Microkinetic Modeling of CO Oxidation on Ionic Palladium-Substituted

Article pubs.acs.org/IECR

Microkinetic Modeling of CO Oxidation on Ionic PalladiumSubstituted Ceria Ravi Kiran Mandapaka and Giridhar Madras* Department of Chemical Engineering Indian Institute of Science, Bangalore 560012, India ABSTRACT: This study presents a plausible dual-site mechanism and microkinetic model for CO oxidation over palladium-substituted ceria incorporating the theoretical oxygen storage capacity of different catalysts into the kinetic model. A rate expression without prior assumption of rate-determining steps has been developed for the proposed microkinetic model using reaction route analysis. Experiments were conducted using various percentages of palladium in ceria that were synthesized by solution combustion. Obtained catalysts were characterized by X-ray diffraction, X-ray photoelectron spectra, and Brunauer−Emmett−Teller surface area measurements. A detailed mechanism was developed, and the kinetic parameters and rate expression were validated with the conversion data obtained in the presence of the catalysts. Furthermore, a reduced rate expression based on rate-determining step and most abundant reactive intermediate approximation was obtained and tested against the original rate expression for different experimental conditions. From the results obtained it was concluded that the simulated rate predictions matched the experimental trend with reasonable accuracy, validating the kinetic parameters proposed in this study.

1. INTRODUCTION Ceria-based catalysts have been extensively used for carbon monoxide abatement.1 The primary reason is the oxygen storage capacity23−6 of these catalysts. Noble metals such as palladium (Pd), platinum (Pt),7 rhodium (Rh), and iridium (Ir), when dispersed on metal oxide supports, have proven to be efficient catalysts for CO oxidation.1,3 This is due to better adsorption of CO on the noble metals.8 To facilitate the bifunctional properties of noble metals and oxygen storage capacity (OSC) of ceria catalysts, noble metals have been dispersed on base ceria using different procedures, such as impregnation, coprecipitation, and sol−gel synthesis, to synthesize highly active metal-impregnated ceria catalysts.1,9−13 These noble metal-impregnated ceria catalysts have been used for a wide variety of applications including various gas-phase reactions14−17 and selective hydrogenation processes.18,19 In addition to these conventional ceria-based catalysts, noble metal ionic catalysts, i.e., noble metal in ionic state substituted ceria catalysts, have also been synthesized and were reported to have high catalytic activity.20,21 This high activity of noble metal ionic catalysts was attributed to the higher dispersion of noble metals in ionic state and increase in surface oxygen vacancies.22 Among the noble metal ionic catalysts, palladium-substituted ceria catalysts are highly efficient for CO oxidation compared to other noble metal-doped and noble metal-impregnated ceria catalysts.5,23−26 Among the various existing methodologies for synthesizing noble metal-substituted ceria catalysts, the solution combustion technique is a cost-effective and rapid procedure to obtain noble metal ionic catalysts.5 This methodology has previously © XXXX American Chemical Society

been adopted to synthesize different bimetallic and monometallic noble metals including palladium in ceria and applied as catalysts for various gas-phase reactions.5,23−25,27 Numerous experimental studies and spectroscopic insights are available for the mechanistic aspects of CO oxidation.7,20,21 Detailed theoretical studies such as density function theory (DFT) approximations for mechanisms involving ceria-based and noble metal-doped ceria catalysts can predict the underlying surface chemistry qualitatively.22,28 However, the applicability of kinetic parameters obtained by DFT to bulk ceria and metal-doped ceria catalysts for packed bed experiments at atmospheric conditions is yet to be established. On the other hand, rate expressions proposed from experimental observations cannot be valid for a wide range of experimental conditions. This limited applicability of rate expressions derived from experimental observations can be attributed to the sparse availability of kinetic parameters and lack of fundamental understanding of kinetics at atmospheric and industrial scale experimental conditions. Earlier studies pertaining to CO oxidation catalyzed by Ce1−xPdxO2−δ report different catalytic activity for different doping fractions of Pd in ceria.20,21,23 Pd impregnated on ceria29and Pd substituted in ceria30 have widely different OSCs, as experimentally verified by temperatureprogrammed reduction (TPR). However, a detailed kinetic Received: December 10, 2015 Revised: February 4, 2016 Accepted: February 11, 2016

A

DOI: 10.1021/acs.iecr.5b04724 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research Table 1. Structural Parameters and Apparent Activation Energy of Catalysts catalyst

lattice parameter, a0 (Å)

Rp

Rwp

specific surface area, a (m2/g)

theoretical OSC (μmol/m2)

activation energy, Aapp (kJ/mol)

Ce0.995Pd0.005O2−δ Ce0.99Pd0.01O2−δ Ce0.98Pd0.02O2−δ

5.4132(5) 5.4126(4) 5.4123(5)

