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At least 451 records · Page 25

Temperature-responsive smart tracers for field-measurement of inter-well thermal evolution: Heterogeneous kinetics and field demonstration

Temperature-responsive smart tracers enable advanced warning of a “premature thermal breakthrough” and may therefore improve reservoir management and reduce financial risk. A successful calculation of inter-well fluid temperatures requires that temperature-dependent kinetics are known, which typically result from homogeneous batch reactor experiments. However, recent meso-scale field experiments at the Altona Field Laboratory involving fluid flow in a discretely-fractured reservoir suggest that silica-fluid interfaces may accelerate hydrolysis kinetics. Here, the Arrhenius parameters of phenyl acetate hydrolysis are investigated under heterogeneous reaction conditions in packed-bed column experiments. The breakthrough curve of the reaction product is compared to an inert reference tracer (carbon-cored nanoparticles). Temperatures experienced during field testing ranging from 10 to 40 °C were studied using a phosphate buffer solution to maintain a near-neutral pH, as found in the reservoir. The empirically-determined pre-exponential factor and activation energy values are subsequently used in a first-order kinetic model to improve calculations of effective reservoir temperatures for these meso-scale field tests. Here, the results suggest that hydrolysis reactions can directly monitor inter-well reservoir temperatures, but only if the influence of solid-fluid interactions are carefully accounted for.

15 GEOTHERMAL ENERGY↗

Kinetic analysis of Cas12a and Cas13a RNA-Guided nucleases for development of improved CRISPR-Based diagnostics

Bacterial CRISPR systems provide acquired immunity against invading nucleic acids by activating RNA-programmable RNases and DNases. Cas13a and Cas12a enzymes bound to CRISPR RNA (crRNA) recognize specific nucleic acid targets, initiating cleavage of the targets as well as non-target (trans) nucleic acids. Here, we examine the kinetics of single-turnover target and multi-turnover trans-nuclease activities of both enzymes. High-turnover, non-specific Cas13a trans-RNase activity is coupled to rapid binding of target RNA. By contrast, low-turnover Cas12a trans-nuclease activity is coupled to relatively slow cleavage of target DNA, selective for DNA over RNA, indifferent to base identity, and preferential for single-stranded substrates. Combining multiple crRNA increases detection sensitivity of targets, an approach we use to quantify pathogen DNA in samples from patients suspected of Buruli ulcer disease. Results reveal that these enzymes are kinetically adapted to play distinct roles in bacterial adaptive immunity and show how kinetic analysis can be applied to CRISPR-based diagnostics.

59 BASIC BIOLOGICAL SCIENCES↗

Metastable formation and disordering kinetics of body-centered orthorhombic CrNi 2 laths in a Cr-Ni binary alloy

Chromium (Cr) alloys combine low density with high-temperature strength but suffer from brittleness and rapid softening. Body-centered orthorhombic (BCO) CrNi 2 laths have been shown to improve Cr-alloy high-temperature strength retention, yet their thermal stability and transformation behavior remain unclear. CrNi 2 conventionally forms through long-range ordering from a face-centered cubic (FCC) phase. Using multiscale microscopy and neutron diffraction, we show that CrNi 2 instead nucleates from a body-centered cubic (BCC) matrix, in a binary Cr 85 Ni 15 alloy. Despite aging above the equilibrium ordering temperature, CrNi 2 persists for ∼220 h at 760 °C before fully disordering, indicating sluggish transformation kinetics. The formation and decomposition follow differing transformation pathways (BCC → CrNi 2 → FCC), revealing kinetic asymmetry not captured by equilibrium Cr-Ni phase diagrams. In conclusion, these findings redefine the transformation behavior of CrNi 2 , establish its metastable kinetic window, and suggest alloying strategies to stabilize CrNi 2 for precipitation strengthening of high-temperature Cr-alloys.

