Analysis of the relative strength of the singular values obtained from the non-parametric kinetic method

Abstract

The non-parametric kinetic method (NPK) is a method for the processing of thermoanalytical data, which does not make any assumption about the functionality of the reaction rate with the degree of conversion or with the temperature. This method has not been widely used due to its mathematical sophistication and difficulty of automation. The original NPK method uses only the first (maximum) singular value whereas additional information could be drawn from the remaining singular values. A hypothetical application of the NPK, which uses all the significant singular values (modified version of the NPK), is the separation of two or more steps of a complex decomposition reaction. Using simulated data, we have demonstrated that the modified version of the NPK is not useful to discriminate among the decomposition steps of a consecutive complex decomposition reaction scheme. Nevertheless, the analysis of the relative strength of the singular values is useful to assess the degree of separability of the temperature and conversion functions, which are the outcome of the NPK. Taking into account the relative magnitude of the first singular value with regard to the remaining singular values, we have proposed an automated two-scan version of the NPK method which guarantees two separable functions. As the separability of both temperature and conversion functions is the imperative assumption of the single-step kinetics approximation, the two-scan NPK method can be used as a testing method for those methods based on this approximation, the model-free and model-fitting methods.