Microkinetic Simulations Research Articles

Kmos: A lattice kinetic Monte Carlo framework

Kinetic Monte Carlo (kMC) simulations have emerged as a key tool for microkinetic modeling in heterogeneous catalysis and other materials applications. Systems, where site-specificity of all elementary reactions allows a mapping onto a lattice of discrete active sites, can be addressed within the particularly efficient lattice kMC approach. To this end we describe the versatile kmos software package, which offers a most user-friendly implementation, execution, and evaluation of lattice kMC models of arbitrary complexity in one- to three-dimensional lattice systems, involving multiple active sites in periodic or aperiodic arrangements, as well as site-resolved pairwise and higher-order lateral interactions. Conceptually, kmos achieves a maximum runtime performance which is essentially independent of lattice size by generating code for the efficiency-determining local update of available events that is optimized for a defined kMC model. For this model definition and the control of all runtime and evaluation aspects kmos offers a high-level application programming interface. Usage proceeds interactively, via scripts, or a graphical user interface, which visualizes the model geometry, the lattice occupations and rates of selected elementary reactions, while allowing on-the-fly changes of simulation parameters. We demonstrate the performance and scaling of kmos with the application to kMC models for surface catalytic processes, where for given operation conditions (temperature and partial pressures of all reactants) central simulation outcomes are catalytic activity and selectivities, surface composition, and mechanistic insight into the occurrence of individual elementary processes in the reaction network. Program summaryProgram title: kmosCatalogue identifier: AESU_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AESU_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 27450No. of bytes in distributed program, including test data, etc.: 2777387Distribution format: tar.gzProgramming language: Python 16.4%, fortran90: 83.6%.Computer: PC, Mac.Operating system: Linux, Mac, Windows.RAM: 100 MB+Classification: 7.8.External routines: ASE, Numpy, f2py, python-lxmlNature of problem:Microkinetic simulations of complex reaction networks with all elementary processes occurring at active sites of a static lattice.Solution method:Efficient lattice kinetic Monte Carlo solution of the Markovian master equation underlying the reaction network.Unusual features:The framework implements a Fortran90 code generatorRunning time:From 10 s to 10 h

Microkinetic Simulation of Ammonia Oxidation on the RuO2(110) Surface

The investigation by microkinetic simulations provide detailed reaction mechanisms about the NH3 oxidation on the RuO2(110) surface. There are 41 elementary reactions involved in the microkinetic model in which all the thermodynamic and kinetic parameters are obtained from density functional theory (DFT) calculations, and the entropy effects of each reaction are considered in the simulation. The differences in reaction mechanisms between the batch type and the steady state were characterized in this study. The selectivities to the oxidation products, including N2, NO, and N2O, depend on the oxidation conditions. The simulated results show that the O2/NH3 ratio, system temperature, and pressure are the controlling factors that could alter the results of the oxidation. The microkinetic modeling demonstrates how these parameters affect the NH3 conversion and the selectivities. The simulations showed that N2 and NO could be a primary product under different oxidizing conditions; however, N2O could only be a minor product because of the nature of its formation mechanism. The highest N2O selectivity obtained in the simulations is 30%.

Pressure Dynamics in Metal–Oxygen (Metal–Air) Batteries: A Case Study on Sodium Superoxide Cells

