Degree of Rate Control: How Much the Energies of Intermediates and Transition States Control Rates

Mechanism of Cobalt-Catalyzed CO Hydrogenation: 1. Methanation

The mechanism of CO hydrogenation to CH₄ at 260 °C on a cobalt catalyst is investigated using steady-state isotopic transient kinetic analysis (SSITKA) and backward and forward chemical transient kinetic analysis (CTKA). The dependence of CH_x residence time is determined by ¹²CO/H₂ → ¹³CO/H₂ SSITKA as a function of the CO and H₂ partial pressure and shows that the CH₄ formation rate is mainly controlled by CH_x hydrogenation rather than CO dissociation. Backward CO/H₂ → H₂ CTKA emphasizes the importance of H coverage on the slow CH_x hydrogenation step. The H coverage strongly depends on the CO coverage, which is directly related to CO partial pressure. Combining SSITKA and backward CTKA allows determining that the amount of additional CH₄ obtained during CTKA is nearly equal to the amount of CO adsorbed to the cobalt surface. Thus, under the given conditions overall barrier for CO hydrogenation to CH₄ under methanation condition is lower than the CO adsorption energy. Forward CTKA measurements reveal that O hydrogenation to H₂O is also a relatively slow step compared to CO dissociation. The combined transient kinetic data are used to fit an explicit microkinetic model for the methanation reaction. The mechanism involving direct CO dissociation represents the data better than a mechanism in which H-assisted CO dissociation is assumed. Microkinetics simulations based on the fitted parameters confirms that under methanation conditions the overall CO consumption rate is mainly controlled by C hydrogenation and to a smaller degree by O hydrogenation and CO dissociation. These simulations are also used to explore the influence of CO and H₂ partial pressure on possible rate-controlling steps.

Mechanism of Cobalt-Catalyzed CO Hydrogenation: 2. Fischer-Tropsch Synthesis

Fischer–Tropsch (FT) synthesis is one of the most complex catalyzed chemical reactions in which the chain-growth mechanism that leads to formation of long-chain hydrocarbons is not well understood yet. The present work provides deeper insight into the relation between the kinetics of the FT reaction on a silica-supported cobalt catalyst and the composition of the surface adsorbed layer. Cofeeding experiments of ¹²C₃H₆ with ¹³CO/H₂ evidence that CH_x surface intermediates are involved in chain growth and that chain growth is highly reversible. We present a model-based approach of steady-state isotopic transient kinetic analysis measurements at FT conditions involving hydrocarbon products containing up to five carbon atoms. Our data show that the rates of chain growth and chain decoupling are much higher than the rates of monomer formation and chain termination. An important corollary of the microkinetic model is that the fraction of free sites, which is mainly determined by CO pressure, has opposing effects on CO consumption rate and chain-growth probability. Lower CO pressure and more free sites leads to increased CO consumption rate but decreased chain-growth probability because of an increasing ratio of chain decoupling over chain growth. The preferred FT condition involves high CO pressure in which chain-growth probability is increased at the expense of the CO consumption rate.

Contrasting the Role of Ni/Al2O3 Interfaces in Water-Gas Shift and Dry Reforming of Methane

Transition metal nanoparticles (NPs) are typically supported on oxides to ensure their stability, which may result in modification of the original NP catalyst reactivity. In a number of cases, this is related to the formation of NP/support interface sites that play a role in catalysis. The metal/support interface effect verified experimentally is commonly ascribed to stronger reactants adsorption or their facile activation on such sites compared to bare NPs, as indicated by DFT-derived potential energy surfaces (PESs). However, the relevance of specific reaction elementary steps to the overall reaction rate depends on the preferred reaction pathways at reaction conditions, which usually cannot be inferred based solely on PES. Hereby, we use a multiscale (DFT/microkinetic) modeling approach and experiments to investigate the reactivity of the Ni/Al₂O₃ interface toward water-gas shift (WGS) and dry reforming of methane (DRM), two key industrial reactions with common elementary steps and intermediates, but held at significantly different temperatures: 300 vs 650 °C, respectively. Our model shows that despite the more energetically favorable reaction pathways provided by the Ni/Al₂O₃ interface, such sites may or may not impact the overall reaction rate depending on reaction conditions: the metal/support interface provides the active site for WGS reaction, acting as a reservoir for oxygenated species, while all Ni surface atoms are active for DRM. This is in contrast to what PESs alone indicate. The different active site requirement for WGS and DRM is confirmed by the experimental evaluation of the activity of a series of Al₂O₃-supported Ni NP catalysts with different NP sizes (2-16 nm) toward both reactions.

