent the surface concentration of intermediate species {units of molecules of Cf(O) [or OCf(O)]/m2 of CeO2}. The two surface concentrations [Oasce] and [Caf] can be related to different parameters linked to ceria and soot particles. For instance, considering that (i) NpCeO2 is the number of ceria particles per m2 of ceria, (ii) Nc is the average number of contacts between a ceria particle and the soot particles, and (iii) sc is the average surface of a contact ceria/ soot, then the total surface of contact between ceria and soot is ScT ¼ NPCeO2 Nc sc

ðunits of m2 of contact=m2 of ceriaÞ ð24Þ

When [Osce] is denoted as the surface concentration of oxygen species on a ceria surface that can be reduced by a reactant, then the surface concentration of the active oxygen species on ceria during the soot oxidation is ð25Þ ½Oasce  ¼ ½Osce ScT ¼ ½Osce NPCeO2 Nc sc where the unit of [Oasce] is active oxygen species/m2 of ceria. Similarly, when [Cf] is denoted as the surface concentration of the carbon defect sites on the soot surface, then ð26Þ ½Caf  ¼ ½Cf ScT ¼ ½Cf NPCeO2 Nc sc where the unit of [Caf] is molecules of Caf/m2 of ceria. At high temperatures, model M2 includes the diffusion of oxygen species (eqs 14-19. It is known that the activation energy of diffusion of adsorbed species is a fraction (corrugation coefficient) of that of desorption.30,31 Taking into account the temperature range of the TPE, implying the Osce species, we consider that the diffusion process (eq 19) can be decomposed into two surface elementary steps: the formation of the diffusing species O*, followed by its fast diffusion to form Oasce species at the ceria/soot contact according to ð27Þ Osce f O rate constant kdf O f Oacsce

ð28Þ

(30) Seebauer, E. G.; Allen, C. E. Prog. Surf. Sci. 1955, 49, 265–330. (31) Tompkin, F. C. Chemisorption of Gases on Metal; Academic Press: London, U.K., 1978.

(32) Perrichon, V.; Laachir, A.; Bergeret, G.; Frety, R.; Tournayan, L.; Touret, O. J. Chem. Soc., Faraday Trans. 1994, 90, 773–781.

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bulk oxygen species, respectively, according to H2 þ Oads f H2O.32,34,35 Perrichon et al.32 using a ceria sample from Rhodia (similar to the present sample) have shown that the amount of hydrogen consumption (μmol/g of ceria) by the oxygen surface species decreases linearly with the decrease in the specific Brunauer-Emmett-Teller (BET) surface area of the sample (see Figure 2 in ref 32). This relationship has been confirmed using magnetic susceptibility measurements. The slope of the straight line provides the amount of hydrogen consumed by m2 of ceria that is estimated in the range of 3.1-4.2 μmol H2/m2 (according to deconvolution procedures used to exploit the response of a thermal conductivity detector), independent of the surface area of ceria. This amount leads to the estimation of [Osce] in the range from 1.8  1018 to 2.5  1018 μmol of Osce/m2 of ceria.32 H2-TPR experiments similar to previous studies32,34,35 have been performed on the present standardized ceria using 1% H2/1% Ar/He. We have observed that the reduction of ceria by hydrogen at high temperatures leads to a significant decrease in the surface area of the solid that is consistent with the literature data.32,35 For the quantification of [Osce], this imposes measuring the surface area of the sample before and after the H2-TPR according to the following experimental procedure using the MS system. The standardized ceria is treated in helium to 873 K and then cooled to 77 K. Its surface area is measured using x% N2/He gas mixtures (x = 10 and 5) as follows: a switch He f 5% N2/ He is performed at 77 K until the same molar fraction is obtained at the inlet and outlet of the reactor (adsorption equilibrium), and then the temperature of the microreactor is progressively increased to 300 K in the presence of 5% N2/He, leading to the detection of a N2 peak that provides the amount of adsorbed nitrogen at 77 K, QN2ads. After a switch 5% N2/ He f He, the temperature is decreased to 77 K and the same procedure is applied using 10% N2/He. The amount of N2 in the monolayer QN2-M that provides the surface area of ceria is obtained using the classical BET equation (with the simplification for C . 1). After the measurement of the surface area, H2-TPR of ceria is performed in the temperature range of 300-1100 K using 1% H2/1% Ar/He (see Figure 4). Similar to the literature data, two hydrogen consumption peaks have been observed at T < 880 K and T > 900 K, ascribed to surface and bulk oxygen species (in the present study, the second peak is not ending at 1100 K).32,34,35 After the H2-TPR, the solid is cooled in helium to 300 K and a switch He f 1% O2/ 1% Ar/He is performed for the reoxidation of the reduced ceria, followed by heating (30 K/min) to 713 K to remove the O2δ- species. After the solid is cooled in helium to 77 K, the surface area of the solid is measured according to the above procedure. Successive H2-TPR/surface area measurement cycles are performed until a pseudo-stable surface area is obtained for ceria that is favorable for the measurement of [Osce]. During the first two cycles, the surface area of ceria decreases significantly (65 m2/g) and the values before and after the H2-TPR are significantly different. Figure 4 gives the evolution of the hydrogen consumption during the H2-TPR of the stabilized solid after five H2-TPR/O2 adsorption cycles; the surface area is ≈27 m2/g before and after the H2-TPR (the inset of Figure 4 shows the desorption of N2 during heating from 77 to 300 K under 5% N2/He). The amount of hydrogen consumption in the first peak with a maximum at TM = 868 K and a shoulder at 737 K because of the reduction of the Osce

