Kinetics of Oxygen Exchange and N₂O Decomposition Reaction over MeO_x/CeO₂ (Me = Fe, Co, Ni) Catalysts

Abstract

MeO_x/CeO₂ (Me = Fe, Co, Ni) samples were tested in an ¹⁸O₂ temperature-programmed isotope exchange and N₂O decomposition (deN₂O). A decrease in the rate of deN₂O in the presence of oxygen evidences the competitive adsorption of N₂O and O₂ on the same sites. A study of isotope oxygen exchange revealed dissociative oxygen adsorption with the subsequent formation of surface oxygen species. The same species, more probably, result from N₂O adsorption and the following N₂ evolution to the gas phase. We supposed the same mechanism of O₂ formation from surface oxygen species in both reactions, including the stages responsible for its mobility. A detailed analysis of the kinetics of isotope exchange has been performed, and the rates of one-atom (R^I) and two-atom (R^II) types of exchange were evaluated. The rate of the stage characterizing the mobility of surface oxygen was calculated, supposing the same two-step mechanism was relevant for both types of exchange. The effect of oxygen mobility on the kinetics of deN₂O was estimated. An analysis of the possible pathways of isotope transfer from MeO_x to CeO_x showed that direct oxygen exchange on the Me–Ce interface makes a valuable contribution to the rate of this reaction. The principal role of the Me–Ce interface in deN₂O was confirmed with independent experiments on FeO_x/CeO₂ samples with a different iron content.

1. Introduction

N₂O is one of the side products of NH₃ oxidation to nitric acid over Pt–Rh gauzes; its emissions into the atmosphere are strictly regulated. It is commonly considered that N₂O decomposition (deN₂O) is initiated by the interaction of gas-phase N₂O with an active site S (oxygen vacancies, in our case), resulting in the gas-phase N₂ and adsorbed oxygen species (O-S):

(1)

N₂O + S ↔ N₂O-S

(2)

N₂O-S → N₂ + O-S

The formation of O₂ can proceed by either direct recombination of two O-S species [1,2]:

(3a)

2O-S ↔ O₂ + 2S

or by direct reaction of gas-phase N₂O with O-S [3] described by the simplified reaction:

(3b)

O-S + N₂O → N₂ + O₂ + S

Reaction inhibition in oxygen presence was observed for most bulk oxide systems [1,2], which can be due to the competitive adsorption of N₂O and oxygen on the same active sites. At 300–600 °C, oxygen desorption was shown to be the rate-controlling step of the reaction [4,5,6]. N₂O decomposition in the ammonia burner with the catalyst located directly under Pt-Rh gauzes is also industrially applied as an attractive technology for N₂O abatement. Such a catalyst operates at above 800 °C. Under these conditions, the importance of oxygen mobility for the deN₂O activity was highlighted for La–Sr–Mn perovskite-type oxides [7] and supported MeO_x/Al₂O₃(CeO₂) (Me = Fe, Co, Ni) [8] and FeO_x/(CeO₂ + Al₂O₃) samples [9], while reaction retardation with oxygen was observed as well. The mechanism of oxygen formation through the recombination of two O-S species (step 3a) is unlikely to fit this case because oxygen species are strongly bonded with anion vacancies and cannot diffuse on the catalyst surface. Kondratenko et al. [10,11,12,13] showed that N₂O decomposition over different Fe-containing oxidic systems used in a wide range of temperatures is better fitted using an intermediate scheme. With this scheme, O₂ and N₂O adsorb on the same active site S, as in the case of the traditional Langmuir-Hinshelwood mechanism. However, oxygen adsorption proceeds without dissociation, and the molecular form of adsorbed O₂ (O₂-S) has been formed by a N₂O reaction with O-S:

(3c)

O₂-S ↔ O₂ + S

(4)

N₂O + O-S $\to$ N₂ + O₂-S

However, samples with preferentially isolated active Fe sites (Fe-ZSM-5, Fe-silicalite, and BaFeAl₁₁O₁₉) have been studied, and non-dissociative O₂ adsorption can be supposed in this case. Data from Boreskov and Muzykantov [14] show that at >~400 °C, oxygen dissociative adsorption proceeds on the surface of bulk α-Fe₂O₃ and NiO. In CeO_2, oxygen from the gas phase first forms adsorbed superoxide or peroxide species which incorporate into the lattice via the following sequence of reactions [15,16,17]:

$${\mathrm{O}}_{2\left(\mathrm{g}\right)}\leftrightarrow {\mathrm{O}}_{2\left(\mathrm{ads}\right)}\leftrightarrow {\mathrm{O}}_{2\left(\mathrm{ads}\right)}^{-}\leftrightarrow {\mathrm{O}}_{2\left(\mathrm{ads}\right)}^{2-}\leftrightarrow 2{\mathrm{O}}_{\left(\mathrm{ads}\right)}^{-}\leftrightarrow 2{\mathrm{O}}_{\left(\mathrm{lattice}\right)}^{2-}$$

Isotopic oxygen exchange in gas-solid systems is widely used in heterogeneous catalysis for studying oxygen activation, characterization of its state on the catalyst surface, and elucidation of kinetic peculiarities of oxygen transfer, including bulk oxide oxygen atoms, depending on sample microstructure. The basic theory is based on the classification of exchange types, depending on the number of surface oxygen atoms participating in an exchange with O₂ (zero-atom, single-atom, or two-atom exchange) [6,18,19,20,21,22]. Regarding the exchange type, one may reveal the most probable mechanisms of oxygen activation on the surface. The unified mechanism was proposed by Muzykantov [14,23,24] for the interpretation of different types of oxygen exchange in oxides. It includes two types of surface oxygen species resulting from oxygen adsorption on the catalyst surface, i.e., O strongly bound with oxygen vacancy (O_v) and O located on the surface (O_s). The last, in turn, can diffuse on the surface and occupy the oxygen vacancy, thus transforming to O_v. Such transformation is reversible: strongly bound oxygen can diffuse to the surface as well. O₂ formation proceeds by recombination of O_v and O_s. According to Muzykantov’s theory, it is the mobility of O_s that determines the type of exchange. Heteroexchange with the participation of two atoms of oxide surface oxygen is realized at a high diffusion rate of O_s, and one oxygen atom participates in the exchange at a low rate of diffusion. Therefore, one can estimate the mobility of surface oxygen from the ratio of different types of exchange. Boreskov and Muzykantov [14] presented the characteristics of surface oxygen mobility of some simple and complex oxides and noted its high value for α-Fe₂O₃. We supposed that the same mechanism of oxygen species recombination could realize in the reaction of N₂O decomposition.

