Isoconversional methods of kinetic

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. 

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. 

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. 

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. 

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... 

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... 

Vyazovkin (1997, 2001) developed an enhanced isoconversional method that allows evaluation of an effective activation energy ( ) as a function of the extent of reaction (a). This methodology, often referred to as model-free kinetics (MFK), is described in Section 3.5. The MFK software allows calculations such as conversion-time plots at selected temperatures that can be compared with actual measured data. It also allows the calculation of DSC curves that can be compared with actual measured DSC curves to help validate the analyses. The same curves analyzed by ASTM kinetics may be evaluated by MFK kinetics, and the same guidance is given. MFK kinetics is very comprehensive in that it is applicable to the simplest as well as to the most complex cure reactions, provided that a baseline can be drawn between a clear beginning and a clear end of the reaction. But it should be pointed out that the software is provided only by Mettler Toledo and Perkin-Elmer. For other users it is possible to measure versus conversion by the ASTM method and generate a spreadsheet with the appropriate MFK equation [e.g., Eq. (3.31) in Chapter 3], to calculate conversion-time plots. 

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]. 

---