Experimental Study and Mathematical Modeling of Self-Sustained

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Experimental Study and Mathematical Modeling of Self-Sustained Kinetic Oscillations in Catalytic Oxidation of Methane over Nickel Elena A Lashina, Vasily V Kaichev, Andrey Aleksandrovich Saraev, Zakhar S. Vinokurov, Nataliya A Chumakova, Gennadii Chumakov, and Valerii I. Bukhtiyarov J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b04525 • Publication Date (Web): 16 Aug 2017 Downloaded from http://pubs.acs.org on August 17, 2017

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The Journal of Physical Chemistry

Experimental Study and Mathematical Modeling of Self-Sustained Kinetic Oscillations in Catalytic Oxidation of Methane over Nickel Elena A. Lashina,†,‡ Vasily V. Kaichev, *,†,‡ Andrey A. Saraev, †,‡ Zakhar S. Vinokurov, †,‡ Nataliya A. Chumakova, †,‡ Gennadii A. Chumakov, ‡,§ Valerii I. Bukhtiyarov†,‡ †

Boreskov Institute of Catalysis, Akademika Lavrentieva Ave. 5, 630090 Novosibirsk, Russia

‡

Novosibirsk State University, Pirogova Str. 2, 630090 Novosibirsk, Russia

§

Sobolev Institute of Mathematics, Akademika Koptyuga Ave. 4, 630090 Novosibirsk, Russia

A B S T R A C T : The self-sustained kinetic oscillations in the oxidation of CH4 over Ni foil have been studied at atmospheric pressure using an X-ray diffraction technique and mass spectrometry. It has been shown that the regular oscillations appear under oxygen-deficient conditions; CO, CO2, H2, and H2O are detected as the products. According to in situ X-ray diffraction measurements nickel periodically oxidizes to NiO initiating the reaction-rate oscillations. To describe the oscillations we have proposed a 5-stage mechanism of the partial oxidation of methane over Ni and a corresponding three-variable kinetic model. The mechanism considers catalytic methane decomposition, dissociative adsorption of oxygen, transformation of chemisorbed oxygen to surface nickel oxide, and reaction of adsorbed carbon and oxygen species to form CO. Analysis of the kinetic model indicates that the competition of two processes, i.e., the oxidation and the carbonization of the catalyst surface, is the driving force of the self-sustained oscillations in the oxidation of methane. We have compared this mechanism with the detailed 18-stage mechanism describing previously by Lashina et al. (Kinetics and Catalysis 2012, 53, 374-383). It has been shown that both kinetic mechanisms coupled with a continuous stirred-tank reactor model describe well the oscillatory behavior in the oxidation of methane under non-isothermal conditions.

1. INTRODUCTION Critical phenomena such as hysteresis, regular self-sustained kinetic oscillations as well as chaotic dynamics are often observed in different heterogeneous catalytic systems. The intensive studies of these nonlinear effects in reaction dynamics have been performed in the last decades of the 20th century.1–5 As a result, harmonic oscillations, relaxation-type oscillations, and chaotic behavior have been discovered to date in approximately 40 catalytic reactions in the wide pressure range from ultrahigh vacuum up to atmospheric pressure, over many types of catalysts including single-crystals, polycrystalline foils, wires, and supported catalysts. The hysteresis effects were mostly observed in the oxidation of CO over supported and unsupported metal catalysts. In general, these investigations

