The Mechanism of Industrial Ammonia Synthesis Revisited

Article pubs.acs.org/JPCC

The Mechanism of Industrial Ammonia Synthesis Revisited: Calculations of the Role of the Associative Mechanism Anna L. Garden†,‡ and Egill Skúlason*,‡ †

Department of Chemistry, University of Otago, P.O. Box 56, Dunedin 9054, New Zealand Science Institute and Faculty of Physical Sciences, University of Iceland, Reykjavík, Iceland

‡

S Supporting Information *

ABSTRACT: Quantum chemical calculations have been used to investigate the rate constant and mechanism of ammonia synthesis on a stepped ruthenium surface at typical industrial conditions. Both the commonly accepted dissociative mechanism and an associative mechanism of ammonia formation are explicitly considered. Uncertainties on the calculated parameters have been estimated using a recently developed functional utilizing Bayesian statistics. A surprisingly stable intermediate is identified in the associative mechanism, which is reached via an accordingly low barrier. This gives rise to a much higher rate constant of ammonia synthesis for the associative mechanism than previously considered. The results confirm that at typical industrial operating conditions the dissociative mechanism is dominant, with a difference in rate constants between the two mechanisms of around 3 orders of magnitude. However, consideration of uncertainties on the calculated parameters indicates that only a small change to the activation energy of the associative mechanism may result in a large contribution to the rate. This offers an additional flexibility for catalyst design to optimize the associative mechanism that could potentially lead to faster and more efficient production of ammonia. Furthermore, it illustrates the need to consider both mechanisms when considering nanoparticle catalysts, which possess a large variety of active sites.

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INTRODUCTION Since the early 20th century, ammonia (NH3) has been primarily synthesized via the Haber−Bosch process, in which gaseous nitrogen (N2) and hydrogen (H2) are passed over a metallic catalyst at a temperature of approximately 400 °C and a pressure of around 200 bar. The original catalyst is a promoted Fe catalyst with Ru later found to be more active toward NH3 synthesis.1,2 Much experimental and theoretical effort has been focused on determining the mechanism and rate-limiting steps of the NH3 synthesis reaction and subsequently optimizing the process. The most vexing issue was whether the nitrogen adsorbed to the catalyst surface is molecular or atomic and whether NH3 forms via a dissociative (eq 1) or associative mechanism (eq 2).3

used electron spectroscopic techniques to directly observe the catalyst surface under ultrahigh vacuum (UHV) conditions. The study was successfully extended to atmospheric pressure, and it was deduced that the dissociative mechanism is responsible for NH3 formation and that the rate-limiting step is dissociation of adsorbed N2.9 Accordingly, most subsequent studies began with the assumption that the dissociative mechanism is dominant, and many studies exist solely on the dissociation of N2, for both Fe- and Ru-based catalysts.10−15 Several kinetic models have been used to extend the results of the UHV experiments beyond atmospheric pressure to highpressure conditions typical of the industrial process.16−18 Such studies are based on the assumption of a dissociative mechanism and the measured properties of adsorbed species on single crystal surfaces under UHV conditions and have been successful in modeling the experimental rate constant of NH3 formation at high pressure to within a factor of 2.16 There have been a large number of density functional theory (DFT) studies on the NH3 synthesis reaction, the vast majority of which have focused on the dissociative mechanism19,20 and the effects of additional adsorbates,21 promoters,22 and various types of stepped surfaces.23−25 The associative mechanism has only been explicitly considered for a flat Ru surface for which the first hydrogenation step to form adsorbed N2H was

N2(g) + 3H 2(g) → 2*N + 3H 2(g) ⇌ 2*NH + 2H 2(g) ⇌ ⇌ 2NH3(g)

(1) N2(g) + 3H 2(g) → *N2H +

5 H 2(g) ⇌ ⇌ 2NH3(g) 2

(2)

Numerous experimental techniques have been used to determine the mechanism of NH3 formation such as kinetic studies,3,4 the effects of coadsorbates,5 isotope tracing experiments,6 stoichiometric arguments,7 and IR spectroscopy.8 The majority of these studies suggested a dissociative mechanism of NH3 formation, although as summed up in a 50 year review of the subject, the problem was not conclusively resolved.3 The most definitive conclusions were obtained by Ertl et al., who © 2015 American Chemical Society

