From First-Principles to Catalytic Turnovers: Ethylene Hydrogenation Over Palladium

Studiesin SurfaceScienceandCatalysis133 G.F.Fromentand K.C.Waugh(Editors) Publishedby ElsevierScienceB.V.,2001

19

From First-Principles to Catalytic Turnovers: Ethylene Hydrogenation Over Palladium Matthew Neurock*, Eric Hansen, Donghai Mei, and Pallassana S. Venkataraman

Department of Chemical Engineering, University of Virginia, Charlottesville, VA, 22903. Abstract We present a first-principles-based dynamic Monte Carlo method which can be used to model the kinetics of metal catalyzed reaction systems by following the explicit atomic surface structure and individual molecular transformations. The approach uses first-principle density functional quantum chemical calculations to build a comprehensive database of adsorption energies, overall reaction energies, activation barriers, and intermolecular interaction energies. The ab initio calculated lateral interaction energies were subsequently used to develop more approximate but universal interaction models that could be used in-situ in the MC. A radial function model and a bond order conservation model were both developed. The simulation algorithm was used herein to examine ethylene hydrogenation over palladium. The results indicate that it is the repulsive interactions in the adlayer that weaken the metal-carbon and metal-hydrogen bonds thus lowering the barriers for hydrogenation from 15 for ethylene to ethyl and 14.5 for ethyl to ethane to 8.5 and 8.0 kcal/mol for the same steps taken at higher surface coverages. The simulation results provide a very good match against known experiment results. The simulation was subsequently used to examine both the effects of alloying and surface structure. The addition of gold decreased the overall turnover number simply because the number of sites was reduced. On a per palladium basis, however, the activity remains approximately the same. The addition of gold indirectly leads to less hydrogen on the surface since it shuts down H2 dissociation steps. This, however, is countered by a reduction in the metal-hydrogen bond strength which helps to enhance the activity. These two features tend to balance one another out as the turnover frequencies remain nearly constant. We provide a simple cursory look at the effects of surface structure by examining the changes in the kinetics over Pd(100) and Pd(111) surfaces. The barriers over these two surfaces are 7.1 and 6.4 kcal/mol respectively suggesting that the chemistry is relatively structure insensitive.

I. Introduction Kinetic modeling of catalytic reaction systems plays a critical role in the design and optimization of chemical reactors and processes. The models that have been developed over the years have been the result of our understanding of the chemistry, available analytical capabilities, and the desired level of the results. Many of the earliest kinetic models were simply power-law models, i.e. empirical relationships between the measured partial pressures (or compositions) and the reaction rate. The earliest models were based solely on overall composition, conversion and yields since that was all that could be routinely determined. Despite their simplicity, power-law models are still used to model a number of industrial chemical processes. They capture the relevant information and can be used to predict daily operation and control of industrial reactors.

20 As our understanding of the elementary catalytic reaction steps and our analytical capabilities improved, the basic kinetic models were expanded in order to reflect this finer level of detail. Langmuir-Hinshelwood and Hougen-Watson (1,2) w e r e some of the first to formulate mathematical models that embody the elementary adsorption, surface reaction and desorption steps. These models have stood the test of time and have played a very valuable role in the chemical process industry as many of the current catalytic processes are modeled via some form of LHHW rate expression. For most of these systems, however, the parameters were (and still are) fit to laboratory data. A number of significant advances in analytical characterization techniques occurred over the past decade that have greatly improved our understanding of the chemistry and resolution of the molecular level0f details. By the late 1980's it became possible to characterize and model the fate of large numbers of the molecular intermediates relevant to the reaction mechanism. Up until the 1980's modeling of complex petroleum feedstocks, for example, had focused on lumping all species into measurable boiling point and solubility fractions and following the kinetics of these "thermodynamically-derived" lumps (3). The 3- and 10-lump models for fluid catalytic cracking of gas oils are classic text-book examples. By the mid 1980's it became apparent that with the increase in analytical capabilities, and computer hardware that more detailed and robust models could be developed that would enable users to span a wider range of process conditions (3). Froment (4,5,2,6),Dumesic (7-10), Stolze and Norskov (11,12), Klein (13-18), Boudart (19,20), and Ertl (21) helped to pioneer what is now termed as microkinetic modeling thus following the detailed reaction mechanisms for a number of different chemical processes. These include fluid catalytic cracking of gas oils, upgrading of heavy petroleum feedstocks, coal pyrolysis, ammonia synthesis, alkane and olefin hydrogenolysis. Microkinetics (7), as defined by Dumesic, "is the examination of catalytic reactions in terms of elementary chemical reactions that occur on the catalytic surface and their relation with each other and with the surface during a catalytic cycle." This definition can easily be expanded into covering non-catalytic systems as well. Microkinetics, for the most part, has focused on analysis or understanding of the reaction mechanism. The approach, however, also holds the promise of being used to aid in the synthesis of new materials. Microkinetic modeling is now an important tool for many of the practicing reaction engineers. This approach enables one to formulate and follow the detailed concentration profile for most if not all of the reaction intermediates. Despite the tremendous progress, the models that have been developed are still simplified descriptions of the molecular transitions of physicochemical processes that govern the kinetics. The kinetic constants used are, in most cases, still fit to experiments on the actual system, thus introducing empiricism. In many of these catalytic reaction systems the adsorption and kinetic terms are considered constant but in fact it is well established that they change as one moves to different processing conditions. Z a e r a (22,23), for example, recently showed that the adsorption constants in a simple Langmuir-Hinshelwood model could only be considered constant if the operating conditions were chosen close to where the parameters were regressed from experimental data. In order to extend their model for NO reduction, it was critical to include coverage dependent adsorption parameters. It is important to stress that many of the models that have been developed are simply just that, "models", and we should exercise caution when in using them outside the range at which they've been parametrized or reading more into the mechanisms than can be justified. There are now many examples in the literature whereby more complicated scenarios concerning different surface sites, competitive and noncompetitive

