kinetics of catalytic oxidation of methane over palladium oxide by wire microcalorimetry

Kinetics of Catalytic Oxidation of Methane over Palladium Oxide byWire MicrocalorimetryYuxuan Xin,† Sydnie Lieb,‡ Hai Wang,‡ and Chung K. Law†,*†Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, United States‡Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, California 90089, UnitedStates

ABSTRACT: The kinetics of catalytic oxidation of methane (1−3% in air) over apalladium oxide (PdO) surface was investigated by wire microcalorimetry at atmosphericpressure and over the temperature range from 560 to 800 K. Wire surface structures andcompositions were characterized by scanning electron microscopy, X-ray photoelectronspectroscopy, and atom force microscopy. It was found that a porous PdO layer with aconstant thickness of 1−2 μm was formed on the Pd wire after it was heat treated innitrogen followed by air at elevated temperatures. Under the condition of theexperiment, the reaction was found to be in the pseudo-first-order regime with respect tothe methane concentration. The apparent rate constant of methane oxidation on PdOwas determined to be kapp(cm/s) = (3.2 ± 0.8) × 104e−(62.8±1.6)(kJ/mol)/RT for 600 < T <740 K. Experimental data were analyzed using a gas−surface reaction model proposedpreviously. Analysis shows that the overall catalytic oxidation rate is governed by equilibrium adsorption/desorption of molecularoxygen, which determines the density of surface palladium sites and dissociative adsorption of methane on these sites. Theequilibrium constant of O2 adsorption and desorption was estimated from literature values of desorption energy and molecularparameters of adsorbed oxygen atoms. The rate coefficient of methane dissociative adsorption was estimated to be k16(cm/s) =(7.7 ± 1.6) × 104e−(59.9±1.2)(kJ/mol)/RT, derived from the equilibrium constant of oxygen adsorption over the same temperaturerange.

I. INTRODUCTION

Catalytic combustion of methane over palladium oxide (PdO)catalyst has been studied extensively over the past few decades.1

As an efficient low-temperature reaction process, catalyticcombustion serves as a promising alternative to convertingenergy from natural gas with minimal soot and NOX emission.It is known that the heterogeneous reaction occurs around andabove a temperature of 550 K.2−5 Toward higher temperatures,the catalytic activity is impacted by Pd/PdO phase equilibrium.PdO was identified as the stable phase below 1070 K in airunder atmospheric pressure.6

Heterogeneous reaction kinetics of methane oxidation overPdO has been examined over supported catalysts2,5,7 and onwires.4 The apparent activation energy was reported to be inthe range from 46 to 105 kJ/mol, while reaction orders areclose to unity and zero for methane and oxygen, respectively. AMars−van Krevelen-type mechanism has been widely accepted.Methane interacts with the lattice oxygen on a PdO surface,thus forming adsorbed methyl radicals. Further dissociation ofthe C−H bonds proceeds rapidly on the catalyst surface,eventually leading to formation and desorption of CO2.

8,9 Theresulting oxygen vacancy is reoccupied by the oxygen from gasphase or support,10 which completes the catalytic cycle.Initial C−H bond breaking in methane has been proposed as

a rate-limiting step in the overall catalytic oxidationprocess.11−13 Fujimoto et al.14 suggested that methaneundergoes physi-adsorption on the surface first and interacts

with neighboring oxygen vacancies, producing surface CH3 andOH species. This mechanism is challenged by the lowprobability of physi-adsorption to account for the surfacereaction rates observed experimentally.2−5 Rather, the initialreaction of methane with the surface probably proceedsthrough dissociative adsorption on a Pd−O dimer, generatingCH3 and OH species bound to the neighboring Pd centers.1,15

Direct observation of dissociative adsorption is difficult tomake, because the products react with the neighboring surfaceoxygen rather rapidly. Theoretically, density functional theory(DFT) has been used to probe the reaction mechanism.Interaction of methane with a single PdO dimer wasexamined,16,17 and the energy barrier was calculated to be102.4 kJ/mol. Recently, methane adsorption over a PdO(101)surface was examined. The energy barrier to dissociativeadsorption was found to be 64.2 kJ/mol.18

