Evolution of heterogeneous catalytic reactions kinetics with time

An overview of development of heterogeneous catalytic kinetic concepts is presented. An emphasis is made on the application of mechanistically sound models, which are needed as a part of the understanding of catalytic reactions on a molecular level as well as of the design and the intensification of chemical processes. Such models should include among other parameters the size and geometry of reacting molecules, size of nanoclusters and deactivation as a part of the reaction mechanism.     

Selectivity of complex heterogeneous catalytic reactions over energetically nonuniform surfaces

The selectivity in parallel and consecutive heterogeneous catalytic reactions over nonuniform surfaces has been analyzed within the framework of the surface electron gas model. Equations for the selectivity are derived in the case of slow adsorption (no rate-limiting steps). Conditions when the nonuniform character of real catalytic surfaces should be taken into account in modeling of the selectivity behavior are discussed.     

Effects of reactant concentration on the internal diffusion retardation of irreversible heterogeneous catalytic reactions

A theoretical analysis is presented for these effects for reactions that are not retarded by products and of orders zero, one, and two. The retardation is found to increase for reactions of fractional order 0n<1 as the reactant is consumed, while first-order reactions are unaffected and higher-order ones show a decreasing effect. The results for zero order are compared with experiment for the catalytic hydrogenation of carbon monoxide.     

Correlation between entropy and enthalpy factors during heterogeneous complex catalytic reactions

The correlation equations are discussed between entropy and enthalpy factors during complex heterogeneous catalytic reactions based on the dependence of the Gibbs energy on the surface coverage. The existence of the entropy heterogeneity in the adsorption layer leads to the correlations between S and H. In the cases where the increase of H is accompanied by an increase of S, i. e. when the entropy factors lead to a decrease of the interval of heterogeneity, the known thermodynamic compensation effect is observed.

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Atmospheric pressure microwave assisted heterogeneous catalytic reactions

The purpose of the study was to investigate microwave selective heating phenomena and their impact on heterogeneous chemical reactions. We also present a tool which will help microwave chemists to answer to such questions as "My reaction yields 90% after 7 days at reflux; is it possible to obtain the same yield after a few minutes under microwaves?" and to have an approximation of their reactions when conducted under microwaves with different heterogeneous procedures. This model predicting reaction kinetics and yields under microwave heating is based on the Arrhenius equation, in agreement with experimental data and procedures.     

Kinetic equation for reversible heterogeneous catalytic reactions

It is demonstrated that when operating far from equilibrium, despite the non-linearity of a complex reaction system, the overall rate of a heterogeneous catalytic reaction is expressed by a classical equation, where the equilibrium constant is determined by the ratio of constants of the forward and reverse reaction, which do not include the lateral interactions in the adsorbed layer.     

Mathematical modeling of heterogeneous catalytic reactions and processes

The problems of heterogeneous catalysis are considered using mathematical modeling of catalytic reactions beginning from the atomic and molecular level. Some problems of the nonlinear dynamics of heterogeneous catalytic reactions are discussed. Mathematical models of these systems were designed using a combination of laboratory and computer experiments. The results of simulation of the nonlinear phenomena involved in the reactions NO+CO, NO+H₂, and CO+O₂, which are important for environmental catalysis, are discussed. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1895–1904, October, 1998.     

Specific features of the catalytic behavior of supported palladium nanoparticles in heterogeneous catalytic reactions

Specific features of the catalytic behavior of supported palladium nanoparticles were analyzed in terms of both the size of the particles and their interaction with the support. The influence of these factors on the activity and selectivity of palladium nanoparticles in carbon-carbon bond hydrogenolysis, hydrogenation of aromatic compounds, olefins, and acetylenes, hydrodechlorination, as well as complete oxidation of organic compounds was discussed. It was shown that the optimal nanoparticle size depends on the type of the reaction and also such factors as the nature of interaction between the nanoparticles and support, absorptivity of the substrates and catalytic reaction products, and electronic and crystal structure of the nanoparticles.     

Kinetic models of heterogeneous catalytic reactions (review)

A complex approach for obtaining comprehensively substantiated kinetic models in heterogeneous catalysis is proposed. The kinetic models of catalytic conversions of different classes of organic compounds, estabished for the first time by this method, are described. Some theoretical premises and the consequences of this study are examined.Review of data from research awarded the Academy of Sciences of the USSR D. I. Mendeleev Prize in chemical sciences for 1990.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2699–2717, December, 1991.     

A device for pulse investigation of heterogeneous catalytic reactions

In the present work a simple device is described for the pulse investigation of heterogeneous catalytic reactions and catalysts. Owing to the possibility for separate adjustment of the gas flow rate in the catalytic reactor and in the chromatographic column, it can be used for kinetic measurements too.