At high temperatures, the bulk oxide oxygen atoms take part in the exchange process. That is why many recent studies focused on the estimation of the rate of bulk oxygen substitution, which may be used for characterizing the mobility of lattice oxygen [7,25,26]. The oxygen exchange behavior at high temperatures in La-Sr-Mn-O samples has been studied with a special emphasis on its relation to catalytic activity in N₂O decomposition [7]. It was shown that the appearance of the second faster pathway of oxygen transfer in the bulk of the catalyst through oxygen vacancies or disordered-free channels in the perovskite structure resulted in increased catalytic activity. Evaluation of the rates of surface oxygen exchange and the coefficient of lattice oxygen diffusion in three La-Sr-Fe-O catalysts with close element content but different phases and surface compositions revealed the direct correlation between the surface exchange rate constant and the rate of N₂O decomposition [27]. The results obtained can be useful for developing active catalysts.

In the present study, we investigated the main features of oxygen transfer on the surface and in the bulk of CeO₂ and MeO_x/CeO₂ (Me = Fe, Co, Ni) samples using ¹⁸O isotope exchange. It allowed us to reveal the interdependence of these processes and the kinetics of the reaction of N₂O decomposition.

2. Materials and Methods

2.1. Samples Preparation and Characterization

Ce, Co, Ni, and Fe nitrates of a purity of 99.0% and citric acid (99.8%) were purchased from Vekton, Saint Petersburg, Russia. Ethylene glycol (99.0%) was purchased from Ecros, Saint Petersburg, Russia.

CeO₂ (S_BET = 1.4 m²/g, pore volume 0.42 cm³/g) used as the support was obtained using calcination of Ce(NO₃)₃·6H₂O at 900 °C for 36 h. MeO_x/CeO₂ samples (Me = Fe, Co, Ni) with Me concentration 6.7 × 10¹⁹ at/m² (0.86–0.91 wt%) were prepared using incipient wetness impregnation of CeO₂ with a water solution of a corresponding Me nitrate (0.37 mol/L) with added citric acid (0.41 mol/L) and ethylene glycol (0.26 mol/L). A solution 2.9 times more concentrated (with regard to all components) was taken for preparation of FeO_x/CeO₂ with an Fe content of 2.5 wt%. After drying first under an IR lamp at continuous mixing and then—at 150 °C for 6 h, samples were calcined at 900 °C for 4 h. S_BET values for FeO_x/CeO₂ samples were close to that of CeO₂ (1.3–1.4 m²/g). X-ray powder diffraction (XRD) patterns were recorded using a Bruker D8 diffractometer with Cu Kα monochromatic radiation. Each sample was scanned in the range of 2θ from 10° to 70° with a step 0.05° of 2θ. The surface composition of the samples was investigated using X-ray photoelectron spectroscopy (XPS) using spectrometer SPECS (SPECS, Berlin, Germany) with Al Kα irradiation (hν = 1486.6 eV). The positions of the peaks of Au 4f_7/2 (84.0 eV) and Cu 2p_3/2 (932.67 eV) core levels were used for calibration of the binding energy (BE) scale.

2.2. Temperature-Programmed Isotopic Exchange (TPIE) of O₂

Before every experiment, the sample loaded into a reactor (quartz tube, i.d. = 3 mm) was kept in 0.5 vol.% ¹⁶O₂ + He flow at 900 °C for 30 min; then, the reactor was cooled down to room temperature in the same flow. At T ≤ 100 °C, this mixture was replaced stepwise by the same one but containing ¹⁸O₂ and Ar (1 vol.%) as an inert tracer, and the reactor was heated up to 900 °C (rate of heating 14.7 °C/min). Gas flow rate and catalyst loading were the same in all experiments and amounted to 5.0 L/h and 0.025 g, respectively. Transient changes in the gas isotopic composition (¹⁶O₂, ¹⁶O¹⁸O, and ¹⁸O₂ concentrations) were continuously monitored using a QMS 200 gas analyzer (Stanford Research Systems, Sunnyvale, CA, USA). ¹⁸O isotope fraction in the gas phase O₂ (α(t)) calculated as α(t) = (¹⁶O¹⁸O + 2¹⁸O₂)/2∑OⁱO^j, where ∑OⁱO^j = ¹⁶O₂ + ¹⁶O¹⁸O + ¹⁸O₂ was a characteristic of oxygen exchange. The general quantity of exchanged oxygen for different samples as related to the mass unit (N_O, at/g) was calculated using the formula

$$N_O=N_A\frac{2C_{O2}U}{g}{\displaystyle \underset{0}{\overset{t}{\int }}({\alpha }^{input}}-\alpha )dt$$

(1)

where α^input is the isotope fraction in the inlet mixture (0.95), C_O2 is inlet O₂ concentration (0.15 × 10⁻² mol/mol), U is the flow rate of the reaction mixture (mol/s), and N_A is Avogadro number.

2.3. Catalytic Activity Measurement

The catalytic activity was measured in a fixed-bed U-shaped reactor (3 mm i.d. quartz tube) loaded with 0.038 g of the sample (particles of 250–500 μm in size) at a flow rate of 18–60 L/h, ambient pressure, and at a temperature range of 600–900 °C. A gas mixture containing 0.15—1.0 vol% N₂O in He was used. To check out the effect of O₂, 3 vol.% O₂ was added to the inlet mixture. Outlet mixture composition was analyzed using a gas chromatograph equipped with Porapack T (i.d. = 3mm, l = 3 m, N₂O analysis) and NaX (i.d. = 3 mm, l = 2 m, N₂ analysis) columns. N₂O conversion (X_N2O) calculated as:

$$X_{N2O}=(C_{N2O}^0-C_{N2O})/C_{N2O}^0\times 100\%$$

(2)

where $C_{N2O}$ and $C_{N2O}^0$ —outlet and inlet concentrations of N₂O were considered a measure of sample activity.

