Effect of Surface Oxidation on Oxidative Propane Dehydrogenation over Chromia: An Ab Initio Multiscale Kinetic Study

An increasingly utilized way for the production of propene is propane dehydrogenation. The reaction presents an alternative to conventional processes based on petroleum resources. In this work, we investigate theoretically how Cr2O3 catalyzes this reaction in oxidative and reducing environments. Although previous studies showed that the reduced catalyst is selective for the non-oxidative dehydrogenation of propane, real operating conditions are oxidative. Herein, we use multiscale modeling to investigate the difference between the oxidized and reduced catalyst and their performance. The complete reaction pathway for propane dehydrogenation, including C–C cracking, formation of side products (propyne, ethane, ethylene, acetylene, and methane), and catalyst coking on oxidized and reduced surfaces of α-Cr2O3(0001), is calculated using density functional theory with the Hubbard correction. Parameters describing adsorption, desorption, and surface reactions are used in a kinetic Monte Carlo simulation, which employed industrially relevant conditions (700–900 K, pressures up to 2 bar, and varying oxidants: N2O, O2, and none). We observe that over the reduced surface, propene and hydrogen form with high selectivity. When oxidants are used, the surface is oxidized, which changes the reaction mechanism and kinetics. During a much faster reaction, H2O forms as a coproduct in a Mars–van Krevelen cycle. Additionally, CO2 is also formed, which represents waste and adversely affects the selectivity. It is shown that the oxidized surface is much more active but prone to the formation of CO2, while the reduced surface is less active but highly selective toward propene. Moreover, the effect of the oxidant used is investigated, showing that N2O is preferred to O2 due to higher selectivity and less catalyst coking. We show that there exists an optimum degree of surface oxidation, where the yield of propene is maximized. The coke, which forms during the reaction, can be burnt away as CO2 with oxygen.


■ INTRODUCTION
Short-chained olefins, such as propene (propylene) and butadiene, are important precursor chemicals in the production of plastics, synthetic rubbers, copolymers, epoxides, various organic acids, acrylonitrile, nylon, and so forth. They are predominantly extracted from higher hydrocarbons during steam cracking and fluid catalytic cracking. 1 Due to the increased demand and environmental concerns, alternative production routes are being developed, among which is dehydrogenation. 2−6 By utilizing propane as a feedstock, which represents a more prudent use than burning it as fuel, hydrogen is produced when the process is carried out nonoxidatively. 7,8 However, the high temperatures required due to the endothermicity of the reaction render it less economical. Alternatively, dehydrogenation can be performed with oxidants, such as air, oxygen, N 2 O, or CO 2 , releasing hydrogen as water in a strongly exothermic reaction.
Propane is a rather inert compound (a heat of formation of −104 kJ mol −1 ) with stable C−H bonds (bond-dissociation energy of 410−420 kJ mol −1 ), requiring high temperatures and pressures for activation. 9 For non-oxidative dehydrogenation to propene and hydrogen, the reaction enthalpy is +124 kJ mol −1 . For the oxidative dehydrogenation, the reaction enthalpy is −118, −200, or +166 kJ mol −1 when using O 2 , N 2 O, or CO 2 as oxidants, respectively. 10,11 In addition to water, N 2 and CO also form.
To steer the reaction toward propene and avoid extensive cracking (non-oxidative) or oxidation (oxidative), appropriate catalysts must be used. In addition to the experimentally 12−16 and theoretically well-researched alumina-supported Pt/Sn catalysts, which underpin the CATOFIN process and operate at 500−700°C and 2−4 bar, chromia-based catalysts are also used extensively. Rather than consisting of (semi-)noble metals, they are made of inexpensive source materials. The catalytic performance under optimum conditions (500−600°C , 1−2 bar) is comparable. Both processes suffer from persistent coking of the catalyst, which must be regenerated or changed often, negatively impacting the catalyst longevity and the process economics.
The use of chromia dates back to the 1930s, 17 while the first commercial technology was the Pacol process from 1968, using alumina-supported platinum catalysts. 1 Already in the 1970s, chromium oxide was used for ethylene polymerization. 18 Soon, the effectiveness of chromia-based catalysts for dehydrogenation had become apparent. Working on chromia-based catalysts, Suzuki and Kaneko already in 1977 proposed a macrokinetic model. 19 Chang et al. showed that doping with Pt improves the performance of α-Cr 2 O 3 (0001) and ZnO(101̅ 0). 20 Zhang et al. investigated the SBA-15-supported chromia. 21 Mentasty et al. showed that the amount of acidic sites of the alumina support strongly affects the catalytic activity. 22 Most importantly, Shee and Sayari showed that Cr(III) and Cr(VI) convert back and forth in mesoporous Cr 2 O 3 /Al 2 O 3 during the reaction. 23 Gascoń et al. performed transient kinetic modeling of propane dehydrogenation, which accounted for the coke formation as well. 24 Chin et al. modeled the reaction in an industrial moving bed reactor, 25 but neither accounted for elementary steps rather than lumped reactions. Nijhuis et al. investigated the catalyst surface with operando spectroscopic analysis and showed that small amounts of coking in fact improved the activity probably due to improved adsorption of propane. 26 Gaspar et al. showed that depending on the chromium contents, supports, and precursor compounds used, the ratio between the Cr 2+ , Cr 3+ , and Cr 6+ sites varies, which strongly affects the productivity of the catalyst: Cr 3+ sites are beneficial for dehydrogenation. 27 Purely first-principles theoretical descriptions of chromiabased catalysts for propane dehydrogenation remain scarce. In our previous studies, we have investigated the non-oxidative dehydrogenation of propane on the reduced α-Cr 2 O 3 (0001) surface using kinetic Monte Carlo (KMC) on DFT-obtained data 28 and butane dehydrogenation in an idealized plug flow reactor using DFT-fed microkinetic modeling. 29 In this work, we used DFT calculations to construct a thorough reaction pathway for propane dehydrogenation when oxidants are cofed on the reduced and oxidized surfaces of α-Cr 2 O 3 (0001). These are used as the two extrema of the realistic catalyst surface. Using extensive KMC modeling, we investigated the kinetic parameters for propane dehydrogenation on each of the surfaces (temperature and pressure dependence), the effect of varying oxidation state (modeled as a varying ratio between the surfaces), and the effect of the oxidant used (none, O 2 , N 2 O, or CO 2 ). We identified the rate-determining steps, the simplified reaction rate law descriptions, and the side products formed. Special emphasis is put on catalyst deactivation, which can manifest as extensive coking (formation of C* and other Ccontaining surface species), reduction of the catalyst surface, or (not-modeled) sintering and phase transitions.
