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Microkinetic Simulation of Temperature-Programmed Desorption Chia-Ching Wang, Jyun-Yi Wu, and Jyh-Chiang Jiang* Department of Chemical Engineering, National Taiwan University of Science and Technology, 43, Keelung Road, Section 4, Taipei, 106, Taiwan S Supporting Information *

ABSTRACT: The temperature-programmed desorption (TPD) spectra were simulated by combining density functional theory (DFT) calculations and microkinetic modeling. In the microkinetic analyses, all kinetic and thermodynamic parameters were obtained from DFT calculations to minimize artificial assumptions. For the case study, the desorptions of NH3 and H2O from the RuO2(110) surface were simulated. The coverage-dependent desorption energies were introduced into the microkinetic model because different adsorbates on the surface will exhibit different desorption behaviors. In addition, temperature-dependent pre-exponential factors were applied to the desorption rate equations. The calculated preexponential factors are ranged from 1014 to 1017 s−1, which are greatly larger than 1013 s−1, a generally accepted empirical value for desorption processes. The desorption temperatures obtained from microkinetic simulations consist with experimental results, and the simulated TPD patterns are also similar to the experimental observations.

1. INTRODUCTION Temperature-programmed desorption (TPD) was first proposed in 1963 by Amenomiya and Cvetanovic,1 which is also known as thermal desorption spectroscopy (TDS). TPD is one of the most straightforward surface science experiments; its techniques are important methods for the determination of thermodynamic parameters and kinetic of desorption processes. In general, a TPD starts by exposing a surface to a specific amount of gas; then, the surface is heated by a constant heating rate. As the gas desorbs from the surface, the molecules are monitored by a mass spectrometer; then, the TPD is obtained by plotting the signals from the mass spectrometer as a function of time. In TPD experiments, the peak temperature directly associates with the desorption energy (Edes) of the sample gas, and the Polanyi−Wigner equation relates the rate of desorption rdes to the desorption energy Edes. The desorption rate by nth order Polanyi−Wigner equation can be written as rdes(t ) = −

dθA * = νnθAn*e−Edes / RT dt

reaction. A microkinetic model can be a convenient tool for the consolidation of fundamental information about a catalytic process and for extrapolation of this information to other reaction conditions and to other catalytic reactions involving related reactants, reaction intermediates, and products. In recent years, there are several remarkable progresses in the implementation of density functional theory (DFT) methods in the development of microkinetic models in the heterogeneous catalysis.3−11 The incorporation of DFT data eliminates the need to make simplifying assumptions in microkinetic models. As such, the models allow estimation of the contribution of each elementary step to the overall rate, the determination of the reversible or irreversible nature of elementary reactions, reaction orders, activation enthalpies, and surface coverages under realistic reaction conditions. In most of theoretical microkinetic studies about heterogeneous catalytic reactions, the catalytic abilities, such as selectivity and turnover frequency, are the major properties that researchers concerned.3−9 In general, the desorption processes were involved in the overall reaction scheme of microkinetic models; however, the details about the desorptions were rarely discussed. Because the TPD is the most straightforward method in monitoring desorption processes, simulating TPD spectra by microkinetic modeling should be a practicable method in investigating properties of desorptions. In the present work, we established a model combining DFT calculations and microkinetics to simulate the TPD spectra on

(1)

where the θA* denotes the surface coverage of the adsorbate A and ν is the pre-exponential factor. Redhead analysis2 is a commonly applied method to extract activation energies from a single desorption spectrum. He assumed that the preexponential factor and the desorption energy are independent of the surface coverage and the desorption follows first-order kinetics. However, this method requires a known value for ν1, and ν1 = 1013 s−1 is a commonly chosen value. The microkinetic modeling was defined to denote reaction kinetics analyses that attempt to incorporate into the kinetic model the basic surface chemistry involved in the catalytic © 2013 American Chemical Society

Received: September 21, 2012 Revised: February 27, 2013 Published: February 28, 2013 6136

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q q kdes = A * e−Edes / RT kads qA *

the RuO 2 (110) surface. Figure 1 gives a schematic representation of the stoichiometric RuO2(110) surface,

(6)

where q is the partition function, and Table 1 summarizes the terms of partition functions applied in this work. For the Table 1. Partition Functions Applied in the Microkinetic Model for TPD Simulationsa type

partition function

translation

⎛ 2πmkBT ⎞3/2 ⎟ qT = ⎜ ⎝ h2 ⎠

rotation (linear)

