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

Abstract

Several linear and nonlinear isoconversional methods have been applied for following non-isothermal thermoanalytical 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 (ΔLE), and Fischer confidence interval obtained for confidence levels of 68.27%, 80%, 90% and 95% by nonlinear method (ΔFE) 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) ΔFE values are substantially greater than ΔLE 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 ΔFE evaluation in which it is assumed that ΔFE correspond to maximum value of Fischer distribution function. According statement (b) it is expected that is a relationship between ΔLE and ΔFE. Both statements suggest that the error in E determined by a nonlinear isoconversional method is equal with ΔLE. Satisfactory fittings of ΔLE vs. ΔFE have be obtained for the relationships: (1) ΔLE=a×ΔFE and (2)ΔLE=b×ΔFE+c×ΔFE2, here a, b and c are parameters which depend on the confidence limit. These relations have been also checked for high density polyethylene (HDPE) decomposition data that were not used for their derivations. For all considered data, the best accuracy of fitting of ΔLE vs. ΔFE has been obtained for Eq. (2) and ΔFE determined for confidence level of 95%. It has been conclude that the evaluation of error in E determined by a nonlinear isoconversional method involves the following two successive steps: the determination of ΔFE for confidence level of 95%, and the application of relation (2).