21 adsorption, and other features are added to the basic Langmuir model in an attempt to better fit the data. These features provide more parameters and usually do a much better job when fit to the experimental data simply because more parameters offer more flexibility. It is implicitly assumed, however, that the Langmuirian models are correct. The problem may not necessarily be in the reaction mechanism but the way in which one idealizes the surface. 9

The classical Langmuir-Hinshelwood model which is used as the foundation for most of the microkinetic approaches is formulated so as to average over the entire surface structure. As such it averages, over all of the local structural and compositional features of the surface and treats them in an average way. This includes the effects of local defect sites, promoters, poisons, bimetallics and metal support interactions. Figure 1 depicts a schematic which identifies various local regions of the metal surface which likely give rise to different reactivity for NO. The classical Langmuir Hinshelwood model, however, would average over the surface and treat each of these NO species as equivalent. We can see, however, that each of the NO Step Edge Covera species may, in fact, be quite different, by virtue of their local environment. Clearly the NO species on the flat terrace should react differently than the one sitting next to defect site Promotors or that next to a promoter or a step edge. The considerable improvements in both analytical as well as computational chemistry Ordered Overlayers that have occurred over Defect Sites the past decade, Figure 1 Schematic illustration of an idealized Rh surface which however, now make it depicts various local regions for NO dissociation. possible to begin to think about moving to atomic and molecular-level descriptions of the surface kinetics, in order to capture a more realistic picture of the surface chemistry and its impact on the catalytic performance. Figure 2, for example, is a recent STM figure from Bowker (24,25) which shows the presence of p(2xl) islands of oxygen on Cu(110). Methanol preferentially attacks at the edges of these islands and reacts to form formaldehyde and water. In the sequence of time progressions shown in Fig. 2, the p(2xl) islands of oxygen are reacted away by methanol and the Cu(110) surface is restored. These islands are highlighted in the overlayed boxes. This figure clearly demonstrates that these advances in spectroscopy are enabling us to begin to image active atomic surface ensembles, at least at well defined conditions. Similar advances, in AFM, HREELS, SFG and EXAFS are also beginning to provide molecular and nanoscale resolution of surface structure, and reactive

22 surface intermediates. The integration of these techniques with traditional kinetic isotopic labeling studies offer the opportunity of elucidating the elementary processes that govern catalytic reactions.

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Advances in computational chemistry and molecular simulation have also reached the stage whereby they can be Used to develop more advanced and robust kinetic models for catalytic systems. First-principle quantum chemical methods, for example, are being used to routinely calculate thermochemistry and kinetics for gas phase chemistry with accuracies on the order of 0.5-2 kcal/mol (26) The situation for the kinetics of heterogeneous reaction systems has also improved considerably but due to the complexity in these systems the accuracy is more on the order of 5-7 kcal/mol (27,28) In addition to the advances in raw computational power and more accurate quantum chemical methods, molecular simulation tools have also made great progress and can now begin to capture detailed quantum chemical results. In this paper, we discuss some of our recent results in coupling ab initio density functional quantum chemical methods along with dynamic Monte Carlo algorithms in order to simulate a detailed myriad of competing molecular transformations that govern the kinetics on metal surfaces. Stochastic models enable us to take full advantages of the atomic detail that is offered from the detailed analytical spectroscopies as well as the information from ab initio quantum mechanical modeling efforts since they can explicitly account for atomic surface structure. Rather than averaging the details over the entire surface by invoking deterministic methods, the Monte Carlo approach follows the position of each atom on the surface as a function of reaction conditions, As such, we can begin to map out the molecular transformations along with kinetic behavior. In particular, we will focus on the hydrogenation of olefinic intermediates. Ethylene is used as a model toward understanding the hydrogenation of complex olefin and aromatic intermediates (29) It is therefore relevant to various hydrocarbon processes. In addition, understanding ethylene hydrogenation kinetics is also important in the manufacturing of high purity ethylene feeds for polyolefin production. It is necessary to remove acetylene from the ethylene feeds for polyolefin