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Complex heterogeneous catalytic reactions. Some aspects of simulation

Heterogeneous catalytic reactions take place by stage mechanisms. The existence of reactants and products (at reactor input and output) and intermediates (not included in final equations of reactions) enables to derive a series of linear algebraic equations observed in stationary conditions in each point of reactor and in each point of catalyst grain. This “theory of stationary complex reactions” was developed first in the works of J. Horiuti and M.I. Temkin. Accounting some relationships of this theory enables to derive the first integrals for the set of the differential equations describing the zero-gradient reactors, flow reactors, and fluidized-bed reactors. Their consideration in the internal diffusion processes results in the relationships of diffusion stoichiometry and similar relationships for the grain surface concentrations and temperature. All the said relationships should be taken into account for calculation of the relevant reactors. Accounting the given relationships provides the correct solution of the relevant problem and reduces the order of the set of the differential equations to be solved. Some calculation features and restrictions in solution of inverse kinetic problems arise also if the mechanism of reactions involves reversible and equilibrium routes. This study systematizes the aforesaid issues and indicates to applicability and importance of the features of complex heterogeneous catalytic reactions for simulation of catalytic processes.     

Steady-state rate of complex reactions under limitation and near equilibrium (one-route mechanism of catalytic reactions)

Explicit equations for the steady-state rate in case when one of the steps is rate-limiting, and in the neighborhood of equilibrium have been derived for a one-route mechanism of a catalytic reaction. Equations have been obtained for a dependence of the observed reaction order and activation energy on the thermodynamic characteristics of the overall reaction.

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Effects of reagent concentration on the rates of reversible heterogeneous catalytic reactions

A theoretical analysis is presented for the effects of reagent concentration on internal diffusion retardation in a reversible catalytic reaction at a porous contact in the form of a plate of infinite extent. The diffusion retardation alters as the equilibrium composition is approached, the nature of the change being determined by the orders of the forward and reverse reactions as well as by the equilibrium constant.We are indebted to V. A. Roiter and M. T. Rusov for interest in the work and valuable comments.     

Stochastic simulation of catalytic surface reactions in the fast diffusion limit

The master equation of a lattice gas reaction tracks the probability of visiting all spatial configurations. The large number of unique spatial configurations on a lattice renders master equation simulations infeasible for even small lattices. In this work, a reduced master equation is derived for the probability distribution of the coverages in the infinite diffusion limit. This derivation justifies the widely used assumption that the adlayer is in equilibrium for the current coverages and temperature when all reactants are highly mobile. Given the reduced master equation, two novel and efficient simulation methods of lattice gas reactions in the infinite diffusion limit are derived. The first method involves solving the reduced master equation directly for small lattices, which is intractable in configuration space. The second method involves reducing the master equation further in the large lattice limit to a set of differential equations that tracks only the species coverages. Solution of the reduced master equation and differential equations requires information that can be obtained through short, diffusion-only kinetic Monte Carlo simulation runs at each coverage. These simulations need to be run only once because the data can be stored and used for simulations with any set of kinetic parameters, gas-phase concentrations, and initial conditions. An idealized CO oxidation reaction mechanism with strong lateral interactions is used as an example system for demonstrating the reduced master equation and deterministic simulation techniques.     

Numerical study of the kinetics of unimolecular heterogeneous reactions onto planar surfaces

In this paper we investigate two-dimensional in space mathematical models of the kinetics of unimolecular heterogeneous reactions proceeding onto planar surfaces. The models are based on Langmuir-type kinetics of the adsorption, desorption, and reaction including the surface diffusion of the adsorbate, surface diffusion of the product before its desorption, and slow desorption of the product from the adsorbent. It is also assumed that the reactant diffuses towards an adsorbent from a bounded vessel and the product diffuses from the adsorbent into the same vessel. Diffusivity of all species and kinetic coefficients are constants. The numerical simulation was carried out using the finite difference technique for four models: one model neglects the surface diffusion of the adsorbate and product, the second one includes the surface diffusion of the adsorbate and product, the third of them includes the surface diffusion of the adsorbate and neglects diffusion of the product along the surface, and the last one neglects the surface diffusion of the adsorbate and includes diffusion of the product along the adsorbent. By changing input parameters effects of the surface diffusion of the adsorbate and product and the slow desorption of the product are studied numerically.     

Influence of pore diffusion on the kinetics of catalytic oxidation of ethylene

Internal diffusion influences the kinetics of ethylene oxidation on an industrial silver catalyst at temperatures higher than 240°C. This influence is completely eliminated when the diameter of the catalyst grains is decreased by a factor of 1/2.

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, 240°C. .