Electrochemical reactions in metal–oxygen batteries come along with the consumption or release of gaseous oxygen. We present a novel methodology for investigating electrode reactions and transport phenomena in metal–oxygen batteries by measuring the pressure dynamics in an enclosed gas reservoir above the oxygen electrode. The methodology is exemplified by a room-temperature sodium–oxygen battery forming sodium superoxide (NaO2) in an electrolyte of diethylene glycol dimethyl ether (diglyme) and sodium trifluoromethanesulfonate (NaOSO2CF3, NaOTf). The experiments are supported by microkinetic simulations with a one-dimensional multiphysics continuum model. During galvanostatic cycling over 30 cycles, a constant oxygen consumption/release rate is observed upon discharge/charge. The number of transferred electrons per oxygen molecule is calculated to 1.01 ± 0.02 and 1.03 ± 0.02 for discharge and charge, respectively, confirming the nature of the oxygen reaction product as superoxide O2–. The same ratio is observed in cyclic voltammetry experiments with low scan rate (<1 mV/s). However, at higher scan rates, the ratio increases as a result of oxygen transport limitations in the electrolyte. We introduce electrochemical pressure impedance spectroscopy (EPIS) for simultaneously analyzing current, voltage, and pressure of electrochemical cells. Pressure recording significantly increases the sensitivity of impedance toward oxygen transport properties of the porous electrode systems. In addition, we report experimental data on the diffusion coefficient and solubility of oxygen in electrolyte solutions as important parameters for the microkinetic models.

Further Theoretical Evidence for Hydrogen-Assisted CO Dissociation on Ru(0001)

Extensive calculations based on spin-polarized density functional theory were carried out to examine how CHx are formed from the dissociation of CO on Ru(0001) in the presence of hydrogen. Common pathways, such as the direct CO dissociation and H-assisted route leading to HCO or COH, including alternative routes that involve the formation of HCOH and CH2O, were examined. The reaction energy and barrier for each elementary step were calculated. The calculations show that the carbide mechanism is not the main reaction pathway for the conversion of CO on Ru(0001). Complementary microkinetic simulations utilizing results from first-principles quantum mechanical calculations indicate that a branch starting from the hydrogenation of CO to HCOH (via COH intermediate) and subsequent C–O bond cleavage is more plausible.

Catalytic properties of extraframework iron-containing species in ZSM-5 for N2O decomposition

The reactivity of mononuclear and binuclear iron-containing complexes in ZSM-5 zeolite for catalytic N2O decomposition has been investigated by periodic DFT calculations and microkinetic modeling. On mononuclear sites, the activation of a first N2O molecule is favorable. The rate of catalytic N2O decomposition over Fe2+ and [FeIIIO]+ sites is very low because of the very high barriers (>180kJ/mol) for the activation of the second N2O molecule necessary to complete the catalytic cycle by O2 formation. The catalytic cycles for N2O decomposition over binuclear [FeII(μ-O)FeII]2+ and [FeIII(μ-O2)FeIII]2+ species are interconnected. The catalytic cycle involves the interconversion of these species upon dissociation of N2O on the former complex. As the coordination of reactive Fe centers changes along the reaction coordinate, there are changes in the spin state of the complexes, which affect the overall potential energy diagram. These changes in spin multiplicities facilitate O2 formation and desorption steps. Based on the DFT-computed potential energy diagrams, microkinetic model simulations were carried out to predict reaction rates and kinetic parameters. The rate of O2 formation is much higher on binuclear sites than on mononuclear sites. For mononuclear sites, the apparent activation energy is ∼180kJ/mol, close to the barrier for dissociating a second N2O molecule. It is consistent with first-order behavior with respect to the partial pressure of N2O. Binuclear sites display much higher reactivity. At low temperature, O2 desorption is rate controlling, whereas at higher temperatures, the rate is controlled by the two N2O dissociation reactions on [FeII(μ-O)FeII]2+ and [FeIII(μ-O)2FeIII]2+. This leads to first-order behavior with respect to N2O. An alternative path involving N2O adsorption and dissociation on [OFe(μ-O)2Fe]2+ is energetically favorable but does not contribute to the catalytic cycle because O2 desorption from the [OFe(μ-O)2Fe]2+ intermediate is preferred over the activation of a third N2O molecule due to entropic reasons.

