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

Abstract

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.