Kinetics and Mechanisms of Solid-Gas Reactions

doi:10.1016/B978-0-444-64062-8.00011-5

Handbook of Thermal Analysis and Calorimetry

Volume 6, 2018, Pages 173-212

https://doi.org/10.1016/B978-0-444-64062-8.00011-5 Get rights and content

Abstract

The kinetic modeling of chemical reactions in gas-solid systems necessitates a mathematical expression of the rate as a function of variables. For a long time the rate equations used for transformations of powders were different from those describing the oxidation of a metal or an alloy. Both approaches and a unified theory that intends to cover any type of reacting solids with the production/reaction of gases are discussed. Owing to kinetic assumptions of pseudo-steady-state and rate-determining step approximations, a general equation of the rate may be established. The rate $\frac{d α}{dt}$ is then a product of two functions, one depending on the thermodynamic variables and the other depending on the geometrical variables and time. According to the various possibilities of geometry, growth direction, rate-determining step localization, nucleation, and/or growth processes, about 40 kinetic models may be obtained for the variations of the kinetic rate with time. The mechanism decomposition in elementary steps is shown to get the calculation of the function, which governs the effect of the thermodynamic variables on the kinetic rate. A series of experimental tests (most of them based on the jump method) are shown to validate the kinetic assumptions and the geometrical modeling.

Section snippets

State of the Art

Among thermal analysis techniques, thermogravimetry (TG) is the most widely used technique for the study of heterogeneous reactions in solid-gas media. Indeed, it allows direct and easy measuring of the kinetic rate at which one or several gases are evolved or incorporated into the solid sample. Since chemical kinetics has been proved to be a powerful method to understand the mechanisms of homogeneous reactions, it looked obvious to apply its concepts to heterogeneous reactions in order to

Pseudo-Steady-State Approximation

As in the case of kinetics of homogeneous reactions, the approach is based on considering elementary steps mechanisms, in which the reaction intermediates are involved, and using approximations in order to simplify the resolution of the system of balance equations on all the intermediate species involved in the reaction. One of them is the steady-state approximation which allows to avoid differential equations by supposing the intermediate concentrations constant. Effectively in homogeneous

Experimental Methods

Numerous experimental techniques allow to obtain kinetic data and the choice often depends on the adequacy between the device and the characteristics of the reaction under study such as the duration of the transformation (linked with its rate), the nature of both gaseous and solid reactive and products or the conditions of temperature and pressures. In most of the studies about solid-gas reactions, researchers used TG. The TG is a continuous macroscopic measure of the solid sample mass. This

Kinetic Geometrical Models and Elementary Mechanisms

This section reporting the physical modeling of gas-solid reactions is divided into two parts. The first one is devoted to the kinetic geometrical models, i.e., models for the S_m function based on both kinetic and geometrical assumptions in which the nucleation, growth, and the morphological features are taken into account along the reaction. The second part resumes the basic knowledge necessary to describe nucleation and growth of the new phase by means of elementary mechanisms, i.e., the

Study of ϕ(T, P_i)

The variation of the ϕ function with temperature and partial pressure of gases may be directly obtained from the ratios of the rates after/before the jump by the elimination of the S_m term as previously mentioned. Therefore, the method consists in achieving a series of jumps, as shown in Fig. 5.13, while keeping the denominator constant and varying the temperature or the partial pressure of one of the gases. No additional assumption than those at the origin of Eq. (5.13) is required. This

Nonisothermal, Nonisobaric Conditions (Case of a Reacting Bed): CIN4 Approach

If experimental procedure does not allow to ensure the absence of gradients of both temperature and gas composition in the thermobalance (cf. Section 5.2) or to design industrial reactors for gas-solid systems, then the knowledge of the chemical kinetics at the particle scale is necessary but not sufficient. Indeed other characteristics such as the shape and size of both the granular medium and the reactor, the heating sources, the gas flow entries and outlets, etc., must also be considered. In

Conclusions

As discussed in this chapter, rigorous methodology of heterogeneous kinetics for solid-gas reactions is a difficult and time-consuming approach. Indeed such solid-gas reactions involve both surface nucleation and growth processes and several reactional zones should be distinguished in the case of the growth process. When both steady-state and rate-determining step assumptions are verified, physically meaningful kinetic model can be established. In accordance with the shape of the solid

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Chapter 5 - Kinetics and Mechanisms of Solid-Gas Reactions

Abstract

Section snippets

State of the Art

Pseudo-Steady-State Approximation

Experimental Methods

Kinetic Geometrical Models and Elementary Mechanisms

Study of ϕ(T, Pi)

Nonisothermal, Nonisobaric Conditions (Case of a Reacting Bed): CIN4 Approach

Conclusions

J. Solid State Chem.

Thermochim. Acta

Thermochim. Acta

Thermochim. Acta

J. Nucl. Mater.

Thermochim. Acta

Chem. Eng. J.

Thermochim. Acta

Solid State Ionics

Thermochim. Acta

Chem. Eng. Sci.

Solid State Ionics

Thermochim. Acta

J. Nucl. Mater.

Surf. Sci.

Cem. Concr. Res.

Chem. Eng. Sci.

Thermal Decomposition of Ionic Solids

High Temperature Oxidation and Corrosion of Metals

Mechanisms of High Temperature Corrosion: A Kinetic Approach

Nucleation and growth processes occurring during the dehydration of certain alums: the generation, the development and the function of the reaction interface

Proc. R. Soc. Lond.

Ecole Nationale Supérieure des Mines de Saint-Etienne, France

Nucleation: Basic Theory With Applications

Crystal Growth for Beginners

Zeitumsatzformeln für heterogene reaktionen an phasegrenzen fester körper, 1. Die entwicklung der mathematischen method und die herleitung von flächeunmsatzformeln

Z. Phys. Chem.

Zeitumsatzformeln für heterogene reaktionen an phasegrenzen fester körper, 2.Die zeitumsatzformeln für ein pulver aus kugelförmigen teilchen

Z. Phys. Chem.

Reaction kinetics in processes of nucleation and growth

Trans. Am. Inst. Metall. Pet. Eng.

Study of ϕ(T, P_i)