23 manufacturing because acetylene leads to a host of different processing problems. Ethylene feeds are first hydrotreated to selectively convert acetylenic intermediates to ethylene. The chemistry, however, is very sensitive to process conditions. Unselective routes lead to ethylene hydrogenation to form ethane. This will sharply decrease the overall selectivity, and can also lead to runaway reactors since ethylene hydrogenation is fairly exothermic. The mechanism for olefin hydrogenation has been debated for well over 30 years. The general chemistry is thought to involve a Horiuti-Polanyi (3~ like scheme. Hydrogen dissociatively adsorbs producing chemisorbed atomic hydrogen on the surface. Ethylene co-adsorbs in either di-~ or n-bound arrangement and then reacts with hydrogen to form the ethyl surface intermediate. The ethyl intermediate can subsequently react with a second surface hydrogen atom to form ethane or dissociate back to form ethylene and atomic hydrogen (29). Although the overall paths appear to be well established, the nature of the active site and the details of what controls the chemistry are still openly debated in the literature. A number of different schemes have been devised in order to appropriately fit the kinetic data (31,8,9,7). They include some of the following ideas: 1) hydrogen and ethylene compete for the same surface sites, 2) hydrogen and ethylene reversibly adsorb into separate islands and reaction occurs at the edges of these islands, and 3) hydrogen is adsorbed on two different sites- one is competitive with ethylene adsorption while the other site is not. There is little evidence, however, to support these ideas other than they provide a better fit the kinetic data. Fitting of the kinetic data alone, however, does not say very much about the mechanism. Westerterp (32) for example, recently showed that over eight different models could be readily correlated with the kinetic results for hydrogenating ethylene and acetylene mixtures. Rather than start with a preconceived notion about the mechanism, we have carried out a comprehensive series of first principle calculations in order to determine the intrinsic activation barriers, heats of adsorption and overall reaction energies for various speculate routes. Transition state theory as well as classical statistical mechanics are used to subsequently establish the Arrhenius factors and thus provide the intrinsic rate constants. One of the critical issues in using first-principles data involves the great difference between the ideal reaction environment that is chosen for the model and the actual environment under operating conditions. Most of the quantum chemical results that have been published over the past decade have examined the zero or low coverage limit in order to avoid introducing coverage effects. In order to model the active surface under reaction conditions, however, we need to explore the effects of the reaction environment. In particular, we focus here on the interactions between species on the surface. We explore these interactions in detail to determine their effects on adsorption and surface reactivity. First principle calculations enable us to easily calculate the interaction between two species coadsorbed to the surface. As we begin to think about more realistic systems, it very quickly becomes apparent that this essentially becomes impossible to do for more than two species because of the infinite number of ways in which adsorbates can assemble on a surface. For example, figure 3 depicts a single snapshot from kinetic Monte Carlo simulation that we performed for NO decomposition over Rh.

24

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We have chosen a smaller unit cell size and also the chemistry in this system is quite limited. Despite these simplifications, this system still contains hundreds to thousands of different configurations for just this single snapshot in time. As we begin to look at the myriad of events that can occur, it becomes clear that it would be simply impossible for us to carry out all of these configurations directly from first-principle calculations. Instead, we use set of first-principle calculations to map both the nearest and next-nearest neighbor interactions. This information is then used to parametrize a semiempirical model which can be called internally within the simulation. The Monte Carlo simulation therefore, builds up the database of calculated rate constants, calculates (through model equations) the influence of the

environment and subsequently simulates the outcome of different reaction steps. The apparent rate constants are subsequently used to calculate a reaction probability distribution, ri/Zri which is then used in the simulation to establish which events occur as we proceed in time. In addition to modeling coverage effects, the Monte Carlo algorithm also enables us to track individual sites, i.e. atop, bridge, hollow sites. It is well known from the surface science literature that while one site may prove to be strongest adsorption site, it may or may not be active site that drives the kinetics. We therefore intrinsically allow for site-specificity in the model.

II. Developing The Intrinsic Kinetic Data Base from Ab Initio Methods We have performed a number of cluster and periodic slab quantum chemical calculations to determine the intrinsic energetics for sequence of adsorption and reaction steps that control ethylene hydrogenation and decomposition. The methods are briefly described below. The (33-36) details can be found in the following papers:

A) OFT Calculations Large nineteen atom palladium clusters were used to model the Pd(111) surface (34). All calculations were performed using spin-polarized Density Functional Theory (DFT) calculations with nonlocal gradient corrections for the correlation and exchange energies. The local exchange correlation potential was modeled using the Vosko-Wilk-Nusair (VWN) potential along with nonlocal gradient corrections from Becke (37) and Perdew (38)for the exchange and correlation terms respectively. DFT-optimized double zeta gaussian type orbital basis sets which include

25 spin polarization were employed for all atoms. (39,40) The spin states were fully optimized for all calculations. The Pd cluster was held fixed at the metal positions of the ideal surface. The adsorbates however were allowed to fully optimize.

B. Periodic Pd(l l l) Calculations To examine higher coverage situations and the effect of surface relaxation, periodic DFT calculations were performed. The results were found to be quite consistent with calculations on the large Pd19 clusters (34) which helps to confirm the cluster results. The Pd(111) surface was described by constructing a supercell which is translated along the lattice vectors that lie in the surface plane to describe ( . ~ x.~/~) R30 ~ and (2x2) surfaces. The surface is defined here by three layers of Pd atoms. A vacuum layer of 10 A was placed above the adsorbate surface to avoid any electronic interactions between the slabs. In previous calculations we examined the effect of the number of metal layers on the binding energies for hydrogen on Pd(111) and found that the energy changes were less than 1 kcal/mol as the slab thickness was increased to three layers and beyond. In addition, the structural changes which occur in going beyond three layers were found to be negligible. Three layers of Pd, therefore, appeared to provide a computationally efficient and tractable model of the Pd(111) surface (41). The Kohn-Sham (KS) equations were solved using a plane wave basis set with a maximum kinetic energy of 40 Rydberg. Eighteen special k-points (Bloch vectors) were used in the description of the first Brillouin zone. The special k-points were chosen based on symmetry by the method developed by Chadi-Cohen. All calculations were performed self consistently by using non-local exchange and correlation potentials in the form of the Perdew-Wang 91 Generalized Gradient Corrections. Scalar relativistic corrections were described through the use of norm-conserving pseudopotentials. The first two palladium layers were allowed to relax in an effort to understand the effects of surface relaxation. The bottom layer was held fixed at the bulk structure of Pd(111). Adsorbates were then spaced in either a ( ~ x,~/~) R30 ~ or a (2x2) surface structure. The ( , ~ x,~/3) R30 ~ structure was found to lead to repulsive interactions between neighboring ethyl intermediates. The (2x2) structure was therefore used to help eliminate any through-space repulsive interactions. The geometries of the first two layers of the surface along with the adsorbates structure were completely optimized. (34)

