Kinetic Studies of Complex Reactions. Part 1: Model Free Kinetics - METTLER TOLEDO

Kinetic Studies of Complex Reactions. Part 1: Model Free Kinetics

Introduction

Model Free Kinetics (MFK) has proven to be an excellent method for describing chemical reactions [1-4]. To apply MFK to dynamic DSC measurements, the reaction has to be measured at three or more different heating rates. MFK assumes that the reaction mechanism does not change with heating rate. In most practical cases, this condition is met. An exception can be the cross-linking reaction of a “hot curing” system. The material may vitrify during the reaction, i.e. pass from the liquid to the glassy state. The reaction kinetics changes from being chemically controlled (in the liquid state) to diffusion controlled (in the glassy state).

This article shows how MFK can be used to identify and describe such a reaction. The experiments were performed using a two-component epoxy resin consisting of the diglycidylether of bisphenol A (DGEBA) and diaminodiphenylmethane (DDM) as hardener or curing agent.

This article is the first part of a two-part study. This first part discusses the experimental approach for the investigation of complex curing reactions and for the evaluation with MFK. The second part [5] presents an extension of MFK that describes the influence of vitrification on the reaction kinetics.

 

Dynamic Curing Measurements

DSC curves of the DGEBA-DDM system measured at different heating rates

Fig. 1 shows a series of dynamic DSC curves measured at different heating rates. It can be seen that the peak maximum of about 105 °C at 1 K/min shifts to about 160 °C at 10 K/min. The glass transition temperature of the unreacted starting mixture (Tg0) is -18.3 °C. The heat of reaction (∆Hreact) is 406 J/g. The glass transition temperature of the fully cured material (Tg1, 166.5 °C) is determined in a second measurement. The reaction peak at heating rates of less than 10 K/min is significantly lower than Tg1. This indicates that the reaction could be influenced by vitrification.

In Figure 2, conversion curves have been calculated from the DSC curves. MFK is then used to calculate a value for the conversion-dependent activation energy from three of the curves. With the material investigated, the activation energy has an almost constant value of 50 kJ/mol if the curves measured at 2, 5 and 10 K/min are used (curve a in Fig. 2). If the kinetics of the reaction does not change, then the activation energy curve should be independent of the heating rate used. 

In the case considered, the activation energy curve however changes significantly when MFK is applied to the conversion curves measured at 1, 2 and 5 K/min. Up to about 85% conversion, the activation energy (curve b) corresponds closely to curve a. Afterward, large differences occur.

The reason for this is the vitrification at 1 K/min. At this heating rate, the actual glass transition temperature has caught up with the sample temperature and the sample changes, at least partially, to the glassy state. The reaction changes from being chemically controlled to diffusion controlled. The reaction rate therefore decreases.

At higher heating rates, the sample temperature changes so rapidly that the actual glass transition temperature is always lower than the sample temperature. The sample is then always in the liquid state and the reaction is chemically controlled. This means that a change in the kinetic behavior of reactions can be detected by means of MFK due to the change in the activation energy curve.

 

Isothermal Measurements of a Reaction

Direct Isothermal Measurements

With isothermal measurements, the sample is inserted into the preheated DSC measuring cell and the heat flow measured as a function of time. An advantage of this method is that the reaction kinetics is not affected by temperature changes. Complete curves are obtained that can be evaluated with the advanced version of MFK.

Conclusions 

The kinetics of a chemically controlled reaction can be described by MFK. Exact predictions can be made for the rate of an isothermal reaction from dynamic DSC measurements performed at different heating rates. If the reaction temperature is less than the Tg of the cured material, vitrification can occur. The reaction changes from chemically controlled to diffusion controlled and the isothermal reaction is not complete. This can have a significant effect on the properties of the material. 

By means of MFK, it is possible to determine whether vitrification occurs from the activation energy curve. This is done by comparing evaluations at different heating rates. If the glass transition temperature as a function of the conversion is known, MFK can be used to predict the vitrification time. Up until vitrification, the predictions of MFK agree well with the measurements. Afterward, the reaction rate decreases because it becomes diffusion controlled. The second part of this study [5] will show how a simple extension of MFK can also describe reaction behavior in this region.

Kinetic Studies of Complex Reactions. Part 1: Model Free Kinetics | Thermal Analysis Application No. UC 183 | Application published in METTLER TOLEDO Thermal Analysis UserCom 18