Kinetic Evaluation and Predictions - METTLER TOLEDO

Kinetic Evaluation and Predictions

Purpose

To show how DSC measurements at different heating rates can be used for kinetic evaluations. The application shows the results that can be obtained from the different evaluation methods and how the predictions can be checked. 

 

Sample

Epoxy resin system consisting of DGEBA and DDM mixed in the stoichiometric ratio of the reactive groups. The measure curves originate the previous examples.

 

Evaluation


Figure 1.

The three dynamically measured DSC curves can be analyzed using kinetics programs. Each measurement can be individually evaluated with the nth order kinetics program or all three curves can be evaluated together using model free kinetics (MFK). In both types of evaluation, the correct choice of baselines is very important. In MFK, the conversion curves are first calculated. As the diagram shows, these conversion curves shift to higher temperatures at higher heating rates. MFK (and advanced MFK) calculates a new curve from these conversion curves that shows how the activation energy changes with conversion. The curve of the activation Ea with increasing conversion clearly shows that Ea does not remain constant during the entire curing reaction as is often assumed. This indicates that the reaction includes complex processes. This is also apparent from the fact that the nth order kinetics yields an activation energy that is significantly larger than the determined from the isothermal experiments (see Section 3.1.3.5) or that is shown by the Ea curve of MFK.

 

Predictions

The aim of kinetic evaluations is to obtain an accurate description of the reaction behavior so that it can be used to predict behavior under other conditions. For example, to predict the conversion curve as a function of time under isothermal conditions at a particular temperature or the time-temperature diagram (Iso-Conversion plot) for a particular conversion. Both can be calculated using model free kinetics or nth order kinetics

Figure 2 shows two possible predictions:

  1. The conversion as a function of time for an isothermal temperature of 160°C
  2. The iso-conversion curve for 70% conversion (right diagram). 

In the left diagram, for example, it can be seen at 160°C a reaction time of 3.6 min is needed for a conversion of 70% if the MFK prediction curve is used (red arrow). Based on the predictions of nth order kinetics, only 1 min would appear to be necessary.

In the right diagram, for example, the reaction temperature can be read off that is necessary to achieve 70% conversion in 5 min reaction time (black arrow)- in this case 55.5°C.


Figure 2.

 

Checking the predictions

The predictions were checked by performing an isothermal DSC measurement at 160°C. The conversion curve calculated from it was also plotted in the above diagram (dashed blue, line, see the example in Section 3.1.3.1).

A comparison of the conversion curves (MFK prediction/isothermal DSC measurement) as a function of time shows that MFK gives a very good prediction up to about 70% conversion. Afterward the measured conversion is lower than the predicted. In contrast, nth order kinetics predicts much shorter times based on one dynamic measurement. This does not agree with the measurement because the curing process is a very complex chemical reaction that cannot be adequately described by just three parameters.

 

Conclusions

The kinetics of one or several DSC curves of a curing reaction can be evaluated by different methods. This is mostly used to describe the reaction rate and to make predictions about behavior at other temperatures. The most reliable results obtained from model free kinetics (MFK). This needs several measurements performed at different heating rates (with advanced MFK, also isothermal measurements). 

The predictions should as far as possible be checked by performing independent experiments. This is easiest to do using an additional isothermal DSC measurement at a temperature that is as close as possible to the desired conditions but still provides a measurable heat flow.

The choice of other experimental conditions (e.g. low temperature) can change the course of the chemical reaction, for example through vitrification. Indications of such changes can be given by the following observations:

  • the shape of the Ea curve
  • a deviation between the predicted conversion curve and that obtained in the control measurement
  • different results based on the evaluation of curves measured at different heating rates

In practice, a reliable kinetic description of the normally complex curing reaction always requires several different DSC measurements. A combination of isothermal and dynamic measurements and use of the advanced MFK software usually yields the most reliable results.

 

Kinetic Evaluations and Predictions | Thermal Analysis Application No. HB12 | Application published in METTLER TOLEDO TA Application Handbook Thermosets, Volume 1