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Rate-determining step or rate-determining configuration? The Deacon reaction over RuO2(110) studied by DFT-based KMC simulations Franziska Hess, and Herbert Over ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.6b02575 • Publication Date (Web): 16 Nov 2016 Downloaded from http://pubs.acs.org on November 16, 2016
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Rate-determining step or rate-determining configuration? The Deacon reaction over RuO2(110) studied by DFT-based KMC simulations Franziska Hessa and Herbert Overa* a
Dept. of Physical Chemistry, Justus Liebig University, Heinrich-Buff-Ring 17, D-35392 Gießen,
Germany *Corresponding author, Tel: +49 461 / 99-34550, E-mail address:
[email protected] Abstract Ab-initio kinetic Monte Carlo (KMC) is successfully applied to simulate the experimentally observed promoting effect of O2 on the HCl oxidation reaction (Deacon process) catalyzed by RuO2(110). Density functional theory (DFT) calculations provide besides the adsorption energies of reaction intermediates and activation energies, also interaction energies between the adsorbates within the cluster expansion approach. KMC simulations with this extended set of energy parameters were analyzed using the concept of “degree of rate control”. Contrary to previous propositions, our simulations indicate that neither the dissociative O2 adsorption (the sterically hindered first reaction step) nor the associative desorption of chlorine (the step with the highest activation energy) are ratedetermining under typical Deacon conditions. Instead, the hydrogen transfer in the water formation determines the rate of the overall reaction. These hydrogen transfer processes are not highly activated, but turn out to be strongly configuration-controlled.
Keywords: Deacon process, HCl oxidation, RuO2, degree of rate control, rate-determining step, Kinetic Monte Carlo simulations, cluster expansion, configuration
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1. Introduction Less than 20 years ago Sumitomo Chemical [1, 2] developed an efficient and stable Deacontype process on the basis of RuO2-coated rutile-TiO2 catalysts. The heterogeneously catalyzed HCl oxidation reaction (so-called Deacon process) over RuO2 based catalysts is a reaction to recover Cl2 from HCl waste omnipresent in industrial processes:
1 2HCl(g)+ O 2 (g) 2
Cl2 (g)+H 2 O(g);
∆ r H 0 =-59kJ/mol
With the Sumitomo-Deacon process chlorine can be recycled from HCl with low energy cost compared to electrolysis and high conversion yield of up to 95 %. [2] The high equilibrium conversion compared to the traditional copper-based Deacon process is the result of a low reaction temperature of 573 K which is determined by the high catalytic activity of the active component RuO2. [2] Besides high activity, the exceptional stability makes RuO2/TiO2 such a versatile catalyst material under the harsh reaction conditions encountered in the Deacon process. It has been shown that the RuO2(110) surface is a proper model system for gaining a molecular-level understanding of the Sumitomo-Deacon process [3]. RuO2 dispersed on rutile TiO2 has been demonstrated in a transmission electron microscopy (TEM) study to preferentially expose the (110) orientation [4], making this surface the model of choice for surface science studies. Mechanistic studies of the HCl oxidation over RuO2(110) and chlorinated RuO2(100) were performed using density functional theory (DFT) calculations [5-10] and high resolution core level shift spectroscopy (HRCLS) experiments [11]. The HRCLS experiments clearly identified the reaction intermediates on the catalyst’s surface, while DFT calculations provided the corresponding energies of adsorption and desorption including the activation barriers of surface processes. From the DFT calculations it can be inferred that the reaction step with the highest activation barrier (228 kJ/mol) is the recombination of two neighboring adsorbed Cl atoms to form the desired product Cl2. Besides this energy-control in the catalyzed reaction, the arrangement of intermediates controls whether the reacting species can access one another on a quasi one-dimensional catalyst such as RuO2(110). [12-16] This interdependence of configuration- and energy-control is all the more important as a pronounced compensation effect has been reported for the HCl oxidation over RuO2based catalysts. [7] The surface coverage terms give rise to compensation between the apparent activation energy and the frequency factor in the Arrhenius equation. So far microkinetic modeling has been restricted to apply the mean field approach [8, 17] which is not able to account properly for the configurational control of the HCl oxidation reaction. Rather kinetic Monte Carlo Simulations are called for. The Deacon reaction over RuO2 is inhibited by both products Cl2 and H2O. [7] The maximum activity for the HCl oxidation over polycrystalline RuO2 has been found for 620 K and atmospheric pressures, while the reaction starts already around 500 K. [9] Pump-probe experiments of O2 and HCl in a TAP (temporal analysis of products) reactor verified a strong dependence of the net Cl2 -2ACS Paragon Plus Environment
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production on the Cl and O coverages on the RuO2 surface: the higher the Cl or O coverage the lower or higher the reaction rate, respectively. [17, 18] Kinetic studies of the HCl oxidation over RuO2 in a flow reactor disclosed a pronounced promoting effect of the reaction rate on the oxygen partial pressure in that the higher the O2/HCl feed ratio the higher is the HCl conversion [9]. Since the adsorption energy of adsorbed O is only 80100 kJ/mol (against ½ O2) [19], oxygen desorption takes place already at temperatures of 450 K under UHV conditions which is much lower than the reaction temperature of 620 K and therefore results presumably in a low surface O coverage. Even more important is the fact that the desorption temperature of adsorbed chlorine is by 200 K higher than that of oxygen [10]. Consequently, the RuO2(110) surface is considered to be overpopulated by adsorbed Cl under reaction conditions of 600700 K, thus blocking active Ru sites for the dissociative adsorption of oxygen molecules. Therefore, oxygen adsorption has been considered to be rate determining in the HCl oxidation reaction, although the elementary reaction step with the highest activation energy is the associative desorption of neighboring adsorbed chlorine atoms to form Cl2. [7, 10, 11, 17] It is therefore safe to say that, although the elementary steps of the HCl oxidation over RuO2 are known in transient experiments under well-defined reaction conditions, the microkinetics of the reaction in the steady state is only poorly understood. In the present paper we apply ab-initio based kinetic Monte Carlo (KMC) simulations including lateral interactions and all known elementary steps in the HCl oxidation reaction over RuO2(110). Because KMC takes into account the arrangement of the intermediates on the catalyst surface, specifically including each adspecies’ individual neighborhoods and site demands, both energy and configuration control can reliably be modeled. Applying the concept of “degree of rate control” as introduced by Campbell [20, 21] we show that oxygen adsorption is not rate controlling for typical Deacon reaction conditions. Rather, the hydrogen transfer between the various surface O species is governing the formation of H2O that is strictly coupled to the production of the desired product Cl2 under steady state conditions. 2. Computational Details 2.1. Elementary steps of the HCl oxidation over RuO2(110) The stoichiometric RuO2(110) surface exposes two kinds of coordinatively unsaturated sites: the one-fold undercoordinated Ru site (Rucus) and the bridging oxygen (Obr) which connects two Ru atoms with six-fold coordination (Figure 1a)). Removal of all Obr leaves these Ru atoms two-fold coordinatively unsaturated (Rubr). For the KMC simulations the surface geometry is simplified to the undercoordinated sites present on the reduced RuO2(110) surface (Rucus and Rubr). These sites are arranged in one-dimensional arrays along the [001] direction, resulting in a coarse-grained representation of the surface as depicted in Figure 1b). -3ACS Paragon Plus Environment
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Figure 1: a) Ball-and-stick model of the RuO2(110) surface (viewed from [001] direction). The rightmost array of sites shows the reduced RuO2(110) surface with Obr removed. b) Left: top view ([110] direction) of a). Right: coarse-grained representation of the lattice configuration. Red stripes on white denote Rucus arrays, purple stripes on grey denote Rubr sites. The undercoordinated sites are marked by black and white crosses. The mechanism of the HCl oxidation over RuO2(110) is decomposed into two catalytic cycles: the formation of Cl2 and the formation of H2O. [3, 10, 22] Since the products, H2O and Cl2, are formed in equal proportion, the two cycles are strictly interconnected. The formation of Cl2 proceeds via adsorption and dehydrogenation of two HCl molecules in the first step (Figure 2a)), which proceeds without activation barrier. [22] The HCl molecules are dehydrogenated by transferring H to the undercoordinated surface O-containing species, such as Obr, Oot, OHbr and OHot, thereby forming OHbr, OHot, H2Obr and H2Oot, respectively.
