Kinetic Regimes in Ethylene Hydrogenation over Transition-Metal

Apr 11, 2016 - A first-principles microkinetic model has been developed and applied to ethylene hydrogenation over close-packed transition-metal surfa...
2 downloads 13 Views 3MB Size
Download PDF
Research Article pubs.acs.org/acscatalysis

Kinetic Regimes in Ethylene Hydrogenation over Transition-Metal Surfaces Christopher J. Heard,*,†,‡ Chaoquan Hu,‡,§ Magnus Skoglundh,‡,§ Derek Creaser,‡,§ and Henrik Grönbeck*,†,‡ †

Department of Applied Physics, ‡Competence Centre for Catalysis, and §Department of Chemistry and Chemical Engineering, Chalmers University of Technology, Göteborg, Sweden S Supporting Information *

ABSTRACT: A first-principles microkinetic model has been developed and applied to ethylene hydrogenation over close-packed transition-metal surfaces of Ru, Rh, Pd, Os, Ir, and Pt. The model is based on density functional theory calculations, which have been used to determine the activation energies of the elementary steps of the reaction according to the Horuiti−Polanyi mechanism. A sensitivity analysis of the activity with respect to the kinetic parameters reveals distinctly different kinetic regimes across the periodic table. For Ru and Ir, the activity is controlled by the activation energy for ethylene to ethyl hydrogenation, whereas the other metals also have a sensitivity to the second hydrogenation step. The analysis shows, furthermore, that the activity could be enhanced considerably with minor reductions of the hydrogenation barriers.

KEYWORDS: microkinetic modeling, DFT, hydrogenation, transition metals, ethylene

1. INTRODUCTION Catalytic hydrogenation is extensively used in a wide range of industrial applications. For the production of fuels, catalytic hydrogenation is, for example, used to improve the combustion properties and stability of biofuels. Hydrogenation is additionally used to convert alkenes to saturated alkanes, which are less toxic and less reactive.1 Alkene hydrogenation over metal surfaces has been studied extensively in the past with ethylene as a model reactant.2−6 The primary mechanism for hydrogenation of simple alkenes over metal surfaces has been established to be the Horuiti−Polanyi (HP) reaction.7−10 In this scheme, the alkene and H2 are adsorbed on the surface. The hydrogen molecule dissociates, and the reaction proceeds via two sequential hydrogen addition steps. Although the overall reaction mechanism on different metal surfaces is known to follow the HP reaction scheme, it has been difficult to establish unambiguous trends across the periodic table.3,11,12 This is due to the high rates at ambient temperatures and the sensitivity to operational procedures. Surprisingly, it is currently not established which are the main factors controlling the activity for a particular metal or how these factors govern the activity trends for different metals. The kinetics of ethylene hydrogenation over transition metals (TMs), primarily Pt and Pd surfaces,2,3,11 nanoparticles,13−17 and bimetallic catalysts,18,19 have previously been studied experimentally. Recently, these types of investigations have been extended to supported metal clusters of Pt and Rh20 and of Ir.21,22 Corresponding theoretical studies, in particular those of Cortright and co-workers,23,24 have shown © XXXX American Chemical Society

that a microkinetic treatment of a slightly modified HP mechanism is able to reproduce kinetic measurements, such as reaction orders and turnover frequencies (TOF). In refs 23 and 24 it was noted that a key requirement is the existence of a pool of hydrogen atoms, which occupy sites that do not compete with ethylene and may interconvert with “activated” hydrogen that reacts with ethylene. Although this reaction step was crucial to obtain correlation with experimental isotopic product distributions, it was not given a structural or physical basis. On the basis of Monte Carlo simulations, Hansen and Neurock found that including lateral repulsion between adsorbates made it possible to recover experimentally obtained reaction orders over Pd(100).25 Later experimental studies by Latusek et al.18 show good agreement with the Monte Carlo simulations25 which indicate that the modified HP mechanism23,24 could be valid for metals other than Pt. Despite the high activity of many metals for hydrogenation, only minor attention has been paid theoretically to transition metals other than Pt and Pd. Currently it is not known whether the kinetic bottlenecks change across the periodic table. By calculation of the sensitivity of hydrogenation activity to different kinetic parameters, conditions which enhance or inhibit the reactivity may be isolated. To our knowledge, there are no published studies that systematically compare the activity of different late TMs. Here, we develop a kinetic model, Received: November 29, 2015 Revised: March 30, 2016

3277

DOI: 10.1021/acscatal.5b02708 ACS Catal. 2016, 6, 3277−3286

Research Article

ACS Catalysis

Table 1. Zero-Point Corrected Adsorption and Activation Energies of the Considered Elementary Steps (in kJ/mol) for a Coverage of 0.33 for Each Surface Speciesa

a

step

Ru

Rh

Pd

Os

Ir

Pt

C2H4π (Ads) C2H4σ (Ads) C2H5 (Ads) H2 (Ads) C2H4π + H → C2H5 C2H5 → C2H4π + H C2H5 + H → C2H6 C2H6 → C2H5 + H

−76 −54 −108 −151 52 42 49 68

−70 −61 −143 −106 50 105 34 24

−54 −66 −133 −123 56 106 51 54

−60 −60 −122 −110 57 111 53 46

−72 −80 −161 −106 63 135 32 32

−52 −84 −154 −101 47 106 53 78

Adsorption steps are denoted Ads.

which is based on density functional theory calculations of elementary steps for hydrogenation of ethylene. The predictions of the model compare favorably with new experimental data for Ru and Pt as well as results from the literature.