Received: August 31, 2015 Published: November 3, 2015 26554

DOI: 10.1021/acs.jpcc.5b08508 J. Phys. Chem. C 2015, 119, 26554−26559

The Journal of Physical Chemistry C

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RESULTS AND DISCUSSION The energy profiles for the first few steps of the associative mechanism and the rate-limiting step of the dissociative mechanism are shown in Figure 1. The calculated energy

postulated to be rate-limiting, due to the existence of a thermochemical barrier of 1 eV, which was the largest of all elementary steps.26 Furthermore, the associative mechanism would incur additional entropic penalties of adsorbing H2 from the gas phase. Recently, a much lower energy configuration of adsorbed N2H was found on a stepped Ru(0001) surface. However, free energy calculations have only been performed in an electrochemical context, where the hydrogen is entering the system in the form of solvated protons, thereby avoiding the entropy loss associated with adsorbing gaseous H2.27 The most comprehensive DFT study of the NH3 synthesis reaction at industrial conditions was performed by Honkala et al.28 With the exception of an experimentally determined distribution of cluster sizes, all results were obtained from first-principles calculations. A dissociative mechanism was assumed and the rate of NH3 formation was predicted within a factor of 3−20 lower than the measured rate. In the current work we use a DFT approach to explicitly investigate the role of the associative mechanism in the NH3 synthesis reaction on a stepped Ru(0001) surface, at industrial conditions. The results are compared with the dissociative mechanism; the relative rates at typical industrial conditions are compared, and the implications for other active sites are discussed.

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Article

COMPUTATIONAL DETAILS

All geometry optimizations and reaction path calculations were performed using a stepped hcp Ru(0001) surface. For the full mechanistic calculations, the surface was constructed with a (6 × 2) surface unit cell of a three-layer slab, where three rows of metal atoms in the top layer were removed to create a strip island three rows wide (30 Ru atoms). In this way the active site is the commonly utilized B5 active site. The bottom layer was held fixed and the two upper layers allowed to relax. A larger slab consisting of eight layers in total was used to converge minima and transition state energies and to compute vibrational frequencies. The slabs were separated by 12 Å of vacuum. The calculated lattice constant for hcp Ru was 2.73 Å (c/a ratio 1.58). For calculations of the transition state energies at higher hydrogen coverage a larger surface unit cell (6 × 3) was used. The calculations were carried out using density functional theory (DFT) with a plane-wave expansion of the wave function, a BEEF-vdW functional description of the exchange and correlation effects,29 and a projector-augmented wave (PAW) representation of the ionic cores.30 All calculations were carried out using the Vienna ab initio Simulation Package (VASP).31−34 The self-consistent electron density was determined by iterative diagonalization of the Kohn−Sham Hamiltonian, with the Kohn−Sham states being smeared according to a Fermi−Dirac distribution with a smearing parameter of kBT = 0.1 eV. All total energies have been extrapolated to kBT = 0 eV. A 2 × 6 × 1 Monkhorst−Pack kpoint sampling was used. The plane wave cutoff was 450 eV, and optimizations were considered converged when the force on any moveable atom was less than 0.01 eV/atom. Kinetic barriers were found from minimum energy paths calculated using the climbing image nudged elastic band (CINEB) method.35,36 The barrier was calculated as the energy of the highest maximum along the MEP minus the initial state energy.

Figure 1. (top) Elementary steps in the associative mechanism (blue lines) of NH3 synthesis on a stepped Ru(0001) surface. The ratelimiting step in the dissociative mechanism is also shown for comparison (red lines). All energies are relative to N2(g) and H2(g). (bottom) Geometries of intermediates and transition states in the associative mechanism.

profile for the dissociative mechanism is in agreement with previously published results,28,37 and thus only the rate-limiting step is discussed explicitly here. The complete energy profile is given in the Supporting Information. After the first hydrogenation step in the associative mechanism, it is more favorable for *N2H to split into *N and *NH rather than being hydrogenated further to *N2H2, which is the process believed to occur in the enzymatic mechanism.38,39 The dissociation of *N2H is not surprising, as the addition of the H adds more coordination to the N2 group, thus weakening the N−N bond and facilitating dissociation. A similar effect is known to exist in other reactions, such as hydrogen-assisted dissociation of CO in the Fischer−Tropsch synthesis.40,41 An interesting point to note concerning the dissociation of *N2H is that many early experiments on deducing the mechanism of NH3 formation assumed either a fully dissociative or fully associative mechanism and that removal of atomic nitrogen from the surface was only possible if a dissociative mechanism was operating.9 It is seen here that the presence and removal of atomic N from the catalyst surface can equivalently be explained by a “mixed” mechanism where the first hydrogenation occurs associatively to molecular nitrogen and subsequent hydrogenation occurs to atomic nitrogen. 26555