We show that the oxidized and reduced surfaces behave radically different and how the oxidants influence the selectivity and activity. Although both surfaces bind saturated hydrocarbons weakly, double and triple bond-containing hydrocarbons are strongly adsorbed on the oxidized surface. As a consequence, the latter exhibit a much greater activity but poor selectivity as CO 2 is mostly produced. Similarly, using O 2 as a strong oxidant increases the activity and suppresses the selectivity in comparison to using N 2 O. Without the oxidant, the oxidized surface is eventually reduced. Using multiscale modeling, we demonstrate a Goldilocks effect. For optimum conversion of propane to propene, the surface should be partially oxidized. Lastly, we show how the catalyst activity decreases due to coking. Our model captures this as an accumulation of CH x * species, which eventually transform into C*. This is, to the best of our knowledge, the first multiscale study of an industrially relevant catalyst in realistic conditions for propane dehydrogenation. Moreover, since the transition between the oxidized and reduced sites is included, this is effectively a model where the catalyst changes during the reaction.
■ COMPUTATIONAL DETAILS Electronic Structure. Theoretical calculations of the electronic structure were performed with VASP 30−33 in the plane-wave approach. The simulation parameters chosen were consistent with our previous work 28,29 for comparability. A GGA functional by Perdew and Wang was used (PW91) 34 with the projector-augmented wave method. 35,36 To mitigate the self-interaction error on Cr when using GGA functionals, the DFT + U approach 37 was used with a Hubbard factor of D − J = 4 eV, 38,39 which had been proved to describe Cr 2 O 3 satisfactorily. 40,41 As Cr 2 O 3 is magnetic, spin-polarized calculations were performed with initial magnetic moments of 3.0 on chromium. The plane waves were expanded to the energy cut-off of 500 eV. The Grimme D3 correction was used to describe the dispersion interactions. 42 Geometry relaxations were performed with a force threshold of 0.03 eV/Å. For the identification of transition states, the dimer method 43−46 was used on rough initial approximations from the nudged elastic band method. 47 All located structures were confirmed with vibrational analysis (a displacement of 0.01 Å) to correspond to local minima (no imaginary frequencies) or saddles (precisely one imaginary frequency) and to obtain the zero-point energies.
Due to the size of the unit cell of Cr 2 O 3 , which was optimized to a 0 = 5.09 Å and c 0 = 13.77 Å, a 4 × 4 × 2 Monkhorst−Pack mesh of k points sufficed. The (0001) surface was modeled with 12 layers, of which the bottom six were immovable in their bulk positions. All calculations were performed on a × 3 3 supercell, where the Brillouin zone was sampled at a Γ point only due to its size (  =  a  3 8.99Å 0 ). There was 15 Å of vacuum between the slabs. The dipole correction was used because the slabs were asymmetrical. 48,49 Thermodynamics and Kinetics. The reaction mechanism consists of surface reactions (Langmuir−Hinshelwood), reactions on the surface involving gaseous reactants (Eley− Rideal), and adsorption/desorption equilibra, which were modeled within the transition state theory approximation. Among the adsorption reactions, we distinguish simple nonactivated adsorptions (for instance, hydrocarbons) and activated dissociative adsorptions (hydrogen, CO 2 , N 2 O, O 2 , etc.). The former is a purely kinetic event (eq 3), while the latter is an ER reaction (eq 2). The reaction rates for these types of reactions are calculated as where Q's stand for partition functions (vibrational from the harmonic approximation, translational, and rotational), T for temperature, E A for activation barriers, p for pressure, A for the effective area of the reaction site, and m for mass. Furthermore, k B denotes the Boltzmann constant and h the Planck constant. All the reactions are reversible: where ΔΔE lateral denotes the difference between the lateral interaction corrections (ΔE lateral = E lattice state − E infinite separation ) to the energy of the initial and final states (ΔE lateral final − ΔE lateral initial ). The reverse of the non-activated adsorption is treated as an ER-type reaction, with E A = ΔE = −E ads . The adsorption energy is intuitively defined as E ads = E slab+adsorbate − E adsorbate − E slab , where E slab+adsorbate stands for the energy of a relaxed slab with the adsorbate, E adsorbate is the energy of the gaseous adsorbate, and E slab is the energy of the empty slab. It is decomposed into the electronic interaction, E int (negative), and the distortion energies of the adsorbate, E dis , and surface, E surf,dis (both positive). It is evident that E int + E dis + E surf,dis = E ads .
The reaction energy, ΔE, is defined as the difference between the final and initial states (E final − E initial ), while for the activation barrier, E A , the transition state must be known (E TS − E initial ). All energies are zero-point energy-corrected.
