Isoconversional kinetic methods

To evaluate the apparent activation energy, the isoconversional methods are use as suitable analysis procedures. These methods are based on the assumption that at a constant extent of conversion degree (a), the decomposition rate da/dt is a function only of the temperature. In methods developed by Friedman and Flynn-Wall-Ozawa, linear functions are obtained from which slopes the apparent activation energy at constant conversion a is achieved. In the free kinetic method set by Kissinger is calculated from the slope of the linear function takes into consideration the relationship between the heating rate and peak temperature of the first-derivative thermogravimetric curve [97]. 

For the very restricted conditions where Eq. (5.2) provides a rigorous description of the reaction kinetics, the activation energy, E, is a constant independent of conversion. But in most cases it is found that E is indeed a function of conversion, E (x). This is usually attributed to the presence of two or more mechanisms to obtain the reaction products e.g., a catalytic and a noncatalytic mechanism. However, the problem is in general associated to the fact that the statement in which the isoconversional method is based, the validity of Eq. (5.1), is not true. Therefore, isoconversional methods must be only used to infer the validity of Eq. (5.2) to provide a rigorous description of the polymerization kinetics. If a unique value of the activation energy is found for all the conversion range, Eq. (5.2) may be considered valid. If this is not true, a different set of rate equations must be selected. 

For this particular case, both a, and a2 are unique functions of conversion, meaning that dx/dt depends only on conversion and temperature i.e., the polymerization kinetics may be described by the phenomenological Eq. (5.1). Moreover, if one of the mechanisms (e.g., the catalytic) predominates over the other one (e.g., the noncatalytic), Eq (5.2) may be used to correlate experimental results and the activation energy may be obtained using isoconversional methods. 

Therefore, for particular values of the conversion of functional groups and temperature, the rate of chainwise polymerizations depends on the concentration of active species which, in turn, depends on the particular thermal history. Thus, phenomenological equations derived from Eq. (5.1), or isoconversional methods of kinetic analysis, should not be applied for this case. 

For chemical scenarios, the kinetic behavior of the reaction, the temperature and pressure increase rate must be known under runaway conditions in the interval between set pressure and maximum pressure. This implies a good knowledge of the thermo-chemical properties of the reaction mass. The required data are traditionally obtained from adiabatic calorimetric experiments [22, 25, 26]. Nevertheless, other calorimetric methods, especially dynamic DSC or Calvet experiments evaluated using the isoconversional approach, can also provide these data with accuracy and an excellent reliability for the temperature increase rate [27], as well as for the pressure increase [28, 29]. 

Vyazovkin and Liimert [56] argue that kinetic data, A and E, values obtained on the assumption of a one-step reaction may be incorrect because the possibility that thermal decompositions proceed by multistep processes has been ignored. This potential error can be avoided by using isoconversional methods to calculate Arrhenius parameters as a fimction of a. A real isokinetic relationship in a multistep process can be identified fi om the dependence of and its confidence limits, on a. The contribution fi om the second reaction step is negligible at the start of chemical change and thereafter rises as ar increases. 

To avoid discarding potentially significant information, the parameters obtained fi om isoconversional methods may be used with the original data to determine the kinetic model [49], although this is often not done. Activation energies determined from isoconversional methods [43] are in good agreement with values from isothermal experiments. 

Methods of kinetic analysis that involve fitting of experimental data to assumed forms of the reaction model (first-order, second order, etc.) normally result in highly uncertain Arrhenius parameters. This is because errors in the form of the assumed reaction model can be masked by compensating errors in the values of E and A. The isoconversional technique eliminates the shortcomings associated with model-fitting methods. It assumes the unknown integrated form of the reaction model, g(a), as shown in Eq. (4), to be the same for all experiments. 

An advantage of the advanced isoconversional method is that it can be applied to study the kinetics under arbitrary temperature programs such as distorted linear (e.g., self-heating/cooling) or purposely nonlinear heating e.g, temperature modulation). To more adequately account for a strong variation of... 

On the other hand, reliable kinetic predictions can be accomplished in entirely model-free way by using the dependence of Ea on a determined by an isoconversional method. The relevant predictive equation [17,87] was originally obtained in the following form... 

Isoconversional kinetics is an efficient compromise between the common single-step Arrhenius treatment and the predominantly encoxmtered processes whose kinetics are multi-step and/or non-Arrhenius. Isoconversional methods are capable of detecting and handling such processes in the form of a... 

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). 

The isoconversional methods are also known as model-free methods. Therefore, the kinetic analysis using these methods is more deterministic and gives reliable values of activation energy E, which depends on degree of transformation, a. However, only activation energy... 

Li and Tang (Li Tang, 1999) have developed an isoconversional integral method which does not make any assumption about the kinetic model and involves no approximation in the Eq. (3) as... 

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