New approach to thermal analysis kinetics by considering several first order reactions

An approach to thermal decomposition kinetics is proposed in which it is assumed that the thermal decomposition of a given material is produced by a large, but finite, number of first order reactions. Initially a set of first order reaction “covering” the thermal analysis curves is selected. Usually between 500 and 1500 first order curves are generated. Then, the problem consists of selecting a finite number or first order reactions (among these previously generated) that best reproduce the experimental curves. If no other considerations are taken into account, the problem is a linear minimum square fitting type. However, a large number of reactions, with small contributions, can appear. Therefore, it is interesting to control the maximum “weight” of a given contribution. In that case, the problem can be formulated as a Mixed Integer Quadratic (or Linear) Programming Problem. The procedure can be iteratively repeated in order to get a fine fit generating a finer grid of reactions around the valued obtained in previous iteration. Finally, a non linear optimization, fitting the number of contributions, can be performed to refine – even more – the final results.