Figure 2: Reaction steps in the mechanism of HCl oxidation over RuO2(110): a) Cl2 is formed by successively dehydrogenating of two HCl molecules. The Clot can recombine to form Cl2 which desorbs. b) H2O can be formed either by recombination of OHbr and OHot (I) or by transferring H from HCl to OHot (II). OHot is mainly formed by hydrogen transfer from OHbr to Oot (I/II). c) The RuO2(110) catalyst surface can be partially chlorinated: first two hydrogen atoms are transferred to a single Obr, resulting in the formation and desorption of H2O. The vacancy is subsequently filled by Cl, thus forming of Clbr defects. -4ACS Paragon Plus Environment
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After dehydrogenation Cl binds on-top of the one-fold undercoordinated Rucus sites (Clot). A Cl2 molecule can be formed by associative desorption whenever two Clot molecules are situated on neighboring sites and the activation barrier for association can be overcome. The activation energies for all elementary steps are compiled in Section S 1.4. The formation of H2O is more complicated because there are many different possible sequences of elementary steps that lead to the H2O molecule. The elementary steps in the formation of H2O on RuO2(110) have been subject to several experimental surface science studies that investigated this reaction in the context of different oxidation reactions (H2 oxidation [23-27], HCl oxidation [10, 11], and NH3 oxidation [28, 29]). Quite naturally, the formation of H2O follows different mechanisms, depending on the hydrogen source. Experimental findings indicate that H2O formation proceeds primarily via Oot/OHot/H2Oot species on oxygen-rich RuO2(110) surfaces in the H2 oxidation due to more favorable energetics for the hydrogen transfer succeeding H2 dissociation. [27] For the NH3 oxidation, Obr has been demonstrated to be almost completely inactive in the formation of H2O. [28, 29] This experimental observation was rationalized by computational studies indicating that OHbr is metastable in the presence of NH2, [29, 30] thus making a dehydrogenation of NH3 by Obr extremely unfeasible, which made it possible to neglect OHbr as an intermediate in KMC simulations of the NH3 oxidation over RuO2(110). [13, 16] The dehydrogenation of HCl, however is fundamentally different from that of H2 and NH3 since the HCl molecule approaching the RuO2(110) surface is prone to dissociate in the presence of undercoordinated O species (Oot/br, OHot/br: to accept H) and Rucus sites (to accept Cl). [9, 22] This makes Obr and Oot equally reactive in the dehydrogenation of HCl if only activation energies are considered. Indeed, in surface science studies the dissociative adsorption of HCl and H2O formation were shown to be equally possible on stoichiometric and oxygen-rich RuO2(110) as well as O2predosed partially chlorinated RuO2(110) surfaces. [10, 22, 31] The availability of Oot and Obr are thus expected to be the decisive factor that controls the dehydrogenation of HCl and the H2O formation pathway. When the coverage of weakly-bound Oot is low (as is the case under typical Deacon reaction conditions), Obr is expected to act as the primary hydrogen acceptor in the dissociative dehydrogenation of HCl. In our KMC simulations all possible hydrogen transfer reactions between HCl, Obr/ot, OHbr/ot and H2Obr/ot are considered. The activation energies for these elementary steps are compiled in Table S 6 in the supporting material. Our simulations point out two main H2O formation pathways through which almost 100 % of the H2O molecules are formed (cf. Figure 2b)). In pathway I H2Oot is formed by recombination of OHbr and OHot. H2Oot subsequently desorbs. In the second pathway (II) a hydrogen atom is abstracted from an incoming HCl molecule by an OHot group, which directly results in the formation and desorption of H2Oot. OHot can be formed in various ways, such as the hydrogen transfer from OHbr to Oot and the dehydrogenation of HCl by Oot. Pathways I and II each account for -5ACS Paragon Plus Environment
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the production of roughly 40-60 % of the H2O molecules. The exact percentages depend on the p(HCl)/p(O2) ratio of the feed. In addition to these steps that lead to the formation of one of the products, the RuO2(110) surface can be partially chlorinated. [32, 33] Only the topmost Obr can be replaced by Clbr. The chlorination of RuO2 mainly proceeds by successive dehydrogenation of two HCl molecules by the same Obr, forming H2Obr (cf. Figure 2c)). The H2Obr can desorb, leaving a vacancy in the bridge row. The vacancy is filled by Clbr through hopping from the on-top to the bridge site. Although it is possible in non-equilibrium experiments under UHV conditions to reach bridge chlorination degrees as high as 76 %,[32] our simulations predict bridge chlorination degrees lower than 10 % under typical reaction conditions (573 K, p(HCl)/p(O2) ≈ 1).