Oxygen adsorption and desorption is another critical processto methane oxidation. The sticking coefficient of O2 wasdetermined over various single- and polycrystalline Pd/PdOsurfaces.19−23 Engel19 studied the adsorption of O2 on Pd(111) by a molecular beam technique and identified thetemperature and coverage dependency of this process. Thesticking coefficient on a bare Pd surface was found to decrease

Received: June 12, 2013Revised: August 30, 2013Published: August 30, 2013

Article

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© 2013 American Chemical Society 19499 dx.doi.org/10.1021/jp4058302 | J. Phys. Chem. C 2013, 117, 19499−19507

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from 0.5 to 0.25 over the surface temperature from 300 to 800K. At certain temperatures the sticking coefficient can decreasenotably with an increase in surface coverage. Goschnick et al.20

examined the oxygen adsorption on Pd (110) by low-energyelectron diffraction (LEED) and mass spectrometry (MS) withsurface temperature ranging from 100 to 600 K. They observeda constant initial sticking coefficient of 0.5 above roomtemperature. Jones et al.21 reported similar results by X-rayphotoelectron spectroscopy (XPS) and molecule beam experi-ments. Matsuchima et al.22 conducted Auger electron spec-troscopy (AES) on O2 adsorption on a polycrystallinepalladium surface. They reported an initial sticking coefficientof 0.8 at 463 K. Carstens et al.23 examined methane adsorptionof methane with PdO supported on zirconia as a function oftemperature and reported an apparently lower binding energyfor oxygen atoms on a crystalline surface of PdO than on ametallic Pd surface.Recently, catalytic combustion of methane has attracted

renewed attention for high-speed combustion. In hypersoniccombustion, the local residence time in an engine can be asshort as a few milliseconds, which approaches the time scale ofcombustion reactions.24 Depending on local thermodynamicconditions, this extremely short residence time can besignificantly less than the time needed to initiate gas-phaseradical processes during the induction time to flame ignition.Nanocatalysis, an approach by which freely suspendednanoparticles induce catalytic surface reaction and local heatrelease, was proposed to address this problem.25 The conceptshares the chemical considerations of traditional catalysisfunctionalized on a wall, but it differs in the physical aspectsof the problem. Catalyst size is substantially smaller than themean free path of the gas. Hence, the oxidation reaction rate islimited by gas−surface reaction kinetics without complicationsfrom mass and heat transfer. In that context, Shimizu et al.25,26

studied the catalytic combustion of methane in a flow reactorby generating PdO nanoparticles in situ from a solubleprecursor. They examined the heterogeneous reaction kineticsof methane oxidation over the surfaces of palladium nano-particles and demonstrated that it is possible to reduce theignition delay time by 1−2 orders of magnitude compared tohomogeneous ignition. Zhang et al.27,28 measured the heatrelease rate of methane oxidation over a PdO surface by wiremicrocalorimetry and extracted kinetic parameters fromexperimental observations. In these earlier studies, a gas−surface reaction model was proposed25 and improvedsubsequently based on experimental observations.26−28 Analysisof the data again shows that in the realm of nanocatalysis, theoxidation rate of methane is largely limited by two principalkinetic processes: adsorption and desorption of O2 anddissociative adsorption of CH4.The present work addresses the ambiguous issues in previous

wire microcalorimetry measurements and updates the kineticand thermodynamic parameters of the reaction model. Inparticular, it is shown that the wire microcalorimetry experi-ments are able to produce a fundamental gas−surface reactionrate coefficient when they are properly designed andconducted. The rate constant of dissociative adsorption ofCH4 was obtained over the temperature range of 600−740 K.

II. EXPERIMENTAL SECTIONWire microcalorimetry has been described in detail else-where.27−30 For a given gas-phase composition, pressure,catalytic material, and surface temperature, microcalorimetry

measures the heat release rate of a surface reaction. A metallicwire with catalytic activity forms its essential component.Mechanically, the wire is suspended in a closed chamber by twocopper columns, which is connected to a dc electrical power.The wire temperature can be determined by its electricresistance. The temperature-dependent resistance of thepalladium material was taken from ref 30.In wire microcalorimetry, a background relationship between

electric power input and wire temperature is established withthe use of an inert gas, typically nitrogen, at a certain pressure.Heat loss from the wire to the surrounding gas balances withthe heat produced by resistive heating. Because of an increasedrate of heat loss, the steady-state power input increases with anincrease in wire temperature, as shown in Figure 1. For a