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were limited by kinetic measurements with the exception of the oxidation of CO over Pt- and Pdbased catalysts, which were studied in detail using various surface-sensitive techniques. It allowed developing numerous mechanisms predicting the rate oscillations and the concentration hysteresis in the catalytic oxidation of CO under certain conditions.6–15 Depending on the pressure range and catalyst nature, the driving force for the oscillations is associated with periodic structural changes of the catalyst surface6–8 or with variation in the subsurface oxygen concentration9 that modulate the sticking coefficient of oxygen and, hence, the catalytic activity. Other mechanisms link the rate oscillations to the periodic deactivation of the catalyst surface because of either accumulation of carbonaceous deposits10 or formation of a surface oxide layer.11 Finally, in some mechanisms, the oscillatory rate of CO2 production is explained by fluctuations of the catalyst temperature12 or influence of the surface coverage with adsorbates to the activation energies of some steps.13–15 At the same time, the isothermal kinetic oscillations in the catalytic oxidation of CO were also observed.8 In all these cases, kinetic models for the oxidation of CO are based on the Langmuir–Hinshelwood mechanism and can be well described by a system of three or four nonlinear ordinary differential equations. In the beginning of the 21st century due to developing in situ surface-sensitive techniques, the interest of researchers has switched to more complicated reactions such as the catalytic oxidation of hydrocarbons.16–22 In particular, the concentration hysteresis in the oxidation of methane over Pt21 and the self-sustained reaction-rate oscillations in the oxidation of methane over Pd20 and propane over Ni17,18 were studied in situ using X-ray absorption spectroscopy and X-ray photoelectron spectroscopy (XPS). The application of these modern techniques combining with mass-spectrometry (MS) showed directly that the chemical state of Pt, Pd, and Ni can change under reaction conditions and thus change the catalytic performance. It should be noted that the self-sustained oscillations of the relaxation type were detected in the oxidation of methane under oxygen-deficient conditions at atmospheric pressure on a variety of catalysts, including Ni wires, foils, and foams, Ni/Cr alloys, Co foils, Pd films and foils, as well as supported Ni, Pd, Rh, and Ru-based catalysts.19,20,23–38 The oscillations were detected of both product and reactant concentrations and the catalyst temperature. Similar oscillations were also observed in the oxidation of ethane and propane over Ni wires and foils.17,18,39–41 All these observations point out that the same oscillatory mechanism is realized in the oxidation of light hydrocarbons. Herein we present the results of our mechanistic study of the oscillatory behavior of the catalytic oxidation of methane over Ni used as a case reaction. In order to elucidate the driving forces of the oscillations we performed the kinetic study in a flow reactor at atmospheric pressure using mass-spectrometry and thermocouples. It allowed us to examine the conditions under which the oscillations appeared, to study the product distributions and the catalyst temperature oscillations. The catalyst was also studied by an X-ray diffraction (XRD) technique in situ, i.e., directly during the ACS Paragon Plus Environment

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oscillations. We also developed the detailed mechanism of the oxidation of methane over Ni based on the 18-steps microkinetics scheme; using mathematical modeling we showed that the mechanism described qualitatively the main features of the oscillatory behavior observed experimentally. Basing on the quasi-steady-state approach, we demonstrated the possibility of a simplification of the reaction mechanism. As a result, we proposed a simple reaction mechanism as well as a kinetic model of three ordinary differential equations, which is similar to the so-called surface oxide STM model developed by Sales, Turner, and Maple for the oscillatory oxidation of CO over Pt, Pd, and Ir.11 The main distinction of our model is that adsorbed carbon species do not desorb back into the gas phase, which causes the possibility of the carbonization of the catalyst surface. The simplified kinetic model shows that both the oxidation and carbonization of the catalyst surface are the driving forces of the selfsustained reaction-rate oscillations in the oxidation of methane over Ni. The corresponding mathematical models for the oxidation of methane in a continuous stirred-tank reactor (CSTR) were also developed. These models were used to generate simulated results for the oscillatory behavior in the reaction under study and to compare oscillation solutions with our experimental data.

2. EXPERIMENTAL METHODS The kinetic experiments were performed under atmospheric pressure using a home-made flow reactor.19 The reactor was constructed from a quartz tube of 18 mm inner diameter and 100 mm length. The reactor was placed inside an electric furnace. The temperature was monitored by a K-type thermocouple. The flows of methane, oxygen, and argon were regulated separately with mass-flow controllers SEC-Z500 (Horiba Ltd.). Rectangular pieces of 0.125 mm thick nickel foil 4×8 mm in size (purity 99.99%, Advent Research Materials Ltd.) were used as the catalyst. The catalyst temperature was monitored with another K-type Compton isolated thermocouple spot-welded directly to the foil edge. The products and reactants were analyzed using a quadruple-type gas analyzer UGA100 (Stanford Research Systems Inc.) connected to the reactor outlet through a stainless steel capillary of 0.175 mm inner diameter and 1 m length. In addition, to establish the changes in the catalyst state during the reaction-rate oscillations, the in situ XRD-MS study was performed using the High-Precision Diffractometry station at the synchrotron radiation facilities of the VEPP-3 storage ring (Siberian Synchrotron and Terahertz Radiation Center, Novosibirsk, Russia). The experiments were carried out on a high-precision X-ray diffractometer equipped with a high temperature reaction chamber XRK-900 (Anton Paar GmbH) and with the same gas analyzer and flow mass controllers which were used in the kinetic experiments. The time-resolved XRD experiments were performed using a position sensitive parallax-free linear OD-3M detector. The X-ray wavelength of 1.724 Å was set by a single reflection of the synchrotron radiation from a Ge(111) double crystal monochromator. ACS Paragon Plus Environment