3.90 3.94 3.83

4.93 4.93 4.85

22 ± 1 22 ± 1 22 ± 1

6.542 6.544 6.545

56 44 38

using a Belsorp surface area analyzer (Smart Instruments) using liquid N2. The results obtained after characterization are tabulated in Table 1. 2.3. Catalytic Activity. The catalytic activity of the catalysts was studied using a packed bed reactor. The catalyst obtained in porous powder form after calcination was made into the form of pellets of mesh size 60/80, and 50 mg of the catalyst pellets were taken in the center of a quartz reactor with internal diameter of 4 mm. The catalytic material was diluted with silica gel beads to make a catalyst bed length of 1 cm and was held firmly between plugs of glass wool. The reactant gases, i.e., CO (99.99% pure supplied by Chemix gases), O2 (99.99% pure supplied by Noble gases), and N2 (99.99% pure supplied by Noble gases) were sent to the reactor in volume percentages of 2.4 vol %, 2.4 vol % (11.4 vol % air), and rest N2, respectively. The outlet gas composition was analyzed using a gas chromatograph (Mayura Analytical, India) equipped with a flame ionization detection (FID) sensor. The temperature of the reactor was varied using a PID-controlled electrical furnace equipped with a thermocouple. To obtain experimental rates at different temperatures, W/FCO was varied by using different volumetric flow rates of inlet gases, i.e., 100, 75, and 50 mL/ min. 2.4. Characterization Results. The observed XRD patterns were refined using Jana 2006 with a Legendre polynomial of 16 terms as background function and a pseudo-Voigt as peak shape function. The refined pattern fitted experimental profile satisfactorily (Figure 1a−c) and confirmed the formation of fluorite, i.e., Fm3̅m, no. 225 structure of ceria. The parameters thus obtained from refinement are tabulated in Table 1. From the results obtained through the refinement analysis, it can be observed that all doped catalysts exhibited lower lattice parameters compared to undoped ceria lattice parameter of 5.414 Å.35−37 It is also noteworthy that the lattice parameters of the doped catalysts decrease with an increase in the doping percentage of palladium. This phenomenon can be understood from experimental findings5 and DFT studies38 that indicate the ionic radius of Pd is less than that of cerium (Ce). Therefore, when a divalent metal such as palladium is doped into the lattice of ceria, reduction in lattice parameters can be observed. Panels a and b of Figure 2 present the XPS spectra pertaining to Pd 3d of Ce0.98Pd0.02O2−δ and Ce0.99Pd0.01O2−δ, respectively. The binding energies of all the elements were calibrated with respect to adventitious carbon spectra (C 1s) value of 284.8 eV. XPS spectra of Pd 3d of different catalysts depict peaks of Pd 3d5/2 and Pd 3d3/2 at 337.6 and 342.8 eV, respectively, for Ce0.98Pd0.02 O2−δ and peaks of 338 and 343.3 eV for Ce0.99Pd0.01O2−δ, respectively. These binding energies indicate the presence of the ionic state of palladium (Pd2+).2,20,23−25,39 This observation indicates the ionic substitution of Pd in ceria lattice.

model covering the catalytic activity and the OSCs with respect to the doping has not been developed. Microkinetic modeling has proven to be an efficient approach for understanding and elucidating various mechanisms presented for gas-phase reactions over various catalysts.31−33 However, validating and developing a rate expression for microkinetic models involving reducible catalysts can be difficult using standard methodologies. Reaction route (RR)34 analysis offers a handy implementation of analyzing various reaction schemes, with its analogy of gas-phase reaction schemes to electric circuitry systems. The primary advantage of the RR analysis is that it offers development of rate expressions for nonlinear kinetics. This paper develops a new microkinetic model for Pd ceria catalysts. Unlike conventional catalysts in which Pd is impregnated in the catalysts, this study investigates the activity of the catalysts in which Pd is substituted in the catalysts, which results in different oxygen storage capacities.30 Thus, the novelty of this study includes incorporating the OSCs of different percentages of Pd substituted in ceria into the kinetic model. The reaction route analysis thus far has been studied only on gas-phase reactions catalyzed by noble metals involving a single-site mechanism, and this was extended to dual sites in this study. Thus, a robust modeling procedure considering the surface chemistry over Pd-substituted ceria, without the assumption of the rate-controlling step, has been derived. This rate expression was validated using different reactor approximations, i.e., differential and plug flow reactor approaches for different % Pd substituted in ceria.