Activation energies were calculated using the climbing-image nudged elastic band (CI-NEB) technique37 as implemented in the transition state tools module for VASP. All transition states located were confirmed with vibrational analysis using the harmonic approximation and finite differences. 2.2. Experimental Details. Alumina-supported Pt and Ru (1 wt %) catalysts were prepared by wet impregnation. Pt(NO3)2 (Heraeus GmbH 15.46 wt %) or Ru(NO)(NO3)3 (Sigma-Aldrich, 1.5%) was diluted in distilled water to form an aqueous solution. Al2O3 (Puralox SBa-200 Sasol) was thermally treated at 973 K for 4 h in a static air atmosphere and subsequently added to the metal precursor solution with strong and constant stirring for 1 h at room temperature. The resulting pastelike slurry was dried at 378 K for 12 h. The obtained Ru/ Al2O3 powder was calcined at 773 K and the Pt/Al2O3 sample at 873 K, both for 4 h in air. Two pulses of 200 ppm of CO in Ar were used to determine the Pt dispersion at room temperature. The first pulse was considered to result in both strongly and weakly adsorbed CO. The second pulse, which followed a period of Ar flushing, was assumed to include readsorption of only weakly bonded CO. The difference between the two pulses was taken as a measurement of the amount of chemisorbed CO on the Pt surface sites of the catalysts. A factor of 0.8 was used38,39 in calculation of the metal dispersion (D): namely, D = nCO/0.8nmetal. The hydrogenation experiments were performed under atmospheric pressure in a tubular fixed-bed reactor with an inner diameter of 4 mm. The reactor was loaded with either 10 mg of the Ru/Al2O3 catalyst or 1 mg of the Pt/Al2O3 catalyst thoroughly mixed with 10 mg of SiO2. Prior to the hydrogenation measurement, the sample was reduced under a stream of 5% H2/Ar at 673 K for 1 h. After the sample was cooled to room temperature (296 K), C2H4 and H2, balanced by Ar, were mixed and introduced into the reactor. The total gas flow was 250 mL/min under standard conditions. The effluent gas was analyzed by a calibrated gas chromatograph (Scion 456-GC, Bruker) equipped with a flame ionization detector (FID) for C2H4 and C2H6 and a thermal conductivity detector (TCD) for H2. The average experimental turnover frequency was calculated from the measured fractional conversion of ethylene (XC2H4) by TOF = (XC2H4FC2H4,inM)/ (0.01WcatDNA), where FC2H4,in is the molar flow of ethylene in the feed, M is the molar mass of Pt or Ru, Wcat is the mass of catalyst, and NA is Avogadro’s constant. From the experimentally observed reaction rates, the maximum value of the Weisz modulus (CWP) was estimated to be 0.03. As CWP < 1, intraparticle concentration gradients can be considered to be negligible. In addition, application of the

2. METHODS 2.1. Electronic Structure Calculations. Calculation of zero point energy-corrected adsorption energies and activation energies was performed within density functional theory (DFT) as implemented in the Vienna ab initio package (VASP 5.2).26−29 The Kohn−Sham orbitals were expanded in a plane wave basis, truncated at an energy of 420 eV. The exchange correlation energy was calculated within the generalized gradient approximation using the Perdew−Burke−Ernzerhof (PBE) formulation.30 Projected augmented wave potentials generated within PBE were used31,32 to describe the interaction between the valence electrons and the core. For the metal atoms, the nd(n+1)s valence shell was treated explicitly. Hydrogen and carbon atoms were treated with one and four electrons in the valence, respectively. Integration over the Brillouin zone was approximated by finite sampling using the Monkhorst−Pack scheme.33 Methfessel and Paxton34 smearing of the Fermi discontinuity was applied to first order, with a smearing width of 50 meV. A threshold of 10−5 eV was used for the convergence of the electronic structure. In the local geometry optimization, the structures were considered to be relaxed when all forces were less than 0.01 eV/Å. All calculations were performed spin restricted, as the considered metals are nonmagnetic and reactants as well as products have closed electronic shells. The surfaces were modeled with four-layer slabs separated by 14 Å of vacuum. The top two layers were allowed to relax in response to adsorption, whereas the bottom two layers were kept fixed at the corresponding bulk positions. Adsorption was considered in a √3 × √3 R30° cell. The k-point grid was chosen to be 7 × 7 × 1. Ruthenium and osmium were treated with hcp symmetry, whereas all other metals were treated with fcc symmetry. The corresponding (0001) and (111) surfaces were cut from the theoretical bulk lattices calculated with the same method and energetic convergence criteria.35 The gasphase molecules were calculated in a cubic box of length 15 Å. The accuracy of the computational method for the reactants was tested, and the relaxed gas-phase C−C and C−H bond lengths in ethylene were found to be 1.33 and 1.09 Å, respectively, which is close to the experimental values of 1.33 and 1.08 Å. The energy of hydrogenation was calculated to be 1.76 eV, which is in agreement with previous calculations and in reasonable agreement with the experimental result of 1.41 eV.36 3278

DOI: 10.1021/acscatal.5b02708 ACS Catal. 2016, 6, 3277−3286

Research Article

ACS Catalysis so-called Mears criterion indicated that interphase concentration gradients could also be neglected.40

adsorbs dissociatively and C2H4 adsorbs associatively in either the σ or π mode. The first hydrogenation step is known to proceed through the π mode.42 For Pt(111), this requires a promotion step, which is taken as the difference between the adsorption energies for C2H4 adsorbed in the two modes (Ep). It is important to note that the two metals differ in their reaction landscapes. Both metals have exothermic paths, with similar energetic gains for the steps. However, whereas the activation energy for the second hydrogenation reaction step is slightly higher than the first on Pt(111), the activation energy for the second hydrogenation step is clearly lower than the first on Rh(111). Such differences may have implications on which reaction steps affect the overall activity across the transition metals.

3. FIRST-PRINCIPLES ENERGY LANDSCAPES Catalytic activity is determined by the relative stability of reaction intermediates together with activation barriers along the reaction pathway. Thus, the potential energy landscape is needed for a fundamental understanding of the reaction and is key to determining the optimal choice of metal and reaction conditions. Here, we have considered the adsorption of ethylene, ethyl, and hydrogen together with the activation energies for hydrogenation. The energetic results are summarized in Table 1. Three carbonaceous species are included, namely π-ethylene (C2H4π), di-σ-ethylene (C2H4σ), and the reaction intermediate, ethyl (C2H5). The C2H4π and C2H5 species adsorb top, whereas C2H4σ adsorbs in a bridge configuration between two metal atoms. The preference for the ethylene adsorption mode varies across the metals. The π mode is preferred for Ru and Rh, whereas the σ mode is adopted for Pd, Ir, and Pt.41 The two modes have similar stability on Os(0001). Molecular hydrogen chemisorbs dissociatively on the considered TMs. Atomic hydrogen preferentially occupies 3fold hollow sites, with a slight preference for fcc over hcp sites. The only exception is Pt, for which the top site is competitive with the hollow sites. One interesting difference between the metals is that the adsorption energy of hydrogen over Ru is considerably higher than that of C2H4. The activation energies for the first hydrogenation step vary from 47 kJ/mol (Pt) to 63 kJ/mol (Ir). In all cases except Pt, the activation barrier for the first hydrogenation step is higher than for the second. From the energetics alone, it is not clear that a comparison of activation barriers will provide the descriptor necessary to predict comparative activities and a full kinetic study is therefore needed. As examples of different profiles, the energy landscapes for ethylene hydrogenation according to the HP mechanism are given for Pt(111) and Rh(111) in Figure 1. The profile starts with a bare metal surface and C2H4 and H2 in the gas phase. H2