C. The Catalytic Potential Energy Surface The low coverage adsorption energies for the relevant intermediates are shown in Table 1. Ethylene binds in both the n and di-cy adsorption states. At the low coverage, the di
26

Species Ethylene (di-cy) (~) Vinyl q2(~tl,~t2) Ethyl Atop Bridge Ethylidyne 3-fold fcc 3-fold hcp Bridge Atomic Hydrogen Atomic Oxygen Atomic Carbon

AEADs Pdl9 (kJ/mol)

AEADs Pd (111) 2x2 (kJ/mol)

Experiment (kJ/tool)

-60 -30

-62 -27

-237

-254

-130 -75

-140 -

-620

-636 (CH3C"quartet) -511 (CH3C-doublet)

-603 -587 -271 -375 -610

-266 -400 -635

-59

-262

Table 1 DFT-calculatedadsorption energies for C2Hxand atomic surface intermediateson the Pdl9 cluster and the Pd(111) 2x2 3 layer slabs [Reprinted from (34) ]. By examining various different configurations for two and three ethylene molecules on the (111) and (100) surfaces, we are able to establish the most basic lateral interactions. For example, ethylene adsorption in the well-defined p(2x2) arrangement shown in Fig. 4 leads to an adsorption energy o f - 8 4 kJ/mol. This indicates that the attractive interactions per pair of ethylene molecules is 11 kJ/mol. As the ethylene molecules move closer or sit perpendicular to one another they become repulsive at about the 8-15 kJ/mol. While these interactions may appear to be small, they become quite important as the coverage is increased because the number of these interactions increases. These are just a few of the interactions that were calculated. These values were subsequently used to parameterize simpler empirical or semiempirical lateral models. Extended Htickel theory, for example, was used in order expand our database of different lateral interactions (42). We let the computer then generate thousands of different plausible surface configurations and their corresponding interaction energies. Hydrogen readily dissociates over Pd(ll 1) to form atomic hydrogen on the surface. The energy for the dissociative adsorption of hydrogen i s - 7 8 kJ/mol. Ethylene hydrogenates to form the ethyl intermediate. Ethyl prefers the atop adsorption site were it binds w i t h - 1 4 1 kJ/mol. Higher coverages weakened the Pd-H interaction by about 10 kJ/mol. The overall reaction energy for the hydrogenation of ethylene from the di-cy adsorption state at zero coverage is +3 kJ/mol. The barrier for the metal catalyzed reaction of ethylene to ethyl at zero coverage is +72 kJ/mol. The reference state for the reactants are ethylene (di-cy) and hydrogen sharing a single metal center. If we use ethylene and hydrogen that are separated from one another as our reference state, the calculated barrier increases to +87 kJ/mol. In the Monte Carlo simulations, the diffusion of ethylene and hydrogen to the reactive site are treated as a separate step. We therefore use the value of +72 as the reference state. As the coverage is increased to 0 = 0.6 ML both of these barriers decrease by about 5 -10 kJ/mol.

27

Figure 4

Ethylene adsorption in p(2x2) arrangement on Pd(100). The specific positioning of ethylene is such that it stabilizes each ethylene pair by 11 kJ/mol due to attractive through-surface interactions. The more interesting situation, however, is that for the n-bound ethylene. At low surface coverages we find that n-bound ethylene does not hydrogenate but simply coverts to the di-cy intermediate. At higher coverages, however, the n-bound state becomes pinned within the adlayer whereby it can no longer translate along the surface to convert to a di-cy species. It can now either react with hydrogen or desorb. We were able to isolate the transition state for the transient n-bound state at high coverage which is shown in Fig. 5. The barrier is reduced from +72 kJ/mol (low coverage) to + 3 6 (high coverage) kJ/mol (36) as we move to higher coverages. Although the di-cy site is the more favorable site, at high surface coverages the n-bound state is actually more reactive.

A)

Figure 5 DFT isolated transition states for ethylene hydrogenation from the di-cyand n-bound intermediates at higher surface coverages (adapted from (36)).

Once ethyl is formed one the surface it can readily dissociate back to form ethylene or undergo successive hydrogenation to form ethane. The DFT calculated barrier for the back reaction is +63 kJ/mol which is lower

28 than that for the forward reaction. The barrier for the addition hydrogen to ethyl to form ethane is +71 kJ/mol. The results suggest that the forward path for ethyl to ethane competes with the reverse path for 13 C-H bond activation which leads back to ethylene. An equilibrium is established between the two. This equilibrium is consistent with known experimental results (43) The final hydrogenation step to form ethane is not very reversible due to the high barrier height for the reverse reaction of ethane C-H bond activation (+105 kJ/mol). In addition, ethane does not readily readsorb. The overall hydrogenation energetics are shown in detail in Fig. 6.

