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Results for “rate-determining step”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4

Formation of three-dimensional bicontinuous structures via molten salt dealloying studied in real-time by in situ synchrotron X-ray nano-tomography

Abstract Three-dimensional bicontinuous porous materials formed by dealloying contribute significantly to various applications including catalysis, sensor development and energy storage. This work studies a method of molten salt dealloying via real-time in situ synchrotron three-dimensional X-ray nano-tomography. Quantification of morphological parameters determined that long-range diffusion is the rate-determining step for the dealloying process. The subsequent coarsening rate was primarily surface diffusion controlled, with Rayleigh instability leading to ligament pinch-off and creating isolated bubbles in ligaments, while bulk diffusion leads to a slight densification. Chemical environments characterized by X-ray absorption near edge structure spectroscopic imaging show that molten salt dealloying prevents surface oxidation of the metal. In this work, gaining a fundamental mechanistic understanding of the molten salt dealloying process in forming porous structures provides a nontoxic, tunable dealloying technique and has important implications for molten salt corrosion processes, which is one of the major challenges in molten salt reactors and concentrated solar power plants.

36 MATERIALS SCIENCE↗

Ligand-modified nanoparticle surfaces influence CO electroreduction selectivity

Improving the kinetics and selectivity of CO 2 /CO electroreduction to valuable multi-carbon products is a challenge for science and is a requirement for practical relevance. Here we develop a thiol-modified surface ligand strategy that promotes electrochemical CO-to-acetate. We explore a picture wherein nucleophilic interaction between the lone pairs of sulfur and the empty orbitals of reaction intermediates contributes to making the acetate pathway more energetically accessible. Density functional theory calculations and Raman spectroscopy suggest a mechanism where the nucleophilic interaction increases the sp 2 hybridization of CO (ad) , facilitating the rate-determining step, CO* to (CHO)*. We find that the ligands stabilize the (HOOC–CH 2 )* intermediate, a key intermediate in the acetate pathway. In-situ Raman spectroscopy shows shifts in C–O, Cu–C, and C–S vibrational frequencies that agree with a picture of surface ligand-intermediate interactions. A Faradaic efficiency of 70% is obtained on optimized thiol-capped Cu catalysts, with onset potentials 100 mV lower than in the case of reference Cu catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Isotope-dependent Tafel analysis probes proton transfer kinetics during electrocatalytic water splitting

Proton transfer plays an important role in both hydrogen and oxygen evolution reactions during electrocatalytic water splitting to produce green hydrogen. However, directly adapting the conventional proton/deuterium kinetic isotope effect to study proton transfer in heterogeneous electrocatalytic processes is challenging. Here we propose using the shift in the Tafel slope between protic and deuteric electrolytes, or the Tafel slope isotope effect, as an effective probe of proton transfer characteristics. Comparison of the Tafel slope isotope effect for diverse hydrogen and oxygen evolution reaction electrocatalysts in different pH environments reveals that proton transfer is both pH and structure dependent. Using ruthenium oxide as an example, we show that local structure modification can change the rate-determining step from an electrochemical, concerted proton–electron transfer step to a chemical step and improve the oxygen evolution activity in acid. The isotope-dependent Tafel analysis will facilitate a better understanding of the proton transfer behaviours during electrocatalytic processes and provide guidance for designing efficient electrocatalysts.

Chemistry↗

Efficient electrocatalytic valorization of chlorinated organic water pollutant to ethylene

Electrochemistry can provide an efficient and sustainable way to treat environmental waters polluted by chlorinated organic compounds. However, the electrochemical valorization of 1,2-dichloroethane (DCA) is currently challenged by the lack of a catalyst that can selectively convert DCA in aqueous solutions into ethylene. Here, in this work, we report a catalyst comprising cobalt phthalocyanine molecules assembled on multiwalled carbon nanotubes that can electrochemically decompose aqueous DCA with high current and energy efficiencies. Ethylene is produced at high rates with unprecedented ~100% Faradaic efficiency across wide electrode potential and reactant concentration ranges. Kinetic studies and density functional theory calculations reveal that the rate-determining step is the first C–Cl bond breaking, which does not involve protons—a key mechanistic feature that enables cobalt phthalocyanine/carbon nanotube to efficiently catalyse DCA dechlorination and suppress the hydrogen evolution reaction. The nanotubular structure of the catalyst enables us to shape it into a flow-through electrified membrane, which we have used to demonstrate >95% DCA removal from simulated water samples with environmentally relevant DCA and electrolyte concentrations.