4. MICROKINETIC MODEL The kinetic model is related to that developed by Cortright and colleagues23,24 for the hydrogenation of ethylene according to the HP scheme over Pt(111). The model in refs 23 and 24 used seven reaction steps: namely, ethylene adsorption, three types of hydrogen adsorption, hydrogen migration, and two hydrogenations. Ethylene is assumed to occupy two surface sites which would correspond to the di-σ mode. Hydrogen occupies one surface site and can be adsorbed competitively or noncompetitively with respect to ethylene. The noncompetitive hydrogen can be either activated or nonactivated; however, it is only the activated hydrogen that participates in the surface reactions. Although the model reproduces experimental reaction orders and activities, the physical origin of the different types of species is unclear. Ethylene decomposition is not considered, as several studies have shown that decomposition products are spectators and merely reduce the maximum total ethylene coverage.43−47 The mechanism and kinetics of these additional reactions have been addressed in the literature through kinetic modeling.48−51 In the present study, sites are defined according to a physical interpretation, in which reactive species may bind atop a metal atom or in a 3-fold hollow site. As the adsorption energies of hydrogen in the hcp and fcc sites are similar, these two sites are considered equivalent in the microkinetic model. Three carbonaceous species are included, namely π-ethylene (C2H4π), from which the hydrogenation reaction proceeds,43,44,52 di-σ-ethylene (C2H4σ) and the reaction intermediate, ethyl (C2H5). The C2H4π and C2H5 species occupy one single top site each, whereas C2H4σ requires two sites, as is known from experiments: e.g., ref 53 and theory.43,52,54−57 Three hydrogen species are included, namely the competitively bound (Ht), which occupies a top site, thus blocking adsorption of ethylene, and two hydrogen species which occupy hollow sites, Hhn and Hhf. The hollow-bound hydrogen atoms are denoted hn (hollow-near) and hf (hollow-far) according to their proximity to the carbonaceous species. This separation of hydrogen species takes into account the lateral repulsion between hydrogen and nearby ethylene (or ethyl), while allowing for adsorption of hydrogen far from the reaction, which is known from experiments.24 Interconversion between reactive (Hhn) and unreactive (Hhf) hydrogen is described in the model by a migration step between hollow sites.58 In total, nine elementary reaction steps are included in the model, involving the six reactive species, and the surface sites *t (top site) and *h (hollow site). The steps are depicted in Figure 2. The first four steps involve adsorption of hydrogen (hollow and top) and ethylene (σ and π). Step 5 corresponds to

Figure 1. Potential energy diagram for ethylene hydrogenation according to the Horiuti−Polanyi mechanism over Pt and Rh. Energy differences for each step and the activation energies for the hydrogenation steps are given in kJ/mol. Ep corresponds to the promotion energy required to convert the di-σ-ethylene species into the π species. 3279

DOI: 10.1021/acscatal.5b02708 ACS Catal. 2016, 6, 3277−3286

Research Article

ACS Catalysis

Figure 2. Schematic diagram of each elementary step included in the microkinetic model. Hydrogen atoms are colored white, carbons atoms are black, and metal surface atoms are gray. *h refers to a vacant hollow site and *t to a vacant top site. Subscript labels for hydrogen are as follows: Hhf is adsorbed hydrogen in a hollow site far from ethylene (or ethyl), Hhn is adsorbed hydrogen in a hollow site near ethylene (or ethyl), and Ht is competitively bound hydrogen on a top site.

migration of ethylene from the σ to the π mode. Steps 6 and 7 describe hydrogen diffusion to the hollow-near site from a hollow-far and top site, respectively. Step 8 is the first hydrogenation step, which converts C2H4π to C2H5. Step 9 is the second hydrogenation step, which results in the desorption of ethane from the surface. The model is described further in the Supporting Information. 4.1. Determination of Kinetic Parameters. Each elementary reaction step is defined according to transition state theory (TST), with a pre-exponential factor and an activation energy Eact. The adsorption steps 1, 2, 3, and 4 were assumed to be nonactivated. The corresponding desorption steps, −1, −2, −3, and −4, are assigned activation energies equal to the adsorption energy of the corresponding species. For the hydrogen migration steps, CI-NEB calculations yielded an activation energy on Pt(111) of 14.5 kJ/mol, between adjacent hollow sites. This barrier was chosen to represent the minimum activation energy for H migration over all metals. The hydrogen migration process, represented by step 6, is assigned a barrier of 19.5 kJ/mol, and the exothermic reverse step, −6, has an activation energy of 14.5 kJ/mol. The presence of low activation energies for reverse steps for hydrogen migration is justified by explicit calculations.58 The 7 and −7 migration steps are assigned barriers of 14.5 kJ/mol for the exothermic step, and ΔE + 14.5 kJ/mol for the endothermic process, where ΔE is the difference in electronic energies between the two states. With the exception of platinum, the migration of Hhn to Ht is unfavorable. Hydrogenation activation energies were calculated for all considered metals (see Table 1). The activation energies of the reverse reactions −8 and −9 are Eact− = Eact + + (EI − EF)

ethylene and hydrogen, the empirical formula derived by Campbell and Sellers is used.61 This model takes the experimental gas-phase entropies of the individual chemical species into account, giving values of 2.1 × 107 and 2.1 × 109 s−1, respectively. The values derived here are similar to those used by Rekoske et al.24 to fit experimental kinetic results. In addition, low pre-exponential factors have been observed for desorption of ethylene and hydrogen in several TPD experiments.62,63 For the migration steps, pre-exponential factors of 1013 s−1 were used and, for the surface reactions, the kinetic pre-exponential factors were calculated by use of transition state theory (see the Supporting Information). The first and second hydrogenation steps have pre-exponential factors of 1.0 × 1012 s−1. The pre-exponential factor for ethane adsorption (−9) is taken from experiments where it has been measured to be ∼1.0 × 10−1 s−1 Pa−1.64 The entropy change in the kinetic model is 153 J/(K mol), which is close to the experimental value of 120 J/K/mol.65 A simple and transferable coverage dependence of the activation energies is included in the model.66 For each elementary step this dependence takes the form Eact = Eact 0 × (1 − (∑ αiθi)) i

(2)