2. EXPERIMENTAL SECTION 2.1. Catalyst Preparation. A detailed description of the methodology used to synthesize palladium-substituted ceria catalysts can be found elsewhere.4,25 In the current study, different atomic percentages of palladium-doped ceria, i.e., 2%, 1%, and 0.5% Pd in ceria, termed as Ce0.98Pd0.02O2−δ, Ce0.99Pd0.01O2−δ, and Ce0.995Pd0.005O2−δ, respectively, were synthesized using glycine, palladium chloride, and ammonium cerium nitrate as precursors. The precursors were dissolved in water to obtain a clear solution, and the precursor solution was then transferred to a muffle furnace at a temperature of 400 °C. The solution boiled initially, evaporating water, then ignited to form porous solid catalyst, releasing a voluminous amount of product gases. The catalysts obtained after synthesis were calcined at 400 °C for 2 h. 2.2. Characterization. Catalytic materials obtained after calcination were characterized using different techniques such as X-ray diffraction (XRD), X-ray photoelectron spectra (XPS), and Brunauer−Emmett−Teller (BET) surface area measurements. For obtaining the XRD pattern, a Bruker D8 Advance X-ray diffractometer with Cu Kα monochromatic beam was used as radiation source with a scan rate of 0.25°/min in 2θ range of 20°−80°. The XPS spectra for the catalysts were obtained using an Axis Ultra-Instrument with Al Kα (1486.6 eV) as the source of radiation. For BET measurements, the catalysts were first regenerated at 120 °C for 2 h and analyzed

3. THEORETICAL MODELING 3.1. Mechanism Development. The mechanism for CO oxidation for doped catalysts has been extensively investigated B


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Industrial & Engineering Chemistry Research

Figure 2. XPS spectra of Pd 3d pertaining to (a) Ce0.98Pd0.02O2−δ and (b) Ce0.99Pd0.01O2−δ.

as compared to bulk reduction of ceria at higher temperatures. Qualitatively, experimental studies propose dissociative adsorption for oxygen on surface vacancies of ceria forming adsorbed oxygen species.1,9,20,21,47 This proposal is in good accord with detailed kinetic modeling procedures42,48 and calorimetric adsorption studies involving oxygen storage by ceria.11,49 Because there are two different adsorption sites for CO and O2, CO oxidation over Pd-substituted ceria proceeds via a dualsite mechanism. This dual-site mechanism for CO oxidation over reducible oxides has been qualitatively used to predict the experimental observations.1,9,41,47 The elementary reaction for the formation of CO2 has also been the subject of much debate in the literature. It has been generally proposed that the adsorbed CO reacts with O2 adsorbed on a vacant ceria site to produce gaseous CO2.42 Transient pulse response experiments50 suggest the reaction of adsorbed CO with back spillover oxygen from a vacant ceria site to Pd site to produce gaseous CO2. DFT considerations51 suggest this phenomenon to be energetically more favorable in metal impregnated on bulk ceria compared to single CeO2 molecule. On the other hand, FTIR and DFT studies pertaining to CO oxidation over Pd impregnated and doped on ceria suggest the presence and formation of carbonate species at higher temperatures.12,45 This suggests the formation of a surface intermediate before the formation of gaseous CO2 product. According to the above considerations, the following mechanism has been proposed in this study for CO oxidation

Figure 1. XRD pattern and profile refinement: (a) Ce0.98Pd0.02O2−δ, (b) Ce0.99Pd0.01O2−δ, and (c) Ce0.995Pd0.005O2−δ.

by theoretical, experimental, and spectroscopic studies ranging from DFT to Fourier transform infrared (FTIR) spectroscopy studies.12,21,40 Different theories involving Langmuir−Hinselwood−Hougen−Watson (LHHW),41,42 Eley−Rideal,43 and Mars−van Krevelen40,44,45 mechanisms have been proposed for CO oxidation on doped catalysts. FTIR studies pertaining to CO adsorption on palladiumdoped and -impregnated ceria suggest adsorption of CO on metallic site, i.e., ionic Pd site for doped catalysts and metallic Pd for impregnated catalysts, respectively.7,12,39 This is also indicated in the DFT studies indicating the metallic site is more favorable for CO adsorption as compared to oxygen vacancy and Ce4+ site.7 The interaction of oxygen and ceria has been a subject of much debate, and the exact nature of this interaction has not been established. DFT studies for doped catalysts suggest that, as compared to nondoped ceria, oxygen is weakly held in doped ceria, indicating a decrease in the vacancy formation energy for doped catalysts.38 This vacancy thus created by the release of loosely held oxygen is replenished by oxygen. However, there is no clear consensus over this oxygen−vacancy interaction as to whether this is a surface phenomenon or proceeds via bulk reduction of ceria. Recent DFT studies46 and calorimetric studies11 suggest the interaction of oxygen and oxygen vacancies to be a surface phenomenon at lower temperatures C

CO + * ⇌ CO*

(1)

O2 + 2Ce‐□ ⇌ 2Ce(O)

(2)

CO* + Ce(O) ⇌ CO2 * + Ce‐□

(3)


