First-Principles Approach to Heat and Mass Transfer Effects in Model Catalyst Studies

Kinetic Monte Carlo simulations for heterogeneous catalysis: Fundamentals, current status, and challenges

Kinetic Monte Carlo (KMC) simulations in combination with first-principles (1p)-based calculations are rapidly becoming the gold-standard computational framework for bridging the gap between the wide range of length scales and time scales over which heterogeneous catalysis unfolds. 1p-KMC simulations provide accurate insights into reactions over surfaces, a vital step toward the rational design of novel catalysts. In this Perspective, we briefly outline basic principles, computational challenges, successful applications, as well as future directions and opportunities of this promising and ever more popular kinetic modeling approach.

CO2-Activation by size-selected tantalum cluster cations (Ta1-16+): thermalization governing reaction selectivity

The reactions of tantalum cluster cations of different sizes toward carbon dioxide are studied in an ion trap under multi-collisional conditions. For all sizes studied, consecutive reactions with several CO₂ molecules are observed. This reveals two different pathways, namely oxide formation and the pickup of an entire molecule. Supported by calculations of the thermochemistry of Ta_nO⁺ formation upon reaction with CO₂, changes in the branching ratios at a particular cluster size are related to heat effects due to the vibrational heat capacity of the clusters and the exothermicity of the reaction.

Bridging the Pressure Gap in CO Oxidation

Performing fundamental operando catalysis studies under realistic conditions is a key to further develop and increase the efficiency of industrial catalysts. Operando X-ray photoelectron spectroscopy (XPS) experiments have been limited to pressures, and the relevance for industrial applications has been questioned. Herein, we report on the CO oxidation experiment on Pd(100) performed at a total pressure of 1 bar using XPS. We investigate the light-off regime and the surface chemical composition at the atomistic level in the highly active phase. Furthermore, the observed gas-phase photoemission peaks of CO₂, CO, and O₂ indicate that the kinetics of the reaction during the light-off regime can be followed operando, and by studying the reaction rate of the reaction, the activation energy is calculated. The reaction was preceded by an in situ oxidation study in 7% O₂ in He and a total pressure of 70 mbar to confirm the surface sensitivity and assignment of the oxygen-induced photoemission peaks. However, oxygen-induced photoemission peaks were not observed during the reaction studies, but instead, a metallic Pd phase is present in the highly active regime under the conditions applied. The novel XPS setup utilizes hard X-rays to enable high-pressure studies, combined with a grazing incident angle to increase the surface sensitivity of the measurement. Our findings demonstrate the possibilities of achieving chemical information of the catalyst, operando, on an atomistic level, under industrially relevant conditions.

Multiscale modeling of damaged surface topology in a hypersonic boundary

In this work, we used molecular dynamics (MD) to perform trajectory simulations of ice-like argon and amorphous silica aggregates on atomically smooth highly ordered pyrolytic graphite (HOPG) and a comparatively rougher quartz surface. It was found that at all incidence velocities, the quartz surface was stickier than the HOPG surface. The sticking probabilities and elastic moduli obtained from MD were then used to model surface evolution at a micron length scale using kinetic Monte Carlo (kMC) simulations. Rules were derived to control the number of sites available for the process execution in kMC to accurately model erosion of HOPG by atomic oxygen (AO) attack and ice-nucleation on surfaces. It was observed that the effect of defects was to increase the material erosion rate, while that of aggregate nucleation was to lower it. Similarly, simulations were performed to study the effects of AO attack and N₂ adsorption-desorption on surface evolution and it was found that N₂ adsorption-desorption limits the surface available for erosion by AO attack.

Combining Planar Laser-Induced Fluorescence with Stagnation Point Flows for Small Single-Crystal Model Catalysts: CO Oxidation on a Pd(100)

A stagnation flow reactor has been designed and characterized for both experimental and modeling studies of single-crystal model catalysts in heterogeneous catalysis. Using CO oxidation over a Pd(100) single crystal as a showcase, we have employed planar laser-induced fluorescence (PLIF) to visualize the CO2 distribution over the catalyst under reaction conditions and subsequently used the 2D spatially resolved gas phase data to characterize the stagnation flow reactor. From a comparison of the experimental data and the stagnation flow model, it was found that characteristic stagnation flow can be achieved with the reactor. Furthermore, the combined stagnation flow/PLIF/modeling approach makes it possible to estimate the turnover frequency (TOF) of the catalytic surface from the measured CO2 concentration profiles above the surface and to predict the CO2, CO and O2 concentrations at the surface under reaction conditions.

