New logarithmic equation of temperature integral for modelling non-isothermal reactions

This article proposes a new logarithmic approximate formula of the Arrhenius temperature integral p(u) for non-isothermal analysis using the Solver algorithm. The proposed formula is presented as - ln p(u) = a + b ln u + cu, and the values for a, b and c are 0.69038, 1.71975 and 1.01249, respectively, for 1 <= u < 20; 0.45891, 1.85919 and 1.00275, respectively, for 20 <= u < 35; and 0.27341, 1.93235 and 1.00060, respectively, for 35 <= u < 100: The validity of the proposed Arrhenius temperature integral formula has been tested by investigating the thermal decomposition kinetics of acrylonitrile-butadiene-styrene (ABS). The activation energy and the pre-exponential factor determined by the proposed formula are 48.7385 kcal mol(-1) and 2.6 x 10(16) s(-1), respectively. The reaction model of ABS thermal decomposition obtained with the method of master plots indicates that the phase boundary reaction model best describes the thermal decomposition reaction of ABS. The accuracy of the proposed Arrhenius temperature integral formula has also been tested by numerical analysis, and deviations from numerical values were compared with those of several previously published approximation formulae. The results show that the proposed formula is superior and is nearly ideal for estimating kinetic parameters from non-isothermal thermogravimetric data.