reactive gas, e.g., a mixture of methane and air, undergoingexothermic catalytic reaction on the wire surface, the wirerequires a smaller power input to reach the same temperature.The difference in the specific power input (Δp) measures thespecific heat release rate due to exothermic surface reactions.Here methane oxidation over a PdO surface was examined at

atmospheric pressure and over the temperature range of 560−800 K. The Pd wire is 10 cm long and 0.01 cm in diameter(99.99%, Aldrich). Methane (99%, Airgas) and high-purity air(21% O2 + 79% N2, Airgas) were used without furtherpurification.The surface composition and morphology of the catalyst wire

was examined by scanning electron microscopy (SEM) beforeand after wire exposure to reactive mixtures at elevatedtemperatures and X-ray photoelectron spectroscopy (XPS)after exposure to oxygen. SEM analysis was carried out using aXL300 FEG SEM, and XPS measurement was accomplishedwith a VG Scientific ESCALAB MKII. Additionally, the wiresurface fine structure was probed by a Vecco Multimode VAFM operating in tapping mode. Silicon AFM tips used in thisstudy have a nominal radius of 9 ± 2 nm and a sidewallinclination of 35°.

III. NUMERICAL SIMULATIONGas-phase composition and surface temperature may beassumed to be invariant along the length of the catalyst wire

Figure 1. Principle of wire microcalorimetry. Symbols areexperimental data; lines are drawn to guide the eye. Difference inpower input p with and without methane is directly proportional to thesurface heat release rate.

The Journal of Physical Chemistry C Article

dx.doi.org/10.1021/jp4058302 | J. Phys. Chem. C 2013, 117, 19499−1950719500

given its large length-to-diameter aspect ratio. To examinebuoyancy-induced natural convection in the chamber, fluidsimulation was conducted using FLUENT by assumingaxisymmetry, as shown in Figure 2. The wire was represented

by an ideal cylinder. The square domain size is 70 times thewire diameter. An increase in the domain size has a negligibleeffect on simulation results. The boundary temperature andpressures are T = 300 K and P = 1 atm, respectively. Thereactive mixture is quiescent on the boundaries. Additionaldetails may be found in ref 27. The Rayleigh (Ra) and Nusseltnumber (Nu) were calculated from pure air environment as afunction of the wire surface temperatures. The relationshipbetween these two dimensionless numbers was compared tothe empirical expression for a natural flow with a reasonableagreement. The gas-phase chemistry is described by USC MechII.32 For surface chemistry, a previously available model28 wasrefined here as will be discussed later.

IV. RESULTS AND DISCUSSIONThe surface of the catalyst wire undergoes chemical andmorphological changes when it was exposed to oxygen ormixtures of methane and oxygen. Figure 3 shows SEM imagesof the cross sections of a Pd wire before and after it wasemployed in a wire microcalorimetry experiment, which used a

2% CH4−air mixture scanning from 500 to 800 K over a 1 hperiod. Morphologically, the wire surface evolved from apolycrystalline structure to a porous layer 1−2 μm in thickness.XPS analysis in that surface region shows both Pd and PdOcrystal structures. Because the reactive mixture is extremely fuellean, there is a sufficient amount of gas-phase molecular oxygenin constant contact with the surface. The reaction oxidized thesurface to form PdO, as expected from thermodynamicconsiderations.6

Modification of the surface resulting in an increase in thesurface area poses a notable challenge in data interpretation. Ina previous study,27 the surface area was only estimated on thebasis of experimental work reported by Rieo et al.4 Usingscanning tunneling microscopy and 18O isotope exchange theyobserved a fact of 2−3 increase in the surface area uponoxidation of a Pd surface to PdO. In the current work, however,the surface area change was carefully examined. Furthermore, amethod was developed that pretreats the surface of as-receivedwires to achieve reliable and repeatable microcalorimetryresults, as discussed in what follows.The wire was first heated in quiescent nitrogen at the surface

