Evaluation of the integral methods for the kinetic study of thermally stimulated processes in polymer science

This paper reports on the accuracy of the integral methods used for the kinetic analysis of degradation and crystallization of polymers. Integral methods are preferred by many authors over the differential ones because often the experimental data obtained, such as thermal degradation studied by thermogravimetry, are integral and the differentiation of the integral data usually produces an unwilling increase of the noise. A problem of the integral methods is the fact that Arrhenius integral function does not have an exact analytical solution. Thus, several approximated equations have been proposed in literature. Some of these approximations lead to a linear relation between the logarithm of g(α) and a predetermined function of T, in such a way that the activation energy can be determined from the slope of the plot of ln g(α) versus the predetermined T function. The most popular approximations to the Arrhenius integral in polymer science are those of van Krevelen et al., Horowitz and Metzger, and Coats and Redfern. Although these three approaches where proposed 50 years ago, they are extensively used nowadays and several hundreds of citations to the original papers can be found in recent polymer science publications. Despite their popularity, there are cast doubts on the accuracy of these approximations, because they provide significant deviations in the determination of the actual values of the Arrhenius integral when used for simulating α-T plots. Nevertheless, a comprehensive study of the systematic errors in the activation energy calculated from these integral methods is still missing. In this paper a comparative study of the accuracy of the different integral methods is performed. The calculated errors are tested with simulated and experimental results.