CrNi2 transformation kinetics↗

Oxide-catalyzed self- and cross-condensation of cycloketones. Kinetically relevant steps that determine product distribution

Metal oxides with acid-base properties can be used to catalyze aldol condensation and potentially obtain valuable chemicals from biomass-derived oxygenates. Understanding the reaction mechanisms could enable the development of effective catalysts with controllable selectivity. In this work, we investigate the reaction parameters that affect the kinetics and product distribution of self- and cross-aldol condensation of cyclopentanone (CPO) and cyclohexanone (CHO) over CeO 2 and ZrO 2 catalysts by combining detailed analysis of experiments and DFT calculations. It is well-known that either the deprotonation of an α-C–H that generates an enolate or the C–C coupling that produces the dimers can be rate-limiting step. Indeed, the detailed kinetics analysis shows that the observed data can be fitted by unimolecular or bimolecular Langmuir-Hinshelwood models. Specifically, on the ZrO 2 catalyst, the unimolecular α-C–H activation is the rate limiting step for the CPO self-condensation, while the bimolecular C–C coupling limits the CHO self-condensation. By contrast, on CeO 2 , the bimolecular C–C coupling step seems to be rate-limiting for both CPO and CHO self-condensation reactions. The adsorption parameters derived from kinetics fitting indicate that when the two reactants are co-fed, the surface is preferentially covered by CHO. So, the condensation rate of [CPO]-activated products ([CPO]CPO + [CPO]CHO) decreases in the presence of CHO, due to the competitive adsorption. However, despite a higher surface coverage, CHO is not an effective electrophile because it imposes stronger steric constraints to the formation of the C–C bond than CPO. Therefore, for a given enolate, the product distribution shows that [CPO]CPO > [CPO]CHO and, similarly [CHO]CPO > [CHO]CHO. Likewise, the yields of [CPO]- and [CHO]-activated products in mixed CPO/CHO feeds are similar because the higher surface coverage and stability of the [CHO] enolate is counterbalanced by the inhibition of C–C coupling by steric constraints when CHO is involved. In summary, the overall rank of products observed experimentally can be explained in terms of a combination of the following effects: relative surface coverage of the reactants, steric constraints for the C–C coupling, stability of the enolate, and effectiveness of the electrophile to accept an electron.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Experimental and computational kinetics study of the liquid-phase hydrogenation of C=C and C=O bonds

Solvent effects on adsorption equilibrium and reaction kinetics are evaluated for hydrogenation reactions catalyzed by Pd/alumina in a series of different solvents. Three reactants – cyclohexene, benzene and benzaldehyde – and three solvents – n-heptane (HEP), methylcyclohexane (MCHA), decalin (DL) – have been investigated. Kinetic analysis of hydrogenation of cyclohexene reveals that hydrogen adsorbs on different sites from those where cyclohexene and the solvents adsorb; however, the presence of hydrogen on these separate sites affects the heats of adsorption of the hydrocarbons. When the solvent is a weakly interacting linear alkane (HEP), the rate determining step of the reaction is the first hydrogenation of adsorbed cyclohexene. Furthermore, this conclusion is supported by DFT calculations that show a higher enthalpy barrier for the first hydrogenation than for the second, while statistical thermodynamics analysis validates the physical significance of the entropy of adsorption parameters derived from the kinetic fitting of experimental data. By contrast, with solvents such as MCHA and DL, which interact more strongly with the metal surface and compete for active sites with the reactant and the surface intermediate, the rate limiting step seems to shift to the second hydrogenation step.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analysis and prediction of reaction kinetics using the degree of rate control

“Degree of rate control” (DRC) analysis provides a quantitative approach for analysing the kinetics of multi-step reaction mechanisms that has been widely applied to both heterogeneous and homogeneous catalysis research, as well as electrocatalysis. The DRC of any given transition state or intermediate is defined as a partial derivative such that it approximately equals the fractional increase in net rate to the product of interest per differential decrease in its standard-state free energy for that species (÷RT), holding constant the standard-state free energies of all other transition states and intermediates. Even very complex mechanisms usually have only a few species with non-zero DRCs and are thus the species whose interactions with the catalyst most strongly affect the net rate. These key DRC values thus offer a simple and intuitive route to optimize catalyst materials, especially with the assistance of computational methods like density functional theory (DFT). These high-DRC species are also the species whose energetics must be most accurately measured or calculated to achieve an accurate kinetic model for any reaction mechanism. In simple cases with a single “rate-determining step”, the DRC for its transition state (TS) is + 1. Catalyst-bound intermediates, on the other hand, often have negative DRCs equal to a small integer times their fractional occupancy of catalyst sites. The apparent activation energy equals a weighted average of the standard-state enthalpies (relative to reactants) of all the species (intermediates, transition states and products) in the reaction mechanism, each weighted by its DRC (+RT). It has been shown that the apparent transfer coefficient in electrocatalysis, an inverted form of the Tafel slope, is a weighted average of the number of electrons transferred to generate each intermediate or product species in the mechanism, weighted again by the DRC. Quantitative analysis of kinetic isotope effects (KIEs, or the ratio of net rates for different reactant isotopes) in complex mechanisms has shown that the logarithm of the KIE equals the weighted average over all species in the mechanism of the difference between the two isotopes in their standard-state free energies (÷RT), again weighted by the DRC. The reaction orders with respect to fluid-phase concentrations of reactants, products and intermediates have also been proven to be directly related to DRCs. Thus, there are numerous experimental observables which equate to short linear combinations of DRCs, so that combinations of experimental measurements might provide access to DRC values. Since its invention for transition states in 1994 and its generalization to include intermediates in 2009, the DRC has thus far mainly been calculated for microkinetic models based either entirely on DFT or on DFT with the key energies (i.e., those for high-DRC species) being fine-tuned to match experiments. The relationships summarized in this work provide new opportunities for using experiments earlier in the development and optimization of microkinetic models that require input from computational catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Numerical schemes for 3-wave kinetic equations: A complete treatment of the collision operator