Catalyst Model. We model the catalyst as the (0001) surface of Cr 2 O 3 with 12 layers. To prevent lateral interactions of adsorbates across the adjoining cells, a × 3 3 supercell is used. Wang and Smith 50 performed extensive first-principles simulations of this surface and constructed a phase diagram. They showed that five surface phases can exist between two extrema (segregated Cr atoms and condensed oxygen). From the lowest to the highest chemical potential of oxygen, chromium-terminated (A), ( 3) 2/9 ML chromylterminated (C), (1 × 1) 1/3 ML chromyl-terminated (D), and (1 × 1) 1/3 ML oxygen-terminated (E) surfaces can manifest. Essentially, these different terminations are congruent with different oxidation states of the chromium atoms at the surface. According to the full potential linearized augmented plane wave calculations on the GGA level of theory, Wang and Smith claim that the E surface is predominant at 850 K and 1 bar O 2 , which are typical operating conditions for propane dehydrogenation over Cr 2 O 3 (CATOFIN process).
Several experimental studies have shown that such descriptions of the surface are appropriate. Maurice et al. used scanning tunnelling microscopy to show that (1 × 1) differently terminated phases occur as predicted by theory within the error bar. 51 Rohr et al. used low-energy electron diffraction (LEED) and reported a (1 × 1) CrO terminated surface, while the reduced phase was discovered below 10 −16 atm oxygen, which is clearly out of the operating conditions for the reaction at hand. 52 Petrosyan et al. studied Cr 2 O 3 in solutions using joint DFT and also investigated the oxygenterminated surface. 53 In a more recent study, Kaspar et al. studied the surface structure of α-Cr 2 O 3 (0001) epitaxial thin films on alumina after activated oxygen exposure using XPS and X-ray photoelectron diffraction (XPD). XPD patterns were found to strongly suggest the Cr−Cr−O 3 termination. 54 Similarly, Lubbe and Moritz performed a LEED analysis on α-Cr 2 O 3 (0001) bulk single crystals and found that "for the chromia surface the results indicate that termination with a single Cr seems not to hold". 55 Bikondoa et al. used XRD to study the surface structure of α-Cr 2 O 3 (0001) and determined that already at an oxygen pressure of 10 −5 atm, the surface is terminated by chromyl species (−CrO). 56 Although studying a different facet (Cr 2 O 3 (101̅ 2)), York et al. also found the oxygen-termination to predominate. 57 However, the situation during the reaction, where oxidants (O 2 and N 2 O) and reducing species (hydrocarbons) are present, is more complicated. First, these conditions are close to a phase transition and a small increase in the temperature or decrease of the oxygen pressure would render the D surface more stable. Second, the accuracy of DFT calculations is limited in terms of chemical accuracy, meaning that surface diagrams can easily be shifted for 100−200 K and several factors for pressure. Third, catalysts are most active near phase transitions. Fourth, while oxygen is an oxidant, propane is a moderate reducing agent. Lastly, in this work, we study the reaction in both, oxidative and non-oxidative regimes, where O 2 (strong oxidant), N 2 O, and CO 2 (soft oxidant) of various concentrations or, alternatively, no oxidant are used. This would necessitate taking into account all five surface structures and their interconversion on-the-fly, which adds too many layers of complexity to a simple model.
Noting that the B, C, and D surfaces are essentially the E surface of different surface oxygen (in the form of chromyl) coverages, we construct a simplified model as an alternative. In our model, we use the A surface, which was already used in our previous studies, 28,29 and the E surface in varying fractions. The model has three types of active sites: chromium atoms on A (Cr red ), oxygen atoms on A (O red ), and oxygen atoms on E (O ox ). The E surface can lose the surface oxygen as O 2 or, more realistically, H 2 O, being converted to A. It, in turn, can be reoxidized to E by N 2 O or O 2 (see the section Reaction Mechanism for more details). As depicted in Figure 1, the lattice has a quasi-hexagonal symmetry, where each chromium atom is connected to six nearest chromium atoms and three nearest oxygen atoms and vice-versa.
KMC Simulations. The kinetic analysis was performed as KMC simulations. Kinetic and thermodynamics parameters, as obtained from the DFT data, were used in the KMC model to probe the reaction at various temperatures, reactant concentrations (effectively pressures), and catalyst compositions. The simulations were performed using Zacros, which is a graphtheoretical implementation of the KMC approach. In this approach, the Hamiltonian is calculated within the energetic model, accounting for the number of adsorbed clusters on the lattice and their interactions. 58−61 The raw output from the simulations is the lattice configuration at each time interval and the amount of gaseous species consumed/formed. From these, turnover frequencies (TOFs) and, in turn, apparent activation barriers, reaction order, rate-determining steps, and degree of rate/selectivity control, and so forth are extracted.
The simulations were carried out on a quasi-hexagonal lattice, as shown in Figure 1, which is commensurate with the lattice of the DFT model. There are two types of surface sites: one corresponding to the exposed chromium atoms and the other to oxygen atoms. Each chromium surface atom (site "Cr") has six neighbors in the hexagonal arrangement. Additionally, each chromium atom connects to three neighboring oxygen atoms (sites "O"). Oxygen atoms are linked to six oxygen atoms in the hexagonal arrangement and the nearest three chromium atoms. In total, each surface site has a connectivity of nine ( Figure 2).
To account for the effect of surface oxidation, two different surfaces are investigated: reduced (A) and oxidized (E). The underlying lattice is the same, but the chromium sites are not exposed on the oxidized surface. Thus, three active site types are considered (O ox , Cr red , and O red ), while the Cr ox sites in the KMC are considered inert (having no physical counterpart, they are only included to construct the lattice more easily). The reaction constants and, consequently, the reaction mechanism are different on the two investigated surfaces and were individually determined by separate DFT calculations.