Advances in fixed-bed reactor modeling using particle-resolved computational fluid dynamics (CFD)

In 2006, Dixon et al. published the comprehensive review article entitled “Packed tubular reactor modeling and catalyst design using computational fluid dynamics.” More than one decade later, many researchers have contributed to novel insights, as well as a deeper understanding of the topic. Likewise, complexity has grown and new issues have arisen, for example, by coupling microkinetics with computational fluid dynamics (CFD). In this review article, the latest advances are summarized in the field of modeling fixed-bed reactors with particle-resolved CFD, i.e. a geometric resolution of every pellet in the bed. The current challenges of the detailed modeling are described, i.e. packing generation, meshing, and solving with an emphasis on coupling microkinetics with CFD. Applications of this detailed approach are discussed, i.e. fluid dynamics and pressure drop, dispersion, heat and mass transfer, as well as heterogeneous catalytic systems. Finally, conclusions and future prospects are presented.

Local-metrics error-based Shepard interpolation as surrogate for highly non-linear material models in high dimensions

Many problems in computational materials science and chemistry require the evaluation of expensive functions with locally rapid changes, such as the turn-over frequency of first principles kinetic Monte Carlo models for heterogeneous catalysis. Because of the high computational cost, it is often desirable to replace the original with a surrogate model, e.g., for use in coupled multiscale simulations. The construction of surrogates becomes particularly challenging in high-dimensions. Here, we present a novel version of the modified Shepard interpolation method which can overcome the curse of dimensionality for such functions to give faithful reconstructions even from very modest numbers of function evaluations. The introduction of local metrics allows us to take advantage of the fact that, on a local scale, rapid variation often occurs only across a small number of directions. Furthermore, we use local error estimates to weigh different local approximations, which helps avoid artificial oscillations. Finally, we test our approach on a number of challenging analytic functions as well as a realistic kinetic Monte Carlo model. Our method not only outperforms existing isotropic metric Shepard methods but also state-of-the-art Gaussian process regression.

Novel in Situ Techniques for Studies of Model Catalysts

Motivated mainly by catalysis, gas-surface interaction between single crystal surfaces and molecules has been studied for decades. Most of these studies have been performed in well-controlled environments and have been instrumental for the present day understanding of catalysis, providing information on surface structures, adsorption sites, and adsorption and desorption energies relevant for catalysis. However, the approach has been criticized for being too far from a catalyst operating under industrial conditions at high temperatures and pressures. To this end, a significant amount of effort over the years has been used to develop methods to investigate catalysts at more realistic conditions under operating conditions. One result from this effort is a vivid and sometimes heated discussion concerning the active phase for the seemingly simple CO oxidation reaction over the Pt-group metals in the literature. In recent years, we have explored the possibilities to perform experiments at conditions closer to those of a technical catalyst, in particular at increased pressures and temperatures. In this contribution, results from catalytic CO oxidation over a Pd(100) single crystal surface using Near Ambient Pressure X-ray Photo emission Spectroscopy (NAPXPS), Planar Laser-Induced Fluorescence (PLIF), and High Energy Surface X-ray Diffraction (HESXRD) are presented, and the strengths and weaknesses of the experimental techniques are discussed. Armed with structural knowledge from ultrahigh vacuum experiments, the presence of adsorbed molecules and gas-phase induced surface structures can be identified and related to changes in the reactivity or to reaction induced gas-flow limitations. In particular, the application of PLIF to catalysis allows one to visualize how the catalyst itself changes the gas composition close to the model catalyst surface upon ignition, and relate this to the observed surface structures. The effect obscures a straightforward relation between the active phase and the activity, since in the case of CO oxidation, the gas-phase close to the model catalyst surface is shown to be significantly more oxidizing than far away from the catalyst. We show that surface structural knowledge from UHV experiments and the composition of the gas phase close to the catalyst surface are crucial to understand structure-function relationships at semirealistic conditions. In the particular case of Pd, we argue that the surface structure of the PdO(101) has a significant influence on the activity, due to the presence of Coordinatively Unsaturated Sites (CUS) Pd atoms, similar to undercoordinated Ru and Ir atoms found for RuO₂(110) and IrO₂(110), respectively.

2D and 3D imaging of the gas phase close to an operating model catalyst by planar laser induced fluorescence

In recent years, efforts have been made in catalysis related surface science studies to explore the possibilities to perform experiments at conditions closer to those of a technical catalyst, in particular at increased pressures. Techniques such as high pressure scanning tunneling/atomic force microscopy (HPSTM/AFM), near ambient pressure x-ray photoemission spectroscopy (NAPXPS), surface x-ray diffraction (SXRD) and polarization-modulation infrared reflection absorption spectroscopy (PM-IRAS) at semi-realistic conditions have been used to study the surface structure of model catalysts under reaction conditions, combined with simultaneous mass spectrometry (MS). These studies have provided an increased understanding of the surface dynamics and the structure of the active phase of surfaces and nano particles as a reaction occurs, providing novel information on the structure/activity relationship. However, the surface structure detected during the reaction is sensitive to the composition of the gas phase close to the catalyst surface. Therefore, the catalytic activity of the sample itself will act as a gas-source or gas-sink, and will affect the surface structure, which in turn may complicate the assignment of the active phase. For this reason, we have applied planar laser induced fluorescence (PLIF) to the gas phase in the vicinity of an active model catalysts. Our measurements demonstrate that the gas composition differs significantly close to the catalyst and at the position of the MS, which indeed should have a profound effect on the surface structure. However, PLIF applied to catalytic reactions presents several beneficial properties in addition to investigate the effect of the catalyst on the effective gas composition close to the model catalyst. The high spatial and temporal resolution of PLIF provides a unique tool to visualize the on-set of catalytic reactions and to compare different model catalysts in the same reactive environment. The technique can be applied to a large number of molecules thanks to the technical development of lasers and detectors over the last decades, and is a complementary and visual alternative to traditional MS to be used in environments difficult to asses with MS. In this article we will review general considerations when performing PLIF experiments, our experimental set-up for PLIF and discuss relevant examples of PLIF applied to catalysis.