temperature of 900 K for 1 h, followed by a 2% methane−airmixture at the same temperature for another hour. Thispretreatment produces a porous PdO layer 1−2 μm inthickness whose catalytic activities were reproducible over thereactant and temperature ranges of interest. We used a two-stepprocedure to determine the surface area. As shown in Figure 4,SEM analysis shows that the wire as received (wire a) has apolycrystalline surface that is smooth at the micrometer level,but at a finer scale AFM probing shows ∼100 nm surfaceislands and ∼10 nm crystal grains and steps. The surface area ofthe untreated wire was determined by integrating the locallyrough surfaces as determined by AFM, which gives a value 1.7times that of an ideal cylinder. Unfortunately, SEM is not ableto determine the surface area of the wire treated in CH4−airmixtures. Figure 4 shows surface pores that were formed duringwire treatment in a 2% CH4−air mixture (wire b). The wirepretreated in 6% CH4 in air at 900 K for 1 h has an even greaterporosity and surface area (wire c). Surface pores have a featuresize around 100 nm, but the depth and distribution of the poresunder the surface is difficult to determine. Hence, the surfacearea has to be measured indirectly using an alternative method.Comparison of the specific heat release rates for 2% CH4

oxidized in air using wires a and b reveals the surface areadifference between them. For wire a, microcalorimetric data canbe obtained reliably only under 650 K. Above this temperature,

Figure 2. Schematic of the computational domain. Boundaryconditions: T = 300 K, P = 1 atm, and fresh reactant mixture.

Figure 3. Scanning electron microscopy images of the wire cross sections before (left) and after (middle) exposing the wire in a 2% CH4−airmixture, scanning from 500 to 800 K, at 1 atm for ∼1 h. XPS spectrum of the wire (right).



drastic surface morphological change accompanies the catalyticreaction and the surface sublayer undergoes oxidation inaddition to surface reactions leading to methane oxidation. Asshown in Figure 5, in the temperature range of 600−670 K theratio of wire b to wire a is around 2 for the specific heat releaserates measured. This difference can only be attributed to anincrease in the surface area. Within the same temperature range,the reaction is expected to be kinetically limited. Evidencesupporting this fact comes from experiments with 2% CH4oxidized over the surface of wire c at 900 K for 1 h. Such a

surface is expected to cause greater diffusional resistance toreaction. Yet, over the 600−670 K temperature range the ratioof specific heat release rates of wire c to wire b is a constant (cf.the inset of Figure 5). Had the reaction been limited by masstransport or heat transport, one would expect the heat releaserate to decrease as the temperature is increased, as is the casefor observations made above 670 K.The above analyses allow us to define the surface area by

combining the AFM measurement with the result of reactivearea measurements, leading to a surface area enhancement of3.5 for wire b compared to an ideal cylinder. The apparentreaction rate may now be defined as

ω =Δ

Δ=

pH T

k3.5 ( )

[CH ]napp

rapp 4

where ΔHr(T) is the enthalpy of combustion of methane(lower heating value). Hence, measurement of the apparentreaction rate allows us to determine the apparent rate constantkapp and the overall reaction order n with respect to theconcentration of CH4. Figure 6 shows the variations of thespecific heat release rate and the apparent reaction rate ωapp as afunction of temperature for 1%, 2%, and 3% CH4 oxidized overthe surface of wire b in air. Within the range of temperature andCH4 concentrations tested, the catalyst surface retained itscomposition and surface morphology after reaction, and theresults shown in the figure are highly reproducible.The overall reaction order n with respect to the CH4

concentration may be obtained from the slope in a plot oflogωapp versus log[CH4]. Figure 7 shows the n values as afunction of wire surface temperature. We found n = 1.03 ±0.03, independent of temperature over its range tested. SinceO2 concentration in the unreacted mixture is substantially

Figure 4. Atomic force microscopy of untreated Pd wire surface (upper left) and scanning electron microscopy images of (a) untreated Pd wiresurface and (b and c) wire surfaces treated in 2% CH4− and 6% CH4−air, respectively, at 900 K and 1 atm for approximately 1 h.