Surface Reaction Barriometry: Methane Dissociation on Flat and Stepped Transition-Metal Surfaces

Accurately simulating heterogeneously catalyzed reactions requires reliable barriers for molecules reacting at defects on metal surfaces, such as steps. However, first-principles methods capable of computing these barriers to chemical accuracy have yet to be demonstrated. We show that state-resolved molecular beam experiments combined with ab initio molecular dynamics using specific reaction parameter density functional theory (SRP-DFT) can determine the molecule-metal surface interaction with the required reliability. Crucially, SRP-DFT exhibits transferability: the functional devised for methane reacting on a flat (111) face of Pt (and Ni) also describes its reaction on stepped Pt(211) with chemical accuracy. Our approach can help bridge the materials gap between fundamental surface science studies on regular surfaces and heterogeneous catalysis in which defected surfaces are important.

Lithium Diisopropylamide: Nonequilibrium Kinetics and Lessons Learned about Rate Limitation

The kinetics of lithium diisopropylamide (LDA) in tetrahydrofuran under nonequilibrium conditions are reviewed. These conditions correspond to a class of substrates in which the rates of LDA aggregation and solvation events are comparable to the rates at which various fleeting intermediates react with substrate. Substrates displaying these reactivities, by coincidence, happen to be those that react at tractable rates on laboratory time scales at -78 °C. In this strange region of nonlimiting behavior, rate-limiting steps are often poorly defined, sometimes involve deaggregation, and at other times include reaction with substrate. Changes in conditions routinely cause shifts in the rate-limiting steps, and autocatalysis is prevalent and can be acute. The studies are described in three distinct portions: (1) methods and strategies used to deconvolute complex reaction pathways, (2) the resulting conclusions about organolithium reaction mechanisms, and (3) perspectives on the concept of rate limitation reinforced by studies of LDA in tetrahydrofuran at -78 °C under nonequilibrium conditions.

Computational investigation of the kinetics and mechanism of the initial steps of the Fischer-Tropsch synthesis on cobalt

A multi-site microkinetic model for the Fischer-Tropsch synthesis (FTS) reaction up to C₂ products on a FCC cobalt catalyst surface is presented. This model utilizes a multi-faceted cobalt nanoparticle model for the catalyst, consisting of the two dominant cobalt surface facets Co(111) and Co(100), and a step site represented by the Co(211) surface. The kinetic parameters for the intermediates and transition states on these sites were obtained using plane-wave, periodic boundary condition density functional theory. Using direct DFT data as is, the microkinetic results disagree with the expected experimental results. Employing an exploratory approach, a small number of microkinetic model modifications were tested, which significantly improved correspondence to the expected experimental results. Using network flux and sensitivity analysis, an in-depth discussion is given on the relative reactivity of the various sites, CO activation mechanisms, the nature of the reactive chain growth monomer, the probable C₂ formation mechanism, the active site ensemble interplay and the very important role of CO* surface coverage. The findings from the model scenarios are discussed with the aim of guiding future work in understanding the FTS mechanism and subsequent controlling kinetic parameters.

CH4 and H2S reforming to CH3SH and H2 catalyzed by metal-promoted Mo6S8 clusters: a first-principles micro-kinetic study

Density Functional Theory (DFT) and microkinetic modelling of CH₄ and H₂S reactions to form CH₃SH and H₂ as a first step in elucidating complex pathways in oxygen-free sour gas reforming was performed.

Connection between macroscopic kinetic measurables and the degree of rate control

Macroscopic kinetic measurables are linked to elementary reaction steps by the degree of rate control.