Choi, Chungseok↗

Understanding the performance of a bisphosphonate Ru water oxidation catalyst

Water oxidation catalysts (WOCs) create electrons that allow generating H 2 from water and sunlight, a promising process for the production of clean energy. Here, the mechanism of water oxidation mediated by Ru(2,2'-bipyridine-6,6'-diphosphonato)(4-picoline) 2 has been studied computationally to comprehend the results obtained in the experiments performed by the Concepcion and Grotjahn groups. Our study was performed at pH = 8 and 1. At pH = 8, the phosphonates are fully deprotonated and the catalysis, which is shown to be more energetically costly than that of the dicarboxylato Ru catalyst counterpart, takes place through a mechanism that involves a bimolecular interaction between two metal-oxo units (I2M). At pH = 1, only one of the phosphonates of the catalyst can deprotonate. After testing all possible pathways and comparing with experimental data, we conclude that the catalysis proceeds neither through a water nucleophilic attack nor via I2M, but rather we hypothesize that the rate-determining step involves both the catalyst and the ceric ammonium nitrate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mechanism of methanol synthesis on Ni(110)

Planewave density functional theory (DFT-PW91) calculations are employed to study the methanol synthesis through CO 2 and CO hydrogenation, as well as the two side reactions: the water gas shift (WGS) reaction and formic acid formation, on Ni(110). For the WGS reaction on Ni(110), we find that the redox mechanism is favored over the carboxyl-mediated mechanism. We show that the formate pathway is the dominant one for formic acid formation. For methanol synthesis through CO 2 and CO hydrogenation on Ni(110), our results reveal that the formic-acid- and dioxymethylene-mediated pathways coexist, in contrast to methanol synthesis on Cu(111) where the formic-acid-mediated pathway dominates. We also find that on Ni(110), hydrogenation of CH 2 O* to CH 3 O* and that to CH 2 OH* both contribute to MeOH synthesis. Based on the derived energetics, we ascertain that CH 3 O* hydrogenation to CH 3 OH* is likely the rate-determining step along the CH 3 O* pathway on Ni(110). Remarkably, CH 3 O* hydrogenation can be facilitated by the presence of HCO*, demonstrating the promotional effect of CO. Furthermore, we show that CO also participates in methanol synthesis directly via its hydrogenation to HCO* and further to CH 2 O*. Additional microkinetic modeling by considering feed composition and reaction conditions would provide further mechanistic insights into methanol synthesis on Ni(110).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Characterization of plasma catalytic decomposition of methane: role of atomic O and reaction mechanism

In this work, we investigated atmospheric pressure plasma jet (APPJ)-assisted methane oxidation over a Ni-SiO 2 /Al 2 O 3 catalyst. We evaluated possible reaction mechanisms by analyzing the correlation of gas phase, surface and plasma-produced species. Plasma feed gas compositions, plasma powers, and catalyst temperatures were varied to expand the experimental parameters. Real-time Fourier-transform infrared spectroscopy was applied to quantify gas phase species from the reactions. The reactive incident fluxes generated by plasma were measured by molecular beam mass spectroscopy using an identical APPJ operating at the same conditions. A strong correlation of the quantified fluxes of plasma-produced atomic oxygen with that of CH 4 consumption, and CO and CO 2 formation implies that O atoms play an essential role in CH 4 oxidation for the investigated conditions. With the integration of APPJ, the apparent activation energy was lowered and a synergistic effect of 30% was observed. We also performed in-situ diffuse reflectance infrared Fourier-transform spectroscopy to analyze the catalyst surface. The surface analysis showed that surface CO abundance mirrored the surface coverage of CH n at 25 °C. This suggests that CH n adsorbed on the catalyst surface as an intermediate species that was subsequently transformed into surface CO. We observed very little surface CH n absorbance at 500 °C, while a ten-fold increase of surface CO and stronger CO 2 absorption were seen. This indicates that for a nickel catalyst at 500 °C, the dissociation of CH 4 to CHn may be the rate-determining step in the plasma-assisted CH 4 oxidation for our conditions. We also found the CO vibrational frequency changes from 2143 cm –1 for gas phase CO to 2196 cm –1 for CO on a 25 °C catalyst surface, whereas the frequency of CO on a 500 °C catalyst was 2188 cm –1 . Here, the change in CO vibrational frequency may be related to the oxidation of the catalyst.