Figure 5. Specific heat release rates measured for oxidation of 2% CH4in air over several wire surfaces. Wire surface area is assumed to be thatof a perfect cylinder. Symbols are experimental data; lines are drawn toguide the eye. Measurements over the untreated Pd wire are unstableabove 650 K. (Inset) Ratios of specific heat release rates.



higher than that of CH4, the heterogeneous reaction occurs as apseudo-first-order reaction. The apparent rate constant kappmay be obtained as the intercept by fitting the measuredreaction rate as logωapp = log kapp + log[CH4], as shown inFigure 8. The resulting rate constant value is plotted as anArrhenius plot as seen in Figure 9. The rate constant may beexpressed as

= ± ×

< <

− ±k

T

(cm/s) (3.2 0.8) 10 e

for 600 740 K

RTapp

4 (62.8 1.6)(kJ/mol)/

where R is the universal gas constant. The value of the apparentactivation energy is consistent with those reported in previousstudies.2−5 Though it is measurable, the amount of heat releasebelow 600 K is too small to obtain an accurate rate constant.Above 740 K, the rate constant appears to fall off as thetemperature increases, which is indicative of the mass transportlimitation.The surface reaction model used here is largely derived from

that in refs 26 and 28, as shown in Table 1. The model isestablished based on experiments conducted on the surfaces ofnanoparticles and wires, for which the support effect cannot betaken into account. Consequently, the model is not applicableto supported catalysts. As in previous studies, critical reactionswere identified by a sensitivity analysis. The overall oxidationrate was found to be sensitive to the reversible O2 adsorptionand desorption

+ ⇄O 8Pd(S) 2O (S)24

(R2)

and methane dissociative adsorption

+ + → +

+ ⇄

CH O (S) Pd(S) CH (S) OH (S)

O 8Pd(S) 2O (S)

k

k

k

44

34

24

16

2b

2f

(R16)

The sensitivity coefficients of these reactions are more than anorder of magnitude greater than those of other reactions overthe entire range of temperature and methane concentrationconsidered. We focus on deriving the rate parameters of R2f,R2b, and R16. In the current model, the rate coefficient of O2adsorption is described in the form of sticking coefficient γ

Figure 6. Heat release (top) and surface reaction (bottom) ratesdetermined for oxidation of CH4 in air over PdO surface. Symbols areexperimental data; lines are drawn to guide the eye.

Figure 7. Reaction order n determined for CH4 oxidation in air over aPdO surface. Symbols are experimental data determined at eachtemperature; line represents the average of the data over thetemperature range shown.

Figure 8. Apparent specific reaction rate versus methane concen-tration. Symbols are experimental data; lines are fits to data assumingthe reaction order n = 1 with respect to methane concentration.

Figure 9. Arrhenius plot for the global oxidation reaction of CH4 in airover a PdO surface. Symbols are experimental data; line represents asimple Arrhenius fit to data.



γπ

=kkTm2f2

O2

where mO2is the molecular mass of O2 and k is the Boltzmann

constant. On the basis of previous studies,19−23 the stickingcoefficient on a bare Pd surface is close to 0.5 at roomtemperature, which decreases with an increase in surfacetemperature and coverage. The current model considers theinfluences of both the surface temperature and the coverage onthe sticking coefficient as the product of two functions

γ γ θ= T F( ) ( )0

where γ0(T) is the sticking coefficient on a bare Pd surface andF(θ) accounts for the dependency on coverage. From amolecule beam experiment of O2 adsorption on Pd (111)surface,19 γ0(T) may be given as

γ = −T e( ) T0

/540

The surface coverage dependency is attributable to the factthat each O atom occupies four surface Pd sites.1 Henceadsorption of each O2 requires at least four adjacent sites thatare available. The number of these adjacent sites decreasesexponentially as the surface coverage increases. The functionF(θ) was computed here by a Monte Carlo simulation in whichO atoms are randomly distributed over a surface. The numberdensity of four empty adjacent sites is counted and normalizedby that of a bare Pd surface. The results are shown in Figure 10.The correlation may be described quantitatively as

θ = θ−F e( ) 8.8

Desorption of O2 from a PdO surface may be determinedfrom the adsorption rate constant and the equilibrium constantof the reversible reaction

+ ⇄O 8Pd(S) 2O (S)k

k

24

2b

2f

The enthalpy of reaction was taken to be 230 kJ/mol.33 Theheat capacity cp and entropy s of surface oxygen may be derivedfrom34