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Industrial & Engineering Chemistry Research CO2 * ⇌ CO2 + *

k4 = A4 ·Γ1·e−E4 / RT

(4)

Equation 1 denotes reversible adsorption of CO on metallic site, i.e., Pd2+. Equation 2 denotes dissociative reversible adsorption of oxygen on a vacant ceria site48 denoted by Ce□. Equation 3 denotes the reaction of adsorbed CO with adsorbed oxygen on a ceria vacant site to produce adsorbed CO2 species, and eq 4 denotes reversible desorption of adsorbed CO2 from a metal site. Note that in the microkinetic model, “i” denotes the forward step of ith surface reaction and “−i” represents the backward step of the ith surface reaction. Note that in eqs 5−12 given below, ki represents the rate constant for forward reaction, k−i the rate constant for the reverse reaction, and Ki the equilibrium constant for the ith k surface reaction where K i = k i . Ai represents the pre-

In eqs 10−12, k−1 represents the rate constant for the backward reaction step of reversible CO adsorption (eq 1), k−2 the rate constant for backward reaction step of reversible dissociative O2 adsorption (eq 2), and k4 the rate constant for forward reaction step of reversible CO2 desorption (eq 4). Note that in eqs 10−12, the pre- exponential factor Ai has units of s−1, site density has units of mol·m−2, and the activation energy has units of kJ mol−1 3.2. Kinetic Parameters. Studies pertaining to adsorption energy of CO on Pd2+ ion-substituted ceria are sparsely reported in the literature. However, it has been proposed from CO adsorption studies21 that the sticking coefficient associated with this adsorption on ionic metal site would be similar to that of CO adsorption on a metallic site.53 This is also indicated in DFT studies7 proposing adsorption energy of CO on an ionic metal site to be in close proximity to the adsorption energy of CO on a metal site. According to the DFT calculations,7 the adsorption energy of CO on a Pt2+ site was found to be 1.39 eV as opposed to 1.45 eV for CO adsorption on Pt(111), indicating a similar trend for other noble metals. The parameters for CO adsorption are taken in accordance with the parameters proposed in our previous study,54 i.e., 0.7 (S0,1 in eq 7) for sticking coefficient, 1017 (A−1 in eq 10) for pre-exponential for desorption, and 142.2 kJ/mol (E−1 in eq 10) for adsorption energy, are considered for CO adsorption on Pd2+. The kinetic parameters associated with dissociative adsorption, i.e., 0.75 (S0,2 in eq 8) for sticking coefficient and 100 kJ/ mol (E−2 in eq 11) for the adsorption energy are taken in accordance with earlier propositions.42,48 This heat of reaction between oxygen and surface vacancies is in good agreement with the earlier modeling studies55,56 and is in close proximity to the optimized value of 123 kJ/mol.47 The pre-exponential factor proposed for the associative oxygen desorption from vacant ceria has been found to be of different values in the literature, i.e., 4.95 × 1010 s−1,56 9.2 × 1015 s−1,55 and 720 000 ± 360 000 s−1.57 These values proposed were obtained using different optimization techniques. Assuming 2.7 × 10−9 mol/ cm2 for site density of ceria,48 the pre-exponential factor proposed by Leistner et al.48 would be 1.35 × 104 s−1, which has been validated using the thermodynamic entropic considerations. 58 Therefore, the pre-exponential for O 2 desorption is taken to be 1.35 × 104 s−1 (A−2 in eq 11) . The energetics and kinetic parameters for CO2 desorption are taken in accordance to the values proposed in our previous study.54 The overall heat of reaction involving CO oxidation and ceria reduction with oxygen interaction has been proposed to be −183 kJ/mol.55,56 No consensus exists in the literature for the activation energy of the forward step of this reaction. Hence, in the study we considered this activation energy to be equal to the apparent activation energy obtained from experimental observations (Table 1), i.e., 38 kJ/mol (E3 in eq 5) for Ce0.98Pd0.02O2−δ, 44 kJ/mol for Ce0.99Pd0.01O2−δ, and 56 kJ/mol for Ce0.995Pd0.005O2−δ. The activation energy for the reverse reaction has been considered to be 44.7 kJ/mol (E−3 in eq 6) for Ce0.98Pd0.02O2−δ, 50.7 kJ/mol for Ce0.99Pd0.01O2−δ, and 62.7 kJ/mol for Ce0.995Pd0.005O2−δ. According to the above presented energetics, the overall reaction enthalpy would be 183 kJ/mol, which is consistent with the proposed overall heat of reaction.54,55 The pre-exponential factor for the forward

−i

exponential, and Ei represents the activation energy for the ith surface reaction. Γ1 and Γ2 represent the surface metallic sites and surface vacancies, respectively. R denotes the universal gas constant, and T is temperature in Kelvin. 3.1.1. Surface Reactions (3, −3). k 3 = A3 ·Γ1·e−E3 / RT