For the desorption steps (−1, −2, −3, and −4) and the migration steps (5, 6, 7, −5, −6, and −7) all species adsorbed at the same site are considered to affect the activation energy. Each species chosen to contribute to a coverage dependence for a particular reaction is given an identical value of αi = 1. A linear coverage dependence is generally too strong at low coverages, while it is too weak at high coverages. This motivates the use of activation energies for the 0.33 coverage in the model (Eact0), as it compensates for the fact that the coverage dependence is too weak at higher coverage. 4.2. Reactor Model. Assuming plug flow in the fixed-bed reactor, the gas-phase composition, surface coverages, and reaction rates can significantly vary axially from inlet to outlet. The catalyst bed was consequently discretized by a tanks-inseries model. In this model, the catalyst mass is distributed over several sections (tanks), each with different gas composition and possibly also coverages.67 The gas flows consecutively

(1)

where + and − refer to reverse and forward reactions and EI and EF are the total electronic energies of the initial and final states, respectively. For adsorption steps, the pre-exponential factors are calculated according to collision theory, with sticking coefficients of 0.1 and 1 for hydrogen and ethylene, respectively. These values are in accordance with experimental results59,60 and yield pre-exponential factors of 1.0 × 102 and 1.0 × 104 s−1 Pa−1, respectively. Details of these calculations are given in the Supporting Information. For desorption of 3280

DOI: 10.1021/acscatal.5b02708 ACS Catal. 2016, 6, 3277−3286

Research Article

ACS Catalysis through each tank in the series. The steady state mole balance for gas phase species i in tank n is given by Fi n − 1 − Fi n + (∑ (νikrk n)csitemcat n)/NA = 0 k

where Fi is the molar flow of species i (mol/s), mcatn is the mass of catalyst in tank n (kg), csite is the site density of the catalyst (1/kg), rk is the rate of reaction k in tank n (1/s), νik is the stoichiometric coefficient for species i in reaction k, and NA is Avogadro’s constant (1/mol). The steady-state mole balance for adsorbed species j on a certain site in tank n is given by

∑ νjkrk n = 0 k

where νjk is the stoichiometric coefficient for species j in reaction k. These mole balances for each gas-phase and surface species in each tank comprise a system of equations which, when solved, yield the reaction rates and species coverages in each tank. For the simulations, the number of tanks in series was set to 10 and the catalyst mass was distributed so that each following tank contained 10% more catalyst than the preceding tank. This distribution of catalyst resulted in a finer resolution of the variables near the reactor inlet, where larger axial gradients were expected. The predicted conversions over the ranges of simulated operating conditions were found to be insensitive to the number of tanks and catalyst distribution. The model-predicted turnover frequencies for ethylene hydrogenation were calculated on the basis of an average of reaction rates weighted by the catalyst mass in each tank and are consequently consistent with the TOFs calculated from the experimentally measured conversions (see section 2.2). 4.3. Comparison with Kinetic Experiments. The parametrization of the model is tested against experimental kinetic data. Platinum and ruthenium were chosen for the experiments, as these metals show distinctly different energy landscapes. Ethylene hydrogenation over transition-metal surfaces is a fast reaction, and therefore, a low weight percentage of 1% metal catalyst was chosen together with low concentrations of the reactive species. In this way, the conversions are controlled by reaction kinetics. Reactant gas pressures are given as mole percent of the total gas pressure, chosen to be 1 atm, in line with the experiments. Three test cases were designed to determine kinetic orders with respect to the reactants, and the results are given in Figure 3. In the first test (I), a fixed 0.7% concentration of hydrogen was chosen, and the ethylene concentration was varied between 0.1 and 1.0% over Ru. In the second test (II), the ethylene concentration was fixed to 0.1%, and the hydrogen concentration was varied from 1 to 20% over Ru. Both of these experiments were performed at room temperature. To compare with the experiments, the kinetic model was explored at a temperature of 300 K and an initial gas flow of 6.82 × 10−5 mol s−1. Kinetic orders from the model (experiment) for tests I and II are 0.1 (0.4) and 0.0 (0.2), respectively. We conclude that there is a good agreement, although the model slightly underestimates the kinetic orders. The corresponding test for platinum(III) includes an ethylene concentration range of 0.1−1.0%, and an H 2 concentration of 1.7%, with the same temperature as for ruthenium. The experimental kinetic order with respect to ethylene is 0.5, while the model gives an average of 0.3 over the studied range. This is again in agreement with a systematic underestimation of the kinetic order. Previous measurements of

Figure 3. Variation of turnover frequency with reaction gas concentrations, which are given as mole percent of the gas feed. Experimental data are denoted by red circles, whereas results from the microkinetic model are denoted by black diamonds. Kinetic orders are indicated. For test I, the hydrogen concentration is 0.7% and the experimental ethylene concentration is varied between 0.1 and 1.0% over Ru. For test II, the ethylene concentration is 0.1 and the experimental hydrogen concentration is varied from 1 to 20% over Ru. For test III, the hydrogen concentration is 1.7%, while the experimental ethylene concentration is varied in the range 0.1−1.0% over Pt.

the kinetic order with respect to ethylene over Pt have reported positive19 as well as negative3,24 values. The negative reaction order is probably related to ethylene self-poisoning by decomposition and side reactions. In the present experiments, the ethylene conversion was stable for several hours and only ethylene and ethane were detected in the GC signal with a carbon balance higher than 99%. When the temperature is varied in the simulation between 240 and 330 K, at intermediate gas-phase concentrations of 0.5% C2H4 and 1.0% H2, the apparent activation energies are calculated to be 58 and 53 kJ/mol for Ru and Pt, respectively. Under these conditions, the hydrogenation is faster over Pt than over Ru both in the experiments and in the simulations. The calculated activation energies (Table 1) for the two hydrogenation steps are 52 and 50 kJ/mol over Ru(0001) and 47 and 54 kJ/mol over Pt(111). It is evident that the apparent activation energies are similar to the hydrogenation barriers; however, further analysis is needed to determine which step controls the reaction to the largest extent. With simplified models, the apparent activation energy could be expressed in an analytical form as the activation energy of the rate-determining step augmented with terms that depend on the heats of adsorption.68 We note that such a simplified Langmuir−Hinshelwood model in which only adsorption of the reactants and the two hydrogenation steps are included does not reproduce the apparent activation energy of the full model.69 In fact, this is further motivation to develop and analyze a more elaborate model. 4.4. Comparison between Metals. With the model verified as able to reproduce the experimental results, we can proceed to investigate activity trends across the metals and isolate possible controlling descriptors. The activities for 3281

DOI: 10.1021/acscatal.5b02708 ACS Catal. 2016, 6, 3277−3286

Research Article

ACS Catalysis

energy of the adsorbate, the activity increased by several orders of magnitude. This effect of the support on ethylene hydrogenation has recently been investigated and confirmed by DFT calculations.22 To investigate whether temperature may influence the kinetic regime, we calculate the TOF as a function of temperature for Pt and Ru with the microkinetic model (see Figure 5). The

hydrogenation of ethylene over Ru, Rh, Pd, Os, Ir, and Pt are calculated at a flow rate of 6.82 × 10−5 mol s−1, with ethylene and hydrogen concentrations of 0.5% and a temperature of 300 K. The calculated activities are reported as a function of the activation energy of the first hydrogenation step and are shown in Figure 4.