In our previous work Walton and Tran (2023), numerical schemes for a simplified version of 3-wave kinetic equations, in which only the simple forward-cascade terms of the collision operators are kept, have been successfully designed, especially to capture the long time dynamics of the equation given the multiple blow-up time phenomenon. In this second work in the series, we propose numerical treatments for the complete 3-wave kinetic equations, in which the complete, much more complicated collision operators are fully considered based on a novel conservative form of the equation. Here we then derive an implicit finite volume scheme to solve the equation. The new discretization uses an adaptive time-stepping method which allows for the simulations to be carried to very long times. Our computed solutions are compared with previously derived long-time asymptotic estimates for the decay rate of total energy of time-dependent solutions of 3-wave kinetic equations and found to be in excellent agreement.

97 MATHEMATICS AND COMPUTING↗

A conservative discontinuous Galerkin algorithm for particle kinetics on smooth manifolds

A novel, conservative discontinuous Galerkin algorithm is presented for particle kinetics on manifolds. The motion of particles on the manifold is represented using both canonical and non-canonical Hamiltonian formulations. Our schemes apply to both formulations, but the canonical formulation results in a particularly efficient scheme that also conserves particle density and energy exactly. The collisionless update is coupled to a Bhatnagar-Gross-Krook (BGK) collision operator that provides a simplified model for relaxation to local thermodynamic equilibrium. An iterative scheme is constructed to ensure collisional invariants (density, momentum and energy) are preserved numerically. Rotation of the manifold is incorporated by modifying the Hamiltonian while ensuring a canonical formulation. Several test problems, including a kinetic version of the classical Sod shock problem, Kelvin-Helmholtz instability on the surfaces of a sphere and a hyperboloid, with and without rotations, are presented. A prospectus for further development of this approach to simulation of kinetic theory in general relativity is presented.

Discontinuous Galerkin↗

Mechanism and kinetic study of rare earth extraction from allanite by direct acid leaching

Direct acid leaching was conducted to recover rare earth elements (REEs) from an allanite ore assaying 9,861.4 ppm of REEs. The effects of operational variables such as acid type, sulfuric acid (H 2 SO 4 ) concentration, temperature, solid/liquid (S/L) ratio, and particle size on the total REE (TREE) recovery were systematically examined. The REE mineralogy and the involved leaching mechanisms were investigated by microscopic characterization and residue re-leaching tests. It was found that approximately 80% of REEs was extracted using 1 M H 2 SO 4 at 75 °C for 2 h. Increasing temperature significantly improved the REE extraction, while changing acid type, H 2 SO 4 concentration, and particle size did not. The TREE recovery also gradually decreased at higher S/L ratios. The low fraction of Si leached (<4.0%) suggested that the extraction did not significantly alter the crystal structure of the dominant mineral. The leaching kinetics of REEs were fast within the first 10 min, followed by a much slower stage (i.e., 10-120 min). The kinetic modeling results showed that each stage may be controlled by both chemical reaction and diffusion (i.e., mix control). The activation energies for REE leaching using 1 M H 2 SO 4 in the 0-10 min and 10-120 min were determined to be 20.3 and 10.8 kJ/mol, respectively. Finally, the residue re-leaching results suggested that the fast leaching kinetics at the beginning may be explained by the preferential decomposition of metamict allanite rather than the formation of silica gel, while the following slower leaching stage was due to the dissolution of difficult-to-leach REE-bearing minerals such as well-crystallized allanite.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Selective dopant segregation modulates mesoscale reaction kinetics in layered transition metal oxide