Figure 2. Evolution of the molar fractions of CO2, O2, and Ar and T during TPO with 1% O2/1% Ar/He for TC-R = 10 after TPE-i (i > 3).

Figure 3. Determination of the activation energy of oxygen consumption during 1% O2-TPO using low temperatures. (b) Experimental data.

it must be considered that Era increases with the decrease in the amount of Oasce species. 3.4.2. Values of the Parameters Providing [Oasce] and [Caf ] in eqs 26 and 27. 3.4.2.1. Surface Concentration of the Oasce Species before TPE. The specific surface area of ceria after several successive TPEs at high temperatures is SBET-ceria ≈ 50 m2/g.14 This provides an average particle diameter of Dp = 17 nm. The average surface, volume, and weight of a particle are SPceO2 = 4π(D/2)2, VPCeO2 = 4/3π(D/2)3, and mPCeO2 = 4/3π(D/2)3F, respectively, with F = 7.1 g/cm3. This provides NPCeO2 =1/(SBETmPCeO2) =1.1  1015 particles/m2 of CeO2. The amount of CO2 produced in the first peak of Figure 1, 154 μmol of CO2/g of soot, gives the amount of Oasce, 30.8 μmol/g of ceria, leading to [Oasce]=3.7  1017 Oasce species/m2 of ceria. 3.4.2.2. Average Number of Contacts between a Ceria Particle and the Soot Particles. According to eq 25, the average number of contacts Nc between a ceria particle and the soot particles can be obtained knowing [Osce] (the concentration of reductible oxygen on ceria) and sc (the average surface area of a ceria/soot contact). The sc values can be estimated as follows: two environmental TEM studies provide characterizations of the catalyst/soot contacts for CeO229 and Ce-Mn-O/Al2O3.33 The dimensions of the catalyst/soot interface are similar in the two studies, ≈21 nm.29,33 Assuming that a ceria/soot interface is circular, then its surface is of sc ≈ 40 nm2. The [Osce] during TPE has been obtained as follows. Different literature data have shown that the evolution of the H2-TPR spectra of different ceria samples is characterized by two successive hydrogen consumption peaks at Tm < 800 K and Tm > 1000 K ascribed to the reduction of surface and (33) Ivanova, A. S.; Litvak, G. S.; Mokrinskii, V. V.; Plyasova, L. M.; Zaikovskii, V. I.; Kaichev, V. V.; Noskov, A. S. J. Mol. Catal. A: Chem. 2009, 310, 101–112. (34) Johnson, M. F. L.; Mooi, J. J. Catal. 1987, 103, 502–505.

(35) Giordano, F.; Trovarelli, A.; de Leitenburg, C.; Giona, M. J. Catal. 2000, 193, 273–282.

