Problems and faulty uses with the Prout-Tompkins description of autocatalytic reactions and the solutions

The investigation of materials containing higher energy, such as peroxides, highly oxidized salts, nitrated organic compounds, leads very quickly to the need for autocatalytic description of decomposition data. The autocatalytic behaviour shows generally a sigmoid change of the conversion. There are several types of autocatalytic equations-one is the Prout-Tompkins (PT) equation. The PT equation is a reaction kinetic model belonging to a series of models with a single reaction rate constant, which are favourably used in the field of reaction kinetic-based thermal analyses. The PT equation was developed and published in the 1940s by E.G. Prout and F.C. Tompkins, which tried to describe reaction kinetically their observations on the thermal decomposition of potassium permanganate. They recognized the autocatalytical behaviour of this decomposition and developed step by step the full autocatalytic description. But, in spite of using the full description with two reaction rate constants, they simplified the expression and kept only the autocatalytic part of the complete reaction scheme and of the rate equation by arguing that this part is much faster than the primary or intrinsic part and determines nearly totally the conversion of the substance. This can be right, depending on the system considered. But this simplification has resulted in a lot of application problems and also in problems to formulate the model in a correct way. In this paper, the problem is analysed and the viable solution will be given, which is called the improved PT model. Further, a lot of papers and applications can be found in the literature, which are a commingling of several concepts. The corresponding equations have an appearance as the PT equation, but in reaction kinetic terms, they are applied in a faulty way. This point is discussed also to dissolve the commingling and to foster the proper application of an autocatalytic description. For completion of the discussed equations and their usefulness in understanding the equations, the characteristic quantities 'time to reach a certain degree of degradation', 'time to maximum rate' and 'conversion at maximum rate' are presented. Finally, some other equations are discussed, which are able to describe autocatalytic behaviour in that they are transformed to the PT equation by choosing the appropriate reaction orders. However, not every sigmoid change in conversion is caused by autocatalysis, and in spite of this fact autocatalytic descriptions are used for such cases and one example of such a faulty use is discussed.