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

(a)dαdt=A exp−ERTf(α)(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. 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.