Kinetic Evaluation of a Vulcanization Reaction (Model Free Kinetics)

Purpose

To demonstrate the evaluation an isothermal vulcanization reaction using Model Free Kinetics.

Sample

Unvulcanized NBR with 50% polymer content 

Conditions

Measuring cell: DSC822e

Pan: Aluminum 40 Pl, pierced lid

Sample preparation: Cubes of approx. 25 mg were cut from the starting material immediately before the measurement.

DSC measurement: Fresh samples were measured at heating rates of 1 K/min, 2 K/min, 5 K/min, 10 K/min, 15 K/min and 20 K/min. The starting temperature was 50 °C. The final temperature depended on the heating rate and was between 190 °C (at 1 K/min) and 250 °C (at 20 K/min). 

Atmosphere: Nitrogen, 50 ml/min

The reaction peak shifts to higher temperatures at higher heating rates. The melting peak remains below 100 °C. 

Evaluation

The conversion curves were first calculated from the heat flow curves. 

With a heating rate of 1 K/min, the conversion curve shows two distinct steps. The reaction begins relatively rapidly. At about 50% conversion, the reaction rate becomes slower. With a heating rate of 20 K/min, the two steps are no longer visible. The reaction kinetics of the vulcanization reaction are heating rate dependent. 

Since the reaction kinetics depend on the heating rate, the curves measured at the three slowest heating rates are used to predict isothermal reaction curves from results of the Model Free Kinetics evaluation.

The activation energy is calculated as a function of conversion from the curves. It can be seen that the first reaction step has an apparent activation energy of about 90 kJ/mol. At 60% conversion, the activation energy increases to about 110 kJ/mol. The activation energy curve can be used to calculate the conversion as a function of time for isothermal reactions at different temperatures. To gain an impression of the accuracy of the calculated isothermal conversion functions, the curve at 130 °C is compared with the curve measured in Section 3.1.3. Measurement of isothermal vulcanization kinetics: 

The measured points in the diagram were obtained from data from the post-vulcanization reaction. The diagram shows that the measured values agree very well with predictions from Model Free Kinetics.

Conclusion

Model Free Kinetics is an excellent and rapid method for obtaining information on the kinetics of reactions and for making predictions about the course of the reaction. If the kinetics of the reaction change with the heating rate, the optimum conditions for the kinetic evaluation have to be carefully chosen. For predictions on isothermal reactions, dynamic experiments with relatively low heating rates should be used. In the case described, the heating rates used were 1 K/min, 2 K/min and 5 K/min. The curves obtained from the prediction can be used to optimize processing conditions. 

^{Kinetics Evaluation of a Vulcanization Reaction (Model Free Kinetics) | Thermal Analysis Handbook No.HB409 | Application published in METTLER TOLEDO TA Application Handbook Elastomers, Volume 1}