methane oxidation↗

Microwave-Assisted Gasification of Biochar: Effect of Operational Parameters and Biochar Composition on Syngas Production

The utilization of microwave-assisted gasification for biomass/plastic is a promising route toward clean energy production, contributing to a reduction in carbon footprint. This method facilitates the conversion of biomass into syngas with enhanced hydrogen (H2) yield, surpassing conventional heating approaches. However, the gasification of biochar, a byproduct resulting from the initial rapid pyrolysis of biomass, appears as a rate-determining step in biomass gasification. To ensure high conversion efficiency, particularly in pilot or larger scales, the maintenance of high biochar reactivity is essential, which can be achieved by introducing catalysts to minimize biochar formation. Furthermore, given the susceptibility of biochar to microwave heating, gaining a comprehensive understanding of its behavior in the presence of microwave-active catalysts under microwave conditions is crucial to obtain valuable insights into the underlying mechanisms, thereby improving overall biomass gasification efficiency. In the previous study, magnetite (Fe3O4) was selected for microwave-assisted gasification for biomass/plastic due to its dual role as a catalyst and microwave absorber and demonstrated considerably enhanced hydrogen production. Herein, Fe3O4 is rationally modified with metal promoters and their synergistic effect toward biochar gasification performance is investigated. The data shows that metal promoted Fe3O4 shows a higher syngas yield than that of pristine Fe3O4 in biochar.

Mai, Duy Hien↗

ALD with Alternative Coreactants: Which Work, Which Do Not, and Why

In this paper, we present a combined experimental and theoretical study that systematically evaluates a series of alcohols (i.e., primary, secondary, and tertiary) as coreactants for trimethylaluminum (TMA)-based atomic layer deposition (ALD) of Al 2 O 3 . We employed in situ quartz crystal microbalance techniques and ex situ X-ray photoelectron spectroscopy to probe growth across a range of temperatures from T = 120 to 285 °C. Dispersion-inclusive hybrid density functional theory was employed to identify potential reaction pathways and compute corresponding Gibbs free-energy barriers and rate coefficients. Experimentally on an Al 2 O 3 surface, sustained thin-film growth, where the rate is constant over many cycles, was only observed with tertiary alcohols (tert-butanol and 2-methyl-2-butanol) at elevated temperatures (e.g., T = 285 °C); for tert-butanol specifically, sustained growth also occurred at T = 240 °C, with no sustained growth at or below T = 210 °C. Growth using primary and secondary alcohols decayed to a negligible value after only 2–3 cycles on an Al 2 O 3 surface at all tested temperatures. Intentional trace additions of H 2 O to anhydrous alcohols restored sustained growth but at reduced deposition rates relative to pure H 2 O. Theoretical analysis supports a bimolecular alkoxy β-H elimination mechanism as the primary reaction pathway: initiated by the formation of a bound alkoxy species, the subsequent β-H elimination step is rate-determining, with a barrier that systematically decreases as the degree of the alcohol coreactant is increased from primary to secondary to tertiary. Computed rate coefficients (k) also indicate a strong temperature dependence (with k increasing by ∼4–5 orders of magnitude from T = 120 to 285 °C) and are consistent with the experimental observation that only tertiary alcohols lead to steady thin-film growth at elevated temperatures. This integrated approach establishes why only certain alcohols can sustain Al 2 O 3 ALD and delivers a predictive framework for identifying effective alcohol coreactants.