∑ ν= −ν ν

=

−−⎛

⎝⎜⎞⎠⎟

c

RhkT

e e[ 1]p

i

Ni h kT h kT

1

3 6( / ) ( / ) 2i i

∑ ν= − − −ν ν

=

−− −⎡

⎣⎢⎛⎝⎜

⎞⎠⎟

⎤⎦⎥

sR

hkT

e e[ 1] ln(1 )i

Ni h kT h kT

1

3 6( / ) 1 ( / )i i

where N is the number of atoms in a species, h is Planck’sconstant, and νi’s are the vibrational frequencies taken from refs35 and 36. Figure 11 shows the equilibrium constant computedin this work. A comparison with the earlier work ofDeutschmann et al.37 shows reasonably good agreementbetween the two studies. The discrepancy is the result of asomewhat larger enthalpy of adsorption used in ref 37 and to alesser extent updated vibrational frequency values used in thepresent work.Calculation of the equilibrium constant just discussed ignores

the impact from surface coverage and thus is valid for a bare Pdsurface only. With an increase in coverage, adsorbed oxygen

Table 1. Surface Reaction Model of Methane Oxidation overPdO above 450 K

rate parametersb

no. reactiona A β E

1f H2 + 2Pd(S) → 2H(S) 1.0c −0.5 01b 2H(S) → H2 + 2Pd(S) 5.33 × 1016 0.992 87.42f O2 + 8Pd(S) → 2O4(S) e−T/540−8.8θdc 0.0 02b 2O4(S) → O2 + 8Pd(S) 3.01 × 1026 −0.5 230.0−120θd

3f H(S) + O4(S) → OH4(S)+ Pd(S)

2.91 × 1018 1.264 94.6−60θd

3b OH4(S) + Pd(S) → H(S)+ O4(S)

2.29 × 1019 1.156 120.3−30θd

4f H(S) + OH4(S) →H2O

4(S) + Pd(S)6.56 × 1015 1.403 31.8

4b H2O4(S)+Pd(S)→

H(S)+OH4(S)2.11 × 1018 1.134 83.8 + 30θd

5f 2OH4(S) → H2O4(S) +

O4(S)3.89 × 1017 1.244 14.5 + 60θd

5b H2O4(S) + O4(S) →

2OH4(S)1.40 × 1019 1.1 40.7 + 60θd

6f H + Pd(S) → H(S) 1.0c 0 06b H(S) → H + Pd(S) 1.32 × 1010 1.1 261.77f O + Pd(S) → O4(S) 1.0c 0 07b O4(S) → O + Pd(S) 1.64 × 1010 1.1 369.7−60θd

8f OH+Pd(S)→OH4(S) 1.0c 0 08b OH4(S)→OH+Pd(S) 1.60 × 1010 1.1 227.5−30θd

9f H2O + Pd(S) → H2O4(S) 1.0c 0 0

9b H2O4(S) → H2O + Pd(S) 1.62 × 1010 1.1 43.8

10 CO(S) + O4(S) → CO2 +5Pd(S)

1.00 × 1019 1.115 59.8

11 C(S) + O4(S) → CO(S)+ 4Pd(S)

1.01 × 1019 1.115 62.8

12f CO + Pd(S) → CO(S) 1.0c 0 012b CO(S) → CO + Pd(S) 1.65 × 1011 1.1 134.013 CH3(S) + 3Pd(S) →

C(S) + 3H(S)1.07 × 1019 1 85.1

14 CH3(S) + 3O4(S) →C(S) + 3OH4(S)

1.07 × 1019 1 25.1

15 CH4 + 2Pd(S) → CH3(S)+ H(S)

4.00 × 105 0 196.0

16 CH4 + Pd(S) + O4(S) →CH3(S) + OH4(S)

7.70 × 104 0 59.9

aPd site occupancy of O(S), OH(S), and H2O(S) is set to 4. Surfacesite density is 1.95 × 10−9 mol/cm2. bRate constant is written in theform k = ATβe−E/RT. Units of A are given in terms of mol, cm, and s. Eis in kJ/mol. cSticking coefficient. dθ is the total occupied site fraction,i.e., θ = 1 − θPd.

