Authors:Jorge Capela, Marisa Capela, and Clóvis Ribeiro
The generalized temperature integral I(m, x) appears in non-isothermal kinetic analysis when the frequency factor depends on the temperature. A procedure based on Gaussian
quadrature to obtain analytical approximations for the integral I(m, x) was proposed. The results showed good agreement between the obtained approximation values and those obtained by numerical
integration. Unless other approximations found in literature, the methodology presented in this paper can be easily generalized
in order to obtain approximations with the maximum of accurate.
The integral methods, which are obtained from the various approximations for the temperature integral, have been extensively
used in the non-isothermal kinetic analysis. In order to obtain the precision of the integral methods for the determination
of the activation energy, several authors have calculated the relative errors of the activation energy obtained from the integral
methods. However, in their calculations, the temperature integral at the starting temperature was neglected. In this work,
we have performed a systematic analysis of the precision of the activation energy calculated by the integral methods without
doing any simplifications.
The results have shown that the relative error involved in the activation energy determined from the integral methods depends
on two dimensionless quantities: the normalized temperature θ=T/T0, and the dimensionless activation energy x0=E/RT0 (where E is the activation energy, T is the temperature, T0 is the starting temperature, R is the gas constant).
= constant is the heating rate. Upon integration over the variables α and T , one can easily obtain the evolution of α ,
where is the temperatureintegral [ 10 ] (in Appendix 1 , we provide some numerical and analytical recipes to evaluate p ( x
Integrating Eq. 2 gives,
where p ( x ) is the famous temperatureintegral, which has no analytical solution [ 11 ]. In the classic integral isoconversional methods, such as Ozawa–Flynn–Wall method (OFW) [ 12 , 13 ], the approximations of p ( x ) [ 14