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that the parameters must be measured at the maximum of [Caf(O)]}. Considering that kra is known, the measurement of the evolution of [Caf(O)] during TPE, for instance using an IR cell for diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS),14 must allow for the measurement of krb. A similar experimental procedure can be proposed to measure kd considering OCaf(O). However, we failed to obtain exploitable DRIFTS spectra of Caf(O) or OCaf(O). This is probably due to the fact that, in addition to the difficulties linked to the recording of IR spectra of SOC species, the amounts of Caf(O) or OCaf(O) species during the TPE are very low. This is supported by the following exploitation of the 1% O2-TPO of TC-R = 10: in Figure 2, at low O2 consumption, RO2(T) is significantly higher than RCO2(T). This is due of the accumulation of Caf(O) and/or OCaf(O) species with rates depending upon particularly the rate constants kra, krb, and kd. The difference between the amounts of O2 consumed and CO2 formed, ≈ 2.5 μmol of O2/g of ceria, provides an estimation of the amount of intermediate species. Assuming that only Caf(O) species are formed, it can be deduced that ≈5  1016 Caf(O) species/m2 of ceria are present on the surface. In comparison to 1.1  1018 Caf/m2 of ceria, this indicates that there is no strong accumulation of intermediate SOC species before the formation of CO2. This rules out the view that krb is significantly lower than kra or that kd is the limiting step of the CO2 production. These different kinetic parameters linked to the elementary steps of models M1 and M2 have been used to obtain, by solving numerically eqs 20-23, a theoretical RCO2(T) curve, which is compared to the experimental data in Figure 1a. 3.5. Kinetic Modeling of the RCO2(T) Curve of TPE for TCR = 10. In this first stage of the modeling, we consider that the TPE follows the plausible kinetic M1 (the Oasce species constitute a finite reservoir) and then model M2 is considered with the contribution of the reservoir of Osce species via a diffusion process. For the rate constants of the surface elementary step, we consider that the pre-exponential factors ν are those provided by the activated complex theory. They are (i) 1013 s-1 for the rate constant of desorption kd (that is supported by experimental data for the rate constant of desorption of SOC species as CO2)25 and the rate constant of the first step of the diffusion process and (ii) 10-6 m2 molecule-1 s-1 for the rate constants kra and krb [the LangmuirHinshelwood (L-H) surface elementary steps]. 3.5.1. Exploitation of the Kinetic Model M1. Using model M1, the theoretical rate of the CO2 production as a function of the temperature is obtained by solving eqs 20-23, considering that dT/dt = R (R = 50/60 in K/s) and assuming that [Caf] remains constant during the TPE because the ceria/soot contacts are maintained during the progressive soot oxidation, whereas [Oasce] decreases progressively. Considering that CeO2 cannot be deeply reduced, we assume that Era increases with the decrease in Oasce. We adopt a linear increase according to ð30Þ Era ðθÞ ¼ Era ð1Þ þ βa ð1 - θOasce Þ kJ=mol

Figure 4. Determination on the surface oxygen concentration on ceria [Osce] using H2-TPR (see the text for more details). (Inset) Desorption of N2 in a 5% N2/He mixture after adsorption at 77 K.

