The determination of the mechanism of solid state reactions from thermogravimetric data

Abstract

The object of this note is to present the salient features of a generalized computer program that was developed with a view to determining the most likely reaction mechanism from thermogravimetric data and also the kinetic parameters of relevance. The data are fitted to different kinds (as many as 13) of mechanistic equations and a residue analysis is carried out. The goodness of fit of the data to the equations has finally been used as a measure to arrive at conclusions regarding the most probable reaction mechanism and the corresponding equation yields the values of the kinetic constants. While carrying out the actual computations, care was taken to ensure that the cases of those equations which lead to unrealistic or irrational values for the kinetic parameters, such as activation energy and pre-exponential factor, were neglected for the purpose of our analysis. Such situations often become possible on account of the fact that the technique applied for determining the reaction mechanism in the program is essentially mathematical in character and also due to the fact that the weight losses which are considered for the analysis are susceptible to experimental errors. The details of the method used in the computer program are as follows. It is well known that the mechanistic equations corresponding to different types of reactions are generally of the form ▪ where α is the weight fraction of chemical decomposed, T the absolute temperature of the reaction environment, A the pre-exponential factor, φ the heating rate, E the energy of activation, R the universal gas constant, and f(α) a function of α. A number of possible reactions and the functions, f(α), connected with them are shown in Table 1 (cf. ref. 1, pp. 7–10). The computer program endeavours to fit the given data to all these equations and calculates, in each case, the sum of squares of the residuals. It then becomes a relatively simple matter to determine which of the equations leaves the least residue and, as a consequence, characterizes the reaction in question.