Incorporation of foreign elements into the cathode material is broadly adopted by both academia and industry to improve the battery performance. The lack of an in-depth understanding for the underlying mechanism, however, makes it a largely try-and-error process with unsatisfactory efficiency and effectiveness. This is particularly true for the electrochemical reaction kinetics that is heterogeneous over a broad range of length scales and is determined collectively by the cathode’s electronic structure, lattice configuration, and micro-morphology. In this work, we unveiled a facet-dependent dopant segregation effect in Zr-modified single-crystal LiNi 0.6 Co 0.2 Mn 0.2 O 2 cathode. By forming kinetically favored corners on the cathode particles, the presence of a trace amount of Zr critically modulates the mesoscale reaction kinetics. Our findings suggest that a delicately controlled dopant distribution is a viable strategy for designing the next-generation battery cathode with superior structural and chemical robustness.

36 MATERIALS SCIENCE↗

Combustion chemistry in the twenty-first century: Developing theory-informed chemical kinetics models

Over the past 20 to 25 years theoretical chemistry (particularly theoretical chemical kinetics) has played an increasingly important role in developing chemical kinetics models for combustion. Theoretical methods of obtaining rate parameters are now competitive in accuracy with experiment, particularly for small molecules. Moreover, theoretical methods can deal with conditions that experiments frequently cannot. In addition to increased accuracy, theory has rejuvenated methods and discovered phenomena that were completely unappreciated, or at least underappreciated, in the 20th century. Our primary interest here is in molecular-level issues, i.e. in calculating rate and transport parameters. However, dealing with kinetics models that involve thousands of reactions and hundreds of species is important for practical applications and is relatively new to the 21st century. Theory, in a general sense, and theoretical methods development have a role to play here too. We discuss in this review all these topics in some detail with an emphasis on issues and methods that have emerged in the last 20 years or so. Even so, our review is selective, rather than comprehensive, out of necessity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An improved semi-global intrinsic kinetics model for high temperature carbon oxidation

Measurements of the oxidation rates of various forms of carbon (soot, graphite, coal char) have often shown an unexplained attenuation with increasing temperatures in the vicinity of 2000 K, even when accounting for diffusional transport limitations and gas-phase chemical effects (e.g. CO 2 dissociation). With the development of oxy-fuel combustion approaches for pulverized coal utilization with carbon capture, high particle temperatures are readily achieved in sufficiently oxygen-enriched environments. Here, in this work, a new semi-global intrinsic kinetics model for high temperature carbon oxidation is created by starting with a previously developed 5-step mechanism that was shown to reproduce all major known trends in carbon oxidation, except for its high temperature kinetic falloff, and incorporating a recently discovered surface oxide decomposition step. The predictions of this new model are benchmarked by deploying the kinetic model in a steady-state reacting particle code (SKIPPY) and comparing the simulated results against a carefully measured set of pulverized coal char combustion temperature measurements over a wide range of oxygen concentrations in N 2 and CO 2 environments. The results show that the inclusion of the spontaneous surface oxide decomposition reaction step significantly improves predictions at high particle temperatures. Furthermore, the simulations reveal that O atoms released from the oxide decomposition step enhance the radical pool in the near-surface region and within the particle interior itself. Incorporation of literature rates for O and OH reactions with the carbon surface results in a reduction in the predicted radical pool concentrations and a very minor enhancement of the overall carbon oxidation rate.