species is of 85 μmol of H2/g of ceria, leading to [Osce] ≈ 1.9  1018 Osce/m2 of ceria, which is a value consistent with the data by Perrichon et al.32 According to eq 25, the different experimental values of the parameters allow for the evaluation of the average number of contacts between a CeO2 particle and the soot particles for the TC-R=10 mixture, Nc=4.38. This indicates that 22% of the ceria surface is in contact with the soot. The experimental Nc value indicates a reasonable homogeneity of TC-R = 10 that is consistent with the analysis of the local composition of this ceria/soot mixture using Raman spectroscopy.14 Moreover, it must be noted that the size of the elementary soot particles (spherules) are in the range of 1050 nm36 and, for diesel soot, in the range of 20-30 nm,37 which are values similar to that of the ceria particles. For a perfect mixing of particles having the same diameter, a hexagonal compact arrangement can be expected, leading to a maximum Nc value of 12. Clearly, different factors prevent considering this situation for the ceria/soot mixtures and justify the experimental value of Nc ≈ 4.4, such as (i) the exact shapes and sizes of the particles,36 (ii) the homogeneity of the mixture, and (iii) the ceria/soot ratio. 3.4.2.3. Surface Concentration of the Caf Species. The value of [Caf] can be obtained from eq 26 after an estimation of the concentration of the carbon defect sites on the soot surface [Cf]. According to eqs 4 and 5, the Cf sites are formed by the desorption of the SOCs. The amounts of CO and CO2 desorbed in the temperature range of 300-1100 K on the pure standardized soot are 4010 and 944 μmol/g, respectively.14 The total amount of SOCs desorbed, 4954 μmol/g of soot, leads to [Cf] ≈ 5.9  1018 molecules/m2 of soot, considering the surface area of the standardized soot, ≈510 m2/g. For R = 10 and Nc=4.38, eq 26 leads to [Caf]=1.1  1018 Caf/ m2 of ceria. This quantity is considered constant during TPE-i (i>3) because the ceria/soot contacts are maintained, whereas a small amount of soot (in comparison to the total amount of soot present in the reactor) is consumed. 3.4.3. Characterization of the Rate Constants krb and kd. An experimental procedure to measure krb can be suggested, considering eq 21. After the substitution of dt=dT/R, it can be observed that the curve [Caf(O] = f(T] presents a maximum for d[Caf(O)]/dT = 0, providing the following relationship: [Caf(O)]m = (kra(Tm)/krb(Tm)][Caf]m {indice m indicates

with θOasce =([Oasce](T))/([Oasce](300 K)), the coverage of the Oasce species, and Era(1) = 188 kJ/mol. The values of βa are provided by the best fit between experimental and theoretical curves RCO2(T). A similar expression is used for Erb Erb ðθÞ ¼ Erb ð1Þ þ βb ð1 - θOasce Þ kJ=mol ð31Þ

(36) Stanmore, B. R.; Brilhac, J. F.; Gilot, P. Carbon 2001, 39, 2247– 2268. (37) Mathis, U.; Mohr, M.; Kaegi, R.; Bertila, A.; Boulouchos, K. Environ. Sci. Technol. 2005, 39, 1887–1892.

with Erb and βb values that must be close to those of Era and βa. Finally, the kinetic parameters that have not be estimated 4788

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Table 1. Kinetic Parameters for the Kinetic Modeling of RCO2(T) Observed during the TPE of TC-R = 10a kinetics parameters

values

surface area of ceria particle size of ceria density of ceria average area of a ceria/soot contact average number of contacts between a ceria particle and the soot particles surface concentration of reductible O species on ceria, [Osce] surface concentration of the active oxygen species, [Oasce] particule size of a elementary soot particle spherule surface concentration of carbon defect sites on a desorbed (≈1100 K) soot, [Cf] surface concentration of active carbon defect sites, [Caf] pre-exponential factor of the rate constant of an H-L elementary steps pre-exponential factor of the rate of desorption for a first-order kinetic activation energy of oxidation of the Caf as a function of the coverage of the Oasce species, Era activation energy of oxidation of the Caf(O) as a function of the coverage of the Oasce species, Erb activation energy of desorption of the OCaf(O) species as CO2, Ed activation of the Osce species for the diffusion, Edf amount of Osce species surface concentration of SOC oxidized at low temperatures, [Cf(O)] activation energy of oxidation of the Cf(O) species, E0 rb activation energy of desorption of the OCf(O) species, Ed a

b

unit 2

50 17b 7.1 40b 4.38b 1.9  1018b 3.9  1017b 20 5.9  1018b 1.1  1018b 10-6 1013 187b þ 56(1 - θOasce)c

m /g nm g/cm3 nm2

178b þ 50(1 - θOasce)c

kJ/mol

< ≈181 288c þ 83(1 - θOasce)c 5[Oasce] 3.9  1015c 140 þ 52(1 - θCf(O))c 180 kJ/mol. Note that Ed values 900 K. 3.5.2. Exploitation of the Kinetic Model M2. The experimental curve RCO2(T) shows that there is a second CO2 production peak at T > 900 K (inset of Figure 1) that cannot be fitted considering model M1. This can be modeled considering that there is a diffusion of Osce and Obce species (eqs 14 and 19) to the ceria/soot interface, forming new Oasce species. The activation energy of diffusion of the Osce species (eq 27) must be similar to that of desorption of O2 from ceria. Punta et al.38 have determined the activation energy of desorption of an adsorbed oxygen species on CeO2, Ed = 260 kJ/mol. The authors consider that this species was weakly adsorbed in comparison to the enthalpy for the removal of O2 from