Figure 4. Variation of the calculated hydrogenation activity with the barrier for the first hydrogenation step (reaction 8) across the considered metals. The line of correlation connects Rh and Ir, which are the metals where the activity is determined by the first hydrogenation step.

Figure 5. Variation of turnover frequency with temperature for Pt and Ru calculated with the microkinetic model. The inset shows the natural logarithm of the TOF.

Although the activation energy varies over a range of only 15.4 kJ/mol, the results show that there is some correlation between turnover frequency (TOF) and the activation energy of the first hydrogenation step (reaction 8). The line of correlation connects Rh and Ir, which are the metals where the activity is determined by the first hydrogenation step (see analysis below). The use of first-principles kinetic modeling allows us to isolate the rate-determining step, which is difficult without explicit kinetics, as the activation energies for the two hydrogenation steps are similar for the studied metals. For particular metals, previous work has often assumed the first hydrogenation step to be rate determining,22,54,70,71 however, without explicitly clarifying which elementary step that controls activity in practice. From Figure 4, we conclude that the assumption that activity stems solely from the first hydrogenation step barrier may be incomplete. Rhodium is found to have the highest inherent activity, with a TOF of 35.1 s−1. Platinum is also predicted to be highly active with a TOF of 34.8 s−1. These results are consistent with the early work of Beeck et al., who measured rhodium to have the highest activity, and to be similar to platinum.2,11,72,73 Ruthenium is found to underperform with respect to the linear correlation. Interestingly, uniquely for ruthenium, reaction 8 is slightly endothermic, due to high adsorption energies, particularly for hydrogen. As a result, the reverse reaction step (−8) is faster than that over the other metals. The sensitivity of the TOF to the reverse barrier shows that a variation of only 10 kJ/mol may change the activity dramatically. The kinetic parameters of ruthenium are such that the reaction rates may be tuned acutely by varying this reverse barrier. Other metals are insensitive to such changes, due to the highly exothermic forward reaction. Iridium is found to have a particularly low activity (TOF relative to Rh is 4 × 10−2). We note that the adsorption energy of ethylene along with the activation energy of the first hydrogenation step is high for Ir. Argo et al. showed that the strong bonding of hydrogen and ethylene to iridium clusters cause a dramatic reduction in the catalytic activity.21 When the metal was supported on substrates which reduce the binding

ethylene and hydrogen concentrations are in this case 0.5 and 1.0%, respectively. Pt is known to be a good low-temperature catalyst, with appreciable rates below room temperature.11 The low-temperature activity of Ru is not as well studied. Decomposition of ethylene on Pt(111) is known to occur at elevated temperatures, which irreversibly poisons the surface,74−76 and therefore temperatures considerably higher than room temperature are unlikely to represent realistic conditions for modeling ethylene hydrogenation over TM surfaces in the absence of C1 products. For ruthenium, ethylidyne is known to form at room temperature,77 and Gupta et al. observed78 that, by delaying the addition of hydrogen to an ethylene-covered Ru surface, the C2H6 formation is reduced. This suggests the possibility of C−C scission down to temperatures below 375 K. Given this information about ethylene decomposition, we have chosen to study the temperature dependence between 150 and 350 K. The close to exponential increase in reaction rate with temperature shows that there are no significant coverage or kinetic limitations to the activity up to 350 K and that the ratedetermining step is unchanged over this temperature range. Pt is the more active metal over the entire temperature range with, for example, an activity 4 times that of Ru at 300 K. In the model of Rekoske et al.,24 a low desorption energy of hydrogen leads to a ethylene-covered platinum surface and thus a negative reaction order with respect to ethylene. In our model, we predict a surface partially covered with ethylene and hydrogen with proportions which vary with metal and temperature. For platinum, the hollow sites are filled to 74% at 150 K, which decreases to 52% by 350 K. The top sites have a coverage of 84% at 150 K and show a similar decrease at high temperatures, down to 61% at 350 K. The top site coverage is predominantly made up of ethylene at low temperatures. With increased temperature and higher activity, the top sites are also covered with ethyl, which suggests that the second hydrogenation step becomes limiting at high activities. On ruthenium, the hollow site coverage is higher than that over platinum and similarly decreases as the temperature increases, from 91% at 150 K to 70% at 350 K. The top site 3282

DOI: 10.1021/acscatal.5b02708 ACS Catal. 2016, 6, 3277−3286

Research Article

ACS Catalysis

Figure 6. Sensitivities of turnover frequency to the reaction barriers of the first and second hydrogenation steps over the considered metals. The TOF is in each case depicted as a fraction of the maximum rate determined for the considered metal under the conditions of Figure 4 (T = 300 K, P = 1 atm, flow rate 6.82 × 10−5 mol/s). ΔEact(rxn n) is the change in activation energy for the elementary reaction step n. Degree of rate control values (χi) for the two reaction steps are displayed in the bottom-right corner.

coverage decreases less rapidly in comparison to that over platinum, from 76% at 150 K to 60% at 350 K. Ruthenium does not undergo any significant changes in top site coverage profile, as the ethyl and top-hydrogen coverages are negligible at all temperatures. The differences between Pt and Ru reflect the differences in the potential energy surfaces. 4.5. Sensitivity Analysis. We have found that the activity across the periodic table may be predicted to some extent by the activation energy of the first hydrogenation step. However, the factors that control the specific activity within a particular metal may be more complex, and the variation between metals remains to be explained. Here we investigate the sensitivity of ethylene hydrogenation activity to the hydrogenation barriers for all six metals. To study the influence of the hydrogenation barriers, the activation energies Eact for reactions 8 and 9 over the metals are varied over a range of 40 kJ/mol around the calculated barrier heights, (see Figure 6). To isolate the extent of the control exerted by each hydrogenation step, these variations are independent of all other kinetic parameters. The TOF is depicted as a fraction of the maximum rate determined for the considered metal at 300 K with reactant concentrations of 0.5%. Over most metals, it is notable that the calculated activation energies (denoted by a cross) do not correspond to the maximum activity. Therefore, the activity may be increased significantly by decreasing the appropriate activation energies. In fact, small changes in activation energy may result in significant variations of the reaction rate, which implies that catalysts could be designed with activity higher than that for the metals in their native state. For example, a decrease in both

