The NPK method: An innovative approach for kinetic analysis of data from thermal analysis and calorimetry
Introduction
It is possible to make use of the kinetic analysis in thermal analysis with two different purposes. The first one is to obtain conclusions about the mechanism of a reaction or to extract reference values of certain parameters, such as activation energies. The second purpose is just to obtain a model to predict the behaviour of a reaction under certain conditions. In this case, it is not intended to obtain a mechanistic model, but an operative one.
Classical methods are based on assuming a possible kinetic model and fitting its parameters [1]. Usually, they assume that the rate of change of conversion or reaction rate can be described using two independent functions: f(T) representing the influence of the temperature and g(α) representing the influence of the conversion.f(T) is commonly accepted to correspond to the Arrhenius law and g(α) is usually associated to an a priori established equation. Some new methods, such as “model free” [2], [3], [4], avoid the use of explicit kinetic models, but remain tied to the Arrhenius law. The use of a method completely free of a priori established models, seems that it should be the natural next step. The “non-parametric kinetics” NPK method was developed to fit this objective [5], [6]. In this paper the basic theory of the NPK method and its application to two different chemical systems are exposed.
Section snippets
Theory
Consider a bidimensional () function f(x,y) that corresponds to the product of two independent functions f1(x) and f2(y). Fig. 1 shows the values for the function:Take into account that only the values at the crosses of the graphic are known. They can be represented as a table or a matrix, A, as shown in Table 1. If a singular value decomposition (SVD) a common method of decomposition of matrices is applied on the data of f(x, y)
Experimental
Dicyclohexylidene diperoxide is prepared according to the method described by Sanderson et al. [7]. DSC curves are obtained using a Mettler-Toledo Stare system with a DSC821 cell, using standard aluminium crucibles (ME-51119870) with a perforated lid (ME-51140832) under a flow of 80 ml min−1 of nitrogen. Samples from 2 to 4 mg are recorded at 1, 2, 5 and 7 K min−1.
A 1% (w/w) of AIBN solution in freshly distilled methyl metacrylate is prepared and stored at 4 °C. DSC curves are obtained using a
Results
The application of the NPK algorithm to the decomposition of dicyclohexylidene diperoxide gives the results shown in Fig. 4, Fig. 5. In this case, the vector seems to correspond to a simple kinetic model, and the Arrhenius plot of ln(u) versus 1/T gives a value of 148 kJ mol−1 for the activation energy. The shape of vector could be identified as a SB model (g(α)=αn(1−α)m). Their parameters are easily obtained by direct regression of the elements of versus conversion. However, the produced
Conclusions
The NPK method applied to simple processes can be used to identify a kinetic model, and to obtain their kinetic parameters. Moreover, using the NPK method itself does not make necessary any model to carry out predictions, even in the case of complex chemical behaviour.
Acknowledgements
One of the authors (R. Serra) would express his gratitude to the “Comissionat per a Universitats I Recerca de la Generalitat de Catalunya” for its pre-Ph.D. grant that has been made possible his participation in this project.
References (11)
- et al.
Thermochim. Acta
(1998) - et al.
J. Loss Prev. Process Ind.
(1991) - M.E. Brown (Ed.), Handbook of Thermal Analysis and Calorimetry: Principles and Practice, Vol. 1, Elsevier, Amsterdam,...
- et al.
J. Chem. Inf. Com. Sci.
(1996) J. Therm. Anal.
(1997)
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