Example:


Figure: Calculated reaction progress (DSC, normalized signals) of a low-temperature decomposed substance as a function of time under isothermal conditions. The values of the temperature in °C are marked on the curves.


Comments:

Thermoanalytical measurements under isothermal conditions are usually investigated in a narrow temperature range due to experimental problems (particularly too short at high temperature or too long at low temperature reaction times). Therefore, these measurements may not contain the necessary information on the time-temperature dependence of a selected property for the correct identification of the complexity of a process:

· Under isothermal conditions, one may be faced with an apparent kinetic system involving the contribution of one reaction only whereas under non-isothermal conditions it would be necessary to consider several reactions. This is due to isothermal measurements being usually carried out over a narrow temperature range (generally 20-40K) as compared to the non-isothermal experiments. In such narrow temperature ranges, the isothermal reaction progress may be well described by using a single kinetic model not expressing the complexity of the total reaction process.

· Depending on the temperature window and type of reactions, truly isothermal conditions cannot be accomplished and applied for the very low and very high ranges of the reaction progress  . The simulated curves for the decomposition of hydromagnesite under isothermal conditions presented in the next figure clearly indicate the difficulties of the measurement of the  -t dependencies at the beginning of the decomposition. The isothermal experiments cannot be carried out at temperatures when the reaction rate is too fast and significant decomposition may occur during settling of the experimental temperature at the beginning of the experiments.

Example: For hydromagnesite, isothermal experiment should be carried out at temperatures below 150°C (see next figure) to avoid the influence of the temperature settling on the kinetic characteristics. Nevertheless, the time necessary to reach significant decomposition extent is not measurable from the experimental point of view (>1000 years at 150°C to reach about 25% decomposition extent). To obtain reasonable scanning times (<24h), temperatures above 350°C should be chosen. However, at such temperatures, the problem related to the temperature settling occurs. Therefore, truly isothermal conditions cannot be accomplished for the very low and very high ranges of the reaction progress  . This explains the difficulties of investigating thermoanalytical measurements under isothermal conditions and the choice of a narrow temperature range.


Figure: Extent of the decomposition of hydromagnesite under isothermal conditions. The values of the temperature in °C are marked on the curves. Isothermal experiment should be carried out at temperatures below 150°C to avoid the occurrence of the temperature settling problem. However, investigation scanning times for such temperatures are just not practical.

The above observations indicate that comparison of the kinetic parameters obtained under isothermal and non-isothermal conditions can be aggravated by unavoidable experimental phenomena that affect the kinetic data calculated from the isothermal conditions. In the isothermal temperature window, the maximum rate of decomposition usually occurs at the beginning of the reaction. At these temperatures, a reaction progress of a few percent is reached after a very short period of time, which clearly indicates the limitations of applications of very low values in kinetic calculations for isothermal conditions. The solution is the determination of the kinetic parameters from non-isothermal experiments carried out over a wide temperature range. Non-isothermal experiments, starting with low temperatures, suppress the temperature settling problem at the beginning of the reaction (see next figure) and consequently the limitations of measuring the reaction progress under isothermal conditions. If the kinetic data are able to correctly describe the full temperature range, then they can be employed for the prediction of the isothermal reaction progresses occurring at temperatures lying inside the range of the non-isothermal experiments. This is especially important for multi-step processes which are accompanied by additional phenomena such as melting, polymorphic transformation, sublimation, etc. For such processes, the accurate mathematical transformation of isothermal data to non-isothermal data is impossible, whereas the inverse procedure is feasible.


Figure: Simulated reaction rates d/dt (DTG, normalized signals) as a function of the temperature for a heating rate of 10 K/min with different starting temperatures To = 50, 150, 250, 350°C (marked on the curves).
The problem of the settling of the experimental temperature depends essentially on the kinetic characteristics of a reaction process and on the temperature at which the experiments under isothermal conditions are carried out.