DOI: 10.1021/acs.jpcc.5b08508 J. Phys. Chem. C 2015, 119, 26554−26559

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The Journal of Physical Chemistry C To deduce the rate constant for the associative mechanism, first the rate-limiting step must be identified. At temperatures and pressures typical of the industrial process, the concentrations of the adsorbed N2 and H2 are low and in equilibrium with the gas phase and the activation barrier of the first hydrogenation step can be referenced to the reactants in the gas phase and the clean catalyst surface.37 In this way, the activation barrier for the first hydrogenation step (denoted A1) is only 0.34 eV. The activation barrier of the next step, *N2H dissociation (denoted A2), is 0.29 eV. Subsequent hydrogenation steps of atomic nitrogen show the formation of *NH3 (denoted A3) to have the highest activation barrier of 1.4 eV. To determine which of these three steps in the associative mechanism is rate-limiting, rate constants of each step can be estimated using harmonic transition state theory. The rate constant for the first hydrogenation step is given as k T qTS, A1 (ETS,A − E0)/ kBT 1 k A1 = B e h q N qH 2

2

Figure 2. Calculated rate constants for the associative (blue) and dissociative (red) mechanisms of NH3 formation. The total pressure is 200 bar, and the N2:H2 ratio is 1:3.

pressure and n(H2) = 3n(N2). The relative contribution to the rate from the associative mechanism increases with temperature. At 700 K the difference in rate constants between the two mechanisms is ∼2500 times. These results show that at typical industrial conditions NH3 is indeed likely formed via the dissociative mechanism. The results presented above use raw, calculated data from DFT. However, calculated properties using density functional theory are often highly dependent on the functional used. The present work utilizes the BEEF-vdW functional, which explicitly includes van der Waals interactions and has been shown to yield accurate predictions of adsorption energies.29 An additional benefit of the BEEF-vdW functional is that it allows for error estimation. A Bayesian error estimation (BEE) ensemble of functionals is employed, from which a range of predictions may be extracted for a given quantity. This range represents uncertainties on the exchange-correlation parameters in DFT. A BEE ensemble of 2000 functional variations is employed herein to ascertain the statistical significance of the calculated transition state energies and resulting rate constants. The energies of the transition states in both the associative and dissociative mechanisms, as calculated using the 2000 functional variations in this study, are shown in Figure 3a. The uncertainties on the transition state energies are rather large; the standard deviations for the dissociative and associative mechanisms are 0.41 and 0.37 eV, respectively. Within these bounds of uncertainty, little can be concluded about the respective transition state energies. The present study is focused on the differences in rate constants for the two mechanisms under consideration, rather than accurate prediction of the absolute rate constants. As such, it is more meaningful to compare the difference in the transition state energies, ΔETS = ETS,A − ETS,D and the uncertainty associated with this quantity. Figure 3b shows the quantity ΔETS as calculated using the 2000 functional variations. Clearly the uncertainty associated with the difference in transition state energies is greatly reduced compared to the uncertainty of the absolute transition state energies. This arises because a large degree of error cancellation occurs due to the similarity of the initial and transition state configurations in both mechanisms. A similar phenomenon has been noted previously in relation to NH3 synthesis. Medford et al. computed the uncertainties in the rate of NH3 synthesis via the dissociative mechanism for a series of transition metal catalysts.42 When the absolute rates were considered, the

(3)

where the quantity in front of the exponential is the prefactor, AA1. The prefactor contains rotational, vibrational, and translational contributions from gaseous N2 and H2 as well as a vibrational contribution from the *N2H species in the transition state. Zero-point vibrational correction has been included for all species. At 700 K and ptot = 200 bar, AA1 = 2.5 × 104 s−1. In contrast, the second and third steps involve only adsorbed species so the rotational and translational partition functions can be assumed to be negligible. Furthermore, as both the initial and transition states contain the same atoms in similar configurations, the vibrational contributions can be assumed to be equal and cancel out. The prefactors for steps A2 and A3 are thus simply kBT/h or ∼1013 s−1 at 700 K. Including the activation barriers, the rate constants at 700 K of each of the steps are kA1 = 48 s−1, kA2 ∼ 1.2 × 105 s−1, and kA3 ∼ 900 s−1 for the first hydrogenation step, *N2H dissociation, and the later hydrogenation step forming *NH3, respectively. From this we can conclude that the first hydrogenation step to form *N2H is rate-limiting in the associative mechanism. To assess the relative role of the associative mechanism, it is necessary to compare the rate constant with that of the commonly accepted dissociative mechanism, which has a barrier of 0.14 eV in the rate-limiting step. Rate constants for the rate-limiting steps in each mechanism can be estimated, again using transition state theory, where the rate constant for the associative mechanism is given above in eq 3 and for the dissociative mechanism is k T qTS,D (ETS,D − E0)/ kBT kD = B e h qN (4) 2