Pathways and kinetics of methane and ethane C–H bond cleavage on PdO(101)

We used conventional density functional theory (DFT) and dispersion-corrected DFT (DFT-D3) calculations to investigate C-H bond activation pathways for methane and ethane σ-complexes adsorbed on the PdO(101) surface. The DFT-D3 calculations predict lower and more physically realistic values of the apparent C-H bond cleavage barriers, which are defined relative to the gas-phase energy level, while giving nearly the same energy differences between stationary states as predicted by conventional DFT for a given reaction pathway. For the stable CH4 η(2) complex on PdO(101), DFT-D3 predicts that the C-H bond cleavage barriers are 55.2 and 16.1 kJ∕mol relative to the initial molecularly adsorbed and gaseous states, respectively. We also predict that dehydrogenation of the resulting CH3 groups and conversion to CH3O species are significantly more energetically demanding than the initial C-H bond activation of CH4 on PdO(101). Using DFT-D3, we find that an η(2) and an η(1) ethane complex can undergo C-H bond cleavage on PdO(101) with intrinsic energy barriers that are similar to that of the methane complex, but with apparent barriers that are close to zero. We also investigated the dissociation kinetics of methane and ethane on PdO(101) using microkinetic models, with parameters derived from the DFT-D3 relaxed structures. We find that a so-called 3N - 2 model, in which two frustrated adsorbate motions are treated as free motions, predicts desorption pre-factors and alkane dissociation probabilities that agree well with estimates obtained from the literature. The microkinetic simulations demonstrate the importance of accurately describing entropic contributions in kinetic simulations of alkane dissociative chemisorption.

Macro‐ and Microkinetic Simulation of Diesel Oxidation Catalyst: Effect of Aging, Noble Metal Loading and Platinum Oxidation

AbstractIn automotive exhaust aftertreatment simulation, both macro‐ and microkinetic models are commonly used. In this contribution both models are applied for the simulation of diesel oxidation catalysts (Pt/γ‐Al2O3) with different catalyst loading and degree of thermal aging. The study proves that the structure insensitive kinetics of the considered catalysts can be described with the same rate equations only by scaling the rate constants of the different reaction steps with the catalytically active Pt surface, which is accessible by CO adsorption or light‐off measurements. In addition, NO oxidation is strongly influenced by a reversible, slow transformation of Pt into Pt‐oxide.

Microkinetic Simulation of Temperature-Programmed Desorption

The temperature-programmed desorption (TPD) spectra were simulated by combining density functional theory (DFT) calculations and microkinetic modeling. In the microkinetic analyses, all kinetic and thermodynamic parameters were obtained from DFT calculations to minimize artificial assumptions. For the case study, the desorptions of NH3 and H2O from the RuO2(110) surface were simulated. The coverage-dependent desorption energies were introduced into the microkinetic model because different adsorbates on the surface will exhibit different desorption behaviors. In addition, temperature-dependent pre-exponential factors were applied to the desorption rate equations. The calculated pre-exponential factors are ranged from 1014 to 1017 s–1, which are greatly larger than 1013 s–1, a generally accepted empirical value for desorption processes. The desorption temperatures obtained from microkinetic simulations consist with experimental results, and the simulated TPD patterns are also similar to the experimental observations.

H2S splitting on Cu(110): Insight from combined periodic density functional theory calculations and microkinetic simulation

Practical copper (Cu)‐based catalysts for the water–gas shift (WGS) reaction was long believed to expose a large proportion of Cu(110) planes. In this work, as an important first step toward addressing sulfur poisoning of these catalysts, the detailed mechanism for the splitting of hydrogen sulfide (H2S) on the open Cu(110) facet has been investigated in the framework of periodic, self‐consistent density functional theory (DFT‐GGA). The microkinetic model based on the first‐principles calculations has also been developed to quantitatively evaluate the two considered decomposition routes for yielding surface atomic sulfur (S*): (1) H2S → H2S* → SH* → S* and (2) 2H2S → 2H2S* → 2SH* → S* + H2S* → S* + H2S. The first pathway proceeding through unimolecular SH* dissociation was identified to be feasible, whereas the second pathway involving bimolecular SH* disproportionation made no contribution to S* formation. The molecular adsorption of H2S is the slowest elementary step of its full decomposition, being related with the large entropy term of the gas‐phase reactant under realistic reaction conditions. A comparison of thermodynamic and kinetic reactivity between the substrate and the close‐packed Cu(111) surface further shows that a loosely packed facet can promote the S* formation from H2S on Cu, thus revealing that the reaction process is structure sensitive. The present DFT and microkinetic modeling results provide a reasonably complete picture for the chemistry of H2S on the Cu(110) surface, which is a necessary basis for the design of new sulfur‐tolerant WGS catalysts. © 2013 Wiley Periodicals, Inc.