Figure 10. Surface coverage dependency of O2 on a Pd/PdO surface.Symbols are results of Monte Carlo simulation; line is a fit to data.



becomes less stable, leading to a significantly reduced enthalpyof adsorption. In the gas−surface reaction model proposed byWolf et al.38 the enthalpy of oxygen adsorption on a Pd/PdOsurface is linearly proportional to surface oxygen coverage. Inaddition, the adsorption enthalpy of O2 on a fully coveredsurface was chosen to be 110 kJ/mol. The same value was usedin the current work. As in a previous study,26 the variation ofthe enthalpy of O2 adsorption was assumed to be a linearfunction with respect to coverage using the value justmentioned as the limit for a fully covered surface and 230kJ/mol for a bare surface.The rate expression for reaction R16 was determined from

the experimental heat release rates observed for 2% CH4 in airto be

= ± ×

< <

− ±k e

T

(cm/s) (7.7 1.6) 10

for 600 740 K

RT16

4 (59.9 1.2)(kJ/mol)/

The results are plotted in Figure 12. The above rate expressionis subject to uncertainties in the equilibrium constant, the rateconstant of O2 adsorption, and to an extent the surface areadiscussed earlier. We note that the activation energy is in close

agreement the DFT energy barrier of 64.2 kJ/mol for CH4dissociative adsorption of over a PdO (101) surface.18

The above rate expression, along with the reaction model ofTable 1, gives heat release rates closely matching theexperimental observation for all three CH4 concentrations, asseen in Figure 13. Analysis of the computational results

suggests that under the experimental conditions tested thereaction is largely kinetically controlled without complicationsfrom buoyancy-induced natural convection or gas-phase speciesconcentration gradients near the surface of the catalyst wire.Under this condition, the overall rate of methane oxidation overa PdO surface is governed by dissociative adsorption ofmethane, as expected, with the reaction rate given by

θ θ− =t

kd[CH ]

d[CH ]4

16 4 O (S) Pd(S)4

Neglecting surface species other than O4(S), this expressioncan be simplified to

θ θ− = −t

kd[CH ]

d[CH ] (1 )4

16 4 O (S) O (S)4 4

With or without reaction R16, the θO4(S) value changes by

<0.1%. In addition, O2 adsorption and desorption is inequilibrium; consequently, methane adsorption affects surfaceoxygen coverage to only a minor degree. Hence, k16 may bederived from the apparent rate constant kapp determined earlieras

θ θ=

−k

k

(1 )16app

O (S) O (S)4 4

Since θO4(S) is determined by equilibrium oxygen adsorption

and desorption, the uncertainty of its equilibrium constantdirectly impacts the accuracy of the k16 expression. Unfortu-nately, there is little to no direct measurements available toverify the accuracy of the equilibrium constant experimentally.Hence, the k16 expression derived here is implicitly coupledwith and must be used together with the specific equilibriumconstant shown in Figure 11.

Figure 11. Equilibrium constant of O2 adsorption on a bare Pdsurface. Solid line, this work; dashed line, ref 37

Figure 12. Arrhenius plot of k16 measured in this work. Symbols areexperimental data; line is an Arrhenius fit to the data.

Figure 13. Heat release rates measured (symbols) and predicted(lines) for oxidation of 1−3% CH4 in air.



V. CONCLUSIONSCatalytic oxidation of CH4 diluted in air was investigated over aPdO surface at atmosphere pressure by microcalorimetry.Under the conditions considered, the catalytic reaction ispseudo first order with respect to the methane concentrationand has a lack of buoyancy-induced natural convection or gas-phase species concentration gradients near the surface of thecatalyst wire. The global kinetic parameters were extracted fromexperimental data, which yielded unity reaction order inmethane and an activation energy 62.8 ± 1.6 kJ/mol. Overthe examined temperature range of 540−800 K the oxidationrate of methane is determined by its dissociative adsorption ona PdO surface, which combines the effects of surface oxygencoverage and the intrinsic rate of methane dissociativeadsorption on a vacant Pd site surrounded by PdO. Theapparent rate constant for the overall oxidation rate wasobtained as kapp(cm/s) = (3.2 ± 0.8) × 104e−(62.8±1.6)(kJ/mol)/RT

for 600 < T < 740 K. The intrinsic rate constant of thedissociative adsorption of methane was derived to be k16(cm/s)= (7.7 ± 1.6) × 104e−(59.9±1.2)(kJ/mol)/RT from the oxygenadsorption/desorption equilibrium constant estimated here andthe apparent rate constant over the same temperature range.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected].

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe authors acknowledge support for this work by the AirForce Office of Scientific Research through a MURI programon Nanocatalysts in Propulsion under the technical monitoringof Dr. Michael R. Berman.

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kinetics of catalytic oxidation of methane over palladium oxide by wire microcalorimetry

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