3. Results and Discussion

3.1. Qualitative Analysis of Oxygen Isotope Exchange Process

The changes in α(t) during the TPIE O₂ on CeO₂ and different MeO_x/CeO₂ samples depending on T are shown in Figure 1. The ¹⁸O fraction in O₂ first decreases as isotope exchange between gas phase oxygen and catalysts starts. Then it goes across the minimum and returns to the initial value after the complete substitution of exchangeable oxygen in the catalyst. One can see that exchange in CoO_x/CeO₂ starts at lower temperatures and thus proceeds much faster than in other samples. The quantity of exchangeable oxygen (N_O) in the CoO_x/CeO₂ sample is 6.4 × 10²¹ atoms/g (

Table 1. Quantities of exchangeable oxygen during TPIE (N_O, 1 × 10²¹ at/g), rate values R, R^I, R^II (mole/m²s) for different types of oxygen exchange at reference temperature 750 °C and their activation energies E_R (kJ/mole) for different samples.

Sample	NO	R × 105	RI × 105	RII × 105	RII/R	ER
CeO2	4.5 1	0.42 (±0.02)	0.03 (±0.01)	0.4 (±0.02)	0.95 (±0.05)	170 (±10)
NiOx/CeO2	2.2 2	0.52 (±0.02)	0.03 (±0.01)	0.5 (±0.02)	0.96 (±0.55)	170 (±10)
FeOx/CeO2	5.4 1	1.4 (±0.08)	0.1 (±0.02)	1.3 (±0.08)	0.93 (±0.04)	175 (±10)
CoOx/CeO2	6.4	26 (±1)	41 (±1)	5.5 (±0.5)	0.21 (±0.02)	160 (±10)

¹ not complete exchange (see Figure 1). ² not complete exchange (heating up to 820 °C only, afterward, the constant temperature was kept, see Figure 1).

), which is close to the stoichiometric quantity of O atoms in CeO₂ lattice (~7 × 10²¹ atoms/g). A lower quantity of oxygen was exchanged in other samples because temperature-programmed heating stopped at 900 °C, while the exchange started at higher temperatures. Based on the similarity of α(t) curves for all samples, we supposed that all oxygen of CeO₂ participates in the exchange therein.

At the same time, a principally different distribution of labeled O₂ molecules was observed during TPIE (Figure 2). So, in CeO₂, NiO_x/CeO₂, and FeO_x/CeO₂ samples, ¹⁶O₂ appears in the gas phase first, and its fraction in O₂ (f₃₂) exceeds that of ¹⁶O¹⁸O (f₃₄) for a long period of time. In the CoO_x/CeO₂ sample, on the contrary, ¹⁶O¹⁸O appear first, and f₃₄ is higher than f₃₂ for all period of monitoring. Klier and Muzykantov [21,28] proposed the theory of isotope exchange of oxygen with solid oxides, which is currently widely used for the interpretation of mechanisms of oxygen transfer in solids [29,30,31]. With this theory, there are three kinetically distinct types of exchange depending on the number of oxygen atoms from the solid phase participating in the exchange reaction, zero-atom (R⁰), single-atom (R^I), and two-atom (R^II). The overall rate of heteroexchange R = 0.5R^I + R^II. Both qualitative and quantitative interdependence between the type of exchange and distribution of isotope molecules during the exchange was determined within the framework of this theory. The observed character of the curves preferentially evidences the two-atom type of exchange in CeO₂, NiO_x/CeO₂, and FeO_x/CeO₂ samples where two O atoms of the catalysts participate in every act of exchange:

¹⁸O₂ + [¹⁶O]_cat + [¹⁶O]_cat → ¹⁶O₂+ [¹⁸O]_cat + [¹⁸O]_cat

In turn, only one O atom participates in the exchange in CoO_x/CeO₂ sample:

¹⁸O₂ + [¹⁶O]_cat → ¹⁶O¹⁸O+ [¹⁸O]_cat

3.2. Quantitative Estimates of Oxygen Isotope Exchange Rates

Numerical analysis of α_g (T), f₃₂(T), and f₃₄(T) was performed to make quantitative estimates of the rates of isotope exchange with an account of types of exchange using the model of flow reactor including diffusion of oxygen isotopes in the bulk of the catalysts (see Appendix A). It revealed that oxygen substitution in the bulk of all samples is determined by the rate of “gas phase–surface” exchange. Diffusion of isotopes in the bulk proceeds very fast. Their concentration in bulk is close to that in the surface layer, which evidences the high mobility of the lattice oxygen. Estimated values of the rates of single-atom (R^I) and two-atom (R^II) exchange, as well as overall rates of heteroexchange (R) and contributions of two-atom exchange to the overall rate (R^II/R), have been presented in Table 1. The accuracy of estimation of the overall rates of heteroexchange is reasonably high, and the calculating error lies within ±5%. The values of the rates of different types of exchange are estimated with lower accuracy (±10%). One can see that R, R^I, and R^II values change in the following order: CeO₂ ≤ NiO_x/CeO₂ < FeO_x/CeO₂ < CoO_x/CeO₂. R^II values vary within one order of magnitude, and differences are more substantial for R and R^I. R^II/R values are as high as 0.9 for CeO₂, NiO_x/CeO_2, and FeO_x/CeO₂ and are only 0.2 for CoO_x/CeO₂. Therefore, a substantially higher rate of exchange in the CoO_x/CeO₂ sample compared with other CeO2-based samples is due to one-atomic exchange in the former of them.

