Alternative approach to the problem of additivity

Abstract

Conditions for additivity of nonisothermal reactions in a general sense and in a sense of Scheil are discussed. Scheil’s additivity rule can be applied to a reaction additive in a general sense if, and only if, the time from the approximating isothermal reaction can be presented as a product of a function only of the temperature and fraction transformed. Thus, the reactions additive in the sense of Scheil are a subset of the reactions additive in a general sense. It is proved rigorously that Cahn’s assumption for the reaction rate, as a function of the temperature and fraction transformed, is not sufficient for additivity in the sense of Scheil. It is sufficient for additivity in a general sense, but not necessary, which means that the class of the additive reactions in a general sense, is wider than that defined by the Cahn’s condition. Alternative statements of the additivity rule and its application limits are discussed, on which basis methods are proposed that allow direct determination of the end temperature of the transformation. A method, to check geometrically whether a given isothermal function or a family of isothermal kinetics curves is consistent with the additivity rule, is also proposed.