Non-parametric kinetic analysis of autocatalytic reactions

Commonly, classical kinetic approaches using a Šesták and Berggren (SB) model, α˙=k·α^m·(1−α)ⁿ, describes the behaviour of autocatalytic processes after their initiation. However, the SB model does not consider any initiation reaction. Therefore, such a model has simulation restrictions and could not predict induction times, which have relevance in process safety, i.e. in thermal explosion/runaway prevention or in curing of some thermosetting resins. Some procedures for simultaneously considering both initiation and autocatalytic propagation reactions were proposed. Perhaps one of the most traditional is the model suggested by Dien et al. in the 1990s. According to this model, two reactions are considered (A→B; A+B→2B), and a combined kinetic equation, α˙=k₁·(1−α)^p+k₂·α^m·(1−α)ⁿ, is used to describe the process. Despite of this model could be considered realistic, the dramatic different sensitivity of its parameters make the numerical fitting of experimental data a quite impossible task if sets of senseless parameters have to be avoided. The non-parametric kinetics, (NPK) method developed by our group has been used to identify and describe single processes. Nevertheless, intrinsically NPK gives information about all simultaneous transformations taking place in a process. This work exposes how the different processes appear overlapped in the results of NPK. NPK methodology has been applied to the thermal decomposition of 2,4-dinitrophenol (DNP) and the curing reactions of Araldite Standard^® and diglycidyl ether of bisphenol A (DGEBA) with diethylenetriamine (DETA). In all the cases, only the first pair of vectors – u₁ and v₁ – has significance in the reconstruction of the original data. The straight simulation of the experimental data using u₁ and v₁ without requiring theoretical models gives excellent results in all of the cases, demonstrating once again the potential of NPK. However, only one function of temperature or kinetic constant can be obtained for the whole process. NPK results confirm the suggestion of Dien et al., indicating that an autocatalytic process can be properly described as the sum of a 1st order reaction (RO) and a truncated Šesták and Berggren (SB) model. However, having only one expression for the kinetic constant, the final equation has the form α˙=A·e^{−E_a/(R·T)}·[(1−α)+γ·α^m·(1−α)ⁿ]. This model enables the prediction of induction times, improving working and safety conditions.