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3. EXPERIMENTAL RESULTS In the first part of our study we investigated the catalytic oxidation of methane in the flow reactor at different CH4:O2 molar ratios. In these experiments we fixed the CH4 flow at 20 sccm and varied the flows of O2 and Ar to the reactor. The total flow was 50 sccm and the reactor temperature was 993 K. CO, CO2, and H2 were detected as products (Fig. 1). Unfortunately, oscillations of the water vapor pressure were not detected because of the high intensity of the background signal from H2O. In full agreement with the previous studies,28,29 the regular self-sustained oscillations were observed under the oxygen-deficient conditions at the CH4:O2 molar ratios in the range between 15:1 and 2:1. In the rich mixtures the catalyst usually was in the high-active state and periodically passed to the lowactive state. As a result, sharp positive peaks were observed in the MS signals of methane and oxygen and, correspondingly, synchronous inverted, negative peaks were observed in the MS signals of CO, CO2, and H2. The inverse picture was observed at the CH4:O2 molar ratio of 2:1 when the catalyst usually was in the low-active state and periodically passed to the high-active state (Fig. 1). When the CH4:O2 molar ratio was 4:1, the duration of high-active and low-active half-periods was almost the same and the shape of oscillations was similar to the meander. It should be underlined that the peaks of CO and CO2 which corresponded to products of the partial and total oxidation, respectively, appeared synchronously. In order to establish the changes in the catalyst state during the reaction-rate oscillations in situ XRD-MS measurements were performed. Figure 2 shows the characteristic XRD patterns obtained for the low-active and high-active states of the catalyst. The high intensity of the NiO(111) and NiO(200) reflections at 41.4° and 48.2°, respectively, are observed when the catalyst is in the lowactive state. The transition to the high-active state is accompanied by a significant increase of the Ni(111) and Ni(200) reflections at 49.5° and 57.9°, respectively, and a complete disappearance of the nickel oxide patterns. Hence, the self-sustained reaction-rate oscillations in the oxidation of methane over Ni are accompanied by periodical oxidation and reduction of the catalyst. This finding is in good agreement with our in situ XPS-MS study17,18 where it is shown that the self-sustained reaction-rate oscillations in the oxidation of propane are controlled by the reversible oxidation of Ni to NiO.


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Figure 1. Self-sustained oscillations in the catalytic oxidation of methane over Ni foil at different CH4:O2 molar ratios. The temperature of the flow reactor is 993 K. Argon is used as a balance.

Figure 2. XRD patterns of the Ni foil obtained during the low-active half-period (1) and the highactive half-period (2). The CH4:O2 molar ratio is equal to 4:1.


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The period of oscillations nonmonotonically depended on the CH4:O2 molar ratio. In our experiments we fixed the methane flow to provide the partial pressure of methane in the reactant mixture at 400 mbar whereas the partial pressure of O2 was varied. Under these conditions the period ranged between 200 and 1000 s. The shortest period was observed at approximately 80 mbar of oxygen that corresponded to the CH4:O2 molar ratio equal to 5:1 (Fig. 3). In contrast, in our previous study19 we observed that the oscillation period increased exponentially when the partial pressure of methane was reduced at fixed partial pressure of O2. In fact, the period depends on the partial pressure of reactants, the feed flow, the catalyst type, and the catalyst loading as well as on the reactor temperature. Indeed, earlier Zhang et al.28,29 studied the oscillations in the oxidation of methane over Ni wires and foils and found that under similar conditions in the first case the oscillations appeared in the temperature range of 1003-1073 K, whereas in the second case the oscillations appeared in the temperature range of 1033-1173 K. In contrast to our results, the period of oscillations ranged between 20 and 60 s.28

Figure 3. Period of self-sustained oscillations and amplitude of temperature oscillations as functions of the partial pressure of O2 in the reactant mixture. The partial pressure of CH4 is 400 mbar. The oscillations of products and reactants were accompanied with synchronous oscillations of the catalyst temperature. The temperature oscillations had a complex shape (Fig. 1) and its amplitude achieved 170 K (Fig. 3). The amplitude increased almost linearly with the increasing partial pressure of O2. One can see sharp negative and positive peaks indicating that both exothermic and endothermic processes occur during the self-sustained oscillations.19 The typical waveform of the oscillations observed at the CH4:O2 molar ratio of 3:1 is depicted in Fig. 4. At least four stages can be identified in the oscillation pattern. Stage I corresponds to the low-active state when the temperature ACS Paragon Plus Environment