2.2. Kinetic Monte Carlo modeling of the HCl oxidation An accurate and reasonably fast way to follow the time evolution of a system of chemically reacting molecules on the catalyst’s surface is provided by Kinetic Monte Carlo simulations (KMC) [34-38] which account for fluctuations, correlations and the spatial distribution of the reaction intermediates on the surface. In KMC simulations, the RuO2(110) surface is represented by a periodic lattice consisting of a two dimensional array of on-top sites (Rucus) and bridge sites (connecting two Rubr) (cf. Figure 1b)). These metal sites can either be vacant or accommodate the reactants/intermediates during the simulation, depending on the applied reaction conditions. In addition, our simulations feature directional hydrogen bonds formed by OH and H2O species. The hydrogen bonds are modeled by keeping track of the direction where a hydrogen bond is pointing during the simulation. OH species are modeled with one hydrogen bond, H2O with two hydrogen bonds. Hydrogen bonds can only point toward the four nearest neighbors. All species considered in the simulation can accept hydrogen bonds. The hydrogen bond energies are listed in Table S 5 in the supporting material. The KMC simulations presented here take explicitly into account the interaction between the molecules via a cluster expansion (cf. Section 2.4), the diffusion of the intermediates on the surface, adsorption/desorption of the reactants/intermediates including different site demands and the activation barriers for elementary reaction steps. Within the transition state theory, the kinetics of elementary steps are determined by the activation energy and the frequency factor (this approach is described in detail in Section S 2 of the supporting material). The activation barriers of elementary steps in the reverse direction result directly from the detailed balance constraint, ensuring the overall thermodynamic consistency in KMC simulations. The binding energies and the energy barriers are exclusively determined from density functional theory (DFT) studies. The interaction between the intermediates is modeled by a cluster expansion including pairwise and three-body interactions and hydrogen bonds. The adsorption processes are treated within the kinetic gas theory, assuming a sticking coefficient of unity. -6ACS Paragon Plus Environment
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In general, KMC simulations provide atomic scale information, most notably about i) the number of turnovers per active site and second; ii) the spatial distribution of reactants on the surface at a particular time; and iii) the number and kind of elementary recombination steps contributing to the overall reaction rate. The rate-determining step can be inferred by numerically computing the degree of rate control XDRC as described in Section 2.5.
2.3. Density Functional Theory computations The Density Functional Theory (DFT) calculations were conducted using the PBEfunctional [39] of the Generalized Gradient Approximation (GGA) family. The calculations were performed using the Vienna ab-initio Simulation Package (VASP), version 5.3.5. [40, 41] The RuO2(110) surface is described in a symmetric slab model with five oxide trilayers separated by 25 Å of vacuum. All oxide layers were relaxed during the geometry optimization. The plane-wave cut-off energy was converged at 500 eV with 6×12×1 k-points in the (1×1) super cells. For larger super cells the number of k-points was adapted to keep the k-point density in reciprocal space constant. This approach ensures that the adsorption energies are converged within 0.2 meV, and total energies are converged within 14 meV per atom. Transition states were calculated using our own implementation of the Growing String Method. [42, 43] Similar to the frequently applied Nudged Elastic Band (NEB) method the minimum energy path (MEP) is approximated using a series of images which are relaxed perpendicular to the MEP. Both methods give the same results, [42] however we prefer the Growing String Method because it saves computational time compared to NEB. [42]
2.4. Cluster expansion approach The parameter sets for KMC simulations contain configuration-dependent adsorption energies, activation energies and diffusion barriers. All the parameters employed in the simulations are presented in the supporting material in tabulated form (Sections S 1.1 through S 1.3). The surface energy Esurf,C for configuration C is expressed by a cluster expansion ∞
Esurf ,C = ∑ ci ,cε i i =1
Eq. 1
,
where i denotes the interaction cluster, ci,c denotes the number of occurrences of the cluster i in the configuration c, and εi the energy of cluster i. This form of the cluster expansion (taking an infinite number of interaction parameters) is exact, which means that the surface energy of any configuration can be described accurately by such a sum of interaction energies, and the interaction energies can be determined unambiguously. The εi encompass all kinds of interactions of adsorbates with the surface and other adsorbates, e.g., the adsorption energy at infinitely low coverage, n-tupel interactions and
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hydrogen bonds. For practical application, it is necessary to restrict the sum to a finite number of terms: Esurf ,C ≈
n par
∑ ci ,C ε i .
Eq. 2
i =1
The number and kind of parameters are chosen such that both the error and number of parameters are minimized. The necessary number of parameters scales with the number of different species on the surface and the distance within which the interactions are to be considered in the simulation. Lateral interactions affect also the activation energies of elementary steps because they change the reaction energies. This is modeled by a simple Brønstedt-Evans-Polanyi (BEP) relationship [44, 45] for the activation energy of step i under the influence of lateral interactions EA,i: E A,i = E A,0,i + α∆Er
Eq. 3
.