Kinetic aspects of chain growth in Fischer–Tropsch synthesis

Microkinetics simulations are used to investigate the elementary reaction steps that control chain growth in the Fischer–Tropsch reaction. Chain growth in the FT reaction on stepped Ru surfaces proceeds via coupling of CH and CR surface intermediates. Essential to the growth mechanism are C–H dehydrogenation and C hydrogenation steps, whose kinetic consequences have been examined by formulating two novel kinetic concepts, the degree of chain-growth probability control and the thermodynamic degree of chain-growth probability control. For Ru the CO conversion rate is controlled by the removal of O atoms from the catalytic surface. The temperature of maximum CO conversion rate is higher than the temperature to obtain maximum chain-growth probability. Both maxima are determined by Sabatier behavior, but the steps that control chain-growth probability are different from those that control the overall rate. Below the optimum for obtaining long hydrocarbon chains, the reaction is limited by the high total surface coverage: in the absence of sufficient vacancies the CHCHR → CCHR + H reaction is slowed down. Beyond the optimum in chain-growth probability, CHCR + H → CHCHR and OH + H → H₂O limit the chain-growth process. The thermodynamic degree of chain-growth probability control emphasizes the critical role of the H and free-site coverage and shows that at high temperature, chain depolymerization contributes to the decreased chain-growth probability. That is to say, during the FT reaction chain growth is much faster than chain depolymerization, which ensures high chain-growth probability. The chain-growth rate is also fast compared to chain-growth termination and the steps that control the overall CO conversion rate, which are O removal steps for Ru.

CO oxidation on Rh-doped hexadecagold clusters

Exploring the unique catalytic properties of gold clusters associated with specific nano-architectures is essential for designing improved catalysts with a high mass-specific activity.

Direct carbon-carbon coupling of furanics with acetic acid over Brønsted zeolites

Effective carbon-carbon coupling of acetic acid to form larger products while minimizing CO2 emissions is critical to achieving a step change in efficiency for the production of transportation fuels from sustainable biomass. We report the direct acylation of methylfuran with acetic acid in the presence of water, all of which can be readily produced from biomass. This direct coupling limits unwanted polymerization of furanics while producing acetyl methylfuran. Reaction kinetics and density functional theory calculations illustrate that the calculated apparent barrier for the dehydration of the acid to form surface acyl species is similar to the experimentally measured barrier, implying that this step plays a significant role in determining the net reaction rate. Water inhibits the overall rate, but selectivity to acylated products is not affected. We show that furanic species effectively stabilize the charge of the transition state, therefore lowering the overall activation barrier. These results demonstrate a promising new route to C-C bond-forming reactions for the production of higher-value products from biomass.

Analysis of reaction schemes using maximum rates of constituent steps

We show that the steady-state kinetics of a chemical reaction can be analyzed analytically in terms of proposed reaction schemes composed of series of steps with stoichiometric numbers equal to unity by calculating the maximum rates of the constituent steps, rmax,i, assuming that all of the remaining steps are quasi-equilibrated. Analytical expressions can be derived in terms of rmax,i to calculate degrees of rate control for each step to determine the extent to which each step controls the rate of the overall stoichiometric reaction. The values of rmax,i can be used to predict the rate of the overall stoichiometric reaction, making it possible to estimate the observed reaction kinetics. This approach can be used for catalytic reactions to identify transition states and adsorbed species that are important in controlling catalyst performance, such that detailed calculations using electronic structure calculations (e.g., density functional theory) can be carried out for these species, whereas more approximate methods (e.g., scaling relations) are used for the remaining species. This approach to assess the feasibility of proposed reaction schemes is exact for reaction schemes where the stoichiometric coefficients of the constituent steps are equal to unity and the most abundant adsorbed species are in quasi-equilibrium with the gas phase and can be used in an approximate manner to probe the performance of more general reaction schemes, followed by more detailed analyses using full microkinetic models to determine the surface coverages by adsorbed species and the degrees of rate control of the elementary steps.