R qlinear =

rotation (nonlinear)

vibration

Figure 1. Ball-and-stick model of the stoichiometric RuO2(110) surface.

rdes(t ) = kdesθA *

(4)

1−e

electronic

q = (2S + 1)e−Eg / kBT

Total

q = q Tq R q V q E

⎞ ⎟ ⎠

E

The PA in eq 7 is the partial pressure of A in the gas phase, and mA and kB are molecular mass of the adsorbate and Boltzmann constant, respectively. The rate of adsorption is then defined as: rads =

FASc CT

(8)

The Sc in eq 8 is the sticking coefficient, which is the probability that collisions with the surface lead to the adsorption, and CT (m−2) is the Rucus concentration of reaction sites per unit area on the surface (CT = 5.05 × 1018 m−2 in this work). The sticking coefficient depends on the fractional surface coverage and temperature, and it can be expressed by Sc°(T)f(θ), a value on a clean surface multiplied by a function of surface coverage.25 Here we assumed the S°c (T) equals 1 and f(θ) equals the fraction of free reaction sites θ* and replaced the partial pressure PA in eq 7 with PTYA (PT is the total pressure and equal to 2 × 10−10 Pa in this work), then PT YAθ rads = * C 2πm k T

where k (s−1) is the rate constant, and the dimensionless θ and Y are the coverage on the surface and mole fraction in gas phase, respectively. For the first-order Polanyi−Wigner equation, the definition of the desorption rate from eq 1 is analogous to eq 4, and it generates ν = kdese Edes / RT

1 −hυi / kBT

molecules adsorbed on the catalytic surface, they will be treated as static bodies that cannot translate or rotate, and only the vibrational and electronic terms of partition functions will be involved. To obtain the desorption rate constant kdes, we derived the adsorption rate constant (kads) from the collision theory. The following equation defines the number of gas-phase molecules colliding with a surface per unit area and per unit time by the collision theory PA FA = 2πmA kBT (7)

where A*, A, and * denote the adsorbed molecule, free molecular, and the free site on the surface, respectively. From the microkinetic model, the rates of the adsorption (rads) and desorption (rdes) can be defined as (3)

⎛

∏ ⎜⎝

h is Plank’s constant, V is the volume of the system, σ is the symmetry factor, A, B, and C are rotational constants, υi is the vibrational frequency of the ith mode, DF is the degree of freedom (3N−5 for linear molecules and 3N−6 for nonlinear molecules), S is the total spin angular momentum, and Eg is the electronic energy from the ground state.

(2)

rads(t ) = kadsYAθ *

DF

qV =

3/2 1 ⎛ kBT ⎞ π ⎟ ⎜ ABC σ⎝ h ⎠

a

2. METHODS In the heterogeneous system, the desorption−adsorption equilibrium can be represented by the following equation: A* ↔ A + *

R qnonlinear =

i

which presents exposed rows of two-fold coordinated oxygen atoms (Obr) and five-fold coordinated Ru atoms (Rucus; cus = coordinatively unsaturated site), all along the [001] direction. The RuO2(110) surface exhibits the high catalytic activity in CO oxidation,12,13 NH3 oxidation,14−17 and HCl oxidation.18,19 Because plenty of experimental and theoretical studies have been performed in investigations of catalytic reactions on the RuO2(110) surface, it is a very suitable material for the case study. In this work, the TPD spectra of NH3 and H2O from the RuO2(110) surface were simulated. Recently, the kinetic Monte Carlo (KMC) method had been applied in TPD simulations.20−23 However, in KMC simulations, a single desorption energy and a specific pre-exponential factor are generally applied to the rate equation of a single reaction step.16,21−24 To obtain more realistic TPD spectra, we established a microkinetic model including coverage-dependent desorption energies and temperature-dependent pre-exponential factors.

1 kBT σ hB

(5)

T

In the adsorption−desorption equilibrium, the rate constants kads and kdes are related by

A B

(9)

and 6137

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PT C T 2πmA kBT

adsorbate molecule in gas phase, and EA/RuO2 is the total energy of the adsorption system. A positive value of Edes indicates an endothermic desorption process. In this work, all of the energies introduced into the rate equations were corrected by the zero-point energy (ZPE).