At 700 K, qTS,A is approximately three times higher than qTS,D due to the additional degrees of freedom. However, the largest difference in the prefactors of the two mechanisms arises from the contribution of the gaseous H2 term. Clearly, the associative mechanism will have a lower prefactor due to the additional requirement of adsorbing H2 from the gas phase, which has an associated large loss of entropy. Combined with the higher barrier, it is evident that the associative mechanism will have a smaller rate constant than the dissociative mechanism. The temperature dependence of the rate constants for the associative and dissociative mechanisms is shown in Figure 2, calculated at a typical industrial pressure of 200 bar total 26556

DOI: 10.1021/acs.jpcc.5b08508 J. Phys. Chem. C 2015, 119, 26554−26559

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Figure 4. Probability of a given ratio of rate constants for the dissociative mechanism to associative mechanism, log(kD/kA). A cumulative distribution function of the data is also shown with dotted and dashed lines indicating the probability that kD is less than 2 or 3 orders of magnitude larger than kA, respectively. The BEEF-vdW calculated value is shown as a solid point, with the horizontal error bars indicating ±1σ. Inset: Probability that kD = 100 × kA (dotted line) and kD = 1000 × kA (dashed line) as a function of total pressure, at 700 K.

Thus, at a given temperature, the associative mechanism becomes more favored as the total pressure increases. A similar phenomenon has been observed for CO methanation when at very high H2 pressure an unusually low prefactor is observed, which is attributable to a change of regime from CO dissociation to hydrogen-assisted CO dissociation.40 The inset in Figure 4 demonstrates the relative dominance of the associative and dissociative mechanisms as a function of pressure. At the pressure (∼1 bar) used in the early surface science experiments, the dissociative mechanism would indeed be completely dominant for NH3 formation on a Ru surface, with only a 4% probability that the rate constants are within 3 orders of magnitude. Considering the energies for the stable intermediates in the dissociative41 and associative mechanisms27 on an Fe surface, a similar situation would be expected for an Fe-based catalyst. However, as the pressure approaches industrial pressure, a small contribution to the rate of NH3 formation from the associative mechanism is a possible scenario. All of the above calculations have assumed zero coverage of hydrogen or other intermediates in the reactions, namely adsorbed N, NH, NH2, and NH3. Honkala et al. performed grand canonical Monte Carlo simulations of the local environment of the B5 active site for N2 dissociation on Ru nanoparticles, under industrial conditions. It was found that at a total pressure of 100 bar there was a high coverage of adsorbates in the vicinity of the active site. Furthermore, it was found that the barrier for N2 dissociation was highly sensitive to the local environment. The coverage that was found to contribute most to the rate was that in which one H atom was adsorbed on the upper step next to the active site. Obviously, the system of Honkala et al. that considered a dissociative mechanism and a pressure of 100 bar is different from the present consideration of both mechanisms and 200 bar pressure. However, as N2H is found to dissociate after the first hydrogenation step, many of the reaction intermediates in the associative mechanism are similar to those in the

Figure 3. (a) Transition state energies for the dissociative (red) and associative (blue) mechanisms, as calculated using the BEE ensemble of functionals. (b) Difference between transition state energies, ΔE = ETS,A − ETS,D. The BEEF-vdW calculated values are shown as solid points, with the horizontal error bars indicating ±1σ.

uncertainties were such that no confident conclusion could be drawn as to whether one metal was a better catalyst than another. However, when the relative rates were compared the uncertainties were small enough to confidently distinguish the relative activities of each metal toward NH3 synthesis. The present result further illustrates this strength of DFT for predicting relative trends in heterogeneous catalysis, here for comparing different mechanisms, rather than different metals. To assess the uncertainty in the relative rate constants, the ensemble of relative transition state energies are transformed to relative rate constants at 700 K, a N2:H2 ratio of 1:3, and a total pressure of 200 bar (see Figure 4). It is clear that there is a significant spread in the difference between the rate constants, with a standard deviation of around 1 order of magnitude in the difference between the rate constants. The cumulative distribution function of the difference between the rate constants is shown in Figure 4. It shows a rather gradual increase, consistent with the relatively large standard deviation in the calculated rate constants (an order of magnitude). The probability that the calculated difference in rate constants for the dissociative and associative mechanism is within 2 and 3 orders of magnitude is 6%, and 29%, respectively. Thus, it is possible that there is at least a small contribution to the rate of NH3 synthesis at industrial conditions by the associative mechanism. At a constant temperature, the rate constants of both the associative and dissociative mechanisms of NH3 formation depend on N2 and H2 pressure according to kD ∝ p(N2)