36 MATERIALS SCIENCE↗

Mechanistic Studies of an Iron-Catalyzed Intermolecular C–H Amination Reaction under Catalytic Conditions and Having a Large KIE

The conversion of C–H bonds into amines by nitrene insertion is an attractive transformation since it is both atom- and step-economical, and provides a direct route to functionalizing hydrocarbons. Using an iron catalyst [{( tBu pyrr) 2 pyr}Fe(OEt 2 )] (1-OEt 2 ) (( tBu pyrr) 2 pyr 2– = 3,5- t Bu 2 -bis(pyrrolyl)pyridine), we recently demonstrated the catalytic conversion of weak C–H bonds into secondary amines using aryl azides as the nitrene source [Zars, E.; Angew. Chem., Int. Ed. 2023, 62, e202311749]. Here, we describe detailed mechanistic studies of this intermolecular C–H amination reaction under catalytic conditions. We find by Variable Time Normalization Analysis (VTNA) that the conversion of xanthene (2-H 2 ) and 2,4,6-trimethyl-phenyl azide ( Me 3) catalyzed by 1-OEt 2 is an overall 3/2 order process, being 1 st order in 2-H 2 and half order in Me 3. A kinetic isotope effect study (KIE) using 2-d 2 results in a significant decrease in the rate (KIE = 61(15)), which clearly implicates the C–H insertion step as rate-determining. Furthermore, treatment of 1-OEt 2 with one equivalent of N 3 -2,6- i Pr 2 –C 6 H 3 yields the mixed-valence C–N coupled product [( tBu pyrr) 2 pyrFe-N═C(2,6 i Pr 2 –Ph)═N-(2,6 i Pr 2 –Ph))Fe tBu pyrrpyr(2-H-pyrr)] (5 iPr ). Quantum chemical calculations confirm the electronic structure of the mixed-valence dimer in 5 iPr and rationalize the Hammett correlation by a delicate balance in the dinuclearization of the catalytically active monomers. Calculations further indicate significant tunneling for the pivotal H atom abstraction by the iron-imidyl complex. Combining all these results allows us to propose a mechanism consisting of imido formation in equilibrium with a radical-coupled diiron system, followed by stepwise C–H insertion via a linear H atom abstraction transition state and subsequent radical rebound.

azides↗

Concerted Proton–Electron Transfer Minimizes Substituent Effects on Adsorbed Phthalocyanine Electrocatalysis

Molecularly modified electrodes (MMEs) are potent electrocatalysts, but few principles exist for their rational design. Electrocatalysis by soluble molecules depends strongly on substituents that tune the catalyst redox potential (E 1/2 ), but it is unclear if this parameter similarly impacts MME catalysis. Herein, we employ the hydrogen evolution reaction (HER) as a test case for comparing carbon-adsorbed cobalt phthalocyanine (CoPc/C) and cobalt hexadecafluoro-phthalocyanine (CoFPc/C). By correlating HER activity and voltammetric data to total Co surface concentration across a wide range of catalyst loadings, we find that only 5–25% of adsorbed Co sites contribute to the Co(II/I) redox wave and that this subpopulation poorly correlates with catalytic activity. Instead, in the low-loading limit, catalytic activity correlates linearly with the majority Co(II/I)-silent Co population, revealing per-site turnover frequency (TOF) values for HER. Despite a 230 mV difference in Co(II/I) redox potentials, CoPc/C and CoFPc/C display TOF values differing by less than a factor of 3 when compared over a wide potential range. Mechanistic studies point to an inner-sphere concerted proton–electron transfer step as rate-determining, suggesting that the Co–H bond dissociation free energy (BDFE) rather than the Co(II/I) E 1/2 is thermodynamically relevant. Computational studies indicate that the fluoro-substituents lead to compensatory changes in Co(II/I) E 1/2 and Co(I) basicity, leaving the Co–H BDFE largely unchanged between CoPc and CoFPc and thereby manifesting in similar catalytic rates. Furthermore, these results highlight the limited effect of E 1/2 -tuning on MME catalytic activity and motivate the development of methods to directly alter active site–substrate BDFE.

