Single heating rate methods

The fundamental flaw of single heating rate methods is that they produce significantly differing kinetic triplets, most of which provide quite satisfactory description of the same dataset [85]. This occurs because of the mutually compensating correlation of E and A. Known as a compensation effect, this correlation takes the following form... 

X.-G. Li, M.-R. Huang, G.-H. Guan, and T. Sun, Kinetics of thermal degradation of thermotrr ic poly(p-oxybenzoate-co-ethylene terephthalate) by single heating rate methods. Polymer International, 46,289 (1998). 

Analysis of tga data for thermal decomposition reactions has been the subject of a major comparative review (the ITACT project) of the application of various methods to both experimental and simulated data (34 7). The final conclusion is that isoconversional analyses tend to work fairly well and that kinetic analysis using single heating rate methods should no longer be considered acceptable (37). 

Single-heating-rate methods and those that assume at the outset a specific reaction model (e.g., first-order) are not recommended. 

An algorithm to fit the experimental data to this model was made in Fortran using a least square method by Fletcher [10], In order to achieve the best result, the model was constructed to fit the frequency factor, A, and a, while the influence of p on the residual sum of squares had to be tested manually. As for the previous models, the model was used to fit data at a single heating rate and to fit data at three heating rates simultaneously. The best fit for the simultaneous fit to three heating rates was obtained with p = 0.055. This value was subsequently used to fit the data individually. Table 3 lists the kinetic parameters and Fig, 5A and 5B shows the fit to the data curves for fits to individual curves and simultaneous fit to all three curves. 

The tpd profiles were determined using a Stanton-Redcroft TG 762 thermogravimetric balance with on-line Commodore CBM computer for data collation and analyses.(3.4) The profiles were analysed using the single heating rate, variable coverage (SHR) method. (4.)... 

Figure 3. Activation energy of desorption of n-hexane from 0 Na-Theta-1 (Na,H)-Theta-1 O H-Theta-1 as a function of sorbate loading in molecules per unit cell. Single heating rate tSHR) method of analysis.

It has been experimentally demonstrated [17,75,85] that the model-free equations give rise to reliable predictions, whereas substitution of the kinetic triplets, obtained from a single heating rate run, into equation (44) yields fundamentally erroneous predictions. It has also been shown that the model-free predictions are superior to the predictions based on the ASTM method (equation... 

Many methods have been developed for evaluating a kinetic triplet by fitting rate equations to data obtained at a single heating rate. For example, rearranging Eq. (3.17) gives... 

One reason for the higher values obtained using the single constant heating rate method (e.g., Eq. 9.3, [70]) is probably due to the different reactions proceeding in a mixed and complex manner. If this is true, it is difficult to evaluate the correct value of each elementary reaction, because the E value is calculated as an apparent value from the slope of the total plot made up of multiple reactions. 

Performing a reaction under isothermal conditions is somewhat more complex. It requires two temperature probes, one for the measurement of the reaction mass temperature and a second for the jacket temperature. Depending on the internal reactor temperature, the jacket temperature is adjustable. The simplest method is to use a single heat carrier circuit to act either on the flow rate of cooling water or on the steam valve. With a secondary heat carrier circulation loop, the temperature controller acts directly on the heating and cooling valves by using a conventional... 

The supported catalysts were characterized for their basicity distribution by temperature programmed desorption (TPD) of CO2 from 50 to 950 C at a linear heating rate of 20°C.min in a flow of helium(40cm. min ). The surface area of the catalysts was determined by the single-point BET method, using a Monosorb surface-area analyser (Quanta Chrome Corp. USA). 

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