The KMC simulations were performed on the 12 × 6 lattice, which corresponds to 288 sites. As seen in Figure 1, their relative ratio was varied by changing the size of the E "island" in the bottom left corner.
Preliminary testing showed that quadrupling the lattice does not change the calculated TOFs noticeably (less than 2%). Lateral interactions were calculated for all C x *−H* pairs up to the first nearest neighbor. The simulations were run with 19 different seeds and then averaged. Adsorption and diffusion reactions were treated as fast equilibrated events (stiffnessscaled). 62 A typical simulation was terminated after 3 million events, which sufficed to reach a steady performance. Convergence testing of three different simulations (one for each surface type) with 2 million, 3 million, and 4 million events showed that the obtained TOFs differed by less than 1%.
The model is checked to be thermodynamically consistent. All reactions paths on the catalyst (on the oxidized or reduced surface) yield the same reaction energy as is the energy difference between the products and reactants in the gaseous phase. In the kinetic model, two sets of adsorption energies and reaction barriers are available, depending on the oxidation state of the active site.

■ RESULTS AND DISCUSSION
Adsorption. Saturated hydrocarbons, of which methane, ethane, and propane were included in the model, interact with the surfaces merely through weak and non-specific van der Waals interactions. This results in high barriers for their activation (see the section Reaction Mechanism and Table 4), low surface coverages during the reaction, and negligible surface perturbation. As summarized in Table 1, the adsorption is weaker on the oxidized surface (0.23 eV vs 0.36 eV for propane, 0.21 eV vs 0.23 eV for ethane, and 0.11 eV vs 0.14 eV for methane), whereas the surface and adsorbate distortion energy due to perturbation is negligible. Molecular hydrogen does not bind to the surface. The attractive interaction is wholly due to electronic effects being weaker on the oxidized surface due to the higher electron density on the surface, repelling the saturated hydrocarbons. A Bader charge analysis shows that on the oxidized surface, oxygen atoms with a Bader charge of −0.68 are exposed, whereas the reduced surface is terminated with chromium atoms with a charge of +1.56, while the three neighboring oxygen atoms have a charge of −1.05. Effectively, the oxidized surface exhibits an acidic character with exposed oxygen atoms, which readily take on hydrogen atoms.
Hydrocarbons with multiple bonds (propene, propyne, ethene, and ethyne) react with the two surfaces differently. While on the reduced surface they bind to an exposed chromium atom by the interaction of their π electron cloud, they bind with the sp 2 or sp carbon atoms to oxygen atoms of the oxidized surface. The latter interaction is approximately 1 order of magnitude stronger, accompanied by the strong electronic interaction and geometric effect. For instance, propene adsorbs strongly (−3.00 eV) despite the large distortion energies of the surface (+1.20 eV) and adsorbate itself (+2.68 eV). Such strong interactions have a profound effect on the reaction selectivity as the intermediates do not readily desorb but instead undergo further dehydrogenation or cracking, as shown later on.
KMC simulations offer insight into the behavior of the catalyst structure with an atomistic resolution provided sufficient input data are available. Lateral interactions are key to transcending a mean-field description. In Table 2, we list lateral interactions between the co-adsorbed H* and every other intermediate in the reaction network. This was shown to be sufficient in our previous work, 28 while including all possible lateral interactions is impractical due to the sheer number of combinatorial possibilities. With a few exceptions, these interactions are weaker on the oxidized surface, where they are also generally repulsive.
Surface (Re)-Oxidation. On the reduced surface, hydrogen atoms bound to oxygen atoms can only recombine into H 2 and desorb. 28,29 However, the oxidized surface can lose its surface oxygen as it gets reduced. Recombination of hydrogen atoms on two adjacent oxygen surface atoms yields chemisorbed water, which can desorb. The ensuing oxygen vacancy can migrate across the surface with a kinetic barrier of 0.63 eV (see reaction 3 in Table 3). This migration is limited to the oxidized part of the catalyst (this is relevant only in the mixed composition). If all surface oxygen atoms are lost, the oxidized surface (E) is equivalent to fully reduced (A). The oxygen vacancy can be replenished by N 2 O in an exothermic reaction, yielding N 2 and the fully oxidized surface. The use of CO 2 , however, is calculated to be less effective due to a high barrier and strong endothermicity. When two adjacent oxygen vacancies form, they are easily filled by dissociative adsorption of O 2 . This reaction is two-step. First, O 2 strongly adsorbs near the vacancies and then it dissociates. These reactions, effectively enabling a transformation between A and E, are summarized in Table 3 and included in the kinetic model. See Figure 3 for the structures involved.
The surfaces (A) and (E) represent two extrema. During the reaction, the catalyst exists in an intermediate state, which is characterized by the fraction of oxygen vacancies (V*) on the surface (E).
Reaction Mechanism. The reaction mechanism for propane dehydrogenation, although consisting of 74 individual steps, is composed of only four types of reactions (adsorption, ER reactions, diffusion, and Langmuir−Hinshelwood reactions). The steps with the corresponding barriers and reaction energies are listed in Table 4. Propane, propene, propyne, ethane, ethene, ethyne, and methane can adsorb (vide supra), while molecular hydrogen interacts weakly and non-specifically with either surface (steps 8−15). However, it readily dissociates and binds as H(−O) (step 16) and diffuses across the surface (step 17). The carbon species either bind too  strongly (all unstable intermediates and multiple bondcontaining species on the oxidized surface), rendering them immobile, or too weakly, making diffusion comparable with desorption. The difference in the acidity of the surfaces is noticeable, as the hydrogen adsorption energy is −1.69 eV on the oxidized surface and −0.14 eV on the reduced surface (relative to 1/2H 2 (g)).