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of the catalyst is constant. According to the in situ XRD data (Fig. 2) the catalyst is in the oxidized state in this case. Stage II corresponds to the transition from the low-active to high-active state when a sharp increase of the CO and CO2 yield is observed. During this stage, the catalyst temperature first increases sharply and then drops dramatically. As a result, one can see the sharp temperature peak with amplitude of approximately 40 K, after which the temperature decreases to an even lower value comparing with the temperature of the catalyst in the low-active state. We suggest that the decreasing in temperature at stage II is due to endothermic reactions such as the reduction of nickel oxide by 0 = +50.9 kcal/mol). It should be noted that the methane: NiO + CH4 = Ni + CO + 2H2 ( ∆H 1000

reduction of NiO by carbon is also endothermic process and cannot be excluded from under 0 consideration as well: NiO + C = Ni + CO ( ∆H 1000 = +29.4 kcal/mol); 2NiO + C = 2Ni + CO2 0 ( ∆H 1000 = +17.9 kcal/mol). We believe that the sharp positive peak is due to burning the surface 0 0 = –94.3 kcal/mol) and С + 0.5О2 = СО ( ∆H 1000 = –26.8 carbon depositions: С + О2 = СО2 ( ∆H 1000

kcal/mol). Unfortunately, carbonaceous deposits cannot be detected by XRD. However, recently, it was shown that the carbonization of the catalyst surface occurs in the self-sustained oscillations in the oxidation of methane over Pd.16 Moreover, it is well known that carbon laydown is a major deactivation mechanism for Ni-based catalysts in the syngas production.

Figure 4. Characteristic temperature oscillations accompanied the self-sustained oscillations of the rate of the catalytic oxidation of methane over the Ni foil. The molar ratio CH4:O2 is 3:1. It is very important to note that Zhang et al.28 also observed a decrease in the catalyst temperature during the self-sustained oscillations in the oxidation of methane over Ni foil. The temperature profile consisted of a sharp positive peak following a negative sharp peak. In contrast to


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our explanation, they suggested that these peaks originated due to CO2 production from the highly exothermic reaction and CO production from endothermic reactions, respectively. In our experiments the decrease in temperature at stage II is simultaneously accompanied by the increase in both CO and CO2 production (Fig. 4). Stage III corresponds to the high-active state when the catalyst temperature increases monotonically due to a high rate of the oxidation of methane to CO and CO2 over metallic nickel. 0 Indeed, both these reactions are exothermic: СН4 + 2О2 = СО2 + 2Н2О ( ∆H 1000 = –191 kcal/mol), 0 СН4 + 0.5О2 = СО + 2Н2 ( ∆H 1000 = –5.2 kcal/mol). During stage III the slow decrease of the

conversion of methane takes place which is accompanied with the decrease of the CO yield. It means that the activity of the nickel foil falls steadily due to the slow oxidation of nickel: Ni + 0.5O2 = NiO 0 ( ∆H 1000 = –56.2 kcal/mol). In addition, the decrease in activity may also occur due to blocking the

catalyst surface by carbon formed by the decomposition of methane.19 Finally, at stage IV the transition from the high-active state to the low-active state occurs and we detect a decrease in the CO and CO2 signals simultaneously with an exponential decrease in the catalyst temperature. Hence, we can conclude that the self-sustained oscillations originate from the reversible oxidation of Ni to NiO. The high-active catalyst surface is represented by metallic nickel, whereas it is covered with a layer of NiO during the low-active half-periods. Indirectly it was confirmed earlier by the visual observation of the color changes due to periodical variation of the Ni valence state during the oscillatory oxidation of methane over Ni foam.34 The increase of the catalyst temperature is mainly due to the combustion of methane over metallic nickel. Since the peaks of CO and CO2 appear synchronously, the total and partial oxidation of methane occurs over metallic nickel with a high rate. Recently analogous results were obtained in the in situ XPS study of the self-sustained oscillations in the oxidation of propane over Ni.17,18 In full agreement with this hypothesis, the amplitude of temperature oscillations increases with the partial pressure of oxygen (Fig. 3) because under these conditions this leads to an increase in the conversion of methane. In spite of the large amplitude of the temperature oscillations, we believe that the thermal instability is not the main reason for the self-sustained reaction-rate oscillations in the oxidation of methane over nickel. Indeed, the amplitude of these temperature oscillations depends on reaction conditions: the flows of reactants, the type of catalysts used, and the type of the catalytic reactor. For example, Zhang with co-authors27 observed, under certain conditions, the temperature oscillations with amplitude of 6-7 K only, which were nevertheless accompanied by strong oscillations of products and reactants in the gas phase.