barriers of only 10 kJ/mol over platinum would induce an increase in normalized turnover frequency from 48% to the maximum TOF. The opposite is true for rhodium, where the calculated activation energies are located in a largely barrierindependent region of parameter space. There are overall trends in the activity profiles across the periodic table. The group 8 and 10 metals have similar values for the first and second hydrogenation activation energies and are located in a sensitive region of parameter space close to, but not directly upon, the area at which the maximum TOF is predicted. The group 9 metals (Rh and Ir) have particularly low activation energies for the second hydrogenation step, which yields a lack of dependence on this reaction step. As a result, Rh and Ir show a sensitivity profile which is entirely related to the first hydrogenation step. A related way to analyze the sensitivity of the turnover frequency to the elementary steps is given by the degree of rate control analysis.79−81 This normalized numerical measure (χi) indicates to what extent a reaction step i promotes (0 < χi ≤ 1) or inhibits (−1 ≤ χi < 0) the overall reaction. χi is given by ⎛ ∂ ln r ⎞ χi = ⎜ ⎟ ⎝ ∂ ln ki ⎠ K

i

(3)

where r is the total rate of the overall reaction and ki and Ki are the rate constant and equilibrium constant for reaction step i, respectively. When the rate constant (or the forward and reverse activation energies) of one reaction is varied, with the other rate constants kept fixed, the role of the investigated step can be isolated. 3283

DOI: 10.1021/acscatal.5b02708 ACS Catal. 2016, 6, 3277−3286

Research Article

ACS Catalysis

slightly. Unlike the group 8 and 9 metals, Pd has an ∼10% coverage of ethyl over the entire activity profile. This is due to the trapping of the reaction between the first and second hydrogenation steps. Whereas the reverse reaction from ethyl to ethylene and hydrogen is prohibited by a large activation energy, the forward second hydrogenation barrier is notably larger than that for rhodium. This kinetic basin reduces the reaction rate with respect to rhodium, but not as extensively as for ruthenium, for which the reverse reaction is fast. The π:σ ratio for Pd is similar to that of ruthenium. It is 83% at the point of calculated activation energies and in the range of 92− 83% within the full activity profile. Furthermore, the total top and hollow site coverages are close to the results of ruthenium. To summarize, the studied metals show different kinetic regimes in ethylene hydrogenation. The reaction is solely dependent on the activation energy of the first hydrogenation step only over Rh and Ir. The activities of the other metals are, to different degrees, dependent on both reaction steps.

The degrees of rate control are indicated in Figure 6. For Rh and Ir, the χ values are close to 1 for the first step and 0 for the second step. This is in full agreement with the activity profiles. The degree of rate control for the other metals show that both hydrogenation steps contribute to the rate control. Pd and Os have higher χ values for the first hydrogenation step. In the activity profiles, this is visualized by the fact that the TOF could be increased to a larger extent by reduction of the first barrier than by a similar reduction of the second barrier. The converse applies for Ru and Pt, which have a higher sensitivity to the second step. The calculated activation energies for Pd and Os as well as for Ru and Pt are all located close to the vertex of the kinetic regime with high activity. Thus, minor changes in the activation energies could alter which of the two hydrogenation steps that are rate determining. We note that, although the activity profiles for Pd and Pt are similar, the calculated χ values are markedly different. Pd has a χ value of 0.78 for the first step, whereas the corresponding value for Pt is 0.05. For the second step, the highest value is calculated for Pt (0.92) while the value for Pd is 0.13. These differences demonstrate that this is a reaction where it is necessary to consider the full parameter landscape in order to understand the kinetic regime. The sensitivity analysis provides a handle to understand the lack of complete correlation between the activity and the activation energy of the first hydrogenation step (Figure 4). The activities of Rh and Ir are solely dependent on the activation energy of the first hydrogenation step and are therefore used to define the linear correlation. The other metals are scattered with respect to this line, as they show a dependence on both activation energies. Pt and Ru are located below the line of correlation. These are metals that are more sensitive to the activation energy of the second hydrogenation step than to the first. Pd and Os have a higher dependence on the activation energy of the first hydrogenation step and are located above the line of correlation. The surface coverages of the catalyst vary significantly with activation energies and across the periodic table. For ruthenium, the hollow site coverage increases significantly from 22% at the low barrier regime (denoted α in Figure 6) to 80% at the point of the calculated activation energies. The top site coverage, however, remains largely invariant to barrier heights, decreasing only slightly from 83% at point α to 75% at the point of the calculated activation energies. The top site coverage consists primarily of ethylene, with a π:σ ratio of 0.82 at the calculated activation energies. This ratio varies from 90 to 82% as the activation energies increase. The coverages do not change notably on moving to β in the activity profile. Over ruthenium, there is a negligible coverage of ethyl, owing to the low barrier for converting ethyl back to ethylene and hydrogen. Similarly, there is zero coverage of top site hydrogen. At the calculated activation energies, the hollow site coverage is 18% for rhodium, which is considerably lower than that over ruthenium. The higher overall activity of rhodium shows that a hollow site coverage is not required for high activity. This is in line with the low kinetic order observed for hydrogen. However, the top sites are occupied over rhodium with coverages of 88% at α and 86% at the point of the calculated activation energies. This is due to a higher ethylene coverage. The π:σ ratio is 0.93 at the point of the calculated activation energies. For ruthenium, there is a negligible coverage of ethyl and top site hydrogen under all considered reaction conditions. Over palladium, which shows activity intermediate between those of ruthenium and rhodium, the surface coverages differ

5. SUMMARY AND CONCLUSIONS We have studied ethylene hydrogenation over a range of closepacked transition-metal surfaces according to the Horiuti− Polanyi mechanism using DFT calculations and first-principles microkinetic modeling. The physically motivated model gives results in agreement with new experimental results for Pt and Ru, as well as literature data. We find that there is some correlation between the activity and the first hydrogenation barrier height across the metals. Although this often has been assumed, this is to our knowledge the first time the correlation has been explicitly tested. Interestingly, there are significant and systematic deviations from linearity for some metals, which show a dependence on the second hydrogenation barrier which varies from negligible to complete. This result shows the importance of considering all reaction steps along the reaction pathway and reveals different kinetic regimes for the different metals. The kinetic model suggests that the parameters of the reaction over the considered metals are in most cases not optimal and, thus, it would be possible to increase the activity by an appropriate catalyst design. In fact, minor reductions of the activation energy would result in pronounced enhancement of the activity. In general, the study shows the predictive power of first-principles-based kinetic modeling in analyzing catalytic reactions and that kinetic modeling provides information that is not available from total energy calculations alone. Simultaneously, obtaining kinetic parameters from first principles provides the means to develop physically justified models.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acscatal.5b02708. Details of the kinetic model, assessment of mass transport limitations, and experimental kinetic data (PDF)