3.3. Comparison of the Rates of N₂O Decomposition and Oxygen Isotope Exchange

Dependences of the rates of N₂O decomposition (R_N2O) versus reverse temperature over different samples have been presented in Figure 3. Their values at 750 °C and activation energy values (E_RN2O), as determined from the Arrhenius dependence on temperature, are presented in

Table 2. Rates of the reaction of N₂O decomposition (R_N2O) and oxygen isotope exchange (R, R^II) at 750 °C. Inlet reaction mixture compositions: 0.15% N₂O in He and 0.5% O₂ in He, respectively.

Sample	RN2O × 106, mol/m2s	ERN2O, kJ/mole	RII/RN2O	R/RN2O
CeO2	0.27	152	15	16
NiOx/CeO2	0.73	153	7	7
FeOx/CeO2	3.2	156	5	5
CoOx/CeO2	3.7	138	14	70

.

One can see that activity in N₂O decomposition changes in the following order: CeO₂ < NiO_x/CeO₂ < FeO_x/CeO₂ < CoO_x/CeO₂ excluding the temperature interval above 750 °C where R_N2O value for FeO_x/CeO₂ and CoO_x/CeO₂ become close. One can suppose that such approaching activity values at the distinct difference between R^I and R^II can be due to the different phase composition of the CoO_x/CeO₂ sample under oxygen-deficient conditions (case of deN₂O) and in the presence of oxygen. Indeed, the reduction of Co₃O₄ to CoO took place at above 750 °C during temperature-programmed heating in the inert [8,32,33], while oxygen presence shifted the temperature of the beginning of Co₃O₄ reduction to substantially higher temperatures [32,33]. At the same time, CeO₂, NiO, Fe₂O₃, and supported Ni(Fe)O_x/CeO₂ samples were stable during TPD in He up to 900 °C, at least [8].

R_N2O values are substantially lower than R^II and R, but R^II/R_N2O values for all samples are comparable and lie within 10 (±5), while R/R_N2O values vary from 5 to 70. Therefore, some correlation between R_N2O and R^II, but not R, can be supposed. Below, we attempted to derive steady-state rates kinetic equations using known conceptions about the mechanisms of these reactions. Finally, the R^II/R_N2O ratios were derived through reaction rate constants and initial concentrations of the reagents.

3.4. Mechanism and Form of Rate Equation for Oxygen Isotope Exchange in Oxides

A certain set of mechanisms can describe every type of oxygen exchange (with the participation of one or two oxygen atoms) in oxides. Single-atom type of exchange is more often described by the Eley–Rideal mechanism that considers the formation of three atomic surface complexes, including two atoms of molecular oxygen and one oxygen atom of the catalyst [34]. The two-atom mechanism is usually interpreted using the two-step mechanism of Bonhoeffer and Farkas [35]. Reversible dissociation of the O₂ molecule proceeds in the first stage resulting in two equivalent atoms of adsorbed oxygen. In the second stage, the incorporation of adsorbed oxygen to the lattice of oxide proceeds, followed by isotope exchange between adsorbed and lattice oxygens. However, these are the anionic surface defects (oxygen vacancies) that are responsible for the activation of O₂ on the oxide surface. As a rule, their concentration is low, and it is doubtful whether simultaneous interaction of O₂ with two defects, which is necessary for molecule dissociation, is possible. We consider that the two-step mechanism proposed by Muzykantov and Boreskov [14,23,24] and presented in Scheme 1 is the most well-grounded.

According to this mechanism, the O₂ molecule dissociates on oxygen vacancy [ ]_v resulting in a strongly bound oxygen atom O_v which is included in the oxide lattice, and oxygen atom O_s weakly bound with the oxide surface (Scheme 1, stage 1). Formation of O₂ proceeds by recombination of O_v and O_s. At a high rate of surface diffusion O_s can find and occupy another vacant site [ ]_v resulting in the formation of O_v (Scheme 1, stage 2). This stage is reversible, i.e., strongly bound oxygen can leave this place and come on the surface. As a matter of fact, the second stage characterizes the mobility of O_s. This mechanism allows the interpretation of both two- and single-atomic exchanges. Two-atom exchange is realized according to the following pathway: step 1 (r₁) → step 2 (r₂) → step −2 (r₋₂) → step −1 (r₋₁), while the single-atom mechanism includes only two steps: step 1 (r₁) → step −1 (r₋₁). The selectivity of the reaction of isotope exchange by pathway corresponding to the two-atom exchange (S) is determined by the ratio of the rates of step −1 and step 2:

$$S=\frac{r_2}{r_2+r_{-1}}=\frac{1}{1+r_{-1}/r_2}$$

(3)

Muzykantov et al. derived an equation for the rate of two-atomic exchange for the case of its strong limitation by stage 2 (Scheme 1) using this mechanism [14,23,24]. They supposed as well that the degree of the population of [ ]_v by strongly bound oxygen (O_v) is close to 1, while surface coverage by O_s → 0. In this case, the order of reaction for O is close to 0.5. In our study, we considered a more general case when the rate-determining step is unknown. No restrictions will be imposed on the concentration of O_v as well, and only the degree of surface coverage by O_s will be supposed as negligible. In this case, rate equations for stages 1 and 2 (Scheme 1) can be represented as follows:

$$r_1=k_1{C}_{O2}(1-{\theta }_V)(1-{\theta }_S)\approx k_1{C}_{O2}(1-{\theta }_V)$$

(4)

$$r_{-1}=k_{-1}{\theta }_V{\theta }_S$$

(5)

$$r_2=k_2(1-{\theta }_V){\theta }_S$$

(6)

$$r_{-2}=k_{-2}{\theta }_V(1-{\theta }_S)\approx k_{-2}{\theta }_V$$

(7)

Here, θ_V and θ_S are the concentrations of O_v and O_s, respectively, and k_i are the reaction rate constants of the ith stage. Under the conditions of adsorption-desorption equilibrium, the rates of direct and reverse reactions are equal:

$$k_1{C}_{O2}(1-{\theta }_V)=k_{-1}{\theta }_V{\theta }_S$$

(8)

$$k_2{\theta }_S(1-{\theta }_V)=k_{-2}{\theta }_V$$

(9)