EA,0,i denotes the activation energy at zero coverage (as listed in Table S 6 in the supporting material),
∆Er equals the change of the reaction energy due to the lateral interactions and α describes the position of the transition state along the reaction coordinate ξ for the forward (exothermic) reaction. For the backward (endothermic) reaction the transition state is located at the position (1-α), i.e., 0 ≤ ξ ≤ 1. Our simulations assume α = 0.5, which has been shown to be a good choice for surface reactions by experiment-based KMC simulations [14] and DFT calculations. [46]
2.5. Rate determining step analysis The rate-determining step (RDS) is defined as the step in the mechanism on which the overall reaction rate critically depends. A universally applicable concept to measure the kinetic influence of one reaction step on the total reaction rate is the degree of rate control XDRC,i (DRC) introduced by Campbell. XDRC,i measures how strongly the rate constant ki of an elementary step i influences the overall rate r of the reaction [20, 21] and is defined as: X DRC ,i =
ki r
∂r ∂ki K i , k j ≠i ,
Eq. 4
where Ki is the equilibrium constant for step i, and kj (j ≠ i) denotes all other rate constants. The partial derivative of the rate with respect to ki given in Eq. 5 requires keeping the equilibrium constant Ki of step i unchanged, as well as all other rate constants kj. XDRC,i is evaluated numerically by changing the rate constant ki (but adjusting the rate constant of the corresponding reverse reaction to keep the equilibrium constant Ki fixed) by a small amount and re-executing the simulation, thus determining the total reaction rate r’i:
X DRC ,i
k = i r
r 'i −1 ∂r ki (r 'i − r ) ≈ = r . ∂ki K i , k j ≠i r (k 'i − ki ) k 'i − 1 ki
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Eq. 5
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The change in ki must be small enough, so that the response of r is linear, but large enough to make the change measurable over the statistical noise in the KMC simulation. To be more precise, the degree of rate control is the limit of XDRC,i as k’i/ki approaches 1 (i.e., the change becomes infinitesimally small). However, since we face the problem of noise in KMC simulations, the rate constants are changed by a relatively large magnitude (k’i/ki = 2), thus giving an approximation of XDRC,i. To further reduce noise in the calculations, the XDRC,i were averaged over three simulation runs. We have found our calculated DRC to be stable with respect to the rate constant variation up to k’i/ki ≈ 5. This corresponds to a variation of the activation barriers by ±0.08 eV at 573 K: XDRC,i can assume values between -1 and 1. Positive values indicate a promotional effect of the
elementary step, i.e., an increase of the rate constant increases the overall rate of product formation. Negative values indicate that the elementary step inhibits the reaction, leading to a decrease of the overall rate when the rate constant is increased. When XDRC,i is zero, changing the rate constant has no measurable effect on the total reaction rate. Since
∑ X DRC ,i = 1 , [21]
Eq. 6
i
the degree of rate control indicates how the rate control is distributed over the elementary steps. Only when one of the elementary steps has an XDRC,i that is significantly higher than all the rest, this step can be considered as rate-determining. When several steps have similar (highest) values of XDRC,i, the rate control is mixed. If XDRC,i is 1, only step i determines the rate, and this step is called the rate-limiting step. The concept of rate control is in principle applicable to all numerical microkinetic models, including KMC models as was demonstrated by Meskine et al. [47]. For the present simulation model, however, this approach imposes a problem because there is no unique rate constant for each elementary step: the rate constants themselves depend on the lattice configuration due to the lateral interactions which affect the activation energies. Therefore, the actual change in the rate constant of an elementary step upon changing the activation energy or the pre-exponential factor can neither be predicted nor measured easily during the simulation. This means that k’i - ki in Eq. 5 is not welldefined. However, the method can be used as an approximation provided that the distribution of intermediates on the surface does not change. In practice, this can be accomplished by running the simulation to the steady state with the original rate constants, then conducting several short simulation runs starting from the steady state with the varied rate constants and finally averaging over all runs. This approach ascertains that the distribution of reactants does not equilibrate, resulting in little or no change of the reactant distribution.
3. Results and discussion 3.1. Rate-determining step under oxidizing conditions
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The HCl oxidation was simulated at T = 573 K, p(HCl) = 250 mbar, p(Cl2) = p(H2O) = 4 mbar and variable p(O2) between 50 mbar and 1000 mbar. A plot of the TOF as a function of p(O2) is given in Figure 3a) (blue curve). The TOF increases with p(O2) but saturates around p(O2) = 400 mbar. The reaction order in O2, as determined from the slope of the log-log plot of TOF versus p(O2), is 0.18 between 50 mbar and 400 mbar and decreases to zero beyond 400 mbar. Increasing the product partial pressures to 60 mbar lowers the total TOF, but raises the reaction order to 0.39 (cf. Figure 3b), orange curve).
Figure 3: a) TOF as a function of p(O2) for T = 573 K, p(HCl) = 250 mbar for different product partial pressures. Blue curve: p(H2O) = p(Cl2) = 4 mbar, orange curve: p(H2O) = p(Cl2) = 60 mbar; b) log-log plot of the same data. Reaction orders are given by the slope of the curve as indicated in the figure; c) and d) Simulation snapshots at p(O2) = 50 mbar and p(O2) = 800 mbar for p(H2O) = p(Cl2) = 4 mbar. From the KMC simulations further information about the surface state of the catalyst can be extracted by examining simulation snapshots. Figure 3 c) and d) show configurations at p(O2) = 50 mbar and 800 mbar. A striking feature of both snapshots is the low bridge chlorination
degree of 1-3 %, which is considerably lower than the maximum chlorination degree obtained in UHV -10ACS Paragon Plus Environment
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experiments (76 %). Most of the bridging sites are occupied by Obr, some of which are hydrogenated. These OHbr groups are formed upon dehydrogenation of HCl and persist on the surface over extended periods of time. Most of the Rucus sites are occupied by Clot. Due to the strong lateral repulsion between neighboring Clot, however, some Rucus sites remain vacant or are occupied by Oot. Already at near-stoichiometric conditions (Figure 3b)) Oot is frequently encountered on the RuO2(110) surface, suggesting that the adsorption of Oot may not be the bottleneck of the HCl oxidation reaction. Oot was found to displace Clot at p(O2) ≥ 400 mbar, resulting in the reduction of number of Clot-Clot pairs capable of recombining to Cl2. This causes the observed saturation of the TOF around 400 mbar (cf. Figure 3a)), followed by a slight decline at p(O2) ≈ 5000 mbar (not shown) .
Figure 4: Degree of rate control (XDRC) for significant elementary steps in the HCl oxidation over RuO2(110) under oxidizing conditions (T = 573 K, p(HCl) = 250 mbar, p(Cl2) = p(H2O) = 4 mbar). The degree of rate control (XDRC) was computed numerically for the formation rates of H2O and Cl2 as described in Section 2.5 from the simulation data presented in Figure 3a) (blue curve). It does not matter if the Cl2 or H2O production or O2 or HCl consumption rates are used for the calculation of the DRC because these rates are coupled via their stoichiometric coefficients in the steady state (resulting in equal degrees of rate control for H2O and Cl2 formation). The XDRC for the most significant steps are plotted as a function of p(O2) in Figure 4. Under the given conditions, we find that the two elementary steps with the highest degrees of rate control (the OHbr + Oot ⇌ Obr + OHot reaction and (ad-/de-)sorption of HCl) are almost equally rate-determining, indicating mixed rate control. Before discussing the details of these elementary steps (Sections 3.1.1 and 3.1.2), we will
provide first an overview over the observed trends. The step with the highest degree of rate control under oxidizing conditions (50 mbar ≤ p(O2) ≤ 1000 mbar) is the hydrogen transfer from OHbr to Oot (OHbr + Oot ⇌ Obr + OHot), i.e., the formation of OHot as indicated in paths I and II in Figure 2b). This does not necessarily imply that OHot is exclusively formed by this elementary step. It only indicates that increasing the rate constant raises the net reaction rate. -11ACS Paragon Plus Environment
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For the other steps plotted in Figure 4, XDRC strongly depends on the gas feed composition. Under near-stoichiometric conditions (p(O2) ≈ 50 mbar to 100 mbar) the step with the second highest degree of rate control is adsorption and desorption of Cl2, i.e., the removal of the product, which is strongly adsorbed to the catalyst surface and must desorb in order to free active sites on the catalyst. Adsorption and desorption are considered simultaneously because the definition of Campbell’s degree of rate control requires the equilibrium constant of an elementary step to remain constant. The surprisingly low degree of rate control obtained for Cl2 (ad-/de)sorption is caused by readsorption of the product from the gas phase, which allows the backward reaction (Cl2 depletion) to occur. Changing the rate constant of Cl2 adsorption by the same magnitude as the rate constant of Cl2 desorption thus increases readsorption as well as product desorption, resulting in the low degree of rate control observed here. Upon increasing p(O2), Clot is partially displaced by Oot so that the desorption of Cl2 loses significance in terms of rate control. Instead, the adsorption of HCl becomes the second most important elementary step. Its degree of rate control is almost as high as that of the OHbr + Oot ⇌ Obr + OHot reaction. All the other elementary steps, including the (ad-/de-)sorption of O2, are of minor importance over the whole range of p(O2), indicated by their low values of XDRC. From this overview of the RDS analysis we can preliminarily conclude that the overall reaction rate is controlled by the OHbr + Oot ⇌ Obr + OHot reaction and the (ad-/de-)sorption of HCl for p(O2)>100mbar. As will be explained in more detail in the following subsections, these two
elementary steps are representative for the two pathways for H2O formation displayed in Figure 2b). Paths I and II each account for approximately 50 % of the H2O molecules formed in the steady state. This is also consistent with the almost identical degrees of rate control for the OHbr + Oot ⇌ Obr + OHot reaction and the HCl (ad-/de-)sorption obtained in the RDS analysis. As H2O and Cl2 are produced in equal proportion in the steady state, their formation rates must be equal. We thus find that the overall reaction (2 HCl + ½ O2 ⇌ Cl2 + H2O) is limited by the formation of the side product H2O, rather than the main product Cl2.
