An Introduction to n-th Order and Autocatalysis Reactions

7. Example: Thermocuring of Epoxy Resin - a Comparison of Different Reaction Types

7. Example: Thermocuring of Epoxy Resin - a Comparison of Different Reaction Types

For a homogeneous system, we’ve already discussed in detail the characteristic reaction progress for different reaction types (n-th order, auto-catalysis, and combined auto-catalysis). Here we will use a DSC example of the curing of epoxy resin. By comparing the kinetics model-fit results, we are trying to help our customers understand the difference between these reaction types visually and intuitively.

Here we carried out DSC tests on curing process of epoxy resin at different heating rates (5, 10, 20 K/min), and obtained the following exothermal curing peaks. The experimental curves are present in the Figure 6:

Fig.6 Three experimental DSC curves for different heating rates

There are some articles which prove that the curing of epoxy resin (EP) is some kind of auto-catalysis reaction [3]. However, here we will put all of these existing conclusions aside and suppose we don’t know what’s going on chemically inside of the material at all. We will therefore try to apply different reaction types to carry out curve-fitting, and decide what the possible reaction type is from the fit quality alone.

Fig.7 Kinetics fit of curing curves using reaction of n-th order Fn

In the Fig.7, the points are measured data points, and the lines are calculated fit-optimized curves using n-th order reacton type (Fn). We already know that the DSC signal is directly proportional to the reaction rate.

If we compare the fit curve with the measured curve and focus on the early stage, we find that the n-th order reaction has no obvious induction period and the increase in the reaction rate is relatively smooth. While for the measured signal, the starting part is more horizontal and the later acceleration is more strong (the left side of the peak is sharper than for the fit curve). This indicates that the reaction can involve an auto-catalysis mechanism.

Fig.8 Kinetics fit of curing curves usingautocatalytical Prout-Tompkins reaction Bna

In Fig.8 we will attempt to use the pure auto-catalysis Prout-Tompkins reaction type, namely Bna, to carry out a curve fit. The overall fit quality is greatly improved, but the early stage of reaction is still not so properly fitted. If we focus on the solid line (fit curve), we’ll find that the pure auto-catalysis function has a longer induction period during which the reaction rate is close to zero (nearly a horizontal line); after that, the reaction rate accelerates faster than it does in reality.

Fig.9 Kinetics fit of curing curves using autocatalytic reaction Cn which is the partial case of Kamal-Sourour reacton

Finally, we will use the combined auto-catalysis reaction Cn to carry out a curve fit. In Fig.9, the calculated curve fits almost perfectly with the measured curve. This indicates that the reaction mechanism might possibly be a combination of n-th order and auto-catalysis paths:

with weighting factor Kcat=1.34. Other parameters listed here:

Ea = 46.2 kJ/mol

lgA = 2.5 lg(1/s)

n = 1.7

All these values are in a chemically sensible range, which proves this reaction type is reasonable.

8. Conclusion

Thermokinetics is a branch of science which combines chemical kinetics with thermal analysis techniques. It filters and abstracts from the various factors influencing reaction rate, simplifying to a relatively basic function of temperature and conversion. It can be used:

  • to mathematically conclude the measurement data,
  • to predict the measurement result under different temperature programs, or
  • to help optimize the process temperature program under a certain rate-control requirement.

The reaction systems can be classified into homogeneous and heterogeneous systems. The common reaction types for homogeneous systems are:

  • n-th order,
  • auto-catalysis types.

Besides the temperature factor, the rate change in n-th order reactions only follows the consumption of reactants, while the auto-catalysis reaction further introduces the accelerating effect from product generation. In some reaction systems, n-th order and auto-catalysis paths may take place in parallel.

Different reaction types can be described by different reaction models in Thermokinetics, and exhibit different behaviors (induction, accelerating, decelerating, etc.) in thermal analysis curves. In circumstances where knowledge regarding chemical mechanisms is lacking, we can try different mechanism functions to carry out curve fitting and compare the results with measured thermal analysis curves. The possible reaction mechanism could thus be surmised based on the fit quality and on whether the obtained kinetics parameters are within a reasonable range.

9. References

1.  M. E. Brown:Handbook of Thermal Analysis and Calorimetry, Vol. 1, Chapter 3.  © 1998 Elsevier Science B.V.

2. Thermal Safety of Chemical Processes: Risk Assessment and Process Design.   Author: Francis Stoessel (Switzerland), Chinese version translator: Wanghua Chen, Jinhua Peng, Liping Chen,Revised by Ronghai Liu, Science Press, Aug. 2009.

3. SergeyVyazovkin, Alan K. Burnham, Loic Favergeon, Nobuyoshi Koga, Elena Moukhina, Luis A.Pérez-Maqueda, NicolasSbirrazzuoli, ICTAC Kinetics Committee recommendations for analysis of multi-step kinetics, Thermochimica Acta 689 (2020) 178597,