We expressed θ_v and θ_s solving Equations (8) and (9) simultaneously. Finally, substituting them in Equations (4)–(7), we obtained:

$$r_1=r_{-1}=\frac{k_1{C}_{O2}}{1+\sqrt{k_1{C}_{O2}{k}_2/k_{-1}{k}_{-2}}}$$

(10)

$$r_2=r_{-2}=\frac{\sqrt{k_1{C}_{O2}{k}_2{k}_{-2}/k_{-1}}}{1+\sqrt{k_1{C}_{O2}{k}_2/k_{-1}{k}_{-2}}}$$

(11)

$$S=\frac{1}{1+r_{-1}/r_2}=\frac{1}{1+\sqrt{k_1{C}_{O2}{k}_{-1}/k_2{k}_{-2}}}$$

(12)

The rate of the reaction of two-atomic exchange can be expressed with the following equation:

$$R^{\mathrm{II}}=r_{1}S=\frac{k_1{C}_{O2}}{1+a_1\sqrt{k_1{C}_{O2}{k}_2/k_{-1}{k}_{-2}}+k_1{C}_{O2}/k_{-2}}$$

(13)

where

$$a_1=1+k_{-1}/k_2$$

(14)

Detailed derivation of the Equations (10)–(14) is given in Appendix B

In the case $r_2>>r_{{}_{-1}}$ (stage 2 is not rate-determining), the following approximate equation is applicable for the description of the two-atomic isotope exchange:

$$R^{\mathrm{II}}\approx \frac{k_1{C}_{O2}}{1+\sqrt{k_1{C}_{O2}{k}_2/k_{-1}{k}_{-2}}}$$

(15)

According to Equation (15), the rate equation can have an order dependence on oxygen concentration (n) varying from 0.5 to 1, depending on the value of the $k_1{C}_{O2}{k}_2/k_{-1}{k}_{-2}$ ratio. In the case of $k_1{C}_{O2}{k}_2>>k_{-1}{k}_{-2}$ (reaction equilibrium is shifted to direct steps and, thus, θ_v → 1), the n value will be close to 0.5. In the opposite case ($k_1{C}_{O2}{k}_2<<k_{-1}{k}_{-2}$) n → 1. According to Equation (13), the n value can be even less than 0.5 in the case $k_1{C}_{O2}>k_{-2}$ (the rate of two-atomic exchange is strictly determined by stage 2).

3.5. Mechanism and Equation Rate for N₂O Decomposition Reaction

We observed a decrease in N₂O conversion in the presence of oxygen in the reaction mixture over FeO_x/CeO₂ and CoO_x/CeO₂ (

Table 3. Effect of oxygen presence in the 0.15% N₂O in He mixture on N₂O conversion over CeO₂-based samples. 900 °C.

Sample	N2O Conversion, %
	0.15% N2O in He	0.15% N2O + 3% O2 in He
FeOx/CeO2	72.8	63.8
CoOx/CeO2	70.8	65.4

) and FeO_x/(CeO₂ + Al₂O₃) [9] samples, which can be due to the competitive adsorption of N₂O and oxygen on the same active sites. Therefore, O₂ formation by step 3 is preferable for CeO₂-based samples. However, oxygen species localized in anionic vacancies (O_v) are strongly bound with cations, and it is doubtful whether they can diffuse easily on the catalyst surface.

We supposed that the recombination of two oxygen atoms proceeds with the same mechanism as at oxygen exchange, i.e., with the interaction of O_v with O_s. The last, in turn, is capable of diffusing on the surface and can result from O_v (lattice oxygen) coming to the surface. The mechanism of N₂O decomposition accounting for the above reactions is represented in Scheme 2.

We consider that oxygen re-adsorption by reverse stage 3N (Scheme 2) is negligible because of low oxygen concentration at low N₂O conversion values in the experiments done for reaction rate evaluation and fast oxygen washing out from the reactor. In this case, the degree of surface coverage with O_s under reaction conditions can be supposed as negligible, like in the reaction of oxygen isotope exchange. One can see that direct and reverse stages 2N and 3N (Scheme 2) are represented in the scheme of oxygen isotope exchange (Scheme 1) as well. Therefore, the rates of these stages can be expressed in terms of rate constants of isotope exchange as follows:

$$r_{2N}=k_2(1-{\theta }_V){\theta }_S$$

(16)

$$r_{-2N}=k_{-2}{\theta }_V$$

(17)

$$r_{3N}=k_{-1}{\theta }_V{\theta }_S$$

(18)

Designating the rate constant of the stage of N₂O adsorption as k_1N, one can obtain the equation for r_1N:

$$r_{1N}=k_{1N}{C}_{N2O}(1-{\theta }_V)$$

(19)

Under the steady state: $r_{1N}=r_{-2N}-r_{2N}=r_{3N}$, so the system of steady-state equations looks as follows:

$$2k_1{}_N{C}_{N2O}\times (1-{\theta }_V)=k_{-1}\times {\theta }_V\times {\theta }_S$$

(20)

$$k_{-2}\times {\theta }_V=k_{-1}\times {\theta }_V\times {\theta }_S+k_2\times (1-{\theta }_V)\times {\theta }_S$$

(21)

Solving Equations (20) and (21) simultaneously, we found θ_V and θ_S. Finally, substituting them in the expression for r_1N, we obtained the following kinetic equation for the rate of reaction of N₂O decomposition (see details in Appendix C):

$$R_{N2O}=2k_{1N}{C}_{N2O}(1-{\theta }_V)=\frac{2k_{1N}{C}_{N2O}}{1+a_2\sqrt{2k_{1N}{C}_{N2O}{k}_2/k_{-1}{k}_{-2}}+k_1{}_N{C}_{N2O}/k_{-2}}$$

(22)

where

$$a_2=\sqrt{1+k_{-1}/k_2}$$

(23)