33 ADVANCED PROPULSION SYSTEMS↗

On the prediction of pressure effects for the combination kinetics of two alkyl radicals with the geometric mean rule

Here, alkyl combination reactions, along with their reverse alkane unimolecular decomposition reactions, are widely present in pyrolysis and combustion systems. These reactions occur mainly at temperatures at which their rate coefficients depend on pressure, and only a few studies have explored this dependence for large size alkyls. The accurate calculation of these kinetic data is limited by the size of the alkyl fragments involved, since the theoretical methods used are computationally expensive. Therefore, little reliable data is available for the modeling of real fuels alkane decomposition kinetics. In this paper, we propose an alternative approach that allows an accurate estimation of pressure-dependent kinetic rates for the combination of long-chain alkyl radicals, based on tabulated reaction models. The rates of combination of linear alkyls radicals forming ethane to pentane were calculated using the CASPT2-F12/cc-pVDZ-F12 level within VRC-TST theory combined with master-equation simulations. The computed high-pressure limit rate coefficients showed that n-propyl could be a minimum-size representative structure for larger n-alkyl chain, but this approach fails to capture the pressure dependence of the reaction that remains size-dependent for larger alkyls. The Geometric Mean Rule (GMR), a simple rule that links the self and cross-reactions of three alkyl radicals, is used to address this issue. Our theoretical calculations show for the first time that the GMR applies not only at the high-pressure limit, but also for every pressure explored. The GMR is shown to be accurate, with a maximum 22 % deviation in the falloff region for the estimation of rates for small alkyl combinations. Using this method, we propose a tabulated reaction rate rule for the combination of alkyl radicals up to C5+C5. The use of computed rate coefficients with the GMR approximation opens ways to develop pressure-dependent reaction rate rules for large n-alkyl combinations, based on accurate and computationally expensive theoretical calculations on smaller alkyl fragments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Surface oxygen exchange kinetics of mixed conducting oxides: Dilatometric vs electrical conductivity relaxation study

The surface oxygen exchange kinetics of mixed ionic-electronic conducting (MIEC) oxides play a crucial role in a variety of applications, including solid oxide fuel/electrolysis cells (SOFCs/SOECs), permeation membranes and sensors. To date, a variety of methods, including isotope exchange, electrical conductivity, optical absorptivity and thermogravimetry relaxation, and impedance spectroscopy have been used to measure the oxygen exchange coefficient of MIEC oxides. Each of these methods have their advantages and limitations, depending on the physical and chemical properties of the investigated materials and their sample dimensions and densities. Here, we demonstrate the ability to precisely measure the surface oxygen exchange coefficient (k chem ) of MIEC model material Pr 0.1 Ce 0.9 O 2-δ (PCO) by use of dilatometric relaxation measurements, particularly of interest for materials that exhibit larger chemical expansion coefficients. This is achieved by use of porous bulk specimens to ensure that the contribution of oxygen exchange to the overall kinetics is dominant. We demonstrate that k chem values extracted from chemical expansion relaxation measurements on PCO are nearly identical to those derived from electrical conductivity relaxation measurements. As a result, this provides the opportunity to precisely investigate the oxygen exchange and chemical expansion kinetics of a wide range of materials used in high-temperature applications, particularly where more conventional methods are difficult or inappropriate to apply.

(Pr,Ce)O2-x↗

A dynamic kinetic model captures cell-free metabolism for improved butanol production

Cell-free systems are useful tools for prototyping metabolic pathways and optimizing the production of various bioproducts. Mechanistically-based kinetic models are uniquely suited to analyze dynamic experimental data collected from cell-free systems and provide vital qualitative insight. However, to date, dynamic kinetic models have not been applied with rigorous biological constraints or trained on adequate experimental data to the degree that they would give high confidence in predictions and broadly demonstrate the potential for widespread use of such kinetic models. In this work, we construct a large-scale dynamic model of cell-free metabolism with the goal of understanding and optimizing butanol production in a cell-free system. Using a combination of parameterization methods, the resultant model captures experimental metabolite measurements across two experimental conditions for nine metabolites at timepoints between 0 and 24 hours. Here, we present analysis of the model predictions, provide recommendations for butanol optimization, and identify the aldehyde/alcohol dehydrogenase as the primary bottleneck in butanol production. Sensitivity analysis further reveals the extent to which various parameters are constrained, and our approach for probing valid parameter ranges can be applied to other modeling efforts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Observation of Stepwise Ultrafast Crystallization Kinetics of Donor–Acceptor Conjugated Polymers and Correlation with Field Effect Mobility