4. MATHEMATIC MODELING AND DISCUSSION


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4.1. “Starting” reaction mechanism The mechanism of the catalytic oxidation of methane over transition metals has been the focus of numerous studies because of its relevance to industrially important applications. As a result, two main groups of different reaction mechanisms have been proposed. As early as in 1946, Prettre et al.42 postulated that the reaction pathway involves the initial conversion of a part of the methane feed to CO2 and H2O followed by steam reforming, CO2 reforming, and water-gas shift reactions. This assumption is accepted by some researchers (see Ref. [43] and references therein). The mechanisms of the other group are based on the direct oxidation via methane pyrolysis, as proposed by Hickman and Schmidt.44,45 The authors suggested that the dissociation of methane is an initial step for the CO and H2 production, while CO2 is the secondary product of the CO oxidation. Later, this hypothesis was confirmed by the experimental results46–49 and several microkinetic schemes characterized by different levels of detail were proposed. Most of them are based on the Langmuir–Hinshelwood mechanism. One of the simplest kinetic models developed by Slinko et al. ten years ago consists of 10 reaction steps.50 The main feature of this model is that the partial oxidation of methane to CO and H2 occurs over Ni in the metallic state, whereas the total oxidation of methane to CO2 and H2O proceeds over NiO only. This model predicts the thermo-kinetic oscillations due to the periodic oxidationreduction of the catalyst surface, while no isothermal oscillations are found in the model. Unfortunately, this model cannot describe the synchronous appearance of the CO and CO2 peaks observed in our experiments. Afterwards, several research groups developed more detailed microkinetic schemes of the catalytic oxidation of methane over Ni based on the gas-surface interaction law.51–53 The schemes include 18 elementary reaction steps. In short, these steps describe the dissociative adsorption of the reagents on metallic Ni with the formation of O, C, and H atoms, which can further react to form CO, CO2, H2, and H2O. It is very important that the scheme implies that adsorbed oxygen can transform Ni to NiO that can be reduced by C, H or CO. By the MonteCarlo methods it has been shown that the microkinetic scheme predicts the oscillatory behavior in the oxidation of methane over nickel under both isothermal and non-isothermal conditions.51,53 It should be noted that the Monte-Carlo methods cannot reproduce time parameters and for comparison with experimental results mathematic modeling based on numerical integration of a set of differential equations is more preferable. Moreover, in the last case it is possible to use the methods of qualitative theory of dynamical systems for studying the possible states of the variables depending on the initial conditions and parameters (i.e., to consider the structure of the phase space of the dynamical system). In this study, to perform mathematical modeling we used a similar 18-stage microkinetic scheme of the catalytic oxidation of methane over Ni. In accordance with the results of a pulse


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study,46 steps (1) – (6) in our mechanism describe adsorption and stepwise dehydrogenation of methane to C and H adsorbed species: CH4(g) + [*] → [CH4*],

(1)

[CH4*] → CH4(g) + [*],

(2)

[CH4*] + [*] → [CH3*] + [H*],

(3)

[CH3*] + [*] → [CH2*] + [H*],

(4)

[CH2*] + [*] → [CH*] + [H*],

(5)

[CH*] + [*] → [C*] + [H*].

(6)

An asterisk (*) represents the adsorption sites on the reduced catalyst surface. Correspondingly, [CH4*], [CH3*], [CH2*], and [CH*] denote supposedly inactive surface intermediates; i.e., those not participating in oxidative reactions; [C*] and [H*] are carbon and hydrogen atoms adsorbed on the reduced catalyst surface. Hydrogen desorbs from the reduced catalyst surface to the gas phase: 2[H*] → H2(g) + 2[*]

(7)

Oxygen adsorbs on the reduced catalyst surface dissociatively to form chemisorbed oxygen species: O2(g) + 2[*] → 2[O*].