The following approximate kinetic equation is applicable in the case $k_1{}_N{C}_{N2O}/k_{-2}$ (stage 2N is not rate-determining):

$$R_{N2O}=2k_{1N}{C}_{N2O}(1-{\theta }_V)\approx \frac{2k_{1N}{C}_{N2O}}{1+\sqrt{2k_{1N}{C}_{N2O}{k}_2/k_{-1}{k}_{-2}}}$$

(24)

One can see that the equations for R_N2O, Equation (22) and R^II Equation (13), are close by the form. In the general case, the ratio between the rates of these reactions is determined with the following equation:

$$\frac{R^{II}}{R_{N2O}}=\frac{k_1{C}_{O2}}{2k_{1N}{C}_{N2O}}\frac{1+a_2\sqrt{2k_{1N}{C}_{N2O}{k}_2/k_{-1}{k}_{-2}}+k_1{}_N{C}_{N2O}/k_{-2}}{1+a_1\sqrt{k_1{C}_{O2}{k}_2/k_{-1}{k}_{-2}}+k_1{C}_{O2}/k_{-2}}$$

(25)

In the case when stages 2 (Scheme 1) and 2N (Scheme 2) are not rate-determining for both reactions, the ratio between rates of these reactions is determined with the following approximate equation:

$$\frac{R^{II}}{R_{N2O}}\approx \frac{k_1{C}_{O2}}{2k_{1N}{C}_{N2O}}\frac{1+\sqrt{2k_{1N}{C}_{N2O}{k}_2/k_{-1}{k}_{-2}}}{1+\sqrt{k_1{C}_{O2}{k}_2/k_{-1}{k}_{-2}}}$$

(26)

According to literature data, on oxides, the rate is usually proportional to C_N2O or has a slightly lower order due to the inhibition of produced oxygen [36]. In line with this, the dependence of the rate on N₂O concentration (varied from 0.15 vol.% to 1.0 vol.%) was around 0.97 for FeO_x/CeO₂ (Appendix D). Such close to 1 order means that the value of $\sqrt{2k_{1N}{C}_{N2O}{k}_2/k_{-1}{k}_{-2}}$ in Equations (24) and (26) is much less than unity. In this case, the ratio between the rates of reactions of two-atomic exchange and N₂O decomposition depends on the values of rate constants of the stages of oxygen and N₂O adsorption and their concentrations.

3.6. Mobility of Surface Oxygen and Rate Determining Steps of Two Atomic Isotope Exchange and N₂O Decomposition Reaction

According to the proposed mechanisms of isotope exchange and N₂O decomposition, the mobility of surface oxygen is characterized by the rate of the same stage designated as stage 2 (Scheme 1) and 2N (Scheme 2). One can estimate the rate of this stage in the reaction of isotope exchange directly from experimental data. So, at known ratios of R^I and R^II (Table 1) to the overall rate of oxygen adsorption-desorption, one can estimate the selectivity of exchange running by different pathways. The rate of oxygen adsorption-desorption is equal to the sum of R^I and R^II:

$$r_{-1}=r_1=R^{\mathrm{II}}+R^{\mathrm{I}}$$

(27)

Therefore, the selectivity of the reaction of isotope exchange with the pathway corresponding to the two-atomic exchange (S) will be determined in the following way:

$$S=\frac{R^{\mathrm{II}}}{r_{-1}}=\frac{R^{\mathrm{II}}}{R^{\mathrm{II}}+R^{\mathrm{I}}}$$

(28)

At a known $r_{-1}$ and S, one can calculate the rate of stage 2 (Scheme 1) using Equation (3):

$$r_2=r_{-1}S/(1-S)$$

(29)

Calculated values of S and the rates of different stages of isotope exchange in the samples have been presented in

Table 4. Selectivity to two-atom exchange (S) and rates of different stages of oxygen isotope exchange.

Sample	S	(r1 = r−1) × 105 mol/m2s	(r2 = r−2) × 105 mol/m2s	r2(−2)/r1(−1)
CeO2	0.93 (±0.04)	0.43 (±0.03)	8 (±3)	20 (±10)
NiOx/CeO2	0.94 (±0.04)	0.53 (±0.03)	15 (±7)	30 (±20)
FeOx/CeO2	0.92 (±0.04)	1.4 (±0.1)	16 (±5)	12 (±5)
CoOx/CeO2	0.12 (±0.01)	46 (±1.5)	7 (±1)	0.15

. The value of S for CoO_x/CeO₂ is low, and the estimation of r₂ = r₋₂, in this case, is quite precise. The higher the selectivity, the less precise the estimate.

The values of θ_V and θ_S in the reaction of N₂O decomposition can differ from those in isotope exchange, thus resulting in the change of the ratio between rates of these stages. So, the r₋₂/r₋₁ ratio in the reaction of isotope exchange is determined with the values corresponding rate constants and θ_S value:

$$\frac{r_{-2}}{r_{-1}}=\frac{k_{-2}{\theta }_V}{k_{-1}{\theta }_V{\theta }_S}=\frac{k_{-2}}{k_{-1}{\theta }_S}$$

(30)

The ratio r_−2N/r_3N that determines the rate-determining stage in the reaction of N₂O decomposition is the same:

$$\frac{r_{-2N}}{r_{3N}}=\frac{k_{-2}{\theta }_V}{k_{-1}{\theta }_V{\theta }_S}=\frac{k_{-2}}{k_{-1}{\theta }_S}$$

(31)

The formation of weakly bound oxygen O_s proceeds with both stage 2N and stage of oxygen adsorption 3N (Scheme 2). Gas phase oxygen concentration under the conditions of N₂O decomposition (<0.01% on average by the length of the catalyst layer) is much less than during isotope exchange experiments (0.5%). Accordingly, we consider that the θ_S value in the reaction conditions cannot be higher than at isotope exchange. In this case

$$\frac{r_{-2N}}{r_{3N}}\ge \frac{r_{-2}}{r_{-1}}$$

(32)

$r_{-2}$ >> $r_{-1}$ for CeO₂, NiO_x/CeO₂, and FeO_x/CeO₂ samples. Therefore $r_{-2N}$ >> $r_{3N}$ as well. In this case, stages 2 (Scheme 1) and 2N (Scheme 2) are not rate-determining in the reaction of oxygen isotope exchange and in N₂O decomposition. The ratio between the rates of these reactions is thus determined with Equation (26) and depends mainly on the ratio of rate constants of the stages of oxygen and N₂O adsorption and their concentrations.