Real-Time Gas-Phase Imaging over a Pd(110) Catalyst during CO Oxidation by Means of Planar Laser-Induced Fluorescence

The gas composition surrounding a catalytic sample has direct impact on its surface structure, which is essential when in situ investigations of model catalysts are performed. Herein a study of the gas phase close to a Pd(110) surface during CO oxidation under semirealistic conditions is presented. Images of the gas phase, provided by planar laser-induced fluorescence, clearly visualize the formation of a boundary layer with a significantly lower CO partial pressure close to the catalytically active surface, in comparison to the overall concentration as detected by mass spectrometry. The CO partial pressure variation within the boundary layer will have a profound effect on the catalysts’ surface structure and function and needs to be taken into consideration for in situ model catalysis studies.

Kinetic modelling of heterogeneous catalytic systems

The importance of heterogeneous catalysis in modern life is evidenced by the fact that numerous products and technologies routinely used nowadays involve catalysts in their synthesis or function. The discovery of catalytic materials is, however, a non-trivial procedure, requiring tedious trial-and-error experimentation. First-principles-based kinetic modelling methods have recently emerged as a promising way to understand catalytic function and aid in materials discovery. In particular, kinetic Monte Carlo (KMC) simulation is increasingly becoming more popular, as it can integrate several sources of complexity encountered in catalytic systems, and has already been used to successfully unravel the underlying physics of several systems of interest. After a short discussion of the different scales involved in catalysis, we summarize the theory behind KMC simulation, and present the latest KMC computational implementations in the field. Early achievements that transformed the way we think about catalysts are subsequently reviewed in connection to latest studies of realistic systems, in an attempt to highlight how the field has evolved over the last few decades. Present challenges and future directions and opportunities in computational catalysis are finally discussed.

A high pressure x-ray photoelectron spectroscopy study of CO oxidation over Rh(100)

We have studied the oxidation of CO over Rh(100) using high pressure x-ray photoelectron spectroscopy under CO and O2 pressures ranging from 0.01 to 1 mbar. The results show a very low or no conversion for the CO covered surface found at low temperatures, while the activity rises slightly when the temperature is high enough for some CO to desorb, exposing surface sites for dissociative O2 adsorption. As the temperature is increased further, more CO desorbs and oxygen replaces CO as the dominating species at the surface. At the same time we find a sudden increase in the reactivity, such that all CO that reaches the surface is instantly transformed into CO2. We find that the O coverage in the active state is highly dependent on the total pressure and, although we do not detect any presence of a surface oxide as in previous surface x-ray diffraction studies, the highest O coverage indicates that the surface is close to being oxidized.

Density functional theory simulations of complex catalytic materials in reactive environments: beyond the ideal surface at low coverage

Advanced DFT models of complex catalysts, such as amorphous silica–alumina and supported subnanometric platinum particles, bridge the gap between the ideal surface model and the industrial catalyst.

In situ x-ray photoelectron spectroscopy of model catalysts: at the edge of the gap

We present high-pressure x-ray photoelectron spectroscopy (HP-XPS) and first-principles kinetic Monte Carlo study addressing the nature of the active surface in CO oxidation over Pd(100). Simultaneously measuring the chemical composition at the surface and in the near-surface gas phase, we reveal both O-covered pristine Pd(100) and a surface oxide as stable, highly active phases in the near-ambient regime accessible to HP-XPS. Surprisingly, no adsorbed CO can be detected during high CO(2) production rates, which can be explained by a combination of a remarkably short residence time of the CO molecule on the surface and mass-transfer limitations in the present setup.

An in situ set up for the detection of CO2 from catalytic CO oxidation by using planar laser-induced fluorescence

We report the first experiment carried out on an in situ setup, which allows for detection of CO(2) from catalytic CO oxidation close to a model catalyst under realistic reaction conditions by the means of planar laser-induced fluorescence (PLIF) in the mid-infrared spectral range. The onset of the catalytic reaction as a function of temperature was followed by PLIF in a steady state flow reactor. After taking into account the self-absorption of CO(2), a good agreement between the detected CO(2) fluorescence signal and the CO(2) mass spectrometry signal was shown. The observed difference to previously measured onset temperatures for the catalytic ignition is discussed and the potential impact of IR-PLIF as a detection technique in catalysis is outlined.