Kinetics Of Heterogeneous Reactions Research Articles

Determining Accurate Kinetic Parameters of Potentially Important Heterogeneous Atmospheric Reactions on Solid Particle Surfaces with a Knudsen Cell Reactor

One of the most important applications of the Knudsen cell reactor is in determining heterogeneous reaction kinetics of potentially important atmospheric reactions. Knudsen cell measurements involving gas reactions on atmospherically relevant particle surfaces, including salt, carbon black, soot, and mineral dust, are often obtained using powdered samples. In this study, we have investigated the importance of gas diffusion into the underlying layers of powdered samples when determining kinetic parameters from Knudsen cell experiments. In particular, we show that the use of the geometric surface area of the sample holder is, in general, not justified in determining initial uptake coefficients or reaction probabilities because the interrogation or probe depth of gas-phase molecules into the bulk powder can be anywhere from tens to thousands of layers deep. One problem encountered by current models used to account for gas diffusion into the underlying layers is that the diffusion constant of the gas through the powdered sample must be known. Typically, diffusion constants for gases into powdered samples are unknown and are difficult to measure or accurately calculate. One way to circumvent this problem is to use thin samples such that the thickness of the sample is less than the interrogation depth of the gas-phase molecules. Under these conditions, the observed initial uptake coefficient is directly proportional to the surface area of the entire sample. This region is termed the linear mass-dependent regime and can be experimentally accessed for many, but not all, heterogeneous reactions. Several examples discussed here include heterogeneous reaction of NO2 on γ- and α-Al2O3, α-Fe2O3, carbon black; HNO3 on CaCO3; and acetone on TiO2.

Electrothermography apparatus for kinetics of rapid high-temperature reactions

A computer-assisted electrothermography setup has been developed to determine the intrinsic kinetics of rapid heterogeneous reactions under conditions of high heating rate. In this method, metal wires are heated in a reactive gas atmosphere to desired temperature in a controlled manner by passing electric current, and then by measuring time-dependence characteristics of electric power applied to the wire, the reaction kinetics is extracted. The described setup allows heating rates up to 3×105 K/s and permits investigation of reaction kinetics over time scale of few milliseconds to seconds. Other applications are also possible that require fast heating and temperature control.

The kinetic effects of decreasing catalytic activity on a simple rate expression

When kinetics are studied for a catalyzed reaction, the active catalyst surface available affects the results. This article illustrates the effect of a progressively decreasing available surface on the heterogeneous kinetics of a gas-phase reaction in a closed system. The present contribution focuses on the effect of simple mth order surface deactivation on a simple nth order kinetic expression. The basic analysis and general results are unchanged if more complex equations are used. It is shown that there are certain common anomalous characteristics of kinetic expressions involving deactivation. In particular, the apparent rate constant and the apparent order are usually dependent on both the actual and initial pressures of the reactant, and the reaction may not go to completion. © 2000 John Wiley & Sons, Inc. Int J Chem Kinet 32: 7–16, 2000

Catalysis in the nm‐regime: manufacturing of supported model catalysts and theoretical studies of the reaction kinetics

We briefly review the methods employed to fabricate model supported nm catalysts, including wetness impregnation, vacuum vapor deposition, electron‐beam lithography, spin‐coating, and vesicle‐mediated deposition. Recent simulations of the kinetics of heterogeneous reactions occurring on supported catalyst particles are discussed as well. The attention is focused on such effects as reactant supply via the support, interplay of the reaction kinetics on different facets and edges, and adsorbate‐induced reshaping of catalyst particles.

On the Derivation of Heterogeneous Reaction Kinetics from a Homogeneous Reaction Model

A simple homogeneous reaction model in one dimension is presented in the context of silicon oxidation. We investigate two different (canonical) regimes for the oxidant diffusivity and show how these lead in the limit of fast bulk reactions to distinct sharp interface models for oxidation. The resulting heterogeneous models are moving boundary problems which correspond to the classical Stefan problem or to the Stefan problem with kinetic undercooling. The results are relevant for more general reactions but illustrate some of the peculiarities associated with silicon oxidation.

Simulations of the kinetics of rapid reactions on supported catalyst particles

Recent simulations of the kinetics of heterogeneous reactions occurring on supported catalyst particles are briefly reviewed. The attention is focused on such effects inherent for nanometer chemistry as reactant supply via the support, interplay of the reaction kinetics on different facets, and adsorbate-induced reshaping of catalyst particles. In addition, original Monte-Carlo simulations are presented illustrating the contribution of the facet edges to the reaction rate.

Chemically induced diffusion-limited interface growth

Employing a lattice-gas model, we study the Monte Carlo kinetics of heterogeneous reaction resulting in the growth of a new phase on the top of the solid in the case when the process is limited by reactant diffusion via the film. For the simplest set of particle-particle interactions and Metropolis diffusion dynamics, the model proposed predicts the power-law growth of the film thickness, $h\ensuremath{\propto}{t}^{\ensuremath{\alpha}},$ with $\ensuremath{\alpha}\ensuremath{\simeq}0.3.$ Such low values of the growth exponent are usually attributed to the reactions involving grain-boundary diffusion. We have however shown that the growth slowdown might result from the formation of a thin dense layer just on the bottom of the newly formed phase. The model introduced is rather flexible. Choosing other types of the particle-particle interactions or diffusion dynamics, one can easily get diverse regimes of the growth.