As shown in Figure 4, we systematically include all possible dehydrogenation steps, where a hydrogen atom is removed from the adsorbate. We distinguish "normal" and deep dehydrogenations. As it takes two steps (two hydrogen atoms must be removed) to convert a single bond to a double bond, dehydrogenation reactions generally link a stable hydrocarbon and a monoradical (either as a reactant or as a product). Deep dehydrogenation reactions violate this rule, yielding multiple radicals. While they are generally unlikely on the reduced surface, the oxidized surface is so active that deep dehydrogenations readily proceed, occasionally surpassing normal dehydrogenation routes (for instance, CH 3 CH 2 is preferentially deep-dehydrogenated to CH 3 CH instead of forming ethene). Intramolecular hydrogen migrations are omitted because their activation barriers exceed those of the dehydrogenation reactions.
Upon a weak physisorption of propane (0.36 eV on the reduced surface and 0.23 eV on the oxidized surface), the reaction proceeds rapidly on the oxidized surface. Due to very low barriers (E A = 0.19 and 0.11 eV), both CH 3 CH 2 CH 2 and CH 3 CHCH 3 form. On the reduced surface, the barriers are much higher but nearly identical (E A = 1.25 and 1.27 eV), meaning both intermediates also form, albeit much more slowly. However, on the reduced surface, CH 3 CHCH 3 is more susceptible to further dehydrogenation (E A = 0.84 eV), yielding propene. On the oxidized surface, CH 3 CHCH 3 is dehydrogenated to propene (E A = 0.69 eV), as expected, while CH 3 CH 2 CH 2 undergoes deep dehydrogenation and yields CH 3 CH 2 CH instead (E A = 0.55 eV). On the reduced surface, propene converts to propyne via CH 3 CCH 2 (E A = 1.22 and 1.31 eV). On the oxidized surface, CH 3 CH 2 CH is dehydrogenated to CH 3 CHCH (E A = 0.21 eV) and propyne (E A = 0.96 eV), while propene yields propyne via CH 3 CCH 2 (E A = 0.23 and 0.83 eV). Further dehydrogenation to CH 3 CC is possible on the reduced and especially oxidized surface (E A = 0.92 and 0.95 eV, respectively), where it is exothermic. The potential energy surface of the reaction steps is depicted in Figure 5. In a nutshell, dehydrogenations are exothermic and kinetically more accessible on the oxidized surface and endothermic with higher barriers on the reduced surface.
Although C2 hydrocarbons enter the reaction as partially dehydrogenated species formed in various cracking reactions of the C3 intermediates, we model the entire pathway. On the reduced surface, ethene is formed in two steps (E A = 1.42 and 1.42 eV), while on the oxidized surface CH 3 CH 2 (E A = 0.28 eV) preferentially dehydrogenates via CH 3 CH (E A = 0.43 eV) and CH 2 CH (E A = 0.13 eV) to ethyne directly (E A = 0.13 eV). Consequently, very little ethene is formed. Methane is unlikely to dehydrogenate on the reduced surface, while the oxidized surface is conducive to full dehydrogenation to coke (C*), which has lower barriers and is exothermic. The ensuing C* cannot utilize adjacent surface oxygen atoms and desorb as CO or CO 2 because of the strong endothermicity of such a reaction.
The increased reactivity of the oxidized surface is mirrored in much greater cracking activity as well. While on the reduced surface, most cracking reactions have high barriers (above 2.5 eV) and are very endothermic, on the oxidized surface, there are kinetically very accessible C−C cleavage reactions. For instance, CH 3 CH−C and CH 2 −C are exothermic and with barriers lower than 1.0 eV. C2 species fragment even more readily (CH 2 −C and C−C are especially prone to cleavage). On the reduced surface, fewer cracking reactions are accessible, although there are rare instances of reactions that occur on the reduced surface and not on the oxidized surface (CH 3 −CCH, CH 3 C−CH 3 , CH 3 −CCH 2 , and CH 3 −CH). As it will be shown later on, this greater activity of the oxidized surface manifests in both higher TOFs for the production of olefins and increased cracking, causing the formation of C2 and C1 products, and coking. The coke formed is usually burnt away with cycles of excess oxygen as CO 2 .
Kinetic Modeling. Temperature Effect. Using no oxidant, the products of propane dehydrogenation are propene and hydrogen and the reaction is endothermic. When an oxidant is used, propene, CO 2 , side products (propyne, ethene, etc.), and H 2 O are produced in an exothermic reaction. On the reduced surface, the elementary step with the largest activation barrier is C 3 H 8 → CH 3 CHCH 3 + H (1.27 eV), while on the oxidized surface, that is, CH 3 CHCH 3 → CH 3 CHCH 2 + H (0.69 eV). However, on the oxidized surface, the formation of water (E A = 1.19 eV) and its desorption (ΔE = + 1.36 eV) also play an important role.
The true apparent activation energies are shown in Figure 6. For the production of propene, this value is 1.34 eV with O 2 and 1.10 eV with N 2 O. The larger value for O 2 does not imply that the reaction proceeds slower, which is clearly shown in Figure 6. Instead, the larger value reflects a great temperature dependence, while the overall TOF is still larger. CO 2 is   Table 3.