(5)

k −3 = A −3 ·Γ1·e−E−3 / RT

(6)

As it was assumed that surface reaction of adsorbed CO and adsorbed O takes place on palladium surface, the metal site density has been taken for this surface reaction. This assumption is consistent with earlier propositions52 that the CO oxidation reaction proceeds on the metallic sites and adjacent active surface vacancies. In eqs 5 and 6, k3 and k−3 represent the rate constant for forward and backward reaction steps (eq 3), respectively, of surface reaction of adsorbed CO with adsorbed O. 3.1.2. Adsorption Reactions (1, 2, −4). k1 = s0,1

RT ·e−E1/ RT 2πMCO

(7)

k 2 = s0,2

RT ·e−E2 / RT 2πMO2

(8)

k −4 = s0, −4

RT ·e−E−4 / RT 2πMCO2

(9)

In eqs 7−9, S0,i represents the sticking coefficient of the ith surface reaction. k1 represents the rate constant for the forward reaction step of reversible CO adsorption (eq 1). k2 represents the rate constant for the forward reaction step of reversible dissociative O2 adsorption (eq 2), and k−4 represents the rate constant for backward reaction step of reversible CO 2 desorption (eq 4). MCO, MO2, and MCO2 are the molecular weights of CO, O2, and CO2, respectively. Note that in the eqs 7−9, the sticking coefficients are unitless,

RT 2π M i

, where i is CO,

O2, or CO2 has unit of m·s−1, and activation energies have units of kJ mol−1. 3.1.3. Desorption Reactions. k −1 = A −1·Γ1·e−E−1/RT

(10)

k −2 = A −2 ·Γ2·e−E−2 / RT

(11)

(12)

D


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Industrial & Engineering Chemistry Research reaction has been approximated from experimental findings, and for the reverse step, the pre-exponential factor has been considered to be 1013 s−1 (A−3 in eq 6)31. 3.3. Calculation of Site Densities. Site densities are important parameters pertaining to the implementation and validation of kinetic models.31 These parameters can be theoretically predicted59 using the lattice parameters (a0). Site density for a (111) surface can be predicted as shown in eqs 13 and 14. surface atom density of Ce =

4 3 ·(a0)2

obtained and are presented in eqs 17−20. To predict the ratedetermining step (RDS) of the system, values of individual step resistances have been plotted against experimental temperature range at constant inlet mole fraction of reactant gases. 1+ R1 =

R2 =

(13)

For example, for Ce0.98Pd0.02O2−δ, surface atom density of Ce is 7.8934 × 1018 atoms/m2 = 1.3105 × 10−5 mol/m2. surface atom density of O =

2·4 3 ·(a0)2

R3 =

(14)

For Ce0.98Pd0.02O2−δ, surface atom density of O is 2 × 7.8934 × 1018 atoms/m2 = 1.5762 × 1019 atoms/m2 = 2.61 × 10−5 mol/ m2. This value for surface oxygen atoms for ceria is consistent with 1.58 × 1015 atoms/cm2.60 It has been previously proposed that the theoretical oxygen storage capacity would be onefourth of the total surface oxygen atoms.1,60 Accordingly, the theoretical oxygen storage capacity (Γ2) would be given as

R4 =

(15)

This value of 0.65 × 10 mol/m for theoretical oxygen storage capacity is consistent with a value of 5.4 μmol/m2.60 As proposed earlier, divalently doped noble metal ionic catalysts show superior performance compared to their counterparts of impregnated catalysts.4,20,21 This was attributed to the ionic nature, better dispersion of the metallic dopants, and increase in surface oxygen vacancies,39 as verified experimentally in earlier studies.26,30 Thus, it is clearly evident from the above calculations that the theoretical OSC is inversely proportional to the lattice parameter. The increase in doping percentage of metal in ceria leads to the decrease of the lattice parameter and ultimately leads to the increase in OSC. It has also been proposed that in doped catalysts, the metallic divalent dopants are located on the surface of the catalysts, i.e., doped into the crystal lattice of the base reducible oxides.4 This is clearly depicted in the plots of XRD patterns and XPS spectra, which show no significant peak for metallic Pd as evident for impregnated catalysts.23 The use of solution combustion methodology results in doping of atomic percentage of noble metal with respect to cerium atoms.4 Using this, the number of surface Pd atoms or surface site density of palladium (Γ1) can be computed by 2

Γ1 = (1.31· (metal doping fraction) × 10−5) mol/m 2

⎜

K4

⎞ PCO2 ⎟ K4K3 K 2PO2 ⎠

k1PCO

⎛ ⎜1 + ⎝

(

PCO2 K4K3K1PCO

(17)

⎞2 ⎟ ⎠

)

k 2PO2 ⎛ ⎜1 + ⎝

PCO2

(18)