Catalysts↗

Thiol-promoted catalytic synthesis of high-performance furan-containing lubricant base oils from biomass derived 2-alkylfurans and ketones

About 97% of lubricant base oils are currently sourced from petroleum and the majority of the rest is produced from vegetable oils. We demonstrate a promising catalytic route to produce base oils from lignocellulosic biomass-derived 2-alkylfurans and ketones via carbon–carbon coupling in neat conditions. Among several homogeneous and heterogeneous acid catalysts tested, a perfluorinated sulfonic acid (Aquivion PW79S) exhibits the best catalytic performance and yields up to 90% renewable furan-containing base oils with the use of a thiol promotor. The effects of the acid strength of the catalysts, molecular size and structure of thiols and ketones, and fraction of thiols are studied. Electronic structure calculations elucidate the reaction pathway and indicate that the thiol reduces the barrier of the rate-determining dehydration step. The structure and properties of base oils can be tuned by using different synthons. Here, these base oils have excellent properties and can be competitive with or surpass the commercial synthetic alkylnaphthalene and furan-containing bio-ester base oils.

09 BIOMASS FUELS↗

Machine Learning Accelerated First-Principles Study of the Hydrodeoxygenation of Propanoic Acid

The complex reaction network of catalytic biomass conversions often involves hundreds of surface intermediates and thousands of reaction steps, greatly hindering the rational design of metal catalysts for these conversions. Here, we present a framework of machine learning (ML)-accelerated first-principles studies for the hydrodeoxygenation (HDO) of propanoic acid over transition metal surfaces. The microkinetic model (MKM) is initially parametrized by ML-predicted energies and iteratively improved by identifying the rate-determining species and steps (RDS), computing their energies by density functional theory (DFT), and reparameterizing the MKM until all the RDS are computed by DFT. The Gaussian process (GP) model performs significantly better than the linear ridge regression model for predicting both the adsorption free energies and transition state free energies. Parameterized with energies from the GP model, only 5–20% of the full reaction network has to be computed by DFT for the MKM to possess DFT-level accuracy for the TOF and dominant reaction pathway. While the linear ridge regression model performs worse than the GP model, its performance is greatly improved when only transition states are predicted by the regression model and adsorption energies are computed by DFT. Overall, we find that a high accuracy in adsorption free energies is more important for a reliable MKM than a high accuracy in TS free energies. Lastly, based on the GP model with GOH and GCHCHCO as catalyst descriptors, we build two-dimensional volcano plots in activity and selectivity that can help design promising alloy catalysts for HDO reactions of organic acids.

adsorption↗

Transition Path Sampling Study of the Feruloyl Esterase Mechanism

Serine hydrolases cleave peptide and ester bonds and are ubiquitous in nature, with applications in biotechnology, in materials, and as drug targets. The serine hydrolase two-step mechanism employs a serine–histidine–aspartate/glutamate catalytic triad, where the histidine residue acts as a base to activate poor nucleophiles (a serine residue or a water molecule) and as an acid to allow the dissociation of poor leaving groups. This mechanism has been the subject of debate regarding how histidine shuttles the proton from the nucleophile to the leaving group. To elucidate the reaction mechanism of serine hydrolases, we employ quantum mechanics/molecular mechanics-based transition path sampling to obtain the reaction coordinate using the Aspergillus niger feruloyl esterase A (AnFaeA) as a model enzyme. The optimal reaction coordinates include terms involving nucleophilic attack on the carbonyl carbon and proton transfer to, and dissociation of, the leaving group. During the reaction, the histidine residue undergoes a reorientation on the time scale of hundreds of femtoseconds that supports the “moving histidine” mechanism, thus calling into question the “ring flip” mechanism. We find a concerted mechanism, where the transition state coincides with the tetrahedral intermediate with the histidine residue pointed between the nucleophile and the leaving group. Moreover, motions of the catalytic aspartate toward the histidine occur concertedly with proton abstraction by the catalytic histidine and help stabilize the transition state, thus partially explaining how serine hydrolases enable poor nucleophiles to attack the substrate carbonyl carbon. Rate calculations indicate that the second step (deacylation) is rate-determining, with a calculated rate constant of 66 s –1 . Altogether, these results reveal the pivotal role of active-site dynamics in the catalytic mechanism of AnFaeA, which is likely similar in other serine hydrolases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Complete Phase Transformation of Ir Nanowire Network into Defect-Rich Oxide Catalyst for High-Performance PEM Water Electrolysis