Figure 5. Comparison of the experimental (curve a) and theoretical (curve b) RCO2(T) curves for TC-R=10 during TPE-i (i >3) using the plausible kinetic model M1. Curves c, d, and e, evolutions of the coverages of the Oasce, Cf(O), and OCf(O) species, respectively, during TPE-i (i>3) according to model M1 (see the text for more details).

ceria, 774 kJ/mol according to 4 CeO2 f 2Ce2O3 þ O2.38 The Ed value is consistent with the fact that, for stoichiometric oxides (the situation of ceria in the present study after adsorption of O2 at 300 K) having a fluorite structure, the activation energy for oxygen diffusion is very high but strongly dependent upon the presence of impurities, 202 kJ/mol for PuO2, in the range of 248-273 kJ/mol for UO2, and 226-322 kJ/mol for CeO2, decreasing to 136 kJ/mol in the presence of trivalent impurities (see ref 39 and references therein). Density functional theory (DFT) calculations indicate that the activation energy of diffusion of O* adatom on the stoichiometric CeO2 surface is 1.58 eV on CeO2(111),40 1.42 eV on CeO2(111), and 1.70 eV on CeO2(110).41 These values are consistent with the corrugation coefficient.30,31 Moreover, it has been shown by different experimental42,43 and DFT studies40,44 that the oxygen diffusion (39) Kamiya, M.; Shimada, E.; Ikuma, Y.; Komatsu, M.; Haneda, H. J. Electrochem. Soc. 2000, 147, 1222–1227. (40) Chen, H. T.; Chang, J. G.; Chen, H. L.; Ju, S. P. J. Comput. Chem. 2009, 30, 2433–2442. (41) Huang, M.; Fabris, S. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 75, No. 081404(R). (42) Steele, B. C. H.; Floyd, J. M. Proc. Br. Ceram. Soc. 1971, 72, 55–76.

(38) Putna, E. S.; Vohs, J. M.; Gorte, R. J. J. Phys. Chem. 1996, 100, 17862–17865.

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Figure 6. Comparison of the experimental (discontinue line) and theoretical (continue line) RCO2(T) curves for TC-R = 10 during TPE-i (i > 3) using the plausible kinetic model M2 (see the text for more details).

Figure 7. Comparison of the experimental (discontinuous line) and theoretical (continuous line) RCO2(T) curves for TC-R = 10 during TPE-i (i > 3) using the plausible kinetic model M2 associated with the oxidation of a small amount of SOC species at low temperatures (see the text for more details).

for non-stoichiometric ceria (CeO2-x) is easier, i.e., 0.52 eV for CeO1.92 by experimental procedure and 0.64 eV by DFT calculations.40 Taking into account these literature data, we have considered that the Osce species must diffuse before the Obce species and that only Osce species are involved in the kinetic modeling at T < 970 K. The full line in Figure 6 that fits the experimental data at high temperatures has been obtained considering that the oxygen reservoir of Osce species is larger by a factor of 5 as compared to the reservoir of Oasce species and that the activation energy for eq 27 is Edf = [Edf(1) þ βc(1 - θOsce)] (in kJ/mol), with θOsce = (Osce(T))/ (Osce(300 K)), Edf(1) = 288 kJ/mol, and βc = 83 kJ/mol. The linear increase in the activation energy with the decrease in the Osce species mimics the fact that CeO2 cannot be deeply reduced. However, in agreement with the literature data,40,42-45 the activation energy of eq 28 may decrease with the progressive reduction of the surface (this has no impact on the kinetic modeling because the rate of diffusion of the O* species is significantly faster than the rate of formation, eq 27). Note that Edf(1) = 288 kJ/mol is not strongly different from the activation energy of desorption of O2 from CeO2 measured by Punta et al.,38 260 kJ/mol. In the temperature range of Figure 6, the content of the Osce reservoir decreases by 36%. In the inset of Figure 1, the second CO2 peak for T > 970 K must probably involve the diffusion of Obce species. Note that neither model M1 nor model M2 considers the desorption of the Caf(O) species as CO. However, at high temperatures, this reaction may explain the CO production, in particular because of the fact that the amount of oxygen species available in the ceria particles (Oasce, Osce, and Obce) is strongly decreased. 3.5.3. Improvement of the Theoretical RCO2(T) Curve at Low Temperatures. The theoretical curve in Figure 6 does not closely fit the experimental curve at T < ≈670 K. This suggests that a small amount of C-containing species, with kinetic parameters different from those associated with the oxidation of Caf, contributes to the CO2 production. For instance, it can be considered that SOC species, remaining on the soot surface after TPE at 1100 K, are oxidized. The presence of SOCs can be due to the fact that, at the end of the TPE when ceria is significantly reduced to CeO2-x, the oxidation rate of the Caf(O) species is decreased and these species may remain on the surface (see curve d in Figure 5), considering that they have a high activation energy of