(8)

Adsorbed oxygen and carbon react to form adsorbed CO, which desorbs to the gas phase: [C*] + [O*] → [CO*] + [*],

(9)

[CO*] → CO(g) + [*].

(10)

The following step describes the interaction of oxygen and carbon monoxide adsorbed on the reduced catalyst surface, which leads to the formation and following desorption of CO2: [CO*] + [O*] → CO2(g) + 2[*].

(11)

Interaction of adsorbed hydrogen and oxygen atoms leads to the formation of hydroxyl groups, which in turn can react with adsorbed hydrogen and produce H2O: [H*] + [O*] → [OH*] + [*],

(12)

[H*] + [OH*] → H2O(g) + 2[*].

(13)

In fact, steps (1) – (13) proceed on the reduced catalyst surface and reflect the direct oxidation mechanism proposed by Hickman and Schmidt.44,45 At the same time, some authors suggest that the self-sustained oscillations in the oxidation of methane over Ni are accompanied with repetitive oxidation and reduction of the catalyst.34 Moreover, our experimental results presented above also support this hypothesis. To take this process into account, the following step describing the transformation of chemisorbed oxygen to surface nickel oxide was used: [O*] → [NiO].

(14)

We postulated that the surface oxide species block the catalyst surface and prevent CH4 and O2 adsorption. However, the nickel oxide species can be reduced via the interaction with some intermediates adsorbed on the metallic surface. To describe this pathway, the next three steps were used: ACS Paragon Plus Environment

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[C*] + [NiO] → [CO*] + [*],

(15)

[CO*] + [NiO] → CO2(g) + 2[*],

(16)

[H*] + [NiO] → [OH*] + [*].

(17)

It should be noted that earlier we analyzed a similar mechanism of the oxidation of methane over Ni under isothermal conditions.52 We found that the system has a stable state corresponding to the catalyst surface completely covered by oxygen species. In order to avoid this critical situation some modification of the mechanism is needed. It is well known that the oxidized Ni-based catalysts, which contain nickel oxide, are active in the oxidation of methane, and that NiO undergoes the reduction under reaction conditions.46 This effect can be explained by the assumption that the oxidation of methane can proceed via the Eley–Rideal mechanism according to which surface oxygen species can react with gaseous methane molecules. Indeed, under certain conditions, this mechanism could satisfactorily fit the experimental results of kinetic studies.54–57 Considering this hypothesis, we inserted the following step in our microkinetic scheme: CH4(g) + 4[NiO] → 2 H2O(g) + CO2(g) + 4[*].

(18)

To estimate the thermal effects and rate parameters for each reaction step, we assumed that for all the steps apart from steps (1) and (8) the reaction rate constants can be calculated by the Arrhenius equation, in which the activation energies and pre-exponential factors are fixed in the entire temperature range. The activation energies and thermal effects for the steps that involve nickel oxide were taken from the previous works.51–53 The parameters for the Eley–Rideal step (18) were taken from Ref. [56]. The pre-exponential factors for other steps were estimated from the transition state theory,58,59 while the activation energies and thermal effects of reactions were calculated using the unity bond index-quadratic exponential potential (UBI-QEP) method developed by Shustorovich et al.60–62 The UBI-QEP method is based on algebraic manipulations with the experimental values of the enthalpy of atomic adsorption on single-crystal metals and the total gas phase bond energies. It allowed us to estimate the enthalpy of adsorption of the reaction intermediates and the activation energy of the dissociation and recombination. This method provides the energetic characteristics of the elementary surface reactions with typical accuracy of 1–3 kcal, which is comparable with the accuracy of ab initio/DFT calculations.60–62 The main advantage of this approach is that the UBI-QEP method appreciably decreases the time required for calculations of the energetic characteristics. It should be stressed that DFT calculations can provide more precise values of the activation energy of different elementary steps.63 However, the rate of surface reactions depends strongly on the structure of the catalyst surface, the presence of defects, and the size of supported nanoparticles.64,65 From this point of view, the use of the UBI-QEP theory for developing our mechanism is valid.