Theoretical Investigation of Structure-Sensitivity of Styrene Epoxidation on Ag(111) and Ag(110) Surfaces

The selective oxidation of styrene on oxygen-covered Ag(110) and Ag(111) surfaces is studied by density functional theory (DFT) calculations with the periodic slab model. On the Ag(110) surface, a pre-adsorbed oxygen atom prefers the 3-fold hollow site (3h) with an adsorption energy of-3.59 eV. On the Ag(111) surface, the most stable adsorption site for a pre-adsorbed oxygen atom is the fcc site, and the adsorption energy is-3.69 eV. The reaction process of the selective oxidation of styrene includes two steps: the formation of surface intermediates (branched oxametallacycle and linear oxametallacycle) and the subsequent formation of different products. The calculated results show that the formation of styrene oxide via the linear oxametallacycle (i.e., the pre-adsorbed atomic oxygen bound to the methylene group in styrene) is the favorable reaction mechanism on both Ag(110) and Ag(111) surfaces. The reaction barriers for the different reaction steps of styrene epoxidation on the Ag(110) surface are generally higher than those on the Ag(111) surface. Moreover, the micro-kinetic simulation results indicate that the relative selectivity towards the formation of styrene oxide on the Ag(111) surface is much higher than that on the Ag(110) surface (0.38 vs 0.003) because the energy barrier for the styrene epoxidation is smaller than that for the formation of phenyl acetaldehyde and its combustion intermediate on Ag(111) surface. The reverse trends occurred on the Ag(110) surface. (Article)

Microkinetics of steam methane reforming on platinum and rhodium metal surfaces

We have investigated the most important elementary reaction steps in the steam methane reforming (SMR) process for planar and stepped Pt surfaces (dissociative CH4 adsorption, CHads–Oads recombination, H2O activation) and compared activation barriers for Rh surfaces. Compared to Rh, the lower reactivity of Pt results in (i) higher barriers for dissociative CH4 adsorption and (ii) endothermic formation of OHads and Oads. Microkinetic simulations show that Rh nanoparticle catalysts will be more active than Pt ones. The rate-controlling step is dissociative CH4 adsorption occurring on low-coordinated surface atoms (edges, corners, step-edges). The stepped surfaces are much more reactive than planar surfaces of the corresponding metals. For stepped Pt surfaces, CO formation via recombination of Cads+OHads is favored because of the low Oads coverage. At higher temperatures, deactivation may occur due to poisoning by carbonaceous species because the rate of OHads/Oads formation becomes too low compared to the rate of CHads formation. This occurs at lower temperature for Pt than for Rh because of the lower Pt–O bond energy.

Modeling spatially resolved data of methane catalytic partial oxidation on Rh foam catalyst at different inlet compositions and flowrates