⎞

( ) + (K P

1 CO)⎠(1

K4

⎟

K 2PO2 )

+

k 3K1PCO K 2PO2

(19)

(1 + (K3K1PCO K 2PO2 ) + (K1PCO)) k4K3K1PCO K 2PO2

(20)

From the resistance graphs depicted in Figure 3a−c, it can be observed that resistance 3, which denotes the reaction of adsorbed CO with adsorbed O, is clearly dominant across the experimental range for all experimental conditions. Therefore, it can be concluded that this reaction step is the rate-determining step (RDS) for the above system. Note that in eqs 17−20, PCO, PCO2, and PO2 represent the pressure of gas-phase species CO, CO2, and O2, respectively Because there is a single RDS for the above system, the rate expression for the overall reaction34 is given by

Γ2 = (2.61/4) × 10−5 mol/m 2 = 0.6542 × 10−5 mol/m 2 −5

⎛

PCO2

( )+⎝

· rOR =

1 − (ZOR )1/2 2R3

1− · rOR =

(21)

⎛ ⎞1/2 PCO2 2 ⎜ ⎟ 2 2 ⎝ K 2(K1K3K4) PO2PCO ⎠

⎧ ⎛1 + PCO2 + (K P )⎞(1 + ⎪ ⎝ ( K4 ) 1 CO ⎠ 2⎨ k 3K1PCO K 2PO2 ⎪ ⎩ ⎜

⎟

⎫ ⎬ ⎪ ⎭

K 2PO2 ) ⎪

(22) −2 −1

Note that the expression in eq 22 has units of mol·m ·s . To convert it into mol·g−1·s−1, the rate expression in eq 22 is multiplied by specific surface area (a) of the catalyst (m2/g). · rOR = (a) ·rOR

(23)

rCO = 2rOR

(24)

⎛ ⎛ ⎞1/2 ⎞ PCO2 2 ⎟ ⎟ a ·⎜⎜1 − ⎜ 2 2 ⎝ K 2(K1K3K4) PO2PCO ⎠ ⎟⎠ ⎝ rCO = ⎧ ⎛1 + PCO2 + (K P )⎞(1 + K P ) ⎫ 2 O2 ⎪ ⎪ ⎝ ( K4 ) 1 CO ⎠ ⎨ ⎬ k K P K P for,3 1 CO 2 O2 ⎪ ⎪ ⎩ ⎭

(16)

⎜

The kinetic parameters for desorption reactions and surface reactions are dependent on these site densities. As the reaction scheme proceeds through a dual-site mechanism, different site densities have been used in this study to represent the surface metallic sites and surface vacancies. 3.4. Rate Expression Development Using Reaction Route Analysis. The detailed explanation and procedure for obtaining analytical expressions for individual step resistances can be found elsewhere.34 According to the reaction route (RR) analysis, the analytic expressions for step resistances have been

⎟

(25)

3.5. Differential Flow Reactor. Equation 26 shows the dependence of rate on the catalyst weight and flow rate. ⎛ W ⎞ ⎛ XCO ⎞ ⎜ ⎟=⎜ ⎟ ⎝ FCO ⎠ ⎝ rCO ⎠

(26)

The experimental rate was determined using eq 27 E


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Figure 3. Resistance plots against differential reactor proximity temperature range for (a) Ce0.98Pd0.02O2−δ, (b) Ce0.99Pd0.01O2−δ, and (c) Ce0.995Pd0.005O2−δ.

(rCO)exptl =

Figure 4. Arrhenius plot for experimental rate and variation of fraction CO conversion with W/F CO for (a) Ce 0.98 Pd 0.02 O 2−δ , (b) Ce0.99Pd0.01O2−δ, and (c) Ce0.995Pd0.005O2−δ.

XCO

( ) W FCO

(27)

catalysts with varying Pd doping percentages, as depicted in Table 2. The kinetic parameters proposed in Table 2 and rate expression obtained by reaction route analysis (eq 25) have been plotted against the experimentally observed rates at different experimental temperatures for different catalysts. Figure 5 shows the performance of the simulated rate prediction (eq 25) against the experimentally observed rates for Ce0.98Pd0.02O2−δ, Ce0.99Pd0.01O2−δ, and Ce0.995Pd0.005O2−δ. 3.6. Plug Flow Reactor. To evaluate the performance of the simulated rate expression (eq 22) at higher-temperature conditions, an isothermal plug flow reactor (PFR) model (eqs 28 and 29) has been used to validate the experimental conditions for Ce0.98Pd0.02O2−δ catalyst for different flow rates. Details of the PFR model used can be found elsewhere.54,62