ACS Catalysis pubs.acs.org/acscatalysis
Research Article  (Figure 6), the apparent activation barrier is 1.39 eV and the effect of the oxidant is non-existent, which agrees with our previous work. 28 We have also studied a mixed surface, consisting of an equal initial fraction of both types of active surface. As shown in Figure 6, the behavior of this surface is, as expected, between the both extrema. The apparent activation barrier for propene production is 1.15, 1.14, and 1.29 eV with O 2 , N 2 O, and no oxidant, respectively. When using O 2 , CO 2 is still the main product, while with N 2 O, propene begins to predominate at lower temperatures. A simple mathematical reasoning shows that the reactions with higher activation energies start to predominate at higher temperatures. However, it is known experimentally that at higher temperatures, hydrocarbons will convert to CO 2 in oxidative conditions. This apparent inconsistency with our model is reconciled as follows. At higher temperatures, combustion proceeds homogeneously, while we are interested only in the performance of the catalyst, that is, surface reactions. Although the production of propene increases with temperature, this is in real life offset by homogeneous combustion. Second, real-life scenarios deal with significant catalyst deterioration at higher temperatures due to deactivation, coking, sintering, and so forth. While we include coking (vide infra), other transformations of the catalyst have not been included in the model because we are interested in the performance of the catalyst in its pristine reduced and oxidized forms and not in the description of the process per se.
Pressure Effect. The effect of the oxidant used and its pressure on the reaction is shown in Figure 7. At 1 bar of propane and 900 K, the partial pressure of O 2 and N 2 O was varied from 10 −3 to 40 bar over the oxidized and reduced surfaces. On the former, increasing the partial pressure of the oxidant has little effect on the selectivity. The reaction order with respect to O 2 and N 2 O is 0.82 and 0.84 for propene and 0.84 and 0.89 for CO 2 production, respectively. On the mixed surface, the effect is different. Since CO 2 production proceeds only on the oxidized surface, it is not surprising that the reaction order remains virtually unchanged. For the production of propene, the reaction order drops to 0.44 with respect to O 2 and 0.19 with respect to N 2 O. In these more realistic conditions, the effect of oxidant pressure on the selectivity is predicted to have an important effect.    This has clear implications for selectivity, which is shown in Figure 8. On the oxidized surface, the selectivity is poor, mostly below 20%, and does not change noticeably with oxidant pressure. On the mixed surface, the effect is pronounced. Whereas at lower oxidant pressures, the production of propene predominates, the selectivity precipitously drops at higher pressures. With oxygen, above 0.3 bar, selectivity toward CO 2 plateaus at 80%. Using a softer oxidant yields consistently better selectivities, exceeding 90% below 0.1 bar N 2 O.
The influence of propane pressure was investigated at p oxidant = 1.0 bar and T = 900 K and found to be converse (Figure 9). On the oxidized surface, the reaction order of propene production with respect to propane is 0.24 and 0.14 when using O 2 and N 2 O, respectively, while the formation of CO 2 shows a slightly negative reaction order with respect to propane. On the reduced surface, the reaction order with respect to propane is close to unity, consistent with our previous work. 28 The behavior on the mixed surface falls between the two. For the production of CO 2 , the pressure of propane is irrelevant when using O 2 or N 2 O as oxidants (without the oxidant, there is a positive trend with very low absolute TOF, which is attributed to the loss of surface oxygen atoms). For the production of propene, the reaction orders with respect to propane are 0.49, 0.52, and 1.00 with O 2 , N 2 O, and no oxidant, respectively. Higher propane pressures are thus expected to be advantageous for the production of propene.
In Figure 10, we show a stark difference between the performances of the three surfaces at different propane pressures. On the oxidized surface, the selectivity toward   propene remains poor and only marginally improves even when the propane pressure shoots up. On the reduced surface, propane is almost exclusively produced. In the realistic conditions, which are modeled as a mixed catalyst, the selectivity increases with propane pressure from 10% below 0.001 bar to more than 90% above 10 bar. In all instances, N 2 O as a soft oxidant exhibits better selectivity, which is expected.
Surface Oxidation Effect. The analysis so far has focused on the effects of temperature and reactant pressure, which were tested on three arbitrary surface oxidation levels: fully oxidized, fully reduced, and mixed (50:50). While the oxidized surface Figure 9. TOF for the dehydrogenation of propane at p oxidant = 1.0 bar and T = 900 K and varying propane pressure on the oxidized (left), reduced (center), and mixed (right) surfaces. The mixed surface consists of 50% of oxidized and 50% of reduced surfaces and includes diffusion of the intermediates across the phase boundary. The symbol shape denotes the oxidant used: ■ O 2 , • N 2 O, and ▲ none. Full symbols denote propene production and empty symbols denote CO 2 production. Inset values denote the slopes, which correspond to the reaction order with respect to propane. Figure 10. Selectivity toward CH 3 CHCH 2 and CO 2 in conditions as in Figure 9. Lines are guides for the eye. exhibits high activity and low selectivity, the reduced surface has the exact opposite properties. Thus, a closer look into the optimum surface condition is warranted. We construct a series of mixed surfaces, as shown in Figure 1. The overall lattice size is 9 × 9 − there are three active sites per unit cell − where the bottom left corner ("island") represents the oxidized portion of the surface. The size of the island was varied from 0 × 0 to 9 × 9 and kept fixed within the simulation run, probing different degrees of surface oxidation.
In Figure 11, the performances of these surfaces at p CH 3 CH 2 CH 3 = 1.0 bar and p oxidant = 1.0 bar at T = 900 K are shown. As expected, the selectivity toward propene drops as the degree of oxidation increases. The drop is more precipitous when using O 2 as opposed to NO 2 . The selectivity toward CO 2 displays a converse pattern because no other products are produced in any meaningful amounts; temperatures in excess of 1000 K were found to be required for the production of propyne and C 2 products. However, the overall catalyst activity increases with the temperature. Thus, a maximum in propene yield was expected at some intermediate degree of oxidation. When using O 2 , the optimum degree of oxidation seems to be around 0.2, while with N 2 O the optimum lies around 0.5, but the effect is not as large.