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Figure 6

The overall hydrogenation energetics for ethylene hydrogenation as computed by DFT at the zero coverage limit. O. Selectivity I s s u e s

It is well established that ethylene decomposes over Pd to form ethylidyne and carbonaceous surface intermediates (44-49) Decomposition readily occurs at lower partial pressures of hydrogen and leads to a loss in selectivity. Under these conditions, ethylidyne is the primary surface intermediate. While ethylidyne is thought to form directly from the interconversion of ethylene, there is little proof that this is indeed the actual route. We have tried to isolate a direct path for the formation of ethylidyne from ethylene with very little success. The barriers for the direct path are simply too high. We have, however, found a low energy path which involves the C-H activation of ethylene to form surface vinyl. The surface vinyl intermediate can subsequently hydrogenate to form ethylidene which can then undergo a C-H bond scission to form ethylidyne. This indirect path along with the calculated energetics are shown in Fig. 7. The limiting step for this sequence involves the formation of the surface vinyl intermediate at +140 kJ/mol. Subsequent steps occur much more readily leading to ethylidene and ethylidyne. A very similar route has also been suggested from UHV studies for ethylene on Pt by Zaera (43) Although ethylidyne is strongly bound to Pd, its barrier for surface diffusion is fairly low. It's primary role may simply be that as a spectator.

29

E. Lateral Interactions The overall potential energy profile calculated for this system at zero coverage shown in Fig. 6 provides the necessary preliminary input for the simulation. As discussed above, we have calculated a set of basic lateral interactions to determine the pair interactions of ethylene from first-principle calculations. These calculations were supplemented by carrying out over 1750 Extended Hiickel Theory (EHT) calculations in order to develop a semiempirical model for lateral interactions (42) These calculations were determined from the number of plausible scenarios that are generated by the Monte Carlo simulation code. The resulting DFT and EHT results were then fit to the model which is a function of the radial distance between the specific adsorbates. The model allows for both attractive as well as repulsive interactions between adsorbates. In addition, a bond order conservation (BOC) model was parametrized by the DFT lateral interaction results and used to calculate local lateral interactions on the measured activation barriers. As was discussed above, these interactions can markedly affect reactivity and control the predominant surface interactions. In previous Monte Carlo TPD studies for example, we found that the shape of the curve and the peak locations were quite sensitive to lateral interactions. Higher coverages displayed repulsive interactions which lead to a lower temperature of desorption. At lower coverages, lateral interactions became attractive. These attractive interactions stabilized the formation of a p(2x2) ordered overlayer.

vinyl formation

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Catalytic paths for the decomposition of ethylene to ethylidyne. Direct isomerization and the sequential hydrogenation/dehydrogenation processes.

30

IIl. Simulating Reaction Chemistry A. Monte Carlo Simulation Algorithm A variable time step dynamic Monte Carlo simulation algorithm was constructed in order to model temporal surface reactivity and kinetics (42). The algorithm explicitly accounts for all atop, bridge, and hollow sites on the surface. The simulation follows the elementary physicochemical processes as a function of time and can therefore, track the changes in the spatial arrangement and positioning of the molecules that make up the surface adlayer. As such we can simply count the number of product molecules that desorb from the surface as a function of time in order to determine the turnover frequency. The algorithm is based on a variable time step kinetic Monte Carlo approach whereby we examine the entire surface for all possible kinetic events that can occur. The overall structure of the simulation algorithm is shown in Fig. 8.

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~/~. Event1

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Yes

Figure 8.

Schematic for the dynamic Monte Carlo simulation algorithm.

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=

-

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We use these same individual rates (or rate-constants) to calculate the probable selectivity for each specific event. By drawing a second random number we specify which event actually occurs from the cumulative probability distribution. This value is used to compare to the cumulative reaction probability distribution Si (equation2). If the value drawn is between Si and Si+~, event Si is chosen. We update the event and then continue back through the process of monitoring time and events.

Si

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The simulation tracks the detailed occupation of all surface sites along with the identity of all molecules that desorb, diffuse or react thus providing a full accounting of the spatiotemporal behavior. The size of the simulation cell employed is chosen so as to optimize the accuracy and

31 precision with the balance on the CPU requirements. Larger unit cells offer more accurate and precise results. Smaller unit cells averaged over numerous runs can reduce the CPU requirements while maintaining accuracy and precision. We will typically use lattices that are on the order of 40x40 which, for a (100) surface, has over 4800 sites. Before the simulation results are tabulated in a production mode we typically allow the simulation to run for a block of time in order to equilibrate the system. The lateral interactions between molecules are quite important in determining the surface coverage as well as the surface kinetics. B. Monte Carlo Simulation Results 1) Ethylene Hydrogenation over Pd(100) The simulation is currently setup to enable the user to change initial process variables and simulate the output product distributions. As such the simulation can be run as a "virtual experiment". We initially examined the hydrogenation of ethylene over the Pd(100) surface. A series of simulation runs were performed at different temperatures to follow the effects of temperature on the reaction rate. The resulting TOFs were plotted against 1/T in the same way that experimental data would be examined, in order to determine the overall apparent activation energy. In addition, we can also back out the apparent activation barriers for specific elementary adsorption and reaction steps. The resulting potential energy profile for ethylene hydrogenation that results from the simulation is quite a bit different than that established at zero coverage. The activation barrier for ethylene hydrogenation to ethyl is reduced from 15 kcal/mol to 10.8 as we move from the zero coverage limit to the more realistic simulation surface coverages (0.3-0.5 ML). The barrier for the hydrogenation of surface ethyl to ethane is reduced from 14.5 kcal/mol (zero coverage) to 8.1 kcal/mol (reaction simulation coverages). This is shown in the overall potential energy diagram in Figure 9 for ethylene hydrogenation at higher coverages. This reduction in the activation barrier is primarily due to the repulsive interactions between surface intermediates. Repulsive interactions reduce the strength of the metal-adsorbate (M-C and M-H) bonds and thus lower the barrier for hydrogenation. Our DFT calculation results showed a similar effect. The barrier for ethylene hydrogenation at higher ethylene (0.3 ML) and hydrogen (0.3 ML) surface coverages was 8-10 kcal/mol which is 3-4 kcal/mol lower than the 11-15 kcal/mol barriers calculated at the zero coverage limit. The high coverage ethylene hydrogenation barriers calculated from both DFT (8-10 kcal/mol) and Monte Carlo simulation (8-11 kcal/mol) results are consistent with known experimental results which are on the order of 7-12 kcal/mol.