(10)

By introducing eq 10 into eq 6, we obtained the desorption rate constant kdes and the pre-exponential factor ν qA q −E / RT PT * e des kdes = C T 2πmA kBT qA * (11) ν=

qA q * 2πmA kBT qA *

3. RESULTS AND DISCUSSIONS 3.1. TPD of NH3. Table 2 lists the calculated desorption energies of NH3 on the RuO2(110) surface. At different

PT

CT

(12)

Table 2. Stepwise Desorption Energies (eV) of NH3 and H2O From the RuO2(110) Surface at Various Coveragesa

In TPD experiments, the temperature T is a function of time t T = T0 + βt

coverage

(13)

0.25 ML 0.50 ML 0.75 ML 1.00 ML second layerb multilayerc

The T0 and β in eq 13 are the initial temperature and the heating rate, respectively. Combining eqs 11, 13, and 4, the desorption rate equation becomes rdes(t) =−

dθA * dt

CT

(1.56) (1.42) (0.93) (0.71) (0.59) (0.42)

1.13 1.30 1.12 1.30 0.43 0.42

(1.27) (1.43) (1.28) (1.42) (0.54) (0.53)

Values in parentheses are the energies before the zero-point correction. bFrom the desorption of the fifth molecule. cAverage desorption energy of 7NH3(6H2O) molecules beyond the first layer.

(14)

coverages, the stepwise desorption energies of NH3 molecules at first layer are 1.40 (0.25 ML), 1.30 (0.50 ML), 0.78 (0.75 ML), and 0.60 eV (1.00 ML). According to the DFT calculated desorption energies, we fitted a desorption energy curve as a function of first-layer NH3 molecule coverage (θNH3* < 1 ML) in Figure 2a. This energy profile shows a desorption energy

In this study, the TPD spectra were assumed to be recorded in a batch-type reactor, and the adsorbates were preadsorbed on the surface. Because the total pressure in this work is 2 × 10−10 Pa, the adsorption is very slow and can be ignored under this condition. In this microkinetic simulation, the TPD intensity is equal to the desorption rate of the adsorbate, and the relationship between surface coverage of A (θA) and time (t) in the desorption process could be obtained by solving the ordinary differential equation (ODE) of eq 14. All ODEs in this work were solved by numerical method using Mathematica. The partition functions and the desorption energies in this study are obtained by DFT calculations. All DFT calculations were performed using the Vienna ab initio simulation Package (VASP).26−28 The generalized gradient approximation (GGA) was used with the functional described by Perdew and Wang29 and a cutoff energy of 420 eV. Electron−ion interactions were investigated using the projector-augmented wave method;30 spin-polarized calculations were performed for all of the structural optimizations. After structural optimization, a normal-mode frequency analysis was conducted to check the validity of the optimized geometries. The RuO2(110) surface was modeled as a 2-D slab in a 3-D periodic cell. The slab was a 4 × 1 surface having the thickness of two O−Ru−O repeat units, which is equivalent to six atomic layers. The upper four atomic layers were relaxed in all structural optimizations. A 13 Å vacuum space was introduced in the [110] direction to curtail interactions between the slabs. For this (4 × 1)-RuO2(110) surface model, the k points of 4 × 6 × 1 were set by Monkhorst-Pack. The validity of all optimized structures was checked through normal-mode frequency analysis. In the vibrational frequency calculations, the upper two atomic layers and adsorbates were relaxed; all others were fixed. The desorption energies (Edes) of adsorbates were calculated using the formula Edes = (E(n − 1)A/RuO2 + EA ) − En A/RuO2

1.40 1.30 0.78 0.60 0.49 0.34

H2O

a

qA q −E / R(T + βt ) * e des 0 θA * 2πmA kB(T0 + βt ) qA * PT

=

NH3

Figure 2. Desorption energy curve and the corresponding fitting function of NH3 molecules at (a) first layer and (b) multilayer.

difference between 0 and 1 ML and a significant energy drop from 0.5 to 0.8 ML. Figure 3 shows the top view of the NH3 adsorption on the RuO2(110) surface at 1 ML, and the numbers indicate the order of desorption in sequence. The NH3 molecule binds to the surface through the donation of its lone pair of electrons to a surface Ru atom.31 As the coverage increases, the electron-accepting ability of the Rucus atoms from

(15)

This equation defined the stepwise desorption energy, where n is the number of adsorbates, EA is the energy of a single 6138

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The θNH3(I) and νNH3(I) are the surface coverage and the preexponential factors of the desorptions of first-layer molecules, and the θNH3(II) and νNH3(II) are the parameters for multilayer. In the real system, the appearance of multilayer molecules might not be after the first layer is fully occupied; that is, both the first layer and the multilayer adsorbates will exist on the surface at the same time. To determine the initial coverage of multilayer NH3 molecules, we assumed an equation to define the θNH3(II) as a function of θNH3(I):

Figure 3. Top view of NH3 molecules adsorbed on the RuO2(110) surface at θHN3* = 1 ML. The numbers indicate the desorption order in sequence.