In the case of CoO_x/CeO₂, $r_{-2}$ < $r_{-1}$, i.e., stage 2 is rate-determining in the reaction of isotope exchange. However, it is not so obvious for the reaction of N₂O decomposition because $r_{-2N}$/$r_{3N}$ can be higher than $r_{-2}$/$r_{-1}$. Finally, the ratio between rates of these reactions will be determined with Equation (25).

3.7. Role of MeO_x–CeO₂ Interface in the Reactions of Isotope Exchange and N₂O Decomposition

Estimates of the rates of different stages made above were based on the assumption of equivalence of all active sites participating in the reactions. It is true only for CeO₂. Supporting of MeOx produces other sites which can be responsible for efficient O₂ adsorption as well. First of all, these are oxygen vacancies located on the surface of crystalline Fe₂O₃, NiO, and Co₃O₄ particles (Figure 4) detected in the samples or their smaller clusters and on the Me–Ce interface. The relative surface concentration of MeO_x is reasonably low (Me/Ce = 0.13 ± 0.1) (

Table 5. Me/Ce (Me = Ni, Fe, Co) atomic ratios in the surface layers (XPS) of different MeO_x/CeO₂ samples, normalized rates of isotope exchange on MeOx and CeO₂ (R^I _(Me,Ce) and R^II _(Me,Ce)) and rates of reactions of stages 1 and 2 (Scheme 1) of isotope exchange on different sites ((r₁ = r₋₁) _(Me,Ce) and (r₂ = r₋₂) _(Me,Ce)). Me concentration—0.86–0.91 wt.%.

Sample	Me/Ce	RI (Me,Ce), s−1	RII (Me,Ce), s−1	(r1 = r−1) (Me,Ce), s−1	(r2 = r−2) (Me,Ce), s−1
CeO2		0.015	0.245	0.26 (±0.02)	4.8 (±2)
NiOx/CeO2	0.12	0.04	0.68	0.72 (±0.02)	12 (±6)
FeOx/CeO2	0.13	0.4	4.3	4.7 (±0.05)	48 (±15)
CoOx/CeO2	0.14	190	23	210 (±7)	25 (±3)

), but their contribution to the rate of exchange can be prominent.

We estimated the values of R^I and R^II on MeO_x normalized to their concentration (R^I _(Me,Ce) and R^II _(Me,Ce), respectively) using Me/Ce values on the surface as measured with XPS and supposing overall concentration of active sites as 1.67 × 10⁵ mole/m². Then S values and rates of reactions of stages 1 and 2 (Scheme 1) for isotope exchange on different sites ((r₁ = r₋₁) _(Me,Ce) and (r₂ = r₋₂)(_Me,Ce)) were calculated as well using Equations (27)–(29) (Table 5).

It is logical to suppose that exchange between surface and bulk oxygen on oxides proceeds with the participation of strongly bound oxygen O_V. Scheme 3 describes isotope transfer between gas phase O₂ and ceria bulk (O_bulk(Ce)) for this case.

To keep the general rate of heteroexchange and selectivity to the two-atom exchange observed in the experiments, the rate of stage 3 (Scheme 3) should be at least equal to the sum of the rates of stages 1 and 2, i.e., r_surf-_bulk(Ce) ≥ r_1(Ce) + r_2(Ce). An additional pathway of isotope transfer between O₂ and ceria bulk appears in MeO_x/CeO₂ samples with the participation of MeO_x particles (Scheme 4).

This scheme includes two pathways of isotope transfer from the MeO_x particle to O_bulk(Ce). Spillover of weakly bound oxygen from the MeO_x surface to the CeO₂ surface followed by transfer to CeO₂ bulk through O_v(Ce) (stage 3a, Scheme 4) provides for the first pathway. By the second pathway (stage 4a), the exchange proceeds first—between strongly bound oxygen of MeO_x (O_V(Me)) and that in MeO_x bulk (O_bulk(Me))_, and then—between O_bulk(Me) and oxygen in CeO₂ bulk, Ob_ulk(Ce). The overall rate of isotope transfer by stages 3a and 4a cannot be less than r_1(Me) + r_2(Me).

Numerical analysis of isotope experiments showed that isotope diffusion to the bulk of CeO₂ (O_s(Ce) ↔ O_bulk(Ce)) is not the rate-determining step of the isotope exchange reaction. This agrees with the results of earlier studies performed on ceria [37], where higher mobility of the oxygen in the lattice than the rate of exchange with the gas phase has been shown. In contrast with CeO₂, the rate of isotope exchange of the surface and the bulk oxygen in Fe, Co, Ni, or mixed La-Fe-O oxides is much lower than the rate of exchange with gas phase O₂ [37,38,39]. So, in the LaFeO₃ sample representing a mixture of perovskite, α-Fe₂O_3, and La₂O_3, the rate constant of heteroexchange at 800 °C was 8 s⁻¹, while the rate of oxygen diffusion in bulk was three orders of magnitude lower (6 × 10⁻³ s⁻¹). In CeO₂, vice versa, these values were 1.2 s⁻¹ and >0.1 s⁻¹, respectively [39]. Solsona et al. performed ¹⁸O₂ TPIE experiments and showed that the addition of ceria into the NiO catalysts increases the diffusion of oxygen in the bulk of the samples [40]. Hence, we suppose that the rate of stage 4a in all MeO_x/CeO₂ samples is negligible compared with the rate of oxygen exchange on the surface of the MeO_x particle.