Spatially resolved species and temperature profiles measured for a wide range of inlet stoichiometries and flowrates are compared with microkinetic numerical simulations to investigate the effect of transport phenomena on the catalytic partial oxidation of methane on Rh foam catalysts. In agreement with the experimental data, the species profiles calculated at different C/O inlet stoichiometries show that both partial oxidation products (H 2, CO) and total oxidation products (H 2O, CO 2) are formed in the presence of oxygen. At the leaner stoichiometries, both oxygen and methane react in the diffusive regime at the catalyst entrance. At the richest methane stoichiometry (high C/O), surface temperatures are lower and methane consumption is only partly determined by transport. For all stoichiometries, a kinetically controlled regime prevails in the downstream reforming zone after O 2 is fully consumed. The effect of increasing the flowrate shifts all species profiles downstream and also slightly modifies the shapes of the axial profiles, due to the different effectiveness of heat and mass transfer. Despite enhanced mass transfer and increased surface temperature, the shortened contact time causes a reduced CH 4 conversion at high flowrates. The effect of flowrate on the dominant regime is investigated, for both reactants, comparing the resistances calculated in the pure transport regime and in the pure kinetic regime. From a chemical point of view, the model allows for the analysis of the reaction path leading to hydrogen. Due to inhibition of H 2O re-adsorption, it can be proven that H 2 can be a primary product even in the presence of gas phase O 2. The analysis of the surface coverages shows analogous effects on the profiles when decreasing C/O or increasing flow, because in both cases the surface temperature is increased. Syngas selectivity was also evaluated, both from measured and calculated profiles. S H2 is well described by the model at each stoichiometry and flowrate, while S CO is underestimated in every case. From this work, it is also indicated that the Rh catalyst works with CO (measured) selectivities higher than equilibrium. Carbon dioxide only forms in the oxidation zone, for C/O = 1 and 1.3, but in the rest of the catalyst zone, there is no further production despite what would be expected from equilibrium. This confirms Rh does not catalyze the water gas shift reaction. On the other hand, at C/O = 0.8, this reaction becomes active, due to the higher temperature, and the CO 2 is also produced in the reforming zone. This suggests that CO 2 will not rise after the oxidation section if the surface temperature is kept sufficiently low. Sensitivity analyses to the active catalytic surface and to the kinetic parameters are provided.

ChemInform Abstract: Catalyst Synthesis by Analogy

Abstract Catalyst synthesis is discussed in terms of the identification of essential similarities that allow new catalysts to be suggested by analogy with known catalytic processes. Microkinetic simulation employing parameters with direct physical and chemical meaning provides an effective means to interpret, coordinate and generalize diverse experimental studies. Microkinetic simulation studies, therefore, can assist in the identification of similarities by consolidating in a quantitative fashion the experimental, theoretical and semi-empirical information relevant to the catalytic process. This procedure serves to focus our chemical intuition, generalize our experience with related catalytic processes, and use more effectively semi-empirical correlations to suggest new catalytic materials.

Dual reverse spill-over: Microkinetic simulations of the CO oxidation on Pd nanocatalysts

Simulations of cluster-based catalytic oxidation of CO were performed using a dual reverse spill-over microkinetic model (DRSO-MK simulations) in order to improve the description and understand the underlying physics of the experimental turn-over data. The description of mass-selected Pd 13 TOF profiles as a function of mole fraction was reproduced to an excellent level at a range of temperatures. The DRSO-MK model was extended to produce predictions of reactants which are both mobile on the support, illustrating the predictive power of the model and the importance of support interactions in the accurate modelling of cluster-based nanocatalysts.

Oxidation of Hydrocarbons at Surface Defects: Unprecedented Confirmation of the Oxomethylidyne Pathway on a Stepped Rh Surface

The pathway of methylidyne (CH) oxidation on Rh{211} was studied using plane wave density functional theory (DFT) slab calculations and microkinetic simulations. We present ample evidence that the direct decomposition and oxidation mechanism is not the main reaction route to sythesis gas especially during light-off of catalysts. We characterize the transition state for the surface oxidation of CH to oxomethylidyne (CHO) species and subsequent decomposition to CO and H as products to establish the minimum energy pathway.

Fischer−Tropsch Mechanism Revisited: Alternative Pathways for the Production of Higher Hydrocarbons from Synthesis Gas

Evidence from density functional theory calculations that the main reaction pathway for the Fischer−Tropsch process on Co{0001} is not the carbide mechanism but an alternative branch starting with the hydrogenation of CO to an oxymethylidyne species. We show that hydrogenation is the main reaction path at realistic pressure using microkinetic simulations and thereby bridge the pressure gap in heterogeneous catalysis.