To obtain experimental rates at different experimental conditions, a differential reactor approach was used,52 i.e., the fractional conversions of CO were plotted against different W/ FCO at various temperatures (Figure 4 a−c). From the apparent activation energy plots, i.e., Figure 4a−c, and values shown in Table 1, the apparent activation energy decreases as the Pd doping percentage increases. This indicates the possibility of different interaction energies between the adsorbed CO and adsorbed oxygen species.22 This trend has been qualitatively reported for different percentages of rhodium loading, i.e., Rh x+ (0.29)/Ce 0.68 Zr 0.32 O 2 , Rh x+ (0.32)/ Ce0.68Zr0.32O2.61 As discussed earlier, the activation energy for surface reaction (3, −3) has been modified for different F


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Industrial & Engineering Chemistry Research Table 2. Microkinetic Scheme for CO Oxidation on Pd-Substituted Ceria So,i (no units), Ai (s−1)

activation energy, Ei (kJ/mol)

Activation energy, Ei (kJ/mol)

equation number

reaction number

1

1, −1

CO + * ⇌ CO*

0.7

1017

0

142.2

2

2, −2

O2 + 2Ce‐□ ⇌ 2Ce(O)

0.75

1.35 × 104

0

100

3

3, −3

CO* + Ce(O) ⇌ CO2 * + Ce‐□

4

4, −4

CO2 * ⇌ CO2 + *

6 × 10 (for Ce0.98Pd0.02O2−δ) 5 × 105 (for Ce0.99Pd0.01O2−δ) 1.2 × 107 (for Ce0.995Pd0.005O2−δ) 1013

38 (for Ce0.98Pd0.02O2−δ) 44 (for Ce0.99Pd0.01O2−δ) 56 (for Ce0.995Pd0.005O2−δ) 15.9

44.7 (for Ce0.98Pd0.02O2−δ) 50.7 (for Ce0.99Pd0.01O2−δ) 62.7 (for Ce0.995Pd0.005O2−δ) 0

reaction

So,i (no units), Ai (s−1)

4

Figure 5. Comparison of simulated rates versus experimentally observed rate for Ce 0.98 Pd 0.02 O 2−δ , Ce 0.99 Pd 0.01 O 2−δ , and Ce0.995Pd0.005O2−δ. (Symbols represent experimental findings; solid lines represent unreduced rate predictions, and dashed lines represent reduced rate predictions.)

(ρ u)

dyi dz

=

⎛a⎞ ⎜ ⎟M ∑ ν R i,j j ⎝V ⎠ i j

for i = 1...Ns

i=1

for i = 1...Ng (28)

compared to other doping fractions of Pd in ceria. This inferred result is also evident from activation energy values (Table 1), which depict lower apparent activation energy for Ce0.98Pd0.02O2−δ. Figure 6 for Ce0.98Pd0.02O2−δ for different flow rates shows that decreasing flow rate of inlet reactants results in an increase in the residence time and ∼100% conversion at lower temperatures. As mentioned earlier, the surface reaction of adsorbed CO and adsorbed oxygen has been found to be the ratedetermining step of this system. This result obtained from the present study is in good agreement with previously reported observations.47,63 As depicted in Figure 5, the rate expression developed with the proposed kinetic parameters predicted the experimentally observed rates for different catalysts with reasonable accuracy. Figure 6 shows the isothermal PFR model also predicted the experimental trend even at highertemperature conditions, validating the robustness of the proposed model. To obtain a simplified rate expression, surface coverage of different surface species has been plotted across the experimental temperature range for different experimental conditions over Ce0.98Pd0.02O2−δ, using the analytical expressions obtained based on the RDS assumption. As depicted in Figure 7a,b, θCO and θO are the most abundant surface species. It is interesting to note that at higher temperatures θCO2, which denotes the surface CO2 species, becomes considerably significant, which is in good agreement with the FTIR studies. From the most abundant reactive intermediate (MARI) approximation, the rate expression in eq 25 can be further simplified to the form given in eq 30.

(29)

The kinetic parameters used for the simulation are given in Table 3. As depicted in Figure 6, the PFR model predicts the experimental trend to good accuracy. Table 3. PFR Simulation Parameters for Different Catalysts palladium doping (atom %) surface area (m2/g) catalyst loading (mg) internal diameter of reactor volumetric flow rate (Ncm3/min) volume of catalyst bed (cm3) flow composition (volume %) length of catalyst bed (cm) area/volume of catalyst (m−1)

0.003

Figure 6. Isothermal PFR predictions against experimental observations with modified parameters for Ce0.98Pd0.02O2−δ at 75 mL/min and 100 mL/min. (Symbols represent experimental findings; solid lines represent unreduced rate predictions, and dashed lines represent reduced rate predictions.)