and

kA ∝ p(N2)p(H 2)1/2

(5) 26557

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Furthermore, we postulate that the associative mechanism may be active on other active sites on Ru nanoparticle catalysts.

dissociative mechanism, and we postulate that the Monte Carlo simulations of Honkala et al. represent a good first approximation to the likely coverage for the associative mechanism at industrial conditions. Accordingly, to more realistically assess the relative rate constants at industrial conditions, activation barriers for the dissociative and associative mechanisms have been calculated at this coverage with one H adsorbed on the upper step. Barriers for both mechanisms were found to increase in the presence of adsorbed hydrogen, with calculated barriers of 0.20 and 0.42 eV for the dissociative and associative mechanisms, respectively. However, the difference between the two barriers (0.22 eV) is similar to that between the barriers at zero coverage (0.20 eV), and thus it is concluded that the zero coverage results are sufficient to compare the two mechanisms at industrial operating conditions. The new insight offered by the present study is interesting from a fundamental point of view but also offers an additional flexibility for optimizing the industrial catalysts. In engineering an efficient NH3 synthesis catalyst, all previous efforts have focused on facilitating N2 dissociation. Various structural and electronic promoters have been shown to increase the number of active sites for the reaction and to lower the N2 dissociation barrier, respectively, thus increasing the rate of NH 3 formation.42 Our results suggest that the rate could also be increased by lowering the activation barrier in the associative mechanism. At 700 K, kBT = 0.06 eV, and so a decrease in the activation barrier of only 0.14 eV changes e−ETS,A−E0/kBT, and therefore the rate constant, by an order of magnitude. It is clear that only relatively small changes to the geometric or electronic structure of the catalyst may result in a much larger contribution by the associative mechanism and potentially lead to a more efficient industrial catalyst. Finally, the present results hold significance for NH3 synthesis over nanoparticle catalysts. The aforementioned previous study of the rate of NH3 synthesis on Ru nanoparticles assumed a single active site, namely the B5 site that is known to be the active site for N2 dissociation.28 However, a later study showed that there were fewer of these active sites than expected and a number of other edges and steps are present on nanoparticles around 3 nm in size.25 We postulate that some of these other sites, such as the edge sites, may in fact be active toward NH3 formation by way of the associative mechanism. This is perhaps also supported by the underestimate of the experimental rate of NH3 synthesis in the aforementioned study. Further work is ongoing in our research groups to investigate the associative mechanism on other active sites on Ru nanoparticles.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b08508. Elementary reaction steps for both mechanisms, complete energy profile for the dissociative mechanism, binding energies and geometries of all stable intermediates, derivation of rate expressions, vibrational frequencies of species involved in the rate-determining steps (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (E.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Dr. Felix Studt, Dr. Thomas Bligaard, and Prof. Jens K. Nørskov at SLAC/Stanford University and Birta L. Kristinsdóttir, Dr. Ragnar Björnsson, and Prof. Hannes Jónsson at the University of Iceland for helpful discussions. Financial support is acknowledged from the Icelandic Research Fund. The authors acknowledge the contribution of the Science Institute of the University of Iceland and NeSI highperformance computing facilities to the results of this research. NZ’s national facilities are provided by the NZ eScience Infrastructure and funded jointly by NeSI’s collaborator institutions and through the Ministry of Business, Innovation & Employment’s Research Infrastructure programme. URL: https://www.nesi.org.nz

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CONCLUSIONS Rate constants and mechanisms of ammonia synthesis on a stepped ruthenium surface have been investigated using density functional theory. An associative mechanism has been explicitly considered for the first time and the contribution of this mechanism to the rate of ammonia synthesis at industrial conditions have been assessed. Results show that within the uncertainties on the calculated parameters the dissociative mechanism is dominant, but there may be a small contribution by the associative mechanism, due to a surprisingly low activation barrier in the rate-determining step of the mechanism. Thus, there exists the possibility of reducing this barrier to increase the contriubtion of the associative mechanism and increase the efficiency of the industrial catalyst. 26558

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