θNH3(II) = [−0.3 + 0.3 exp(2.6 × θNH3(I))] × θNH3(I) (18)

By comparing simulated TPD spectra and experimental results, we chose proper initial coverages to mimic a TPD pattern similar to experimental one. We fitted an exponential growth function according to these assumed initial coverage to define the relationship between θNH3(I) and θNH3(II). This equation is artificially designed and will not directly affect the desorption temperature because it defines only the initial coverage and will not alter the desorption energy profiles in Figure 2. In the NH3 TPD simulations, the initial temperature is 50 K and the heating rate (β) is 3 K/s (base on the NH3 TPD experiment.)14 Figure 4 shows the simulated NH3 TPD with

the NH3 molecules decreases, which results in the weakening of gas−surface interaction. In addition, the lateral interactions between the first layer NH3 molecules on the RuO2(110) surface are also repulsive forces. Therefore, in the desorption process, the NH3 molecule with more neighbor molecules will be prior to desorption from the surface. As shown in Figure 3, the first and second NH3 desorbed from the surface are both neighbored with the other two molecules, and the third and fourth ones are isolated in their desorptions. Because of the different binding environments on the RuO2(110) surface, the first layer NH3 molecules exhibit a broad distribution in desorption energies. In Table 2, we also listed the desorption energies of ammonia beyond the first layer. After the four Rucus sites on the (4 × 1)RuO2(110) are fully occupied, additional NH3 molecules adsorb on the surface through the hydrogen-bonding interactions. For the second-layer ammonia molecules, the desorption energy was obtained from the fifth NH3 on the surface. This fifth molecule adsorbed on the surface through the hydrogen-bond interactions with the first layer NH3 and the surface Obr atom (the adsorption structure is shown in the Supporting Information), and the desorption energy is 0.49 eV. For the desorption energy of multilayer molecules, the 0.34 eV was obtained from the average desorption energy of seven NH3 molecules beyond the first layer.32 (The structure is shown in the Supporting Information.) Because of the limitation of the computational scale, it is difficult to calculate the desorption energy of ammonia at a really high coverage by DFT calculations. Therefore, we applied the 0.34 eV as the desorption energy of NH3 molecules at infinite coverage. On the basis of these two desorption energies at high coverage, Figure 2b shows the fitted desorption energy curve of NH3 molecules when the coverage is higher than 1 ML. The desorption of NH3 from the RuO2(110) surface is a simple process, and the desorption rate can be represented by the following equation: rNH3(t ) =

dθ dθ * = − NH3* = νNH e−Edes / RT θNH * 3 3 dt dt

Figure 4. NH3 TPD spectra by the simulations combing DFT calculations and microkinetic modeling with different initial coverages. The starting temperature is 50 K, and the heating rate is 3 K/s. The inset is the experimental NH3 TPD by Wang et al.14

different initial coverages by solving the ODE of eq 17 with the fitted desorption energy curves (Figure 2), and the inset is the experimental NH3 TPD done by Wang et al.14 The intensities of TPD spectra in the Figure 4 are defined as the desorption rate of NH3. In the experimental TPD study under UHV environment by Wang et al.,14 the NH3 desorption peaks are α1-NH3 at 420 K, α2-NH3 at 355 K, β-NH3 at 170 K, and γNH3 at 130 K; the α- and β-NH3 were attributed to the desorption from the first and second layers, and γ-NH3 was assigned to multilayer desorptions. In our microkinetic TPD simulations, ammonia desorption peaks locate at 419 (first layer), 155 (second layer), and 128 K (multilayer). According to DFT calculated results, the higher coverage of ammonia will result in a lower desorption energy, which implies the lower desorption temperature. When θNH3* = 0.8 ML, the desorption

(16)

Because the desorptions are contributed by first-layer and multilayer (including second layer) NH3 molecules, the desorption rate equation can be rewritten into two terms: −

dθNH3* dt

⎛ dθNH3(I) dθNH3(II) ⎞ ⎟ =−⎜ + dt ⎠ ⎝ dt = νNH3(I)e−Edes / RT θNH3(I) + νNH3(II)e−Edes / RT θNH3(II) (17) 6139