In addition to temperature effects, we can also simulate changes in reaction kinetics as we increase the partial pressure for each of the reactants. A series of simulation runs were carried out at different partial pressures of ethylene and hydrogen to examine their effect on the rate. The measured turnover frequencies were fit to the following power law expression in order to establish the reaction orders of hydrogen (x) and ethylene (y).

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-

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y

(3)

The turnover frequency is simply the number of ethane molecules that desorb per surface site per time. The reaction orders calculated from the simulation results were-0.16 to +0.03 for ethylene

32 and 0.38 to 0.56 for hydrogen. This is in very good agreement with known experimental results which indicate reaction rates that are zero order in ethylene and half order in hydrogen (50,7) In addition to the overall kinetic properties, the C2H 4 (g)+ H 2 (g) simulation also provides a comprehensive -11 accounting of the atomic positions of all -16.4 of the surface -18.7 intermediates as a i, -19.1 10.8 function of time and process conditions. For C2H4 (g)+ 2H (a) -27.2 C2H6 (g) example, the snapshots C2H 5 (a)+ H (a) -3""].8 shown in Fig. 10 are C2H 4 (a)+ 2H (a) taken at subsequent elementary steps and depict the change in the T= 298 K, PC2H4= 25 Torr, PH2=25 Torr molecular arrangements Figure 9 The "apparent" overall energetic cycle for the hydrogenation of on the surface as a ethylene due to lateral surface interactions. function of time. The majority of the surface is covered with the di-~ bound ethylene intermediate along with hydrogen which is isolated at the 4-fold hollow sites. The surface contains only 1-5% of the n-bound ethylene which is actually the much more reactive intermediate. Our first-principle DFT calculations show that the n-bound ethylene has a barrier that is almost half of that for the di-cy ethylene. The n-bound ethylene is more weakly bound and therefore reacts much more readily than the di-~ ethylene. This is in good agreement with the results by Cremer and Somorjai (45-48) who used Sum Frequency Generation experiments to follow the characteristic stretch modes for the n and di-~ bound ethylene throughout reaction over Pt. Their results suggest that the n-bound ethylene makes up only 4-5% of the surface coverage but is solely responsible for catalytic turnovers. The di-~ intermediate is thought to be only spectator species. In our simulations, we see a much higher rate of reaction from the n-bound intermediates but the di-~ species also plays an important role in the measured rate. Effects of Lateral Interactions Barrie1:v Reduced

The apparent activation barrier for the first hydrogenation step as established by the simulation is slightly greater than the second hydrogenation step. The barrier for the reverse reaction of ethyl dissociation back to ethylene and hydrogen, however, is also rather low. The ethyl that forms readily reacts back to form ethylene and hydrogen rather than hydrogenate to from ethane. This exchange process between ethylene-ethyl-ethylene occurs quite readily with increasing temperatures. This exchange process is well known experimentally over various transition metals (43,49)

33

Event Snapshots

Ethylene Figure 10

Ethyl

Snapshotsfrom the kinetic Monte Carlo simulationfor ethylene hydrogenationover Pd(100).

The detailed information offered from the simulation enables us to point out the molecular features that govern the chemistry. By calculating all of the barriers and reaction energetics from first-principle quantum chemical calculations, the simulations are free of any experimentally regressed parameters. The results for the simulation agree remarkably well with the known experimental data (51,50,31,52,53).A simple power law rate model derived from the simulations is compared with that known from experiments below in Eqs. 4 and 5.

Rsimuta"~

-

9.5 + 2.5 kcal/mol'~po.65_l.Op_o.4_o.o 105.4-+0.0exp(7 RT ) H2 -- C2H4

(4)

8.5 + 2.5 kcal/mol)pO.5_,.op_o3_oo RT ) H2 C2H4

(5)

RExhPern~merit = 1 0 6.3+0.07 exp

-

We didn't expect the match to be this close. In any event, the simulations provide a framework for which we can now begin to test mechanistic ideas. As indicated in the introduction most of the current models in the literature require arbitrary assumptions about site specificity or competitive and uncompetative sites in order for them to match the experimental results. These assumptions provide more flexibility in the model through the introduction of another fitting parameter. We were able to match the experimental results here without invoking assumptions about the different surface sites and different site competitions or fitting parameters. The elementary step rate constants used in the simulation were derived solely from quantum chemical calculations and transition state theory estimates without regression back against the experimental data. One of the limitations of the models posed in the literature is their assumption of "constant" adsorption constants over different inlet partial pressures. Our results here indicate that the lateral repulsive interactions between surface species play a very important

34 role in reducing the activation barriers. Changes in the surface coverage markedly impact the nature of the intermolecular interactions, this dictates the relative surface coverages and as well the reaction rate. All of these features can be easily captured in the Monte Carlo simulation.

