Estimating errors in the determination of activation energy by nonlinear methods applied for thermoanalytical measurements performed under constant heating rates

摘要

Several linear and nonlinear isoconversional methods have been applied for following non-isothermal thermo-analytical data: simulated data for two consecutive first order reactions (12 heating rates), crystallization of (GeS2)(0.3)(Sb2S3)(0.7) (4 heating rates), decomposition of ammonium perchlorate (6 heating rates) and decomposition of poly(vinyl chloride) (PVC) (5 heating rates). It has been considered some pairs "linear isoconversional method + nonlinear isoconversional method". The "differential pair" is "differential isoconversional method suggested by Friedman + nonlinear differential method", while each "integral pair" corresponds to a certain approximation of the temperature integral. The values of activation energy (E), error of E obtained by linear method and applying the method of least squares (Delta E-L), and Fischer confidence interval obtained for confidence levels of 68.27%, 80%, 90% and 95% by nonlinear method (Delta E-F) applying the procedure suggested by Vyazovkin and Wight have been determined for each pair of methods and several conversion degrees. It has been turned out that, for a certain pair of methods, (a) Delta E-F values are substantially greater than Delta E-L values, and (b) the values of E determined by linear method are identical with those determined by the nonlinear method. The statement (a) is explained by the procedure for Delta E-F evaluation in which it is assumed that Delta E-F correspond to maximum value of Fischer distribution function. According statement (b) it is expected that is a relationship between Delta E-L and Delta E-F. Both statements suggest that the error in E determined by a nonlinear isoconversional method is equal with Delta E-L. Satisfactory fittings of Delta E-L vs. Delta E-F have be obtained for the relationships: (1) Delta E-L = a x Delta E-F and (2)Delta E-L = b x Delta E-F + c x (Delta E-F)(2), here a, b and c are parameters which depend on the confidence limit. These relations have been also checked f