The semicrystalline microstructures of donor-acceptor conjugated polymers strongly impact their optoelectronic properties. The control of the microstructure relies on the understandings of the crystallization processes in these polymers, from packing structures to crystallization kinetics. How fast these conjugated polymer chains crystallize and how their chemical structures and pre-existing microstructure history influence their crystallization have so far remained unclear, due to the fast crystallization rate caused by chain rigid structures and strong interactions. Here, ultrafast scanning calorimetry (FSC) is employed to reveal the crystallization behaviors of high perform- ance diketopyrrolopyrrole (DPP)-based conjugated polymers with scanning rates up to 500 000 K/s. Through elaborately designed nonisothermal and isothermal crystallization studies, we probed the fast crystallization kinetics and extracted the two-step crystallization process of these polymers quantitatively. We found that both the rigidity of the chain backbones and the preinduced crystalline microstructures can influence the crystallization rate over an order of magnitude at the same degree of undercooling. We further demonstrated the manipulated crystallization kinetics in the DPP-based polymer films with different amounts of preinduced crystallites and correlate it to the polymers’ charge transport mobility.

36 MATERIALS SCIENCE↗

High-Temperature Fe-Based Fischer–Tropsch Synthesis: Experimentally Validated Kinetic Models Implemented at Pellet and Reactor Scales

Pellet- and reactor-scale models for Fischer–Tropsch synthesis (FTS) with a Fe–K/silica catalyst were developed to investigate the sensitivity of the hydrocarbon products and carbon dioxide selectivity to process conditions and feed composition at high temperature (350–400 °C), moderate pressure (1–10 bar), and a range of H 2 /CO ratios (3–1). The major objective of this paper is to develop, validate, and evaluate a high-temperature FTS model that is then used to assess the feasibility of process integration with syngas production. Since there is limited kinetic data available, in literature at these conditions, bench-scale reactor tests were conducted to obtain operational data for parameter fitting of kinetic expressions used in the model. This resulting kinetic model demonstrated agreement with the experimental data with an R 2 of 0.97 to the testing data set and, thus, was feasible to apply at pellet and reactor scales. Here, multiple pellet sizes were modeled to detail the role of transport limitations as the sphere’s diameter approached and exceeded 1 mm. Application of the reactor model indicated that hydrocarbon selectivity depended strongly on temperature, whereas the ratio of olefin to paraffin products decreased with increasing temperature, pressure, and H 2 /CO ratio. Product selectivity was not sensitive to the conversion of carbon monoxide. Furthermore, the roles of the pressure and H 2 /CO ratio were closely coupled. At a H 2 /CO ratio of 3, only slight variations in selectivity occurred over a pressure range of 1–20 bar, whereas at a ratio of 1, selectivity could vary by as much as 30% over the same pressure range. At pressures below 5 bar and temperatures above 350 °C, minimal selectivity to heavy hydrocarbons (C 12+ ) is obtained, and selectivity to midrange products (C 5–11 ) rapidly declined as pressure dropped below 5 bar, which indicated that an operational pressure of at least 5 bar is needed to achieve reasonable yields in this temperature range. These results, while tentative, provide guidelines for further experimentation and evaluation of integrated FTS processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Single-Molecule Kinetics of Styrene Hydrogenation on Silica-Supported Vanadium: The Role of Disorder for Single-Atom Catalysts

We report a theoretical approach for the study of supported atom catalysis is developed based on recent advances in the study of single-molecule kinetics. This view is particularly useful in exhibiting the role of disorder in single-atom and single-site catalysts on amorphous supports. The distribution of passage times (or waiting times) through a complex catalytic network originating from a set of coupled active sites is described by a probability distribution function (PDF), f(t), that reflects the local environment of the reaction center. An efficient algorithm is developed based on the linear algebra of the Markov transition matrix that produces f(t) or its moments. The kinetics of the hydrogenation reaction of styrene on an organovanadium(III) catalyst supported on amorphous silica is studied. A kinetic model consisting of three intertwined catalytic cycles emanating from three chemically distinct active sites is proposed to describe the chemistry. Density functional theory (DFT) calculations are employed to determine the free energy barriers of the reactions, which are used to construct the rate coefficient matrix. The disorder induced by the amorphous support material is divided into a low-dimensional short-range component reflecting the covalent structures near the reaction center and a weaker long-range component modeling the bulk randomness. The results are computed and analyzed for a wide range of concentration values and disorder scenarios. The unusual structure in the f(t) PDF is found to occur for certain cases that reveal the contribution of multiple catalytic pathways acting in concert.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