Stepwise isothermal approach

The stepwise isothermal approach was first introduced by Sorenson. In this approach, a maximum heating rate and two weight loss... 

Fig. 56. Dissociation of BaC>2 during stepwise heating, approaching quasi-isothermal conditions...

A valuable approach for measuring thermal degradation kinetic parameters is controlled-transformation-rate thermal analysis (CRTA) - a stepwise isothermal analysis and quasi-isothermal and quasi-isobaric method. In this method, some parameters follow a predetermined programme as functions of time, this being achieved by adjusting the sample temperature. This technique maintains a constant reaction rate, and controls the pressure of the evolved species in the reaction environment. CRTA is, therefore, characterised by the fact that it does not reqnire the predetermined temperature programmes that are indispensable for TG. This method eliminates the nnderestimation and/or overestimation of kinetic effects, which may resnlt from an incomplete understanding of the kinetics of the solid-state reactions normally associated with non-isothermal methods. 

As shown by Eq. (8), the kineties governing a thermal decomposition event depend on time, temperature, and rate of decomposition. TG experiments performed at a constant heating rate allow temperature and time to be interehanged in the ease of first order kinetics and one-step decompositions. ] Hi-Res TGA allows the determination of kinetic parameters such as activation energy and reaction order for each step in multiple component materials using four different TG approaches I constant heating rate, constant reaction rate, dynamic heating rate, and stepwise isothermal. 

As a consequence the heating rate must not only be linear but also adapted to the type of reaction which is to be expected. In certain cases stepwise heating may be chosen, since this better approaches the isothermal conditions. Figure 31 shows the effect of the heating rate on the shape of the TG-curve in the case of palygorskite, a complex layer silicate28. Only the low heating rate (0.5 °C/min) allowed to resolve the individual dehydration steps. 

An interesting approach was adopted by Annabi-Bergaya et al. (1979), who determined methanol and isopropanol desorption isotherms on a series of charge-deficient Ca-montmorillonites (prepared from Na- and Li-saturated montmorillonite). Each desorption isotherm was determined after a surface cleaning process with the particular alcohol in order to prevent the irreversible collapse of the interlamellar space. The adsorbent was exposed to the alcohol vapour atp/p° = 0.9 and the stepwise mass... 

In reality it is neither practical nor desirable to step the column oven temperature in 10° increments every minute, nor does the stepwise model predict elution times with sufficient accuracy for our purposes. If we now imagine instead that the oven temperature increases in 1° steps every 6 s or even better in 0.1° increments every 600 ms, we can approach a true linear temperature program rate of 10°C/minute as is encountered in modem gas chromatographic systems. Our isothermal retention data at 50 and 60°C are still valid, and we could calculate the peak positions for each 0.1°C step in a tabular format. The problem is that even this small a step is still too large for accurate prediction of programmed-temperature retention times. Instead, we must to turn to calculus and consider an arbitrarily small step size (dt). A simplified relationship of a single-step linear temperature program to elution time can be expressed as follows [13] ... 

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