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signal of first-layer NH3 molecules raises at 185 K and extends to 440 K; this simulated ammonia desorption pattern is very similar to the experimental TPD observations. Moreover, the shape of peaks from the desorptions of multilayer NH3 molecules also consists with experimental results. In the NH3 TPD simulation, we also introduced a step function of desorption energy into the desorption rate equation (eq 16). This step function is composed of the six desorption energies of NH3 listed in Table 2. The step function and the corresponding TPD spectra are shown in the Supporting Information (Figure S2.) By using the stepwise desorption energy function, the desorption peaks locate at the 410, 392, 236, 185, 158, and 113 K. These six desorption temperatures are in consistence with the experimental results; however, the TPD pattern in six isolated desorption peaks does not match that from the experiment. 3.2. TPD of H2O. In the H2O TPD simulation, the water molecules show a different adsorption behavior from ammonia. Figure 5 shows the adsorption structure of H2O molecules Figure 6. Desorption energy curve and the corresponding fitting function of H2O molecules at (a) first layer and (b) multilayer.

desorption energy profile of first-layer H2O molecules. In the desorption process, the desorption energy is gradually increased and apparently drops when the coverage approached to 0 ML. For the second-layer and multilayer desorption of H2O molecules from the RuO2(110) surface, we applied the same method as the previous section to predict the desorption energies. The desorption energy of the second-layer H2O molecules is 0.43 eV, which is calculated from the desorption of the fifth H2O molecule. Similarly, the desorption energy of multilayer H2O molecules, 0.42 eV, is obtained from the average desorption energy of six water molecules beyond the first layer.32 On the basis of the two desorption energies, Figure 6b shows the desorption energy curve of H2O molecules beyond the first layer. In the microkinetic simulation of H2O TPD, the following equation defines the rate of desorption

Figure 5. Top view of H2O molecules adsorbed on the RuO2(110) surface at θH2O* = 1 ML. The blue rectangles indicate the two water dimers on the surface.

adsorbed on the RuO2(110) surface at θN2O* = 1 ML, and Table 2 lists the desorption energies at different surface coverages. When θH2O* = 0.25 ML, the single H2O molecule is dissociatively adsorbed on the RuO2(110) surface, and the calculated desorption energy is 1.13 eV; at θH2O* = 0.50 ML, the second H2O molecule adsorbs in molecular form on the Rucus site next to the first one, and the corresponding desorption energy is 1.30 eV. Through the strong hydrogen bonding with the first H2O molecule and the Obr atom, the second H2O molecule owns a much higher desorption energy than the first one, and the two molecules form a stable water dimer on the RuO2(110) surface. As the coverage increases, the third and the fourth H2O molecules will follow the same mechanism and form another water dimer on the surface. In Figure 5, the blue rectangles indicate the two water dimers on the surface. From Table 2, it has been observed that the calculated desorption energies for two water dimers on the (4 × 1)-RuO2(110) surface are like wave-type distribution. However, when fitting the desorption energy curve, the desorption energy at θH2O* = 0.75 ML was ignored; we assumed that when strong bonded H2O molecule desorbs from the surface, the weak bonded one will desorb immediately or form a new water dimer with another H2O molecule. In the search for adsorption structures, the dimer form is the most stable one for water molecules adsorbed on the RuO2(110) surface. Additional hydrogenbonding interaction in water dimer makes the average binding energy larger than that of the isolated H2O molecule. Therefore, in the desorption process, when one of the molecules in the water dimer desorbs, another H2O will desorb promptly after the first one. Figure 6a shows the fitted

rH2O(t ) =

dθ dθ * = − H 2O * dt dt

= νH2O(I)e−Edes / RT θH2O(I) + νH 2O(II)e−Edes / RT θH2O(II) (19)

The desorption rate of H2O molecules is contributed by two terms: the desorption from the first layer defined by θH2O(I) and νH2O(I) and that from the multilayer (including second layer) defined by θH2O(II) and νH2O(II). To define the relationship between θH2O(I) and θH2O(II), we applied the exponential growth function with the same coefficients as eq 18 θH2O(II) = [−0.3 + 0.3 exp(2.6 × θH 2O(I))] × θH 2O(I) (20)

Figure 7 shows the simulated H2O TPD spectra with different initial coverage by solving the ODE of eq 19, and the inset shows the experimental H2O TPD done by Lobo et al.33 In the H2O TPD simulations, the initial temperature is 90 K and the heating rate (β) is 4 K/s (based on the H2O TPD experiment.)33 As the initial coverage increased, the desorption 6140

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Figure 8. Pre-exponential factor plots in function of temperature: (a) in desorption of NH3 molecules and (b) in desorption of H2O molecules.