パルス電解ストップトフロー法による電解生成活性種の反応解析

By connecting a column electrolysis method with a stopped-flow technique, a pulse-electrolysis stopped-flow method has been developed. This method has many advantages that it can be applied to the detection and characterization of unstable intermediates as well as the analysis of the reaction kinetics of heterogeneous electrode reactions as homogeneous reactions. In addition, this method can be utilized combined with various spectroscopic methods including UV-visible, resonance Raman (RR) and electrogenerated chemiluminescence (ECL) measurements. In this review, the advantages of this method are demonstrated with many successful results in the analyses of the reaction kinetics and mechanisms involving electrogenerated species obtained by using the pulse-electrolysis stopped-flow method.

Kinetics of Rapid Heterogeneous Reactions Accompanied by the Reshaping of Supported Catalyst Crystallites

Using the Monte Carlo technique, we analyze the steady-state kinetics of the ${2A+B}_{2}\ensuremath{\rightarrow}2AB$ reaction occurring on a nanometer-sized crystallite in the case when its shape depends on the amount of adsorbed $B$ particles. The simulations, carried out with a realistic ratio between the rates of the elementary steps, demonstrate that the adsorbate-induced catalyst reshaping may result in qualitatively new reaction regimes.

The influence of the non-irradiated surface area on the kinetics of heterogeneous photocatalytic reaction in a static reactor

Mathematical modelling, on the basis of the Langmuir-Hinshelwood equation, of a photocatalytic reaction in a static reactor, taking into account in the mass balance the adsorption on the irradiated parts of the catalyst, dark parts of the catalyst and support, reveals that an increase in the surface area of the dark catalyst results in prolonged kinetic curves. If the adsorption on the irradiated and dark parts of the catalyst is ignored in the mass balance, errors can occur in the kinetic parameters calculated from the concentration-time curves. An increase in the surface area of the dark catalyst facilitates the removal of contaminants from the gas or liquid phase to below the threshold permitted concentration (TPC), if TPC corresponds to the surface coverage of the illuminated catalyst with contaminant of higher than 0.37.

A Simple Electrochemical Approach to Heterogeneous Reaction Kinetics

Despite the great importance of reactions involving solids and solutions (dissolution reactions, crystallization reactions, heterogeneous catalysis, adsorption and ion exchange reactions), very few teaching laboratory experiments attempt to inculcate the fundamentals of this type of reaction. A major difference between such heterogeneous reactions and the usual homogeneous reactions in solution is that, in the former, the reactant in solution must reach the solid surface before reaction can take place. As a result, reactions between solids and solutions are often controlled by transport of the reacting solution species to the solid surface.It is not easy to experimentally obtain reproducible mass transport. In the teaching experiment described in this paper, it is shown that reproducible results can be obtained using a solid sample in the form of a rotating disc. However, the principle can also be demonstrated using a fixed sample and a stirred solution. The system studied is the dissolution of a known amount of copper in a solution of iron(III). The reaction time is determined by measuring the potential of the copper, which has been electrodeposited on an inert electrode, as a function of time; the potential increases rapidly when all the copper has been consumed. The reaction rate is shown to be dependent on the stirring of the solution, and is first order with respect to the reactant, iron(III).

Analytical Treatment of a Heterogeneous Reaction

An analytical method has been used to study the kinetics of a generic heterogeneous catalytic reaction, A + B → AB. This reaction includes the elementary steps of adsorption and desorption of reactants A and B, surface reaction through the Langmuir-Hinshelwood mechanism, and desorption of the product AB. Despite its simplicity, this analytical approach shows some of the general features observed by simulating the present mechanism on a large N × N lattice.5–7 The rate of reaction depends on the rate of desorption of reactants with a maximum at a value similar to those found by performing heavy simulations. Coverage fluctuations of reactants, as a function of their rate of desorption on a 2 × 2 lattice, have a behavior similar to that found on large N × N lattices.

Heterogeneous catalytic reaction on a 2×2 lattice

We study a model proposed by Fichthorn, Gulari and Ziff for the kinetics of a generic heterogeneous catalytic reaction, A+B→AB. This reaction includes the steps of adsorption and desorption of reactants A and B, surface reaction through the Langmuir–Hinshelwood mechanism, and desorption of product AB. We solve the model exactly and without any restriction on a 2×2 lattice. Despite the reduced number of sites employed, the solution shows some of the general features observed by simulating the mechanism on a large N× N lattice. The rate of reaction depends on the rate of desorption of reactants with a maximum at a value similar to those found by performing heavy simulations. Also, on a 2×2 lattice, we have coverage of fluctuations of reactants as a function of their rate of desorption, as found on large N× N lattices.