For better insight into the catalyst performance, we study the catalyst surface, whose temporal evolution is shown in Figure 12. We plot the fraction of empty oxidized sites (*), surface oxygen vacancies (Vac*), adsorbed H*, and C 1 , C 2 , and C 3 fragments at different temperatures. The rationale is as follows. The empty oxidized sites are readily available for the reaction. The surface oxygen vacancies actually correspond to the reduced catalyst surface, which is much less active (vide supra) and can be used as a surrogate for reversible catalyst inhibition. The adsorption of H* is transient and does not impede the reaction. Different carbon species, however, constitute irreversible deactivation of the catalyst. While C 3 and most C 2 species adsorb reversibly since they can undergo further dehydrogenation, the buildup of C 1 is indicative of coking. The most abundant C 2 species is CC*, which quickly plateaus and acts as an inhibitor. The C 1 concentration steadily increases with time but can be burnt away with oxygen, regenerating the catalyst (in our model, we do not account for structural changes of the catalyst such treatment might cause). For comparison, the cumulative production of propene and CO 2 and the consumption of propane is also shown on the secondary axes.
We observe a few clear trends. First, the fraction of empty oxidized sites decreases with temperature and is higher under O 2 than under N 2 O, where it drops to zero. Conversely, the fraction of empty reduced sites increases and approaches unity at higher temperatures. In most instances, this is the predominant surface motif. The second most abundant species is initially H*, which predominates at low temperatures. The most common carbon species are C 2 *, followed by C 1 *, which is higher at lower temperatures. Once the reaction reaches a steady state, C 3 * are negligible. These results explain the observed kinetic behavior of the catalyst under different conditions.
It is clear that under N 2 O, the surface is more reduced, which is beneficial for the selectivity toward propene. Moreover, we see that initially only CO 2 is produced (red dashed line) and only when the catalyst is sufficiently reduced is propene also formed (blue dashed line). This transition to the steady state is also accompanied by the decrease of the surface concentration of H* and C 3 *.
Deactivation. Catalyst deactivation is a common problem with oxidation reactions. As coke forms on the catalyst surface, the activity drops. Deactivation is a complex topic, which a first-principles kinetic model cannot fully reproduce. We make no attempt at describing the structural deterioration of the surface, such as sintering, phase transitions, or decomposition. We define deactivation as the buildup of dead-end carbon species, which cannot further dehydrogenate even upon C−C cracking. These are: C*, CH*, CH 2 *, CH 3 *, CC*, CHC*, CH 2 C*, CH 3 C*, CH 3 CC*, CH 3 CHC*, and CH 3 CH 2 C*.
As shown in Figure 13, the deactivation of the catalyst occurs primarily by the accumulation of CC* and C* species. Other species (mostly CHC*) transiently form but are ultimately dehydrogenated. First, CC* is formed, which slowly transforms into C*. This might very well be an artifact of the model as both species describe the coked surface. Thus, we treat both species cumulatively in our analysis. We show that the deactivation of the catalyst can be described with the Arrhenius kinetics. The apparent activation barrier and preexponential factor for the deactivation are dependent on the oxidant used: 1.70 eV and A = 1.4 × 10 8 s −1 for O 2 and 0.81 eV A = 3.6 × 10 2 s −1 for N 2 O. A much stronger temperature dependence when using a stronger oxidant is an expected result. We can compare these values with the previously calculated deactivation parameters on the reduced surface, which are E A = 2.82 eV and A = 1.66 × 10 10 s −1 . This shows that the oxidized surface deactivates faster than the reduced surface when O 2 is used as the oxidant. Soft oxidants, such as N 2 O, cause a much slower catalyst deactivation.
In Figure 13, we show the catalyst surface after 9.4 s. The catalyst surface is partially reduced (Vac*), while the oxidized sites are mostly coked (initially with CHC* and CC* and later with C*). When the catalyst is fully coked (Figure 13), it can be recovered by burning away the coke as CO 2 . Since C* is removed as CO 2 , the surface is briefly reduced and quickly reoxidizes. N 2 O and CO 2 are too weak oxidants for surface recovery. In real operation, cycles of catalyst coking and regeneration repeat with an hourly cadence because the catalyst is not fully oxidized. As shown previously, the reduced surface gets coked much slower. 28 Experimental Relevance. It is difficult and often not very informative to try applying idealized models aimed at understanding the fundamentals in simplified conditions to real-life scenarios. Assumptions (pristine crystal lattice devoid of defects and phase boundaries, constant pressure and temperature, suppression of unwanted side reactions, reactor design, etc.) that make a model neat enough to discern trends can be next to impossible to ensure in experiments. However, some parallels can be drawn.
The experimentally measured adsorption energy of propane by Suzuki and Kaneko is 10 kcal mol −1 (0.43 eV), which is comparable with our values of 0.36 eV for the reduced surface and 0.23 eV for the oxidized surface. 19 The apparent activation barrier for propane dehydrogenation in their study was found to be 33.9 kcal mol −1 (1.47 eV), which is comparable to values from our model (1.39 eV for the reduced surface and 1.34 eV for the oxidized surface).
Gascoń et al. modeled the reaction of propane dehydrogenation over Cr 2 O 3 /Al 2 O 3 with a lumped microkinetic model and found an activation barrier of (308 ± 14) kJ mol −1 (3.21 eV) for the reaction C 3 H 8 → CH 4 + C 2 H 4 . 24 In our model, the decomposition of propane (C 3 H 8 → CH 3 CH 2 + CH 3 ) has activation barriers of 3.23 and 3.02 eV on the reduced and oxidized surfaces, respectively. In the same model, the authors note that the "apparent reaction order of the coking process with respect to the propane concentration is very low", which might be due to "the strong propene adsorption" and its coverage being close to unity. In our model, we also observe a weak dependence of the reaction rate on the propane concentration (see Figure 9) and very strong adsorption of propene on the oxidized surface (3.00 eV).