We tried to estimate whether the rate of stage 3a (Scheme 4) can provide an increase in the rate of heteroexchange in MeO_x/CeO₂ compared with CeO₂. At the known Me/Ce value (Table 5), the rate of transfer of isotope label by stage 3a (Scheme 4) will be not higher than r_2(Ce)/0.11 = 42 (±20) mole/(mole(Me) × s) for any of MeO_x/CeO₂ samples. For the case of FeO_x/CeO₂ and CoO_x/CeO_2, this value is less than r_1(Me) + r_2(Me) (Table 5). Therefore, one can conclude that the increase of the rate of isotope exchange in FeO_x/CeO₂ and CoO_x/CeO₂ samples compared with that in CeO₂ is due to sites on the Me–CeO₂ interface characterized by increased concentration of oxygen vacancies promoting oxygen exchange [41,42,43].

For the case of FeO_x/CeO_2, this is confirmed with ¹⁸O₂ TPIE experiments on the samples with different Fe content. One can see (Figure 5a) that the increase of Fe content in the sample from 0.86 wt% to 2.5 wt% resulted in a high-temperature shift in the isotope fraction curve, thus evidencing a decrease in the rate of exchange. Non-proportional growth of the Fe/Ce surface ratio (as measured with XPS) from 0.13 to 0.19 only with Fe content in the sample can be due to the enlargement of Fe₂O₃ particles decreasing the concentration of sites on the Fe–Ce interface. It is interesting that FeO_x/CeO₂ sample with higher Fe content was also less active in deN₂O (Figure 5b). Therefore, reaction on the Me–CeO₂ interface contributes more substantially to the overall reaction rate than that on Fe sites.

The results of TG-DTA-MS experiments performed in an oxygen-containing stream [33] showed that cobalt in CoOx–CeO₂ catalysts are present in the form of Co₃O₄/CoO particles and a CoO_x–CeO₂ system formed on the cobalt oxide–ceria interface. The decrease of N₂O conversion under oxygen-deficient conditions at T > 800 °C resulted from the reduction of Co₃O₄ to CoO in the particles weakly interacting with CeO₂. The authors, therefore, concluded that the activity of these catalysts originates from the interaction of cobalt oxide with CeO₂. A strong dispersion effect of the cobalt spinel active phase spread over ceria on the turnover rate of deN₂O was observed due to the progressive agglomeration of the Co₃O₄ nanocrystallites into compact domains with the increasing cobalt loading [44]. Model supposing the cylindrical shape of Co₃O₄ domains permitted normalizing the deN₂O reaction rate with respect to the cobalt content and the length of the Co₃O₄/CeO₂ interface periphery. The authors proposed a two-step mechanism operating at the interface, where the redox properties of the cobalt component were responsible for the dissociation of N₂O molecules and formation of oxygen intermediates, whereas the ceria periphery was responsible for the enhanced diffusion and recombination of oxygen adspecies, closing the catalytic cycle.

For the NiO_x/CeO₂ sample, we did not observe the effect of the Ni-ceria interface on the rate of oxygen transfer. Indeed, a minimal red shift of the CeO₂ absorption edge was observed in the UV-vis DR spectra of the NiO_x/CeO₂ sample compared to that in the CeO₂ (Eg value of 3.35 eV and 3.27 eV, respectively). For the CoO_x/CeO₂ and FeO_x/CeO₂ samples, Eg values were substantially lower (3.18–3.22 eV) [8]. It indicates that either (1) Fe/Co ions substitute Ce into the CeO₂ lattice, or (2) the isolated Me ions form a mixed Me–Ce oxide and strongly interact with CeO₂ leading to the electronic structure changes [45]. The additional absorption band at ~20,000–23,500 cm⁻¹ in the spectra of Co(Fe)O_x/CeO₂ samples [8] is due to O₂ adsorption on the structural defect; more obviously, clusters of oxygen vacancies arose on Fe(Co)-CeO₂ interface.

4. Conclusions

Oxygen transfer on the surface and in the bulk of CeO₂ and MeO_x/CeO₂ (Me = Fe, Co, Ni) catalysts was studied using ¹⁸O isotope exchange. The relationship between this process and the kinetics of the reaction of N₂O decomposition was elucidated.

Supporting of MeO_x onto CeO₂ increased the rate of isotope exchange by 20% (Ni), threefold (Fe), and more than ten times (Co). Both single-atom and two-atom exchanges proceed simultaneously in all samples: two-atom exchange predominates in CeO₂, NiO_x/CeO_2, and FeO_x/CeO₂, while the one-atom exchange prevails in CoO_x/CeO₂. One can interpret both types of exchange using a two-step mechanism [14,18,19], considering two forms of surface oxygen. With this mechanism, weakly bound oxygen (O_s) can diffuse on the surface and can transform into a strongly bound form (O_v) after interaction with anionic vacancy. The contribution of every type of exchange to the overall rate of heteroexchange depends on the ratio of the rate of recombination of O_s and O_v and the rate of their interconversion. The last, in turn, characterizes the mobility of the surface oxygen. We obtained estimates of the surface oxygen mobility in CeO2-based samples using such a model. It turned out that CeO₂ promotion using FeO_x and NiO_x increases the mobility of surface oxygen, while it doesn’t change in the case of CoO_x. It is shown that the mobility of surface oxygen can determine the rate of the reaction of N₂O decomposition on CoO_x/CeO₂. On other samples, it is determined by the rate of N₂O adsorption.

Detailed analysis of the kinetics of isotope exchange accounting for the surface concentration of MeO_x made it possible to estimate their contribution to the rates of different types of exchange and quantify the rates of oxygen transfer from MeOx to the bulk of CeO₂ by different pathways. Oxygen transfer from MeOx to the bulk of CeO₂ realized on the Me–Ce interface is shown to be important in FeOx/CeO₂ and CoOx/CeO₂ and makes a prominent contribution to the overall rate of exchange in these samples. Direct dependence of the rate of isotope exchange in FeO_x/CeO₂ samples with different Fe content on the length of the FeO_x-CeO₂ interface was shown. The analogous effect was observed for the rate of deN₂O reaction, which points to the principal role of the interface in both reactions.