Figure 7. Simulated H2O TPD spectra with different initial coverages; the starting temperature is 90 K and the heating rate is 4 K/s. The inset is the experimental H2O TPD by Lobo et al.33

entropy effect of desorption is not negligible. This finding is in agreement with the recent microkinetic study by Cao et al.;11 they showed that in the collision theory model the free energy barriers of the desorption processes are much smaller than the thermal desorption energy in total energy landscape (0 K). DFT calculations could directly provide reaction energies under the zero-temperature conditions, but the entropy effect is not included. In other words, assuming 1013 s−1 as the preexponential factor in kinetic simulations might cause an underestimation of desorption rate or an overestimation of desorption temperature, especially for desorption processes with large entropy change. In this work, if the pre-exponential factors are replaced by 1013 s−1, the desorption temperatures of NH3 will be 149, 179, and 515 K. These desorption temperatures are significantly increased, especially for strongbonded molecules in the first layer. Experimentally, 1013 s−1 is a generally accepted pre-exponential factor in predicting desorption energies; however, this value might not be appropriate for predicting desorption temperatures in theoretical studies. In kinetic simulations, the entropic effects should be considered to acquire reliable information because they strongly affect the desorption rate.

peak of first layer H2O molecules shifts to higher temperature; at νH2O* = 0.8 ML, the simulated desorption temperature is 394 K. For the desorptions of first-layer H2O molecules, the intensity increased at ca. 330 K and dropped rapidly after reaching the maximum point. According to Figure 6a, the desorption energy of water molecules decreases as the coverage decreases at the low coverage region. Therefore, when the thermal energy overcomes the maximum desorption energy in the heating process, the remaining water molecules desorb rapidly, which results in dramatic decreases in the TPD spectra. For the desorptions from the multilayer, only one desorption peak appears at 142 K in the TPD spectra because the desorption energies of the second layer and multilayer water molecules are very similar (Table 2). In the experimental H2O TPD spectra, the desorption temperatures from first-layer and multilayer molecules are 400 and 160 K, respectively.33 Similarly, we designed a stepwise desorption energy function of H2O molecules using the six calculated desorption energies (Table 2) and simulated a TPD spectra by this step function. The step function and the TPD spectrum are shown in the Supporting Information (Figure S2). The TPD spectrum shows three desorption peaks located at 390 (0.50 and 1.00 ML), 330 (0.25 and 0.75 ML), and 142 K (second layer and multilayer). Again, by comparing with experimental results, these desorption peaks from the step function lie in a reasonable range, but the TPD shape does not consist with the experimental one. According to these simulations, we suggest that a detailed desorption energy profile is an important issue in simulating reliable TPD spectra. 3.3. Pre-Exponential Factors. According to the definition of eq 12, pre-exponential factors obtained from the statistical thermodynamics should be temperature dependence. In Figure 8, we plotted the calculated pre-exponential factors from 50 to 500 K; it clearly shows that as the temperature elevated, the value of pre-exponential factors increased from 1014 to 1017 s−1. In addition, the pre-exponential factors of the desorptions from the first layer are always larger than those from multilayer. That is because the stronger bonded adsorbates at first layer gain larger entropy during the desorption processes, which results in larger pre-exponential factors. The pre-exponential factors obtained in this study are significantly larger than the empirical value of 1013 s−1, and this high magnitude implies that the

4. CONCLUSIONS In this study, we successfully established a method for the TPD spectra simulations. The results demonstrate that microkinetic modeling combined with DFT calculations could properly simulate TPD spectra that consist with experimental results. We introduced the coverage-dependent desorption energies and the temperature-dependent pre-exponential factors into the microkinetic model. The proper desorption energy profiles and pre-exponential factors are important issues in the simulations. In our microkinetic model, the desorption energy curve in a function of coverage was applied rather than a single desorption energy. As the coverage changed, both the vertical gas-surface interaction and the lateral interaction between the adsorbates will be different, and the desorption energy will also be altered. For the pre-exponential factors, the calculated values in this work are a function of temperature and ranged from 1014 to 1017 s−1. These pre-exponential factors are significantly higher than 1013 s−1, a generally applied empirical value. The high magnitude of pre-exponential factors comes from the entropic contribution in the desorption processes. The 1013 s−1 might not be an appropriate pre-exponential factor for theoretical 6141