Towards rational catalyst design: a general optimization framework

Rational catalyst design is one of the most fundamental goals in heterogeneous catalysis. Herein, we briefly review our previous design work, and then introduce a general optimization framework, which converts catalyst design into an optimization problem. Furthermore, an example is given using the gradient ascent method to show how this framework can be used for rational catalyst design. This framework may be applied to other design schemes.

Using degrees of rate control to improve selective n-butane oxidation over model MOF-encapsulated catalysts: sterically-constrained Ag3Pd(111)

Metal nanoparticles encapsulated within metal organic frameworks (MOFs) offer steric restrictions near the catalytic metal that can improve selectivity, much like in enzymes. A microkinetic model is developed for the regio-selective oxidation of n-butane to 1-butanol with O₂ over a model for MOF-encapsulated bimetallic nanoparticles. The model consists of a Ag₃Pd(111) surface decorated with a 2-atom-thick ring of (immobile) helium atoms which creates an artificial pore of similar size to that in common MOFs, which sterically constrains the adsorbed reaction intermediates. The kinetic parameters are based on energies calculated using density functional theory (DFT). The microkinetic model was analysed at 423 K to determine the dominant pathways and which species (adsorbed intermediates and transition states in the reaction mechanism) have energies that most sensitively affect the reaction rates to the different products, using degree-of-rate-control (DRC) analysis. This analysis revealed that activation of the C–H bond is assisted by adsorbed oxygen atoms, O*. Unfortunately, O* also abstracts H from adsorbed 1-butanol and butoxy as well, leading to butanal as the only significant product. This suggested to (1) add water to produce more OH*, thus inhibiting these undesired steps which produce OH*, and (2) eliminate most of the O₂ pressure to reduce the O* coverage, thus also inhibiting these steps. Combined with increasing butane pressure, this dramatically improved the 1-butanol selectivity (from 0 to 95%) and the rate (to 2 molecules per site per s). Moreover, 40% less O₂ was consumed per oxygen atom in the products. Under these conditions, a terminal H in butane is directly eliminated to the Pd site, and the resulting adsorbed butyl combines with OH* to give the desired 1-butanol. These results demonstrate that DRC analysis provides a powerful approach for optimizing catalytic process conditions, and that highly selectivity oxidation can sometimes be achieved by using a mixture of O₂ and H₂O as the oxidant. This was further demonstrated by DRC analysis of a second microkinetic model based on a related but hypothetical catalyst, where the activation energies for two of the steps were modified.

Theoretical investigations toward the [3 + 2]-dipolar cycloadditions of nitrones with vinyldiazoacetates catalyzed by Rh2(R-TPCP)4: mechanism and enantioselectivity

The mechanism of Rh₂(R-TPCP)₄-catalyzed [3 + 2]-dipolar cycloadditions between vinyldiazoacetate and nitrone to form 2,5-dihydroisoxazole has been studied by ONIOM methodology calculations including density functional theory and PM6 theory.

Ethylene glycol reforming on Pt(111): first-principles microkinetic modeling in vapor and aqueous phases

Reaction chemistry for vapor- and aqueous-phase reforming of ethylene glycol over Pt(111) is similar with early dehydrogenation steps being rate-controlling.

Possibility of designing catalysts beyond the traditional volcano curve: a theoretical framework for multi-phase surfaces

The current theory of catalyst activity in heterogeneous catalysis is mainly obtained from the study of catalysts with mono-phases, while most catalysts in real systems consist of multi-phases, the understanding of which is far short of chemists' expectation. Density functional theory (DFT) and micro-kinetics simulations are used to investigate the activities of six mono-phase and nine bi-phase catalysts, using CO hydrogenation that is arguably the most typical reaction in heterogeneous catalysis. Excellent activities that are beyond the activity peak of traditional mono-phase volcano curves are found on some bi-phase surfaces. By analyzing these results, a new framework to understand the unexpected activities of bi-phase surfaces is proposed. Based on the framework, several principles for the design of multi-phase catalysts are suggested. The theoretical framework extends the traditional catalysis theory to understand more complex systems.