3.1.1. The OHbr + Oot ⇌ Obr + OHot reaction Under oxidizing conditions, the reaction is thus controlled by only two elementary steps, the OHbr + Oot ⇌ Obr + OHot reaction and the (ad-/de-)sorption of HCl. Inspection of the simulation snapshots (Figure 3b)) and averaged coverages reveals that OHot is virtually not present on the surface in the steady state. However, the product H2O is exclusively formed from OHot as elucidated from counting reaction events in the KMC simulations. This allows us to identify OHot as a short-lived and extremely reactive intermediate required for the formation and subsequent desorption of H2Oot, thus releasing the byproduct H2O (reaction pathways I and II in Figure 2b)). Counting the events in KMC -12ACS Paragon Plus Environment
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simulations reveals that the reactive OHot species are formed almost exclusively by the OHbr + Oot ⇌ Obr + OHot reaction. In configurations that typically occur on the surface this step has a rather low activation energy of 0.38 eV for the forward and 0.35 eV for the backward reaction. Due to the rather low activation energies this step is reversible. With the forward and backward reaction rates being six times as high as the net reaction rate, the equilibrium between OHbr + Oot and Obr + OHot is hardly perturbed by the successive reaction steps. The reaction can thus be considered as equilibrated and the ratio of OHot/OHbr is mainly governed by the availability of Oot on the surface and the equilibrium constant of the OHbr + Oot ⇌ Obr + OHot reaction. However, due to the unfavorable (endothermic) reaction energetics OHbr is more favorable compared to OHot, resulting in considerably higher coverage of inactive OHbr compared to OHot, even if Oot is abundant on the surface. Even so, it is unexpected to find such a high degree of rate control for a quasi-equilibrated reaction step. This finding can be rationalized by considering OHot in active and non-active configurations. Due to the short life time of OHot, H2Oot can be formed only if it is present in a favorable configuration that would enable the formation of H2Oot in a fast successive reaction step. Considering the H2O reaction pathways I and II in Figure 2b), we can identify two active configurations which allow for the formation of H2Oot: OHot + OHbr and OHot + *ot (free cus site), which are displayed again for clarity in Figure 5. Comparing the rate constants for the associated elementary steps in such active configurations (Figure 5) we find that the rate of hydrogen transfer from OHbr to Oot is lower than the rate of the successive OHbr + OHot recombination step in pathway I, but higher than the rate of HCl adsorption in pathway II. As indicated by the arrows for forward and backward reaction, the OHbr + Oot ⇌ Obr + OHot can be assumed as equilibrated only in pathway II, where the hydrogen transfer from OHbr to Oot constitutes the fast step, being two orders of magnitude faster than the successive HCl adsorption (cf. Section 3.1.2). In path I, on the other hand, we find that the rate of the successive OHbr + OHot recombination is faster than the OHbr + Oot ⇌ Obr + OHot reaction by two orders of magnitude. The hydrogen transfer from OHbr to Oot thus constitutes the slow step in pathway I. Consistently with this observation we find a degree of rate control close to zero for the OHbr + OHot recombination in our RDS analysis. We thus conclude that the hydrogen transfer from OHbr to Oot is rate determining only in H2O formation pathway I, where the OHbr + Oot ⇌ Obr + OHot reaction constitutes the slow step in the H2Oot formation. As a consequence, increasing the rate constant of the OHbr + Oot ⇌ Obr + OHot reaction accelerates the rate of H2Oot formation, resulting in the observed high degree of rate control. Since the H2O and Cl2 formation rates are equal in the steady state, accelerating the H2O formation also increases the rate of Cl2 formation. -13ACS Paragon Plus Environment
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Figure 5: Comparison of rate constants at 573 K and p(HCl)= 250 mbar in the two mechanisms of H2O formation (pathways I and II, as indicated in Figure 2b)). The activation energies assumed here are representative for typical configurations that occur during the simulation. Path I: EA,I,1 = 0.38 eV, EA,I,2 = 0.17 eV, EA,-2 = 0.23 eV. Path II: EA,II,1 = 0.38 eV, EA,II,-1 = 0.35 eV, EA,I,2 = 0 eV. The rates are calculated according to Eq. S 2 for pure H transfer reactions and according to Eq. S 3 for dissociative adsorption of HCl. 3.1.2. Adsorption and desorption of HCl The question why HCl (ad-/de-)sorption has such a high degree of rate control can be rationalized in a similar fashion. Counting reaction events in the simulation reveals that only one HCl molecule in 102-103 that adsorb onto the catalyst surface is actually converted to Cl2. All other HCl molecules desorb again, which means that the rates of adsorption and desorption of HCl are higher than the net reaction rate by 2-3 orders of magnitude. This step can therefore be considered as quasiequilibrated, thus behaving in a similar manner as the OHbr + Oot ⇌ Obr + OHot reaction described in Section 3.1.1. Again a high degree of rate control is observed, despite being quasi-equilibrated (as concluded from counting reaction events). It should be noted that, although HCl (ad-/de-)sorption is treated as a unique step by the RDS analysis, it actually comprises several different elementary steps: (1) HCl + Obr ⇌ Clot + OHbr (2) HCl + Oot ⇌ Clot + OHot (3) HCl + OHbr ⇌ Clot + H2Obr (4) HCl + OHot ⇌ Clot + H2Oot. Among these four elementary steps, the first three are indeed equilibrated. The fourth, however, is strongly out-of-equilibrium with the forward reaction being only 1.02 times as fast as the net reaction. The elementary reaction step (4) accounts for 40-60 % of the H2O molecules formed in steady state; the remaining H2O molecules are formed through the OHbr + OHot recombination, cf. Section 3.1.1. Step (4) is the last step in the H2O formation pathway II (cf. Figure 2b) and Figure 5). Comparing the rate constant of this step with the preceding reaction step in pathway II (OHbr + Oot ⇌ Obr + OHot ), we find that the rate constant of HCl adsorption is by two orders of magnitude lower than the rate of the hydrogen transfer from OHbr to Oot (Figure 5). HCl adsorption thus constitutes the slow step in H2O formation pathway II. As a consequence, a high degree of rate control is observed for HCl adsorption, although (ad-/de-)sorption of HCl appears to be equilibrated when simply counting reaction events. -14ACS Paragon Plus Environment