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Table 1. Reaction steps and corresponding pre-exponential factors ( ki0 [s-1], i ≠ 1, 8, 18), activation energies (Ea,i [kcal mol-1]), and thermal effects (qi [kcal mol-1]). Here ki0 = ki [mbar-1 s1 ] for i = 1, 8, and 18. ki0

i

Step

1

CH4(g) + [*] → [CH4*]

70

2

[CH4*] → CH4(g) + [*]

3 4

[CH4*] + [*] → [CH3*] + [H*] [CH3*] + [*] → [CH2*] + [H*]

Еa,i

qi

–

6.8

3.6 × 107

7.9

-6.8

1.3 × 10

12

14

-1.1

1.5 × 10

13

24

-13

13

23

-4.6

5

[CH2*] + [*] → [CH*] + [H*]

1.7 × 10

6

[CH*]+ [*] → [C*] + [H*]

4.8 × 1012

4.5

37

7

2[H*] → H2(g) + 2[*]

2.3 × 1013

23

-22

8

O2(g) + 2[*] → 2[O*]

8200

–

110

9

[C*] + [O*] → [CO*] + [*]

5.6 × 1013

34

0.8

29

-29

17

-15

28

-14

1013

9.7

-5.0

14 [O*] → [NiO]

3 × 108

16

5.0

15 [C*] + [NiO] → [CO*] + [*]

5×105

26

-10

102

17

-17

11

-0.1

26

-13

10 [CO*] → CO(g) + [*] 11 [CO*] + [O*] → CO2(g) + 2[*] 12 [H*] + [O*] → [OH*] + [*]

10

13

4.3 × 10

13 [H*] + [OH*] → H2O(g) + 2[*]

16 [CO*] + [NiO] → CO2(g) + 2[*] 17 [H*] + [NiO] → [OH*] + [*] 18 CH4 + 4[NiO] → 2 H2O(g) + CO2(g) + 4[*]

10

13

10

13

4

5 × 10

4

Since steps (1) and (8) describe the adsorption of CH4 and O2 on the surface of metallic nickel, the corresponding reaction rate constants can be estimated from the following expression:

ki = S i0

1

σ

NA − E  f (θ ) exp a  , 2πM i RT  RT 

i = 1, 8

(19)

where Si0 is the initial sticking coefficient; σ is the surface site density, i.e., the number of surface sites involved in the adsorption; Mi is the molar mass of species i; f(θ) represents some function depending on the coverage θ of free surface sites; R is the universal gas constant; and T is the absolute temperature.66 Under assumption that adsorption occurs with the zero activation barrier, ki does not depend on θ (i.e., f(θ) = 1), and σ for the Ni(111) surface is equal to 1.8×1015 atom/cm2; therefore, we can write the adsorption rate Ri as follows:

Ri = k i Pi = S i0

1

σ

NA Pi , 2πM i RT ACS Paragon Plus Environment

(20) 12

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where Pi is the partial pressure of reactant i, mbar. Using values of the initial sticking coefficients for CH4 and O2,67,68 the reaction rate constants for steps (1) and (8) were calculated. The kinetic parameters and thermal effects of all reaction steps are listed in Table 1.

4.2. “Starting” kinetic model The described microkinetic scheme consists of 18 irreversible heterogeneous reactions involving the molecules of gas phase and 10 surface intermediates. Table 2 shows the list of the surface intermediates and their concentrations ci [mol/cm2], i = 1–10. Table 2. List of the surface intermediates and concentrations. CH4* c1

CH3* CH2* CH* H* C* O* NiO CO* OH* c2

c3

c4

c5

c6

c7

c8

c9

c10

The dynamics of the methane oxidation has been studied on the basis of this microkinetic scheme and the assumption of the ideal adsorption layer. Taking into account the mass (surface) interaction law the following kinetic model is under study:

x&1 = R1 – R2 – R3,

x&2 = R3 – R4,

x&3 = R4 – R5,

x&5 = R3 + R4 + R5+ R6 – 2R7 – R12 – R13 – R17,

x&4 = R5 – R6,

x&6 = R6 – R9 – R15,

x&7 = 2R8 – R9 – R11 – R12 – R14,

(21)

x&8 = R14 – R15 – R16 – R17 – 4R18, x&9 = R9 + R15 – R10 – R11 – R16,

x&10 = R12 + R17 – R13,

where xi = ci/cs is the dimensionless concentration of the surface species i (i = 1–10), cs = 1.8×1015 atom/cm2 is the density of active sites on the catalyst surface, Rj (j = 1–18) is the rate of

the reaction step j that depends on the catalyst temperature (Table 1); PCH4 and PO2 [mbar] are the partial pressures of CH4 and O2 in the gas phase, 10   R1 = k1PCH4 1 − ∑ xi  ,  i =1 

R2 = k2x1,

10   Rj = kj 1 − ∑ xi  xj-2,  i =1 

j = 3, 4, 5, 6,

R7 = k7x52,

2

10 R8 = k8PO2 1 − ∑ xi  ,  i =1 

R13 = k13x5x10,

R14 = k14x7,

R9 = k9x6x7, R15 = k15x6x8,

R10 = k10x9, R16 = k16x8x9,

R11 = k11x7x9, R17 = k17x5x8,

R12 = k12x5x7, R18 = k18PCH4 x84 .