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The Journal of Physical Chemistry C

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and Catalytic Reactivity of the RuO2(110). Surf. Sci. 2000, 287, 1474− 1476. (13) Wang, J.; Fan, C. Y.; Jacobi, K.; Ertl, G. The Kinetics of CO Oxidation on RuO2(110): Bridging the Pressure Gap. J. Phys. Chem. B 2002, 106, 3422−3427. (14) Wang, Y.; Jacobi, K.; Schöne, W. D.; Ertl, G. Catalytic Oxidation of Ammonia on RuO2(110) Surfaces: Mechanism and Selectivity. J. Phys. Chem. B 2005, 109, 7883−7893. (15) Wang, C.-C.; Yang, Y.-J.; Jiang, J.-C.; Tsai, D.-S.; Hsieh, H.-M. Density Functional Theory Study of the Oxidation of Ammonia on RuO2(110) Surface. J. Phys. Chem. C 2009, 113, 17411−17417. (16) Hong, S.; Karim, A.; Rahman, T. S.; Jacobi, K.; Ertl, G. Selective Oxidation of Ammonia on RuO2(110): A Combined DFT and KMC Study. J. Catal. 2010, 276, 371−381. (17) Perez-Ramirez, J.; Lopez, N.; Kondratenko, E. V. Pressure and Materials Effects on the Selectivity of RuO2 in NH3 Oxidation. J. Phys. Chem. C 2010, 114, 16660−16668. (18) Hevia, M. A. G.; Amrute, A. P.; Schmidt, T.; Pérez-Ramírez, J. Transient Mechanistic Study of the Gas-Phase HCl Oxidation to Cl2 on Bulk and Supported RuO2 Catalysts. J. Catal. 2010, 276, 141−151. (19) Zweidinger, S.; Hofmann, J. P.; Balmes, O.; Lundgren, E.; Over, H. In Situ Studies of the Oxidation of HCl over RuO2 Model Catalysts: Stability and Reactivity. J. Catal. 2010, 272, 169−175. (20) Zuniga-Hansen, N.; Calbi, M. M. Thermal Desorption from Heterogeneous Surfaces. J. Phys. Chem. C 2012, 116, 5025−5032. (21) Alas, S. J.; Vicente, L. TPD Study of NO Decomposition on Rh(111) by Dynamic Monte Carlo Simulation. Surf. Sci. 2010, 604, 957−964. (22) van Bavel, A. P.; Ferré, D. C.; Niemantsverdriet, J. W. Simulating Temperature Programmed Desorption Directly from Density Functional Calculations: How Adsorbate Configurations Relate to Desorption Features. Chem. Phys. Lett. 2005, 407, 227−231. (23) Raaen, S.; Ramstad, A. Monte-Carlo Simulations of Thermal Desorption of Adsorbed Molecules from Metal Surfaces. Energy 2005, 30, 821−830. (24) Sinha, N. K.; Neurock, M. A First Principles Analysis of the Hydrogenation of C1−C4 Aldehydes and Ketones over Ru(0001). J. Catal. 2012, 295, 31−44. (25) Cortright, R. D.; Dumesic, J. A. Kinetics of Heterogeneous Catalytic Reactions: Analysis of Reaction Schemes. Adv. Catal. 2001, 46, 161−264. (26) Kresse, G.; Hafner, J. Ab-Initio Molecular-Dynamics for OpenShell Transition-Metals. Phys. Rev. B 1993, 48, 13115−13118. (27) Kresse, G.; Furthmuller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phy. Rev. B 1996, 54, 11169−11186. (28) Kresse, G.; Furthmuller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (29) Perdew, J. P. In Electronic Structure of Solids ’91; Ziesche, P., Eschrig, H., Eds.; Akademie Verlag: Berlin, 1991; p 11. (30) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758− 1775. (31) (a) Wang, C.-C.; Yang, Y.-J.; Jiang, J.-C. DFT Study of NHx (x = 1−3) Adsorption on RuO2(110) Surfaces. J. Phys. Chem. C 2009, 113, 2816−2821. (b) Wang, C.-C.; Yang, Y.-J.; Jiang, J.-C. DFT Study of NHx (x = 1−3) Adsorption on RuO2(110) Surfaces. J. Phys. Chem. C 2009, 113, 21976−21976. (32) For the desorption energy determinations of multilayer NH3 and H2O molecules, there are 11 ammonia molecules and 10 H2O molecules on the surface, respectively. The average desorption energies were determined by the following equation

studies because it might result in an underestimation of desorption rate or an overestimation of desorption temperature.