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3.2. Influence of the O2 dissociation barrier on the dissociative sticking coefficient of O2 In the DRC analysis in Section 3.1 the rate constants of elementary steps are varied only by a factor of 2. Due to the small magnitude of change it is possible to miss influential elementary steps if their rates in the model deviate significantly from the true values. In order to unambiguously rule out O2 adsorption as the rate determining step, we further assess our choice of sticking coefficient (S = 1). It has been considered in the literature whether or not the dissociation of O2 is associated with an activation barrier. UHV experiments indicate that the initial (i.e., zero-coverage) sticking coefficient of O2 is 0.7 at 300 K [48], but this finding may not be easily extrapolated to 573 K. Theoretical investigations suggest that the O2 dissociative adsorption proceeds via a precursormediated multi-step mechanism, yielding a temperature-dependent sticking coefficient. [49, 50] Despite describing the O2 dissociative adsorption by the same mechanism and applying similar methods, the computational studies of Ref. [49] and Ref. [50] came to different conclusions concerning the barrier height for O2 dissociation and thus the effect activated dissociative adsorption of O2 under actual reaction conditions. This is further discussed in Section S 2 in the supporting material.
Figure 6: Elementary steps for the dissociative adsorption of O2 with schematic depictions of the intermediate and transition states. Energies of intermediate states and transition states are given in black and red, respectively. Transition states are placed along the reaction coordinate ξ to reflect the relative position of the transition state between the minima as obtained in the transition state computations. The detailed energy diagrams for the transition state calculations with relative values of ξ are shown in Figure S 4 in the supporting material. The dissociative adsorption of O2 on RuO2(110) was computationally found to proceed in three steps (cf. Figure 6). First, O2 adsorbs terminally on a Rucus site (superoxo species) without activation energy: *cus + O2 → (O2)ot
∆E = -0.770 eV
EA = 0 eV
The superoxo species was first detected experimentally in a TDS study by Kim et al.. [19] In the second step the O2 molecule rotates around the Ru-O bond and tilts downward until it reaches a parallel alignment to the surface, forming a second Ru-O bond with a neighboring Rucus (peroxo state): -15ACS Paragon Plus Environment
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(TS1) → (Oot)2 (O2)ot + *cus
∆E = -0.364 eV
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EA = 0.043 eV
This step was found to have a negligibly small activation energy (< 50 meV). [49, 50] Due to the low activation energy for the transition between superoxo and peroxo states, the superoxo species can only be detected on the surface in TDS experiments if isolated vacancies are present on the surface, which sterically prevents dissociation of O2. [49] Considering the low activation barrier for this step it is questionable if the superoxo state should be treated as a separate minimum at finite temperatures. Our transition state calculation shows that TS1 is located very close to the initial state on the reaction coordinate (cf. Figure S 4 and Figure 6). In the transition state the superoxo group is rotated by 14° around the Ru-O bond. The formation of the second Ru-O bond proceeds without additional barrier, suggesting that an O2 molecule will only adapt the superoxo geometry if it approaches the surface in perpendicular fashion (±14°). If it approaches side-on it should directly enter the minimum of the peroxo state. Considering the small tolerance angle of ±14°, we consider it far more likely that O2 will adsorb as the peroxo species, skipping the first minimum. In the third (second if the superoxo state is not considered) step the O-O bond dissociates, thus forming two separate Oot bound to neighboring Rucus: 2) (Oot)2 (TS → 2 Oot
∆E = -0.771 eV
EA = 0.219 eV
In order to quantify the influence of the dissociation barrier on the rate of dissociative O2 adsorption we performed microkinetic simulations of the two-step mechanism for associative adsorption of O2, neglecting the superoxo state (see Section S 2 for computational details on these simulations).
Figure 7: Sticking coefficient given by the quotient r2-step(T)/r1-step(T) as a function of temperature for a dissociation barrier of 0.219 eV. By defining that S = r2-step(T)/r1-step(T) (with r1-step and r2-step given by Eq. S 12 and Eq. S 9, respectively), effective sticking coefficients can be computed as a function of temperature. The resulting sticking coefficients for our dissociation barrier of 0.219 eV are plotted in Figure 7. At room temperature, an effective sticking coefficient of 0.58 is obtained which agrees with the experimentally obtained value of 0.7 [48] within a small error of ±0.12 or ±20 K (i.e., a sticking coefficient of 0.7 is obtained at 320 K). In the studied temperature range (300 to 700 K) the deviation of k2-step(T) -16ACS Paragon Plus Environment
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compared to k1-step(T) is a factor of two at most, i.e., S ≥ 0.5. A barrier of 0.57 eV as proposed by Pogodin et al. results in an effective sticking coefficient of 10-5-10-4 at room temperature, which strongly disagrees with experimental data. We conclude from the microkinetic simulations that the dissociation barrier of 0.219 eV obtained from our DFT calculations is consistent with available experimental data. At a reaction temperature of 573 K where our simulations were conducted a sticking coefficient of 0.95 is obtained, which barely deviates from 1, as assumed in the present KMC simulation model. In the whole temperature range relevant for the Deacon process (450 K to 600 K [3]) the sticking coefficient is expected to be greater than 0.9. Reducing the sticking coefficient to 0.9 in the KMC simulations has no significant impact on the reaction kinetics, consistent with the observed low degree of rate control of O2 (ad-/de-)sorption observed in Section 3.1.
