Cure rate law

Starting from the cure reaction mechanism, a proper cure rate law, describing the evolution of the system from initial to final state, can be proposed. In the case of a mechanistic approach, in which the reaction model consists of a set of chemical reaction steps, a set of (stiff) coupled differential equations has to be solved to describe the evolution of the important reacting species of the system. In this case, effects of the composition of the fresh reaction mixture (such as a stoichiometric unbalance of resin and hardener, the concentration of accelerator, initiator or inhibitor) and the influence of additives (such as moisture and fibres in composites) can be studied. Because this set of equations may be rather complex and/or even partly unknown, various simplifications have to be made. 

Modelling the Diffusion-Controlled Overall Kinetics and Cure Rate Law of Epoxy Systems... 

Based on the optimised parameters for the cure rate law of the bifunctional epoxy-anhydride and the tetrafunctional epoxy-diamine (see previous section), the TTT and the CHT cure diagrams for both systems can be calculated. Figures 2.30 and 2.31 represent the TTT diagrams for both systems. 

With values of Ej/Bm and FJF, it is a simple matter to calculate Pyj, at any value of Tg (= Te ), and then determine the time to vitrification from an assumed kinetic rate law. Using first order kinetics, which seemed to fit the extent of conversion vs. time data, the temperature of cure vs. the times to gelation and vitrification are shown in Fig. 15. The model fits the data well at low temperatures but appears to... 

The ejq)erimental MTDSC observations on anhydride-cured and amine-cured epoxies, described in the previous section, will now be modelled to illustrate the benefits of the technique to obtain a quantitative law of cure kinetics for such thermosetting systems. Because cure kinetics are often complicated by diffusion limitations and/or mobility restrictions, the effect of diffusion has to be incorporated into the overall reaction rate law. For this purpose, both heat capacity and non-reversing heat flow signals for quasi-isothermal and non-isothermal cure experiments are used. 

Reactivity can also be increased by externally heating the epoxy formulation to a preselected curing temperature. Epoxy resin reactions roughly obey Arrhenius law that for every 10°C rise in temperature, the reaction rate doubles. Certain epoxy resin systems must be heated for any reaction to take place at all. This is beneficial in that these latent adhesive formulations are one-component products that do not require metering or mixing yet have long, practical shelf lives. 

It should be noted that the effects of fillers may be incorporated into the cure and shear-rate effects. The main forms of combined-effects model consist of WLF, power-law or Carreau shear effects, Arrhenius or WLF thermal effects and molecular, conversion or empirical cure effects. Nguyen (1993) and Peters et al. (1993) used a modified Cox-Merz relationship to propose a modified power-law model for highly filled epoxy-resin systems. Nguyen (1993) also questions the validity of the separability of thermal and cure effects in the derivation of combined models. 

Han et al (1997) examined the chemorheology of a highly filled epoxy-resin moulding compound that is characterized by a modifed slit rheometer. Results show that a modified Cox-Merz rule relating dynamic and steady viscosities is established, >7(7 ) = (Tm )-Also the material was shown to exhibit a yield stress at low shear rates and power-law behaviour at higher shear rates. The temperature dependence of the viscosity is well predicted by a WLF model, and the cure effects are described by the Macosko relation. 

The alternative approach involves the determination of the water uptake by the adhesive, checking at the same time that the difihision leading to saturation obeys Pick s two laws, deducing the diffusion constant from the rate of uptake of water and thence calculating the distribution of water in the joint. These steps are outlined by Comyn (1981) together with data on a number of epoxide-curative combinations. The epoxide resins were aU based on the commonly used bis phenol A with various amine curing agents. 

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