Microkinetic simulations of the oxidation of CO on Pd based nanocatalysis: a model including co-dependent support interactions

The catalysed oxidation of CO using mass-selected Pd(13) clusters supported on thin MgO films was modelled using a microkinetic simulation of the reaction. The model of the system includes reverse spill-over calculations which were intrinsically incorporated into the formulation of the kinetics. The spill-over model is based on a capture-zone approach including a co-dependence on the variables of the kinetic equations. The experimental values were determined using dual pulsed-molecular beam measurements and recorded at a range of temperatures. The experiment allowed the turn-over frequency and reaction probability to be determined as a function of mole fraction. Comparison of the kinetic model with the experimental data gives excellent agreement and strongly highlights the importance of substrate effects. In particular, the origin of the low temperature catalysis of the Pd clusters is elucidated. The model allows the mole fraction and temperature dependent values such as the sticking coefficients for these clusters to be predicted.

Adsorption, Diffusion and Desorption of Chlorine on and from Rutile TiO2{110}: A Theoretical Investigation

The adsorption, diffusion and desorption of chlorine on and from stoichiometric, reduced and partially reduced (defective) rutile TiO2{110} are investigated using ab initio density functional theory (DFT) calculations. Theoretical results are compared with experimental investigations, and microkinetic simulations based on DFT values are then used to verify the diffusion mechanisms assumed in the experimental investigations.

Steam Reforming and Graphite Formation on Ni Catalysts

Based on density functional theory calculations, kinetic measurements, microkinetic and Monte Carlo simulations, thermogravimetric analysis (TGA) experiments, extended X-ray absorption spectroscopy (EXAFS) measurements, and experimental results from the literature, we present a detailed and comprehensive mechanistic picture of the steam reforming process on a Ni catalyst. The complete potential energy diagram for the full reaction is presented and compared to experiments. Structures, energies of all reaction intermediates, and activation barriers are identified. We conclude that there are at least two kinds of active sites with different reactivities for steam reforming: a more active one associated with defect (step) sites, and a less active one associated with close-packed facets. It is further suggested that the nucleation of graphite is initiated at the step sites. We show that additives like potassium, sulfur, and gold preferentially bind to the step sites of Ni, and on this basis it is suggested that the promotion by these additives in terms of a higher tolerance toward graphite formation involves the same basic mechanism: blocking of the step sites.

Reaction Kinetics on Heterogeneous Model Catalysts: The CO Oxidation on Alumina-Supported Pd Particles

We have employed multimolecular beam techniques to study the transient and steady-state kinetics of the CO oxidation on alumina-supported Pd model catalysts as a function of particle size and surface structure. The model systems were prepared under UHV conditions on a well-ordered alumina film on NiAl(110) and were previously characterized with respect to their geometric and electronic structure and their morphology. Crossing two molecular beams on the sample surface we have systematically probed the CO2 production rate over a wide range of reactant fluxes and at different sample temperatures. Characteristic differences as a function of particles size are observed in both the transient and steady-state regime. In order to relate these effects to the differences in structure and adsorption properties, we have performed microkinetic simulations of the entire series of transient experiments. Whereas it is found that the kinetics on large and ordered Pd particles can in general be described by a homogeneous surface model, significant deviations remain with respect to the kinetics on small and defect-rich particles. In order to semiquantitatively simulate these effects, we consider a heterogeneous surface model, which takes into account the simultaneous presence of different types of adsorption sites. Depending on their distribution, surface diffusion between these sites is included. It turns out that the differences observed for the small particles can be qualitatively understood by a simple model, where we add a small fraction of weakly CO binding sites to the regular adsorption properties. This type of modified adsorption behavior is in agreement with previous desorption studies.