desorption.19-28 After the reoxidation of ceria at 300 K, these species can be oxidized before the Caf species. The full line in Figure 7 has been obtained considering that RCO2(T) is due to the oxidation of (a) the Caf sites according to model M2 (continuous line in Figure 6) and (b) SOC species [with a structure C(O)] present in small quantities, [C(O)] = 3.9  1015 C(O)/m2 of ceria (this represents 0.25% of the Oasce species), with an activation energy of oxidation that varies with their coverage to mimic the presence of SOCs of different reactivity ð32Þ E 0 rb ðθÞ ¼ E 0 rb ð1Þ þ γð1 - θCðOÞ Þ kJ=mol with E0 rb(1) = 140 kJ/mol and γ = 52 kJ/mol [the desorption of the OC(O) species is considered equal to those of the OCaf(O) species]. It can be observed in Figure 7 that the theoretical RCO2(T) curve fits the experimental curve on the full temperature range, considering the contribution of a small amount of SOC species. 3.6. Impact of the Ceria/Soot Mixture on the RCO2(T) Curve. A priori, the type of ceria/soot mixture, TC-R = 10, TC-R=1, and LC-R=10, can not strongly modify the kinetic parameters implicated in the RCO2(T) curve, except for the number of contacts Nc and the ceria/soot weight ratio R. For LC-R = 10, the value of Nc must be lower than for TC-R = 10, because of the decrease in the homogeneity of the mixture, as observed by Raman spectroscopy.14 Similarly, Nc must be higher for TC-R = 1 than TC-R = 10 because of a lower soot dilution in ceria. Considering this viewpoint, the experimental RCO2(T) curves for TC-R = 1 and LC-R = 10 in Figure 1 have been compared to the theoretical curves using the same kinetic parameters as for TC-R=10 (Table 1), except Nc and R. 3.6.1. Theoretical RCO2(T) Curve for TC-R=1. The number of contacts Nc between a ceria particle and the soot particles for TC-R = 1 can be estimated considering the amount of oxygen adsorbed at 300 K after TPE-i (i > 3), 94 μmol/g of ceria. This value is higher than that on TC-R = 10, 64 μmol/g, indicating that ceria provides more oxygen species for TCR = 1. This must come from a higher Nc value that increases [Oasce]. After the adsorption of O2 at 300 K, the TPE leads to an O2 peak of ≈16 μmol of O2/g of ceria as compared to 10 μmol of O2/g of ceria for TC-R = 10. Assuming that there is a proportionality between the amount of oxygen adsorbed on ceria and Nc, then Nc for TC-R = 1 is obtained considering the values for TC-R = 10, Nc = [4.38(94 - 16)/(64 - 10)] = 6.3. The full line in Figure 8A is obtained using the same kinetic parameters as those in Table 1, except using R=1 and Nc=6.3.

(43) Fuda, K.; Kisho, K.; Yamauchi, S.; Fueki, K. J. Phys. Chem. Solids 1985, 46, 1141–1146. (44) Frayet, C.; Villesuzanne, A.; Pouchard, M.; Matar, S. Int. J. Quantum Chem. 2005, 101, 826–839. (45) Stan, M.; Zhu, Y. T.; Jiang, H.; Butt, D. P. J. Appl. Phys. 2004, 95, 3358–3361.