Here ki [mbar-1 s-1] are the reaction rate constants of steps i = 1, 8, and 18, and k j = k 0j exp− E j  [s-1]  RT 

are the rate constants for steps j = 2–7, 9–17, while R = 1.987 cal (mol K)-1.


13


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Page 14 of 33

Using the methods of qualitative theory of dynamical systems and numerical methods in our previous study we showed that the model (21) at some values of the parameters could qualitatively describe kinetic self-oscillations in the oxidation of methane over Ni. The results presented elsewhere52 indicate that the surface concentrations of carbon and NiO oscillate with large amplitudes and in antiphase, while concentrations of other surface species are relatively small.

4.3. Mechanism of oxidation-carbonization of the Ni surface and the main kinetic model More reasons for careful studying the kinetic model (21) in the oscillatory regime rest on some generalization to the case of more complex reactions such as the catalytic oxidation of ethane, propane, and butane, in which the self-sustained reaction-rate oscillations were also discovered.17,18,39–41 For example, an analogous mechanism for the oxidation of ethane over Ni consists of 36 elementary reactions.69 The experimental results17–20,23–41 indicate that the kinetic oscillations in the oxidation of different hydrocarbons over the metals of Groups 8, 9, and 10 have a similar pattern and belong to the relaxation type. It points that there are several basic kinetic processes which determine the oscillatory behavior. As these processes are revealed, it can facilitate the analysis of the kinetic models. In contrast to the harmonic oscillations, the relaxation oscillations are characterized by two rather different time scales and often can be described as periodic fast transitions (jump up and jump down) between “low-active” and “high-active” states. It means that under reaction conditions there should be some slow and fast chemical processes and that the concentration of some adsorbed intermediates can be very small. Dynamics of such catalytic systems can be efficiently described by means of the quasi-steady-state approximation.70–72 A small parameter should be distinguished in the system of differential equations and, thereafter, a part of variables can be considered quasi-stationary. The main advantage of the quasi-steady-state approximation consists in reduction of the dimension of the system and, correspondingly, in a possible simplification of the reaction mechanism under study. Studying the dynamics of the model (21) near the stable limit cycle (see Ref. [52]) we observed that the surface coverages with CH4, CH3, CH2, CH, H, CO, and OH (variables x1, x2, x3, x4, x5, x9, and x10 in model (21)) vary only slightly near their quasi-steady-state values, which can be obtained as some functions of the surface concentrations of NiO (x8), adsorbed carbon (x6), and adsorbed oxygen (x7): xieq = xieq(x6, x7, x8),

i = 1–5, 9, 10.

The step of methane desorption from the catalyst surface (step 2 in Table 1) proceeds slowly, and we consider the limit case when methane does not desorb back to the gas phase (i.e., R2 = 0 in the model (21)). Thus, the quasi-steady-state concentrations are as follows: x1eq = k1PCH4/k3,

x2eq = k1PCH4/k4,

x3eq = k1PCH4/k5,


x4eq = k1PCH4/k6,

14

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x9eq =

k9 x6 x7 + k15 x6 x8 , k10 + k11 x7 + k16 x8

x10eq =

k12 x7 + k17 x8 , k13

(22)

2

x5eq = −

 2k P + k x eq  2k P (1 − S5 ) 2k1PCH4 + k13 x10eq , +  1 CH4 13 10  + 1 CH4 2k 7 2k 7 k7  

where S5 = x1eq + x2eq + x3eq + x4eq + x9eq + x10eq. Let us consider the quasi-steady-state concentrations xieq (i = 1–4) under conditions when the methane dissociation steps (3) – (6) are fast; i.e., when min{k3, k4, k5, k6} >> k1PCH4. In this case, it follows from system (21) that xieq

Experimental Study and Mathematical Modeling of Self-Sustained

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