3.3. Rate-determining step under reducing conditions Under reducing conditions (with 0 ≤ p(O2) ≤ 50 mbar, p(HCl) = 250 mbar, p(Cl2) = p(H2O) = 4 mbar, T = 573 K) the reaction follows quite different kinetics than under oxidizing conditions. Reducing conditions do not play a role in the practical application of the Deacon Process because complete conversion of HCl cannot be achieved due to shortage of O2 in the gas stream. The RDS analysis was conducted in the same way as discussed in Section 3.1 and the results are plotted in Figure 8. Under very O2-deficient conditions (p(O2) < 20 mbar) the RDS is O2 (ad-/de)sorption. This can be explained by the reduced Oot coverage on the catalyst surface owing to lack of O2 in the gas feed. Since every second Obr site is hydrogenated, the O2 molecules that adsorb on the surface are rapidly consumed by H2O formation. Counting the reaction events reveals that O2 (ad-/de)sorption is not equilibrated, in contrast to oxidizing conditions. Increasing the O2 adsorption rate thus enhances the total reaction rate. The second and third most rate determining steps have equal degrees of rate control over the whole range of conditions plotted in Figure 8. One of them is Cl2 (ad-/de-)sorption, indicating slight product inhibition and the other is the hydrogen transfer from OHbr to Oot, forming the reactive precursor for water production, OHot, as explained in detail in the Section 3.1.1. The diffusion of Clot along the Rucus rows is necessary for the recombination of Cl2 and has a minor degree of rate control over the whole reducing p(O2) range. The adsorption of HCl has negative degree of rate control at p(O2) ≤ 5 mbar, indicating competition for free sites between O2 and HCl. At p(O2) > 5 mbar the
degree of rate control of HCl adsorption is close to zero, indicating little influence of the HCl adsorption rate on the total reaction rate.
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Figure 8: Degree of rate control (XDRC) for significant elementary steps in the HCl oxidation over RuO2(110) under reducing conditions (T = 573 K, p(HCl) = 250 mbar, p(Cl2) = p(H2O) = 4 mbar). With increasing p(O2) the degree of rate control of O2 adsorption decreases, intersecting with the curve for Cl2 desorption and the OHbr + Oot ⇌ Obr + OHot reaction at p(O2) ≈ 35 mbar. At p(O2) > 35 mbar the OHbr + Oot ⇌ Obr + OHot reaction is the step with the highest degree of rate control, which it continues to be up to strongly oxidizing conditions (cf. Section 3.1). This means that even at stoichiometric conditions (p(O2) = 62.5 mbar) adsorption of O2 is not rate-determining. XDRC of the other elementary steps are largely independent of p(O2) except for the HCl adsorption that inhibits the reaction at p(O2) ≤ 5 mbar and becomes more promoting with increasing p(O2). 3.4. Comparison with experimental data Our KMC simulations are capable of reproducing the experimentally found positive reaction order in O2 (oxygen promoting effect). [9, 17] In good agreement with experimental findings, the reaction order in O2 was found to strongly depend on the measurement protocol. When no reaction product is added to the gas feed, a reaction order of 0.4 is obtained in the experiment. [17] However, this number was not considered as very reliable by the experimentalists as the observed enhancement of activity by increasing p(O2) is strongly influenced by the conversion inside the reactor and the actually achieved conversion depends on the p(O2)/p(HCl) ratio. A truly differential measurement of catalytic activity (i.e., at zero conversion) is not possible in a flow reactor. To reduce the influence of the conversion inside the reactor, 60 mbar of Cl2 and H2O were added to the gas stream. Under these conditions a reaction order in O2 of 1.0 was obtained in the experiment. [17] The same effect can be observed in KMC simulations, where the addition of 60 mbar Cl2 and H2O leads to a significant increase of the reaction order from 0.18 (with p(Cl2) = p(H2O) = 4 mbar) to 0.39 (cf. Figure 3a)). Our simulations, however, do not explicitly consider the conversion inside the reactor, mimicking rather a perfectly differential measurement at fixed p(Cl2) and p(H2O). -18ACS Paragon Plus Environment
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The comparison between experiment and theory is further complicated by the fact that with oxidizing educt composition at the reactor inlet the gas stream becomes even more oxidizing further downstream, thus overestimating the reaction order in O2. It is evident from these considerations that a perfectly differential simulation of the catalyst activity as presented here is not capable of quantitatively reproducing the reaction order found in the experiment. Given the strong dependency of the reaction order on the product partial pressures it is difficult to even estimate the magnitude of the error. In principle, obtaining a reaction order from simulations which is comparable to the experiment would require integrating the reaction rate over the length of the catalyst bed. This could be achieved by simulating the reaction at different conversion levels and then numerically solving the differential equation for the plug flow reactor model. This, however, is considered out of scope for the current article. Possibly the biggest source of error is the catalyst itself. A RuO2 catalyst supported on SnO2 was employed in the activity measurements by Teschner et al.. The SnO2 support was found to strongly influence the electronic properties of thin layers of RuO2 and the stability of intermediates adsorbed on the surfaces. [17] This was shown to impact the catalyst activity in a combined DFT/microkinetic study. In addition, the powder catalyst exposes other facets beside the (110) surface, while our model assumes a pure RuO2(110) single crystal surface. For the total activity of the RuO2(110) surface in the HCl oxidation data from batch reactor measurements over an oxidized Ru(0001) single crystal are available. [11] The catalyst activity was measured over 0-50 % conversion under stoichiometric conditions and an average turnover frequency (TOF) of 0.6 s-1 was obtained. We simulated the batch reaction under the same conditions (T = 660 K, p(HCl) = 2 mbar, p(O2) = 0.5 mbar, 0-40 % conversion) and obtained a time-averaged TOF of 8.9 s-1.