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Figure 9. Comparison of the experimental and theoretical RCO2(T) curves for LC-R = 10 during TPE-i (i > 3) using the plausible kinetic model M2 associated with the oxidation of a small amount of SOC species at low temperatures: (a and b) experimental data for TC-R = 10 and LC-R = 10, respectively, and (c) theoretical curve for LC-R = 10. (A) Same kinetic parameters as in Figure 7, except Nc = 3.8. (B) After the modifications of the kinetic parameters for oxygen diffusion and oxidation of Caf(O) (see the text for more details).

Figure 8. Comparison of the experimental and theoretical RCO2(T) curves for TC-R = 1 during TPE-i (i > 3) using the plausible kinetic model M2 associated with the oxidation of a small amount of SOC species at low temperatures: (a and b) experimental data for TCR = 10 and TC-R = 1, respectively, and (c) theoretical curve for TC-R = 1. (A) Same kinetic parameters as in Figure 7, except Nc = 6.1 and R = 1. (B) After the modifications of the kinetic parameters for oxygen diffusion (see the text for more details).

It can be observed that the theoretical curve is consistent with the experimental data, except at high temperatures, where the diffusion of Osce species contributes to the CO2 production. Figure 8B shows the theoretical curve after a slight modification of the activation energy of diffusion, Edf(1) = 277 kJ/mol and βc = 70 kJ/mol, as compared to Edf(1) = 288 kJ/mol and βc = 83 kJ/mol for TC-R = 10. This lower activation energy of diffusion might be due to the higher Nc value. 3.6.2. Theoretical RCO2(T) Curve for LC-R=10. Similar to TC-R=1, the number of contacts Nc between a ceria particle and the soot particles for LC-R=10 can be estimated considering the amount of oxygen adsorbed at 300 K after TPE-i (i > 3), 46 μmol/g of ceria. This value is lower than that on TC-R = 10, 64 μmol/g, indicating that ceria provides less oxygen species than for LC-R = 10. This probably originates from a lower Nc value because of a decrease in the homogeneity of the ceria/soot mixture (this decreases [Oasce]). After adsorption of O2 at 300 K, the TPE leads to an O2 peak at T 3) of the three ceria/soot mixtures can be extended to TPO with low partial pressures of O2, PO2.

Figure 10. Comparison of the experimental and theoretical RCO2(T) curves for TC-R = 10 during TPE-i (i>3) and TPO: (a-c) experimental data for TPE-i (i > 3), 1% O2-TPO, and 5% O2-TPO, respectively, and (d) theoretical curve according to kinetic model M1 associated with the oxidation of a small amount of SOC species at low temperatures, considering [Oasce] and [Caf] constant (see the text for more details).

After eight TPE/O2 cycles, the TC-R = 10 ceria/soot mixture is heated in 1% O2/He (see Figure 2). Figure 10 shows a comparison of the rates of the CO2 productions RCO2(T) in the absence (curve a, classical TPE) and presence (curve b) of 1% O2/He. For 1% O2/He, the highest temperature of curve b is that corresponding to an O2 conversion of 80% (see Figure 2). A similar TPO has been performed using 5% O2/ He, leading to a RCO2(T) curve shown in Figure 10c. The comparison of the three experimental RCO2(T) curves in Figure 10 leads to the following comments: (i) RCO2(T) becomes significant at a temperature Ts ≈ 600 K, independent of PO2; this is consistent with model M1, which considers that the soot oxidation proceeds at the ceria/soot interface via the oxygen species of ceria that are in contact with the soot (Oasce species) (the activation energy associated with those species controls Ts). (ii) After Ts, RCO2(T) is higher in the presence of PO2. This is also consistent with model M1; in the absence of O2, the amount of Oasce species decreases with T (they are consumed), whereas because of the rapid oxygen adsorption, the amount of Oasce remains constant in the presence of O2, even for a significant O2 consumption. (iii) Similarly, after Ts and for low O2 conversion, RCO2(T) is independent of PO2. This is consistent with model M1; regardless of PO2, the rate of adsorption maintains [Oasce] constant. However, at high O2 conversion, the external diffusion of O2 to the surface may limit the rate of adsorption and [Oasce] decreases. 4791