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail for C.J.H.: [email protected]. *E-mail for H.G.: [email protected]. Notes

The authors declare no competing financial interest. 3284

DOI: 10.1021/acscatal.5b02708 ACS Catal. 2016, 6, 3277−3286

Research Article

ACS Catalysis

■

(32) Kresse, G.; Joubert, D. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758. (33) Monkhorst, H. J.; Pack, J. D. Phys. Rev. B 1976, 13, 5188−5192. (34) Methfessel, M.; Paxton, A. T. Phys. Rev. B: Condens. Matter Mater. Phys. 1989, 40, 3616−3621. (35) The bulk PBE lattice constants (in Å) are calculated to be as follows: Ru, 2.73; Rh, 3.85; Pd, 3.96; Os, 2.75; Ir, 3.89; Pt, 99. (36) Kistiakowsky, G. B.; Romeyn, H., Jr.; Ruhoff, J. R.; Smith, H. A.; Vaughan, W. E. J. Am. Chem. Soc. 1935, 57, 65−75. (37) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. J. Chem. Phys. 2000, 113, 9901−9904. (38) Folger, K.; Anderson, J. R. Appl. Surf. Sci. 1979, 2, 331−351. (39) Olsson, L.; Abul-Milh, M.; Karlsson, H.; Jobson, E.; Thormaehlen, P.; Hinz, A. Top. Catal. 2004, 30/31, 85−90. (40) Fogler, H. S. Elements of Chemical Reaction Engineering; PrenticeHall: Englewood Cliffs, NJ, 1999. (41) Heard, C. J.; Siahrostami, S.; Grönbeck, H. J. Phys. Chem. C 2016, 120, 995−1003. (42) Paz-Borbon, L. O.; Hellman, A.; Thomas, J. M.; Grönbeck, H. Phys. Chem. Chem. Phys. 2013, 15, 9694. (43) Cremer, P. S.; Somorjai, G. A. J. Chem. Soc., Faraday Trans. 1995, 91, 3671−3677. (44) Cremer, P. S.; Su, X.; Shen, Y. R.; Somorjai, G. A. J. Am. Chem. Soc. 1996, 118, 2942−2949. (45) Zaera, F. Langmuir 1996, 12, 88−94. (46) Beebe, T. P.; Yates, Y. T. J. Am. Chem. Soc. 1986, 108, 663−671. (47) Backman, A. L.; Masel, R. I. J. Vac. Sci. Technol., A 1988, 6, 1137−1139. (48) Moskaleva, L. V.; Aleksandrov, H. A.; Basaran, D.; Zhao, Z.-J.; Rösch, N. J. Phys. Chem. C 2009, 113, 15373−15379. (49) Zhao, Z.-J.; Moskaleva, L. V.; Aleksandrov, H. A.; Basaran, D.; Rösch, N. J. Phys. Chem. C 2010, 114, 12190−12201. (50) Aleksandrov, H. A.; Moskaleva, L. V.; Zhao, Z.-J.; Basaran, D.; Chen, Z.-X.; Mei, D.; Rösch, N. J. Catal. 2012, 285, 187−195. (51) Aleksandrov, H. A.; Kozlov, S. M.; Schauermann, S.; Vayssilov, G. N.; Neyman, K. M. Angew. Chem., Int. Ed. 2014, 53, 13371−13375. (52) Neurock, M.; Pallassana, V.; van Santen, R. A. J. Am. Chem. Soc. 2000, 122, 1150−1153. (53) Sheppard, N. Annu. Rev. Phys. Chem. 1988, 39, 589−644. (54) Miura, T.; Kobayashi, H.; Domen, K. J. Phys. Chem. B 2000, 104, 6809−6814. (55) Ohtani, T.; Kubota, J.; Kondo, J. N.; Hirose, C.; Domen, K. Surf. Sci. 1998, 415, L983−L987. (56) Kubota, J.; Ohtani, T.; Kondo, J. N.; Hirose, C.; Domen, K. Appl. Surf. Sci. 1997, 121-122, 548−551. (57) Ofner, H.; Zaera, F. J. Phys. Chem. B 1997, 101, 396. (58) Hydrogen migration was calculated with CI-NEB for pathways between 3-fold hollow sites over Pd(111) and Pt(111) in the lowcoverage regime. The process from fcc to hcp sites is slightly downhill in energy but retains a small activation barrier. (59) Luntz, A. C.; Brown, J. K.; Williams, M. D. J. Chem. Phys. 1990, 93, 5240−5246. (60) Tysoe, W. T.; Nyberg, G. L.; Lambert, R. M. J. Phys. Chem. 1984, 88, 1960−1963. (61) Campbell, C. T.; Sellers, J. R. V. J. Am. Chem. Soc. 2012, 134, 18109−18115. (62) Salmerón, M.; Somorjai, G. A. J. Phys. Chem. 1982, 86, 341− 350. (63) Berlowitz, P.; Megiris, C.; Butt, J. B.; Kung, H. H. Langmuir 1985, 1, 206−212. (64) Frennet, A.; Lienard, G.; Crucq, A.; Delgols, L. Surf. Sci. 1979, 80, 412−420. (65) The gas-phase entropies are from the NIST webbook, which collects experimental values from various sources: http://webbook. nist.gov/. (66) Zhdanov, V. P.; Kasemo, B. Surf. Sci. Rep. 1994, 20, 113−189. (67) The variations of the steady-state coverage along the reactor are small. Tests show that the largest coverage variations are less than 1%.

ACKNOWLEDGMENTS The calculations were performed at the C3SE (Göteborg) under a SNIC grant. The work was supported by the Chalmers Area of Advance Transport and the Swedish Research Council. The Competence Centre for Catalysis (KCK) is hosted by the Chalmers University of Technology and is financially supported by the Swedish Energy Agency and the member companies AB Volvo, ECAPS AB, Haldor Topsøe A/S, Scania CV AB, Volvo Car Corporation AB, and Wärtsilä Finland Oy.