Iridium-based catalysts remain the most reliable option for the oxygen evolution reaction (OER) in proton exchange membrane water electrolyzers (PEMWEs). However, their high cost and limited performance represent critical barriers to the commercialization of this green hydrogen production technology. Herein, we report the creation of a metallic Ir nanowire network (IrNWN), which exhibits superior OER performance through its in-situ transition into an oxide structure with high intrinsic activity. At a low loading of 0.25 mgIr/cm2 in PEMWEs, IrNWN achieved a current density of 3.13 A/cm2 at a cell voltage of 1.8 V, outperforming the commercial Ir-based catalyst and surpassing the Department of Energy (DOE) 2026 technical target. Moreover, the high activity of IrNWN was maintained for 900 hours in a durability test at 2 A/cm2, showing a low degradation rate of 0.042 mV/hour. Structural analysis of the electrochemically oxidized IrNWN revealed the presence of mixed Ir oxidation states and a high density of surface terminal oxygen groups (μ1-O), which contributed to a reduced energy barrier for the rate-determining O-O coupling step.

oxygen evolution reaction↗

Three rate-determining protein roles in photosynthetic O 2 -evolution addressed by time-resolved experiments on genetically modified photosystems

Light-driven water splitting by plants, algae and cyanobacteria is pivotal for global bioenergetics and biomass formation. A manganese cluster bound to the photosystem II proteins catalyzes the complex reaction at high rate, but the rate-determining factors are insufficiently understood. Here we trace the oxygen-evolution transition by time-resolved polarography and infrared spectroscopy for cyanobacterial photosystems genetically modified at two strategic sites, complemented by computational chemistry. Our results highlight three rate-determining roles of the protein environment of the metal cluster: acceleration of proton-coupled electron transfer, acceleration of substrate-water insertion after O 2 -formation, and balancing of rate-determining enthalpic and entropic contributions. Whereas in general the substrate-water insertion step may be unresolvable in time-resolved experiments, here it likely becomes traceable because of deceleration by genetic modification. Our results may stimulate new time-resolved experiments on substrate-water insertion in photosynthesis, clarification of enthalpy-entropy compensation in enzyme catalysis, and knowledge-guided development of inorganic catalyst materials.

Bioenergetics↗

Mechanistic manifold in a hemoprotein-catalyzed cyclopropanation reaction with diazoketone

Abstract Hemoproteins have recently emerged as promising biocatalysts for new-to-nature carbene transfer reactions. However, mechanistic understanding of the interplay between productive and unproductive pathways in these processes is limited. Using spectroscopic, structural, and computational methods, we investigate the mechanism of a myoglobin-catalyzed cyclopropanation reaction with diazoketones. These studies shed light on the nature and kinetics of key catalytic steps in this reaction, including the formation of an early heme-bound diazo complex intermediate, the rate-determining nature of carbene formation, and the cyclopropanation mechanism. Our analyses further reveal the existence of a complex mechanistic manifold for this reaction that includes a competing pathway resulting in the formation of an N-bound carbene adduct of the heme cofactor, which was isolated and characterized by X-ray crystallography, UV-Vis, and Mössbauer spectroscopy. This species can regenerate the active biocatalyst, constituting a non-productive, yet non-destructive detour from the main catalytic cycle. These findings offer a valuable framework for both mechanistic analysis and design of hemoprotein-catalyzed carbene transfer reactions.

59 BASIC BIOLOGICAL SCIENCES↗

Modified Energy Span Analysis of Catalytic Parallel Pathways and Selectivity

Mechanistic modeling provides vital insights into catalytic reactions. To analyze complex reaction networks with parallel pathways, we leverage the graph theory approach of the Energy Span Model (ESM) to develop a modified energy span analysis (MESA). A new method of cycle plots is proposed to perform reaction pathways analysis visually. We demonstrate this method on two published models: one describing carbon monoxide oxidation and the other simulating ethylene conversion to propanal via hydroformylation or ethane via hydrogenation. Fundamental insights explain kinetic observables, such as a reactant’s negative reaction order. General principles are revealed, such as rate-determining surface species being outside the primary reaction flux cycle and pathway selectivity being a purely kinetic property when reaction conditions are not near equilibrium. Lastly, we demonstrate MESA’s consistency with published microkinetic modeling results, highlighting this technique’s extension of the ESM to heterogeneous catalysts using collision theory to describe adsorption steps and concentration effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