From the drawbacks of the Arrhenius-f(α) rate equation towards a more general formalism and new models for the kinetic analysis of solid–gas reactions

Abstract

Since many years the kinetic models used for interpreting the kinetic curves α(t) relative to the chemical transformations of solids such as thermal decomposition, reduction, oxidation, etc., rely on very restrictive assumptions to which corresponds the following equation:(a)dαdt=A exp−ERTf(α)where A is called the “pre-exponential term”, E is the “apparent activation energy”, and f(α) is a mathematical function which depends of the kinetic model. This article first presents a critical analysis of Eq. (a) by detailing the conditions in which it is rigorously correct. A more general equation is then proposed on the basis of assumptions related to the nucleation and growth processes of the new phase:(b)dαdt=ϕ(T,Pi)Sm(t,…)Sm(t, …) being a function of α only in very particular cases of instantaneous nucleation or growth, and ϕ being related to the rate-determining step and varying only with thermodynamic variables (temperature, partial pressures Pi, …).The advantages of Eq. (b) are of two types: firstly, the variables temperature and partial pressure of gases may not be separated in the expression of ϕ (no Arrhenius dependence with temperature); secondly, in gas–solid systems, when the nucleation process takes place at the surface of the solid and along the course of the transformation (nucleation and growth processes are simultaneous), the rate cannot be expressed by means of a function of α.Moreover, it is shown that new kinetic models can be obtained considering that the rate-determining step of growth may be located at the surface of the particles, and also the direction of development of the product phase may be outwards, instead of inward as generally considered.In order to simulate kinetic curves and to compare to the experimental ones, a free access software tool has been developed: CIN3. Examples of simulation and optimization are shown, illustrating the determination of constants related to nucleation and/or growth kinetics.