Remarks on the determination of kinetic constants from thermogravimetric data

Abstract

The methods for determining kinetic constants may have significant effects on the estimation results. The two-variable linear correlation method leads to values of the kinetic constants for which the difference between the calculated and measured values is comparable to or greater than the measurement precision. The non-linear method for calculating kinetic constants by searching for the minimum of the error function N S 1 = ~ (rnit --nh)e/N, where ml and mtt are the measured and calculated values, i=l respectively, and N is the number of experimental data, gives very precise results. A simple calculating technique is necessary for the fitting of the minimum point and the confidence region limit at the significance level. An appropriate calculation was made for metal oxidation according to the parabolic law.The estimation of kinetic constants from thermogravimetric data is a specific case of the wide problem of the estimation of mathematical model parameters from experimental data. When the number of observations is greater than the number of parameters estimated, the task consists in choosing the parameter values best describing the phenomenon investigated. The sum of the square differences of the measurement results and the values predicted for the given model parameters is usually assumed as an accordance value.Those values are the best whose sum is the least. The estimation is therefore frequently identified with the least squares method. The problem formulated above is an example of determining the constraintl minimum, where the sum of square differences is the minimized objective function, and the mathematical model equation is the constraint generator for the individual experimental data. For a given constraint system:it is necessary to find the parameter values of the model a T = (o"1, oh, 9 9 tYp) T giving the minimum value of the objective function

Different kinetic equations analysis

“…One finds from the literature [36][37][38][39][40] that the correlation coefficient is not a good index for selecting the proper mechanism, and we must keep in mind that application of statistical criteria is only possible with the assumption that data have a 'normal distribution'. Since the aim of the calculations is to determine parameters that describe experimental data relatively well, the conformity of Yexperimental and Ycomputed (or o~xp and o~a1r is often used as a criterion for selecting the proper f(a) or g(a) function [5,42,43].…”

Kinetic studies on the thermal decomposition of phosphate-doped sodium oxalate

“…It has been reported that correlation coefficient (r) is not a perfect criterion for deciding the best fit [40,41]. Rózycki and Maciejewski [36] has shown that the best fit of experimental and calculated data is gained by using the weighted least squares method using criteria based on the minimization of the difference between the experimental a values (a exp ) and a values calculated (a calc ), on the basis of the equation g(a) = kt ?…”

Thermal analysis

“…The hydrolysis of acetic anhydride was used as the model of simple reaction for this method. The two-variable linear correlation method leads to values of the kinetic constants for which the difference between the calculated and measured values is comparable to or greater than the measurement precision (135). A detailed analysis of the merits and shortcomings of integral methods for the treatment of constant heating rate, nonisothermal kinetic data was presented (70).…”