In their mathematical model of experimental data from the dehydrogenation of a propane-isobutane mixture in a fluidized bed reactor over Cr 2 O 3 /Al 2 O 3 , Vernikovskaya et al. obtained high selectivities toward isobutylene (89−94%) and propylene (81−100%). 63 They decreased as the temperature increased, which is consistent with our model.

■ CONCLUSIONS
We have investigated the mechanism and kinetics of propane dehydrogenation over oxidized and reduced α-Cr 2 O 3 (0001), which yields primarily propene and CO 2 . Other potential products, such as propyne and C2 and C1 hydrocarbons, could also form but only in minute amounts, especially when insufficient oxidant is present. We modeled the surface in the reduced and oxidized form. The reduced surface is Crterminated, while the oxidized surface has chromyl units exposed (−CrO). The kinetic parameters of all possible reaction steps were calculated using a first-principles DFT + U approach using the PW91 functional and D − J value of 5−1 eV. The mechanism was exhaustive, including all possible elementary steps for the dehydrogenation of propane to propene and propyne, cracking of hydrocarbons to C2 and C1 species and catalyst coking.
First, we show that the surfaces exhibit markedly different affinities toward the adsorbates. While saturated hydrocarbons and molecular hydrogen only physisorb on both surfaces, unsaturated intermediates bind much more strongly on the oxidized surface. On the oxidized surface, the reaction energy for the dissociative adsorption of hydrogen is −3.40 eV, while on the reduced surface, it is only −0.85 eV. Similarly, unsaturated C3 and C2 hydrocarbons have interaction strengths of 3−4 eV with the oxidized surface and 0.3−0.6 eV with the reduced surface. The difference stems from electronic effects, that is, surface basicity and nucleophilicity, as the oxidized surface exposes oxygen atoms with a Bader charge of −0.68e 0 , while the exposed Cr atoms on the reduced surface have a positive charge (+1.56e 0 ).
As a consequence, the reaction mechanism is fundamentally different. This is to be expected from the stoichiometry alone as H 2 O is the co-product in the oxidative environment and H 2 in the reducing environment. In the former case, dehydrogenation steps are exothermic with low activation barriers (generally below 1.0 eV), while the reduced surface exhibits higher barriers (typically 1−2 eV) and the steps are generally endothermic. Cracking reactions follow a similar trend, that is, being much more likely on the oxidized surface.
Dehydrogenation over the oxidized surface follows the Mars−van Krevelen mechanism. Hydrogen atoms that shed off the hydrocarbons are picked up by integral surface oxygen atoms, which desorb in the form of water. The ensuing surface oxygen vacancy corresponds to the reduced site. These are replenished with N 2 O, which heals one vacancy and yields N 2 , or O 2 , which donates two oxygen atoms. While both reactions are exothermic, N 2 O functions as a soft oxidant with a higher barrier. O 2 , however, first adsorbs without a barrier in a strongly exothermic step and then readily dissociates, making it a strong oxidant. The reaction with CO 2 was calculated to be too endothermic on this surface and was not studied further.
Chang et al. have shown that the reduced surface with an additional oxygen vacancy is more active than the reduced surface. 20 However, this structure was not predicted to be stable in their phase diagram by Wang et al. 50 Our calculations also showed that this further reducing of the reduced surface is energetically not favorable as the formation energy of such a vacancy is +4.07 eV (with respect to 1/2O 2 ).
These data were cast into a KMC model, which also accounted for lateral interactions. It was shown that the reduced surface produces propene with high selectivity (>99%) but has a low activity. On the oxidized surface, the production of propene is approximately an order of magnitude faster. However, the production of CO 2 is even faster, resulting in low selectivities. The reaction order with respect to propane is ≈1 on the reduced surface and 0.14−0.24 on the oxidized surface using O 2 and N 2 O, respectively. On the oxidized surface, the reaction order is much more dependent on the oxidant pressure (≈0.8). The already low selectivity on the oxidized surface is further depressed if the oxidant pressure increases.
Realistic conditions during the reaction are between the two extrema (oxidized and reduced surface). First, the reaction was studied on the mixed surface, consisting of equal parts of both surface types. This surface exhibited considerably better performance than each individual surface. Additionally, the selectivity and activity were strongly dependent on the oxidant and propane pressure and oxidant type. Further investigation of surfaces with varying degrees of oxidation showed that there exists an optimum degree of surface oxidation, which is 0.2 when using O 2 and 0.5 when using N 2 O.
We have shown that the catalyst also gets slowly deactivated due to the formation of carbon-heavy species. After the transient formation of CHC*, CH 2 *, CH*, CC*, and ultimately C* accumulate on the surface. The deactivation rate is strongly dependent on the temperature and the oxidant used. At higher temperatures with O 2 , the catalyst is very prone to coking, while with N 2 O at lower temperatures, it is less so. The formed coke can be removed by burning with O 2 , while N 2 O and CO 2 are ineffective.
These results extend our knowledge of propane dehydrogenation on Cr 2 O 3 . While our previous work examined the reaction mechanism and kinetics on the reduced surface without co-feeding oxidants, which was shown to produce propene with high selectivity, here, we showed how the catalyst in question performs in more realistic conditions. The addition of the oxidant and consequent partial oxidation of the catalyst improves the activity and can be fine-tuned to avoid excessive CO 2 production.