■

REFERENCES

(1) Zhang, Q.; Feldman, M.; Peterson, C. L. Am. Soc. Agric. Eng. 1988, 881562. (2) Beeck, O. Discuss. Faraday Soc. 1950, 8, 118−128. (3) Zaera, F.; Somorjai, G. A. J. Am. Chem. Soc. 1984, 106, 2288− 2293. (4) Fujikawa, K.; Kita, H.; Miyahara, K.; Sato, S. J. Chem. Soc., Faraday Trans. 1 1975, 71, 1573−1581. (5) Bos, A. N. R.; Westerterp, K. R. Chem. Eng. Process. 1993, 32, 1− 7. (6) Godbey, D.; Zaera, F.; Yeates, R.; Somorjai, G. A. Surf. Sci. 1986, 167, 150−166. (7) Horiuti, J.; Polanyi, M. Nature 1933, 132, 819−819. (8) Horiuti, J.; Polanyi, M. Nature 1933, 132, 931−931. (9) Horiuti, J.; Polanyi, M. Nature 1934, 134, 377−378. (10) Horiuti, J.; Polanyi, M. Trans. Faraday Soc. 1934, 30, 1164− 1172. (11) Beeck, O. Rev. Mod. Phys. 1945, 17, 61−71. (12) Siegbahn, P. E. M.; Blomberg, M. R. A.; Svensson, M. J. Am. Chem. Soc. 1993, 115, 1952−1958. (13) Takasu, Y.; Sakuma, T.; Matsuda, Y. Chem. Lett. 1985, 48, 1179−1182. (14) Zea, H.; Lester, K.; Datye, A. K.; Rightor, E.; Gulotty, R.; Waterman, W.; Smith, M. Appl. Catal., A 2005, 282, 237−245. (15) Song, H.; Rioux, R. M.; Hoefelmeyer, J. D.; Komor, R.; Niesz, K.; Grass, M.; Yang, P.; Somorjai, G. A. J. Am. Chem. Soc. 2006, 128, 3027−3037. (16) Rioux, R. M.; Song, H.; Grass, M.; Habas, S. E.; Niesz, K.; Hoefelmeyer, J. D.; Yang, P.; Somorjai, G. A. Top. Catal. 2006, 39, 167−174. (17) Kuhn, J. N. J. Catal. 2009, 265, 209−215. (18) Latusek, M. P.; Spigarelli, B. P.; Heimerl, R. M.; Holles, J. H. J. Catal. 2009, 263, 306−314. (19) Skoglund, M. D.; Jackson, C. L.; McKim, K. J.; Olson, H. J.; Sabirzyanov, S.; Holles, J. H. Appl. Catal., A 2013, 467, 355−362. (20) Huang, W.; Kuhn, J. N.; Tsung, C.-K.; Zhang, Y.; Habas, S. E.; Yang, P.; Somorjai, G. A. Nano Lett. 2008, 8, 2027−2034. (21) Argo, A. M.; Odzak, J. F.; Lai, F. S.; Gates, B. C. Nature 2002, 415, 623−626. (22) Qi, K.; Zhao, J.-M.; Wang, G.-C. Phys. Chem. Chem. Phys. 2015, 17, 4899−4908. (23) Cortright, R. D.; Goddard, S. A.; Rekoske, J. E.; Dumesic, J. A. J. Catal. 1991, 127, 342−353. (24) Rekoske, J. E.; Cortright, R. D.; Goddard, S. A.; Sharma, S. B.; Dumesic, J. A. J. Phys. Chem. 1992, 96, 1880−1888. (25) Hansen, E. W.; Neurock, M. J. Catal. 2000, 196, 241−252. (26) Kresse, G.; Hafner, J. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 47, 558. (27) Kresse, G.; Hafner, J. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 49, 14251. (28) Kresse, G.; Furthmüller, J. Comput. Mater. Sci. 1996, 6, 15. (29) Kresse, G.; Furthmüller, J. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169. (30) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865−3868. (31) Blochl, P. E. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953. 3285

DOI: 10.1021/acscatal.5b02708 ACS Catal. 2016, 6, 3277−3286

Research Article

ACS Catalysis (68) Chorkendorff, I.; Niemantsverdriet, J. W. Concepts of Modern Catalysis and Kinetics, 2nd ed.; Wiley-VCH: Weinheim, Germany, 2007. (69) We have analyzed the apparent activation energy with a simplified model which is possible to solve analytically. The simplified model includes hydrogen and ethylene π-state adsorption together with the two hydrogenation steps where the first hydrogenation step is assumed to be rate determining. The apparent activation energy is in this model given by Eapp = Eact + 0.5ΔHH2(1 − θH) + ΔHC2H4(1 − 2θC2H4). For hydrogen and ethylene coverages of 0.5, the apparent activation energy is calculated to be 10 kJ/mol, which is much lower than the apparent activation energy in the complete model. (70) Neurock, M.; van Santen, R. A. J. Phys. Chem. B 2000, 104, 11127−11145. (71) Pallassana, V.; Neurock, M.; Lusvardi, V. S.; Lerou, J. J.; Kragten, D. D.; van Santen, R. A. J. Phys. Chem. B 2002, 106, 1656−1669. (72) Beeck, O.; Ritchie, A. W. Discuss. Faraday Soc. 1950, 8, 159− 166. (73) Beeck, O.; Cole, W. A.; Wheeler, A. Discuss. Faraday Soc. 1950, 8, 314−321. (74) Somorjai, G. A.; Van Hove, M. A.; Bent, B. E. J. Phys. Chem. 1988, 92, 973−978. (75) Steininger, H.; Ibach, H.; Lehwald, S. Surf. Sci. 1982, 117, 685− 698. (76) Stöhr, J.; Sette, F.; Johnson, A. L. Phys. Rev. Lett. 1984, 53, 1684−1687. (77) Hills, M. M.; Parmeter, J. E.; Mullins, C. B.; Weinberg, W. H. J. Am. Chem. Soc. 1986, 108, 3554−3562. (78) Gupta, N. M.; Kamble, V. S.; Iyer, R. M. J. Catal. 1984, 88, 457− 465. (79) Campbell, C. T. Top. Catal. 1994, 1, 353−366. (80) Campbell, C. J. Catal. 2001, 204, 520−524. (81) Stegelmann, C.; Andreasen, A.; Campbell, C. T. J. Am. Chem. Soc. 2009, 131, 8077−8082.

3286

DOI: 10.1021/acscatal.5b02708 ACS Catal. 2016, 6, 3277−3286