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According to the procedure developed in previous studies,2-8 two plausible kinetic model (denoted as M1 and M2) of the soot oxidation, via Cf sites, have been selected on the basis of the literature data.17,18 The models are different by the implication (M2) or not (M1) of the diffusion of oxygen species on the ceria surface. In the two models, the ceria/soot contacts are considered as a key kinetic parameter of the soot oxidation; the active oxygen species of ceria and the active sites Cf of the soot are situated at the ceria/soot interface. The properties of this interface, such as Nc, the average number of contact between a ceria particle and the soot particles, and sc, the average surface area of a contact, are included in the mathematical formalism. According to the microkinetic approach, different kinetic parameters have been quantified individually by experimental procedures, such as the activation energy of oxidation of the Cf sites (187 kJ/mol) and Nc for the different ceria/soot mixtures (i.e., Nc = 4.3 for TC-R = 10, and Nc = 6.1 for TC-R = 1). It has been shown that the surface elementary steps of model M1 and their experimental kinetic parameters provide, for the three ceria/soot mixtures, theoretical RCO2(T) curves during TPE, in good agreement with the experimental data for T < 900 K, whereas model M2 must be used at higher temperatures. This is due to the fact that surface oxygen species and then bulk oxygen species of ceria diffuse to the interface, forming new Oasce species. At high temperatures, it is the rate of diffusion of those species that controls the CO2 production. The models have been extended to the soot oxidation in the presence of O2. It has been shows that model M1 provides theoretical curves consistent with the experimental data, considering that the rapid adsorption of oxygen on ceria allows for the amount of Oasce species to remain constant in the absence of external diffusion. The study confirms the interest of the experimental microkinetic approach, for the understanding of the key kinetic parameters controlling a catalytic reaction in the absence of the contribution of physical processes. In particular, for the catalytic oxidation of the soot by mechanical mixtures with a solid catalyst, it provides a mathematical formalism, allowing for the comparison of the performances of different catalysts that can be used as a support for the development of new catalyst formulations.

These remarks allow for the comparison of the experimental RCO2(T) curve in the presence of PO2 to the theoretical curves obtained according to model M1, considering that [Oasce] remains constant because of the fast rate of O2 adsorption. Curve d in Figure 10 is obtained with the kinetic parameters of Table 1, except that [Oasce] is considered constant, [Oasce]=3.9  1017 Oasce species/m2 of ceria. The comparison to TPE is limited to a low soot conversion to assume that Nc remains constant in the presence of O2. It can be observed that curve d is consistent with the experimental curves b and c. However, at a reaction temperature T . TS, the theoretical curve provides higher values than the experimental curves. This can be due to the facts that (i) the increase in the oxygen conversion (see Figure 2) may limit the rate of oxygen adsorption (i.e., contribution of the external diffusion), leading to a decrease in the amount of Oasce species, and (ii) at a significant soot conversion, the total surface area of the ceria/soot interface must decrease, leading to a decrease in [Oasce]. 4. Conclusions The catalytic oxidation of a diesel soot contained in three mechanical ceria/soot mixtures (TC-R = 10, TC-R = 1, and LC-R = 10), different by (i) the ceria/soot contacts (tight and loose contacts denoted as TC and LC, respectively)12,13 and (ii) the ceria/soot weight ratios (denoted as R), have been studied by an experimental microkinetic approach. The main aims were to provide a kinetic model of the rates of the CO2 production, RCO2(T), during TPEs in the absence of O2. It has been shown that, for each ceria/soot mixture, the experimental RCO2(T) curves are reproducible after performing three cycles of TPE followed by O2 adsorption at 300 K with the same sample. In these experimental conditions, the soot oxidation proceeds via the carbon defect sites Cf of the soot (created by the removal of the SOCs) and oxygen species provided by the ceria particles. The RCO2(T) curves present two peaks at low (T < 900 K) and high (T > 900 K) temperatures; the experimental microkinetic approach is mainly dedicated to the kinetic modeling of the CO2 peak at T < 900 K because the surface elementary steps implicated are those associated with the decrease in the light-off temperature of the soot in the presence of ceria.14

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