NS

∑ θi = 1

10

13

2% 22 50 4 100, 75 0.126 2.4% CO, 2.4% O2, 95.2% N2 1 8.78 × 106

4. RESULTS AND DISCUSSION Figure 4a−c shows the applicability of the differential reactor approach for various doped fractions of Pd in ceria. As evident from the figures, the differential reactor approach was valid until the percentage conversion of CO reached 15−20%. Figure 5 shows the experimentally determined rate for different catalysts with respect to temperature, indicating higher catalytic activity of Ce0.98Pd0.02O2−δ even at lower temperatures. From this, it can be concluded that Ce0.98Pd0.02O2−δ shows higher activity as G


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curve-fitting procedure based on experimental observations. Equation 30 is similar to the rate expression obtained using a Mars−van Krevelen mechanism63 when n = 1/2. This study confirms that simpler rate expressions can be obtained using microkinetic models proposed for gas-phase reactions involving dual-site mechanisms for reducible oxides.

5. CONCLUSIONS This study depicts a comprehensive attempt to understand the surface kinetics of CO oxidation on palladium-substituted ceria. A brief review of the existing mechanisms and propositions has been presented. Based on the proposed dual-site mechanism, a detailed microkinetic model has been developed with kinetic parameters obtained from experimental observations, propositions from the literature, and obtained structural parameters. Using the RR analysis, the surface reaction of adsorbed CO and adsorbed O was found to be the RDS of the system. Based on this RDS, a rate expression has been developed for the microkinetic model. The rate expression developed in this study has then been validated against the in-house packed bed experiments at atmospheric conditions. For the experimental studies, catalysts of different palladium doping percentages were synthesized using novel solution combustion synthesis. The obtained catalysts were characterized by XRD, XPS, and BET surface area analysis. The XRD patterns and XPS spectra showed no significant peaks for metallic Pd, thus confirming the ionic substitution of palladium into base ceria lattice. The lattice parameters obtained were then used to estimate the theoretical OSC and surface metallic atomic site density. As depicted in Results and Discussion, the simulated rate predicted the experimentally observed rates to a reasonable accuracy. Furthermore, simulations using an isothermal PFR model with modified parameters predicted the experimental CO conversions to good degree of accuracy even at higher temperatures, thus exhibiting the robustness of the kinetic rate parameters and developed analytical rate expression. MARI analysis showed adsorbed CO and adsorbed O to be the most abundant intermediates. Based on this approximation, a reduced rate expression has been obtained. The validity of the reduced rate expression was tested against the unreduced rate expression for the experimental conditions. As is evident from Figures 5 and 6, the performance of the reduced rate expression was found to be satisfactory for experimental conditions. From this study, it can be concluded that structural parameters when coupled with theoretical propositions can provide valuable insights in understanding the surface kinetics of gas-phase reactions over reducible catalysts.

Figure 7. MARI predictions for experimental conditions of Ce0.98Pd0.02O2−δ at 100 mL/min on (a) ionic Pd site and (b) vacant surface ceria site.

rCO =

k 3aK1PCO K 2PO2 (1 + (K1PCO))(1 +

K 2PO2 )

(30)

The performance of this reduced rate expression (eq 30) is validated against the unreduced rate expression depicted in Figures 5 and 6. From Figures 5 and 6, it can be inferred that the predictions of reduced rate expression are in good accord with the unreduced rate expression predictions. This proposed reduced rate expression (eq 30) is in good accordance with earlier propositions9,41,47 involving a dual-site mechanism. From the rate expression obtained in eq 30, it can be seen that the rate is dependent on the forward rate constant k3 and equilibrium constants K1 and K2. The rate is directly proportional to k3.When K1PCO ≫ 1 and K2PO2 ≫ 1, there is no effect of K1 and K2 on the overall rate. However, when K1PCO ≪1 and/or K2PO2 ≪ 1, then these parameters will have overall effect on the rate. The kinetic parameters and rate expression (eq 30) have significance at different experimental conditions, i.e., lower concentrations of CO and O2. RR analysis holds its hierarchy over the sensitivity analysis in providing explicit rate expressions for mechanisms involving nonlinear kinetics. Sensitivity analysis, on the other hand can be used to understand the importance of rate parameters when provided with an explicit rate expression and numerical solution for the exit gas conversions. The primary advantage of RR analysis over sensitivity analysis is that the RDS of the system can be readily obtained by the comparison of step resistances that represent the individual reaction steps of the mechanism. Often it has been reported in the literature that a rate expression based on a Mars−van Krevelen mechanism predicts the experimental trend for reducible catalysts. However, as pointed out in earlier studies,63 rate expressions based on a Mars−van Krevelen mechanism can be considered only as a

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +91-80-22932321. Fax: +91-80-23601310. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

The authors thank the Department of Science and Technology, India (DST 1362/2014) and the Gas Authority of India Limited (PC 99233) for financial support. G.M. thanks the Department of Science and Technology, India for J.C. Bose fellowship. H


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Microkinetic Modeling of CO Oxidation on Ionic Palladium-Substituted

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