# A Simple Direct Method to Obtain Kinetic Parameters for Polymer Thermal Decomposition
## 5 Discussion  
Although the Arrhenius equation adjusts as much as possible to experimental results, it only approximates the thermal decomposition behavior, which can be perturbed by experimental noise and competing reactions. These limitations make it unlikely that perfect results will be obtained.  
It is useful also to highlight some considerations regarding application of the Lyon and GDM methods. The former is valid only for a reaction first order. The latter is employed using different equations [22] to calculate the reaction order and maximum and minimum of the second \(\alpha\) derivative and to choose the kinetic parameters that best fit the experimental curve.  
In estimating the kinetic parameters at different heating rates, there is a tendency for the activation energy and pre-exponential factor predicted by the Lyon method to vary, which occurs because these quantities are determined using only the \(dm/dT\) maximum as a single reference point. As the \(dm/dT\) maximum moves to higher temperatures with increasing heating rate, the activation energy increases. The GDM produces considerable variation in the estimated kinetic parameters without exhibiting the trend of the Lyon method. The variability results from the methodology of the GDM approach, which prioritizes obtaining a good representation of the experimental response rather than the homogeneity of the equations used.  
The proposed method overcomes these constraints by considering three regions of the curve (beginning, middle, and end) to estimate kinetic parameters characteristic of the entire reaction. The use of several reference points along the course of the reaction may explain why the proposed method does not produce the trend in activation energy and pre-exponential values exhibited by the Lyon method. The new method also produces the narrowest range of E and A values at all heating rates and a smaller dependence on reaction order. Nevertheless, variation in the kinetic parameters with heating rate is still observed. The variability could arise from the influence of heating rate on the nature of the decomposition reactions, where it has been shown [3; 15] that the boundary conditions (including heating rate) employed in the definition of the TGA response can change the temperature at which reactions take place and the kind of material produced upon decomposition.  
Although GDM and Lyon methods can be applied to analyze complex behavior, such as that exhibited by NOMEX, where decomposition occurs by competitive reactions. When it is applied to competitive reactions with more than one step, it is not possible to define a unique and separate peak in the second derivative to calculate kinetic parameters. This  
Figure 15: A comparison of experimental and calculated (**a**) mass and (**b**) \(dm/dT\) for PVC.  
seems to affect the results of these methods, producing worse results when competitive rather than consecutive reactions occur.  
The proposed method is applicable to single, consecutive, and partially competitive reactions, as illustrated by the results shown in Table 6, which show the lowest error under all conditions except for the \(dm/dT\) result of PVC. Special attention should be paid to the analysis of competitive reactions. The new method can be applied to other reaction models by modifying Equation (7) to fit specific circumstances better, such as the first decomposition reactions of PMMA and PVC. However, these objectives are beyond the scope of the present work. The proposed method of calculating average kinetic parameters at different heating rates should enable users to define global kinetic parameters to predict thermal decomposition behavior under a wider range of conditions.