Clarifying mechanisms and kinetics of programmable catalysis
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Engineering topics
Razdan, Neil K.
Publications and source records attributed to Razdan, Neil K..
Concepts Relevant for the Kinetic Analysis of Reversible Reaction Systems
The net rate of a reversible chemical reaction is the difference between unidirectional rates of traversal along forward and reverse reaction paths. In a multistep reaction sequence, the forward and reverse trajectories, in general, are not the microscopic reverse of one another; rather, each unidirectional route is comprised of distinct rate-controlling steps, intermediates, and transition states. Consequently, traditional descriptors of rate (e.g., reaction orders) do not reflect intrinsic kinetic information but instead conflate unidirectional contributions determined by (i) the microscopic occurrence of forward/reverse reactions (i.e., unidirectional kinetics) and (ii) the reversibility of reaction (i.e., nonequilibrium thermodynamics). This review aims to provide a comprehensive resource of analytical and conceptual tools which deconvolute the contributions of reaction kinetics and thermodynamics to disambiguate unidirectional reaction trajectories and precisely identify rate- and reversibility-controlling molecular species and steps in reversible reaction systems. The extrication of mechanistic and kinetic information from bidirectional reactions is accomplished through equation-based formalisms (e.g., De Donder relations) grounded in principles of thermodynamics and interpreted in the context of theories of chemical kinetics developed in the past 25 years. Here, the aggregate of mathematical formalisms detailed herein is general to thermochemical and electrochemical reactions and encapsulates a diverse body of scientific literature encompassing chemical physics, thermodynamics, chemical kinetics, catalysis, and kinetic modeling.
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Rates and Reversibilities in Interconnected Reaction Networks
Mathematical relations prescribing unidirectional forward and reverse rates originally derived based on single-path reaction sequences do not apply to interconnected reaction networks. The presence of branches in reaction networks, leading to alternative stable products, decreases unidirectional rates in reference to those calculated by single-path functional forms, as shown by simulated isotopic exchange rates, but impacts the unidirectional forward and reverse rates equally such that the functional form of effective reversibility remains unchanged. Regardless of stoichiometric numbers and network connectivity, the application of the pseudo-steady-state hypothesis on reactive intermediates in conjunction with consideration of unidirectional rates toward the product of interest and all alternative stable products results in mathematical expressions that accurately reflect simulated isotopic exchange rates. Further analyses based on kinetic resistance, a property akin to electrical resistance, illustrate the manifestation of nodal resistances in addition to the single-path kinetic resistance for interconnected reaction networks. The generalized formalism for assessing rates and reversibilities in interconnected networks derived herein enables us to demonstrate that unidirectional rates cannot be assessed solely from effective reversibilities and net rates of generation of stable species in such networks. Furthermore, isotopic exchange rates, under the condition that each elementary step in the overall reaction sequence forms a unique reactive intermediate that is consumed solely by the subsequent step, can be utilized to determine unidirectional rates and can serve to validate postulated reaction pathways in highly interconnected reaction networks (e.g., CO x hydrogenation).
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Catalytic site ensembles: A context to reexamine the Langmuir-Hinshelwood kinetic description
The Langmuir-Hinshelwood formalism describes catalytic reactions of Langmuirian surface species under the assumption that all adsorbates are randomly-distributed – enabling adjacency of surface-bound intermediates to be determined solely by coverages of single-site occupants. We demonstrate herein that this approximation is inappropriate even for simple catalytic reactions (e.g. A + A → A 2 ) and manifestly neglects islanding of slowly-consumed species and partitioning of highly-reactive species inherently engendered by ≥ two-site elementary steps (e.g. A*–A* → A 2(g) + *–*). Rigorous description of kinetically-consequential islanding/partitioning phenomena requires explicit description of the coverage and chemical dynamics of all multi-site ensembles. Higher-order, ensemble-specific rate terms identify the particular microscopic events relevant to each ensemble, and, in doing so, reveal that each elementary step (e.g. A (g) adsorption) describes not one event (e.g. A (g) + * → A*) , but a sum over all ensemble-specific paths (e.g. A (g) + *–* → A*–* and A (g) + A*–* → A*–A*). De-convoluting each elementary step into its constituent multi-site paths proffers kinetic detail otherwise inaccessible – enabling (i) identification of rate- and selectivity-determining site ensembles, (ii) calculation of rates and degrees of rate control of ensemble-specific elementary steps, (iii) incorporation of adsorbate surface diffusion, (iv) incorporation of lateral adsorbate interactions, and (v) quantitative description of catalysis of multi-site-occupying intermediates (e.g. *C n H m * species in hydrocarbon (de-)hydrogenation and C-C bond coupling/cleavage reactions) which we demonstrate here is inaccessible to the Langmuir-Hinshelwood formalism even if adsorbate surface diffusion is infinitely-fast.
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Kinetic description of site ensembles on catalytic surfaces
Significance The kinetic assessment of catalytic reactions is essential to the design and application of thermochemical processes useful in petrochemical synthesis, energy conversion, and environmental remediation. We demonstrate that the ubiquitously used Langmuir–Hinshelwood formalism is incomplete and fails to correctly describe even simple catalytic reactions (e.g., A + A → A 2 ). An accurate kinetic description requires explicit rate equations for multisite configurations (e.g., A*–A* pairs) to account for the nonrandom clustering/isolation of surface species. We rigorously describe clustering/isolation phenomena by derivation of coverage-dependent stoichiometric coefficients, which capture the distinct influence each elementary step exerts on each catalytic site ensemble—thereby overcoming limitations of the mean-field (i.e., Hinshelwood) assumption in describing reactions of mobile Langmuirian adsorbates on catalytic surfaces.
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Carbidic Mo is the sole kinetically-relevant active site for catalytic methane dehydroaromatization on Mo/H-ZSM-5
Systematic variation of Mo/Al = {0.10, 0.25, 0.35} in Mo/H-ZSM-5 catalysts effects ~20× change of Mo-to-H + ratio during methane dehydroaromatization (DHA) reactions at steady state and on deactivating catalysts. Mo and Brønsted-acid site count, respectively enumerated by ethane hydrogenolysis probe reaction and dimethyl ether chemical titration, evolve disparately during DHA catalysis, indicating the two sites reduce in number by distinct mechanisms. Here, the deactivation of Mo/H-ZSM-5 catalytic activity is uniquely attributed to the loss of active, or accessible, Mo sites, evinced by (i) the non-selective nature of deactivation (i.e. that deactivation occurs without modification of residual active sites), (ii) invariance in product distribution from Mo/H + = 0.10–2.1, and (iii) linear correspondence between Mo-catalyzed ethane hydrogenolysis rate and active site count during DHA on deactivating samples. DHA forward rate – the intrinsic kinetic descriptor of catalyst activity – normalizes by Mo content at steady state and on deactivating catalysts with Mo/Al = 0.10–0.35 for Mo-based contact times in the range τ Mo = 0.79–44 mol Mo s mol –1 C , unequivocally establishing Mo aggregates as the sole kinetically-relevant active site on Mo/H-ZSM-5. Brønsted-acid site content over a ~40× range in τ H+ = 1.4–54 mol H+ s mol –1 C has no discernable correlation with or effect on DHA rate, methane conversion, or product distribution – demonstrating H + does not catalyze any rate- or selectivity-determining steps in the benzene formation pathway and suggesting that the benefits of zeolitic acid sites are only to disperse Mo during catalyst synthesis and, conceivably, to catalyze equilibrated reaction steps.
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