2) Effect of Gold Olefin as well as acetylene hydrogenation is carried out industrially over PdAu, PdAg or PdCu alloys in order to increase selectivity. Palladium catalyzes the hydrogenation of olefins but is also active in catalyzing unselective hydrocarbon decomposition paths. The question of whether gold alters the electronic or the geometric features that control selectivity is still debated. Gold is modeled here by parametrizing a bond order conservation approach with ab initio DFT values, similar to the model described above for Pd. DFT results indicated that ethylene adsorption is reduced by only 30 kJ/mol as we move from Pd (-60 kJ/mol) to Au (-30 kJ/mol), but atomic hydrogen is reduced by almost 80 kJ/mol in moving from Pd (-271 kJ/mol) to Au (-195 kJ/mol). The more strongly bound intermediates are those which are most critically affected by the presence of gold. The DFT results on the pure Pd and Au were subsequently used to estimate the adsorption and reaction energies on the alloyed surfaces through the use of bond order conservation estimates and Eq. 6.

(6)

We have performed a series of simulations on various different PdAu alloyed surfaces. The systems examined along with the corresponding ethane turnover frequencies (on a per Pd atom basis) are given in Table 2. As would be expected, the overall turnover frequency is decreased simply due to ensemble size (geometric arguments) effects. Gold is inactive, and therefore when it is substituted for Pd it reduces reactive sites. The calculated turnover frequency, measured on a per Pd basis, however remains essentially constant over a range of different alloy configurations examined. In these simulations, it is clear that gold acts to shut down sites for hydrogen dissociation. This leads to lower surface coverages of hydrogen which ultimately lowers the rate. On the other hand, gold also acts to weaken the binding energies of both ethylene and hydrogen on the surface. This leads to a faster rate of hydrogenation. These two effects counter one another and therefore there is little measurable change in the TOF on a Pd atom basis. The effect of gold composition and temperature on ethylene and hydrogen coverages and binding energies are shown in Fig. 11 and 12. As the gold composition in the surface is increased from 0 to 12%, the hydrogen surface coverage changes from 0.21 to 0.11 ML. In addition the hydrogen binding energy can decrease from 61 kcal/mol to 59.5 kcal/moi. These changes in the binding energies are much more subtle with gold coverage but their effects are just as important to the rate. The changes in the ethylene coverage and ethylene binding energy as shown in Figures 11 and 12 are much less sensitive to the composition of Au. The ethylene coverage changes by only 0.01 to 0.02 ML. Although Au decreases the number of Pd sites, it does not really change the activity of the remaining Pd atoms. This is shown in Table 2.

35

3713,~o

Hydrogen Surface6"overage

370

Ethylene Surface Coverage

(1 17

35(1

~

i .~3o

330

310

2911

27(1

25.

,

i1(111

1102

(1114

,

0(16

oox

0 i(1

0 12

25(1

o (HI

A u Conll~),ltlon

,

0 (12

,

(1 (14

0 O6

o ()8

o |2

o io

Au Composition

Figure 11

The effect of gold and temperatureon the average surface coverages.

37(1

35o

HydrogenBindingEnergy

/

3711

14.O

2711

2711

2S0

111111

(1112

111111 Au Composition

Figure 12

1) 11~

11111

(112

. iii)

002

004

o116

oo1~

o IO

o.12

Au Compo,ttlon

The effect of gold and temperatureon the average binding energies.

The results presented so far only examine the selective hydrogenation pathways. Carbon formation is not explicitly explored in the Monte Carlo simulation. We have, however, worked out the reaction paths and energetics for ethylidyne and carbon formation from DFT QM calculations. The results indicate that gold shuts down the sites for ethylidyne formation, thus increasing the stability of ethylene and ethyl surface intermediates. The barrier for ethylidene to react to form ethylidyne (see Fig. 7) increases by 30 kJ/mol when gold is substituted into the surface. This helps to improve the reaction selectivity without sacrificing the activity of reactive metal (in this case Pd). The activities reported here (on a Pd atom basis) are essentially constant. This is consistent with what is known experimentally. Davis and Boudart (511 for example, report little changes in the TOF (on a pure Pd basis) as Pd is alloyed with Au. The apparent effects discussed in the literature suggest that the role of Au is simply geometric. Our results herein show that the electronic effect is important in increasing the rate of hydrogenation of ethylene which ultimately compensates the reduced number of sites on activity.

36

I

g m / R B m

Turn-over Frequency

H* Coverage (ML)

0.10

0.15

60.0

10.7

0.1875

0.10

0.27

61.6

9.7

0.176

0.13

0.25

62.3

9.3

0.184

0.11

0.29

61.3

8.5

0.179

0.13

0.27

61.3

10.3

0.176

0.15

0.28

61.2

9.1

0.18

0.14

0.36

62.1

9.1

0.19

0.42

62.5

9.1

0.182

0.14

Eads(H* ) Eads(C2H4*) C2H4" Coverage (kcal/mol) (kcal/mol) (ML)

:ll,

TOF/per Pd

Table 2 The effect of gold on the ethylene hydrogenation turnover frequencies for ethane formation.

