Evaluation of kinetic constants for the solid state reactions under linear temperature increase conditions

The theory of solid state reaction kinetics considers the dependence of reaction rates on temperature (T) and progress of the reaction (α). The term describing the dependence of reaction rates on temperature is usually assumed to be an Arrhenius-type equation: k(T) = Z exp(—E/RT), or the equation predicted by transition state theory: k(T) = ZTb exp(—E/RT). With these assumptions, the equation g(α) = tk(T) has been derived, and this form has been satisfactorily applied for the description of solid state reaction kinetics under isothermal conditions. In this work equations similar to those applied in the case of isothermal conditions are proposed for describing the reaction kinetics under linear temperature increase conditions if k(T) = Z exp(—E/RT) if k(T) = ZTb exp(—E/RT) An attempt has been made to apply the above equations, as well as the differential form from the first equation dα/dt = f(α)Z(1 + E/RT) exp(—E/RT) to a non-isothermal thermogravimetric experiment. The evaluated kinetic constants are in good agreement with those estimated previously by applying widely used methods of calculation. Therefore, these equations may be considered as simpler and more adequate forms for the description of reaction kinetics under linear temperature increase conditions. Two new statistical functions have been applied in this work which permit the evaluation of E and Z from any kinetic equation. These functions may be used instead of the linear interpolation method, because they allow one to distinguish more easily between possible forms of g(α) or f(α) functions. This approach is recommended especially if one intends to use differential kinetic equations.