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ASSOCIATED CONTENT

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AUTHOR INFORMATION

S Supporting Information *

The top view and side view of the (4 × 1)-RuO2(110) surface model (Figure S1), the list of NH3 and H2O adsorption structures and corresponding vibrational frequencies (Table S1), and the simulated TPD spectra by applying stepwise desorption energies (Figure S2). This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author

*E-mail: [email protected]. Tel: +886-2-27376653. Fax: +886-2-27376644. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the support from National Science Council of Taiwan (NSC 101-2113-M-011-004-MY3), and the computer time and facilities from National Center for HighPerformance Computing (NCHC).

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REFERENCES

(1) Amenomiya, Y.; Cvetanovic, R. J. Application of FlashDesorption Method to Catalyst Studies. I. EthyleneAlumina System. J. Phys. Chem. 1963, 67, 144−147. (2) Redhead, P. A. Thermal Desorption of Gases. Vacuum 1962, 12, 203−211. (3) Gokhale, A. A.; Kandoi, S.; Greeley, J. P.; Mavrikakis, M.; Dumesic, J. A. Molecular-Level Descriptions of Surface Chemistry in Kinetic Models Using Density Functional Theory. Chem. Eng. Sci. 2004, 59, 4679−4691. (4) Grabow, L. C.; Gokhale, A. A.; Evans, S. T.; Dumesic, J. A.; Mavrikakis, M. Mechanism of the Water Gas Shift Reaction on Pt: First Principles, Experiments, and Microkinetic Modeling. J. Phys. Chem. C 2008, 112, 4608−4617. (5) Gokhale, A. A.; Dumesic, J. A.; Mavrikakis, M. On the Mechanism of Low-Temperature Water Gas Shift Reaction on Copper. J. Am. Chem. Soc. 2008, 130, 1402−1414. (6) Madon, R. J.; Braden, D.; Kandoi, S.; Nagel, P.; Mavrikakis, M.; Dumesic, J. A. Microkinetic Analysis and Mechanism of the Water Gas Shift Reaction over Copper Catalysts. J. Catal. 2011, 281, 1−11. (7) Novell-Leruth, G.; Ricart, J. M.; Perez-Ramirez, J. Pt(100)Catalyzed Ammonia Oxidation Studied by DFT: Mechanism and Microkinetics. J. Phys. Chem. C 2008, 112, 13554−13562. (8) Kandoi, S.; Greeley, J.; Sanchez-Castillo, M. A.; Evans, S. T.; Gokhale, A. A.; Dumesic, J. A.; Mavrikakis, M. Prediction of Experimental Methanol Decomposition Rates on Platinum from First Principles. Top. Catal. 2006, 37, 17−28. (9) Bjorkman, K. R.; Schoenfeldt, N. J.; Notestein, J. M.; Broadbelt, L. J. Microkinetic Modeling of cis-Cyclooctene Oxidation on Heterogeneous Mn−tmtacn Complexes. J. Catal. 2012, 291, 17−25. (10) Blaylock, D. W.; Ogura, T.; Green, W. H.; Beran, G. J. O. Computational Investigation of Thermochemistry and Kinetics of Steam Methane Reforming on Ni(111) under Realistic Conditions. J. Phys. Chem. C 2009, 113, 4898−4908. (11) Cao, X.-M.; Burch, R.; Hardacre, C.; Hu, P. An Understanding of Chemoselective Hydrogenation on Crotonaldehyde over Pt(111) in the Free Energy Landscape: The Microkinetics Study Based on FirstPrinciples Calculations. Catal. Today 2011, 165, 71−79. (12) Over, H.; Kim, Y. D.; Seitsonen, A. P.; Wendt, S.; Lundgren, E.; Schmid, M.; Varga, P.; Morgante, A.; Ertl, G. Atomic-Scale Structure

Edes = (E RuO2 + nEA − En A/RuO2)/n (33) Lobo, A.; Conrad, H. Interaction of H2O with the RuO2(110) Surface Studied by HREELS and TDS. Surf. Sci. 2003, 523, 279−286.

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dx.doi.org/10.1021/jp309394p | J. Phys. Chem. C 2013, 117, 6136−6142