On the application of mean value theorem to reaction kinetics over inhomogeneous surfaces

The application of a common mean-value theorem for the description of kinetics of heterogeneous catalytic reactions over inhomogeneous surfaces is discussed. Being mathematically correct for integration of multiple integrals, the mean value theorem can provide a correct value of reaction rate for a particular set of parameters, but physical reasons of its application are doubtful, as it obviously contradicts the kinetic regularities. As an example, the kinetics of a two-step sequence on an inhomogeneous surface is discussed.

Positron emission imaging in catalysis

In situ imaging technology developed for nuclear medicine is now being applied to study the kinetics of heterogeneous catalytic reactions under actual process conditions. Minute quantities of molecules (ca. 10 −15 mol), radio-labeled with positron-emitting isotopes such as 11C; 13N; or 15O, are injected as pulses into the feed streams of chemical reactors. Subsequent coincident detection of pairs of gamma photons produced via positron-electron annihilation allows the concentration of reactants, intermediates and products to be mapped as a function of both time and position within the reactor bed. As well as providing qualitative information regarding the mechanism of the reaction under investigation the data obtained can be compared with mathematical models based on the reaction kinetics in order to refine parameters such as activation energies and pre-exponential factors for elementary reaction steps. Since the technique is capable of imaging transient phenomena, information is provided that is not accessible to steady-state techniques.

Paper I: Design and construction of a Knudsen-cell reactor for the study of heterogeneous reactions over the temperature range 130–750 K: Performances and limitations

A new low-pressure flow reactor operated as a Knudsen cell and intended for chemical kinetic studies is described. The reactor is specifically designed to study the kinetics of heterogeneous reactions. Gas-phase species are detected either by mass-spectrometric sampling or by in situ optical techniques, e.g., laser-induced fluorescence, resonantly enhanced multiphoton ionization. A feature of the reactor is its modular design, allowing full interchangeability of several sample holders at minimal effort, allowing the measurement of uptake coefficients ranging from 10−7 to 1.0. Sample supports operating at low and high temperatures have been developed which cover the stated temperature range. Several experimental examples of the utility of the reactor are detailed. The reliability and error bars of the kinetic results due to the errors and uncertainties associated with the experimental procedures are discussed, in particular for fast heterogeneous processes. It is found that even in the molecular flow regime, for fast reaction, the effects of diffusion limitations within the cell must be taken into account. This fact has been shown here from an experimental point of view. In a companion article the phenomena are studied using Monte Carlo simulation of the gas dynamics under molecular flow conditions.

Kinetics of Rapid Heterogeneous Reactions on the Nanometer Scale

Steady-state kinetics of catalytic reactions, occurring on supported catalyst particles of the nanometer size, are analyzed by employing two schemes taking into account respectively (i) the interplay of reactions on different facets of the catalyst particle and (ii) the possibility of adsorption of reactants on the support followed by diffusion to the catalyst. A chosen model reaction, 2 A + B 2 → 2 AB, is assumed to involve monomolecular A adsorption, dissociative B 2 adsorption, and the Langmuir-Hinshelwood step resulting in the formation of AB. This reaction mimics such practically important catalytic processes as CO oxidation on Pt, Rh, or Pd, and its kinetics for the infinite surface have been explored in detail during the past decade. The results obtained in the present study demonstrate that the kinetics on the nanometer-size catalyst particles can be remarkably different from those corresponding to the infinite surface. This conclusion is drawn on the basis of Monte Carlo simulations with realistic ratio between the rates of reaction and reactant diffusion [scheme (i)] and self-consistent equations explicitly describing A diffusion on the support and the reaction steps on the catalyst [scheme (ii)].

Chemical Kinetics Models for Semiconductor Processing

ABSTRACTChemical reactions in the gas-phase and on surfaces are important in the deposition and etching of materials for microelectronic applications. A general software framework for describing homogeneous and heterogeneous reaction kinetics utilizing the Chemkin suite of codes is presented. Experimental, theoretical and modeling approaches to developing chemical reaction mechanisms are discussed. A number of TCAD application modules for simulating the chemically reacting flow in deposition and etching reactors have been developed and are also described.

Investigation of the kinetics of heterogeneous reactions with the aid of an oxygen probe

The feasibility of using a solid-electrolyte oxygen probe to monitor the kinetics of processes which are accompanied by the transfer of oxygen between a gas atmosphere and solid material in a laboratory reactor was shown. The equation describing such processes was derived. It was concluded that the solid-electrolyte probe can be used to control mass transport in commercial heat-treating furnaces.

Integral method to analyze the kinetics of heterogeneous reactions under non-isothermal conditions A variant on the Ozawa-Flynn-Wall method

The paper describes an integral method of investigating the kinetics and methanism of reactions based on the use of the degree of conversion measured at the same temperatures on curves recorded for a reaction carried out at various heating rates. The main advantage of this method is that it is not based on any assumption concerning the temperature integral, giving, thus, a higher degree of precision to the results. Since it is an integral method, the results are expected to be less affected by experimental errors. The method also allows the computation of the pre-exponential factor, A, and of the activation energy, E, if the Arrhenius-type relationship is assumed for the rate constant. The approach may be considered as a variant on the Ozawa-Flynn-Wall method. Theoretical considerations are verified on two sets of generated data from the literature, as well as on the experimental data acquired for the calcium oxalate dehydration reaction.