3) Structure Sensitivity Hydrogenation reactions are known to be relatively structure insensitive. We examine the effects of structure sensitivity by simulating ethylene hydrogenation over Pd (100) as well as Pd(111) surfaces. The relative surface coverages and adsorbate binding energies again appear to be the two factors that control the kinetics. The (100) surface is more open than the (111) surface and therefore allows for slightly higher surface coverages of ethylene and hydrogen. Monte Carlo simulations performed at UHV conditions where T= 100 K, indicate saturation coverages of 0.33 and 0.37 ML for ethylene on P d ( l l l ) and Pd(100) respectively. These are in very good agreement with reported experimental saturation coverages of 0.30 and 0.37 ML for ethylene on Pd(111) (54) and Pd(100) (55) surfaces respectively. The resulting adlayers that form are shown in Fig. 13. Thespacing on the (111) surface is ideal in that it allows for ethylene to begin to order into ('~/'3x'~) R30 ~ patches of ethylene in the adlayer. In the presence of hydrogen, the saturation coverages drop to 0.19 and 0.25 on Pd(111) and Pd(100) respectively. The coverage of hydrogen over Pd(100) in the presence of ethylene ranges from 0.35 ML to 0.20 ML over the range of 250-375 K. The corresponding coverage of hydrogen on the (111) surface is 0.22 to 0.15 ML. The (100) surface therefore can accommodate up to 10-30% more than the (111) surface. The average binding energies calculated from the simulation are slightly lower on the (100) than on the (111) surface. The lower binding energy on the more open surface is the result of increased repulsive interactions which weaken the metal-adsorbate surface bonds. The average binding energy for ethylene changes from 60.0 to 61.5 kJ/mol on Pd(111) whereas the value is about 62.0 kcal/mol on Pd(100). The weaker interactions and the higher surface coverages of ethylene lower the intrinsic activation barrier for hydrogenation on the (100) surface. This will tend to increase the rate of ethylene hydrogenation. This increase however is countered by an increased rate of the reverse reaction of ethyl back to ethylene. As was reported earlier, the rate of ethane formation is

37

controlled by a delicate balance of the first hydrogen addition step, its reverse reaction of ethyl dissociation and the final hydrogen addition step. The lower barriers for hydrogen addition are offset by lower barriers for the reverse reaction back to ethylene and hydrogen. The end result is that the overall apparent activation barrier over Pd(100) and Pd(111) are quite similar. There are hardly any measurable differences in the calculated turnover frequencies on these two surfaces.

Pd(111)

Pd(lO0)

..

,,

~-~'~.~

'

N

Osat at 100 K = 0.37 M L

~i'

'

Osat at 100 K = 0.33 M L

(Experimental Saturation is 0.37 ML) Figure 13

The Pd(100) and Pd(111) ethylene saturation coverages at low temperature UHV conditions.

This is shown in the Arrhenius plot shown in Fig. 14. This is consistent with the experimemal evidence which indicate little or no structure sensitivity for olefin hydrogenation.

,El ./~--- l~l

12

Pd(111)

Ea = 7.17 kcal/mol

,/k

Pd(lO0)

Ea = 6.38 kcal/mol

9

-2

0.0020

,

I

0.0025

,

I

0.0030

,

I

0.0035

,

I

0.0040

,

0.0045

1/T (K'I)

Figure 14

The effect of surface structure on the activation barriers and turnover frequencies for ethylene hydrogenation over Pd. The Pd(100) and Pd(lll) surfaces show nearly identical activtiy. The activation barriers for ethylene hydrogenation are 7.1 and 6.4 kcal/mol respectively.

38

IV. Summary and Conclusions Many of the issues that currently impede the development of robust reaction engineering models are those which target molecular level details. Our analytical and computational capabilities will continue to improve. We can therefore begin to develop molecular and even atomic level reaction engineering models that track the basic elementary surface processes and the intermolecular transformations that govern the catalytic surface chemistry. This will not only improve the depth of our reaction engineering models but should also nicely complement experimental catalyst design efforts. In this paper, we focused our attention on olefin hydrogenation and present just a small subset of what is currently possible in terms modeling and developing structure-property relationships for alloys and structure sensitivity. Herein we coupled first-principle quantum mechanical calculations with kinetic Monte Carlo simulation in order to follow the spatiotemporal changes in the surface adlayer and its effect on the measured catalytic turnover frequencies. The atomic surface structure was explicitly tracked thus providing the ability to examine the effects of the local reaction environment on the intrinsic surface kinetics. Ethylene hydrogenation is controlled by the reactivity of weakly bound ~ and dicy ethylene species. Lateral repulsive interactions that exist between neighboring ethylene and ethylene and hydrogen surface species weaken the metal-adsorbate bond strengths and lower the barriers for hydrogenation. The n-bound intermediate, for example, which is present on the surface at coverages of less than 4% is highly reactive. Although the barrier for the first hydrogenation step is the highest, the reverse reaction.of ethyl dissociation to ethylene and hydrogen can significantly impact the rate by sending the reactive ethyl intermediate back to ethylene and hydrogen. Alloying the surface with gold shuts down the conversion of ethylene to ethylidyne and surface carbon by simple geometric effects. While gold also decreases the number active sites, it has little apparent effect on the activity of the palladium sites. This is due to a balance whereby gold decreases the surface coverage of hydrogen, it also decreases the binding energies for surface hydrogen and ethylene. These two factors counter one another, and thus maintain a nearly constant activity on a per palladium basis. Ethylene hydrogenation appears to be relatively structure insensitive. The (100) surface has an increase in the surface coverage of about 10% over the (111) surface. This acts to lower the barriers for both the first and second hydrogen addition steps. The reverse path of ethyl reacting back to form ethylene is also increased, thereby countering some of the increased activity. The apparent activation barriers on the (111) and (100) surfaces are 7.1 and 6.5 kcal/mol respectively. There is also little change in the turnover frequency. We have focused solely on chemistry issues and improved kinetic models. The fluid mechanics and heat and mass transfer will also be quite important to assess.

Acknowledgments We would like to thank Dow Chemical Company, DuPont Chemical Company, and the National Science Foundation for the financial support of this work.

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