Our simulations overestimate the catalyst activity by a factor of 15, which we consider as satisfactory agreement considering that no empirical corrections were applied to our model. The experimental data themselves are subject to errors, too. For the computation of the number of active sites it was assumed that the Ru(0001) single crystal was entirely covered by RuO2(110), which is generally not the case; as the oxide forms domains on the crystal surface, areas where the metal is left bare are generally present after oxidation. Another source of error is the fact that the batch reactor experiments were not conducted under isothermal conditions. Only the sample was annealed to 660 K, while the gas phase was not, leaving the temperature of the gas phase and sample surface ill-defined. The KMC simulations underlying our batch reactor simulations were conducted at isothermal conditions with T = 660 K, which is another possible source of error here. In summary, our simulations are able to reproduce the observed promoting effect by O2 in the correct range of temperature and partial pressures and correctly account for the effect of product inhibition as illustrated by the increase of the reaction order in O2 upon raising the product partial pressures from 4 mbar to 60 mbar. -19ACS Paragon Plus Environment
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4. Summary and Conclusion O2 has found experimentally to exert a beneficial effect on the HCl oxidation reaction with a clear correlation between the oxygen adsorption energy and the activity [8, 9]. However, O2 adsorption needs not to be rate controlling, as suggested based on experimental data [7, 17], but rather the first step in a sequence of reaction steps to form water by dehydrating HCl. With ab-initio KMC simulations we have shown that the adsorption of O2 is not rate-determining under typical reaction conditions in the Deacon process over RuO2(110). Only under reducing conditions, O2 adsorption has the highest degree of rate control, i.e., O2 adsorption is the rate-determining step. In order to rule out errors in our model that arise from activated dissociation of O2, we have considered in detail the influence of the O2 dissociation barrier. We have shown by microkinetic simulations that the dissociation of O2 is hardly impeded by the small activation energy of 0.219 eV, at temperatures typical for the Deacon process (450 to 600 K). Sticking coefficients greater than 0.9 are obtained in this temperature range, giving no measurable change of the kinetics of the HCl oxidation compared to S = 1, consistent with the low degree of rate control for O2 adsorption determined by the DRC analysis. We found that the transfer of hydrogen from OHbr to Oot and the dehydrogenation of HCl by OHot to have the highest degrees of rate control under stoichiometric and oxidizing conditions. These two elementary steps are representative for the two H2O formation pathways through which almost 100 % of the H2O molecules are formed, as sketched in Figure 2 b). Since the Cl2 and H2O are strictly 1:1 coupled in the steady state, their production rates are identical. We thus find H2O formation, rather than O2 adsorption, to determine the rate of Cl2 production under stoichiometric and oxidizing reaction conditions. This finding is rather surprising, considering that the activation energies associated with hydrogen transfer reactions on RuO2(110) are typically lower than 0.5 eV due to the flexibility of the lattice and favorable distance between active sites that facilitate hydrogen transfer between adsorbed OH species. Indeed, straightforwardly counting reaction events during the simulation reveals that both the hydrogen transfer and the (ad-/de-)sorption of HCl are quasi-equilibrated in the steady state with the forward and backward reaction being up to 1000 times faster than the net HCl consumption. Upon closer inspection, however, it turns out that most of these reaction events lead to inactive configurations, i.e., configurations in which H2O is not formed due to lack of a suitable reaction partner in the direct neighborhood. For the OHbr + Oot ⇌ Obr + OHot reaction, only configurations where the short-lived OHot is situated next to an OHbr (path I) or to an empty cus site (path II) directly lead to the formation of H2O and can thus be considered as active configurations. Comparison of the rate constants of the elementary reaction steps in the two H2O formation paths reveals that the formation of OHot through the OHbr + Oot ⇌ Obr + OHot reaction is rate-determining only in path I, where the hydrogen transfer -20ACS Paragon Plus Environment
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from OHbr to Oot constitutes the slow step, but not in path II, where it represents the fast step. In path II, the slow step is the dehydrogenation of HCl by OHot, resulting in the observed high degree of rate control for HCl adsorption. We emphasize that from simply comparing the rate constants (or activation energies) of all elementary steps, it would be impossible to correctly predict that the OHbr + Oot ⇌ Obr + OHot reaction and the HCl (ad-/de-)sorption are rate-determining in the HCl oxidation because both steps have quite low activation energies compared to the step with the highest activation energy (associative desorption of Cl2). Explicit Degree of rate control (DRC) analysis by Campbell’s method [20, 21] is essential in order to prevent misinterpretation of simulation data: as the present example shows, both ratedetermining steps are quasi-equilibrated, suggesting low degrees of rate control. However, we find that the very specific configurational demands required by the formation of H2O are mainly responsible for the observed rate control because only a small fraction of reaction events actually lead to active configurations where H2O formation is possible. This emphasizes the necessity for Kinetic Monte Carlo simulations for the theoretical investigation for kinetics in heterogeneous catalysis, because the reaction kinetics can be extremely sensitive to the distribution of intermediates on the surface. The distribution is strongly influenced by specific lateral interactions, such as the repulsion between ClotClot pairs and hydrogen bonds that stabilize (or destabilize) specific arrangements of reactants. Proper consideration of such interactions is possible only in KMC simulations which are able to keep track of the specific neighborhood of the reaction intermediates on the surface. The specific neighborhood was shown to play a major role in the HCl oxidation over RuO2(110) through the occurrence of configurations which are either active (cf. Figure 5) or inactive in the formation of H2O. Simple microkinetic simulations based on the mean-field approach [8, 17] are not able to properly account for the configurational control in the present case because the mean-field approach assumes unlimited mixing of reactants on the surface. On the RuO2(110) surface, however, most reactants are confined to the Rucus rows, which practically disables mobility of the reactants on the surface due to the high coverage under reaction conditions. Communication between the Rucus rows is possible only via OHbr groups which allow hydrogen atoms to be passed between different rows, thus partially overcoming the one-dimensionality of the catalyst surface. This intimate interplay between reaction energetics, reactant distribution (given by the lateral interactions) and configurational control can only be properly captured by KMC simulations and is essential for simulating the microkinetics of the HCl oxidation reaction over RuO2(110). The present study thus demonstrates the power of atomicscale KMC simulations in rationalizing experimental observations and providing unprecedented fundamental insight into heterogeneously catalyzed reactions with complex site demands.
Supporting Information Cluster expansion parameters with statistical diagnostics -21ACS Paragon Plus Environment
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Elementary steps and activation energies considered in the simulations Formulas for computation of rate constants Description of microkinetic modeling of O2 adsorption Comparison of simulated O2 thermal desorption spectrum with experiment This material is available free of charge via the Internet at http://pubs.acs.org.
Acknowledgement JLU Gießen is acknowledged for a graduate stipend for Franziska Hess. This project was partly supported by the federal ministry of science and education (BMBF_Deacon: 033R018C). The authors thank the Hessian High Performance Computing Network (HKHLR) and the computing centers of the University Giessen and Technical University Darmstadt for providing computational time and support on the Skylla and Lichtenberg high performance clusters.
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