Autocatalytic cure

The model that best represents the curing kinetics of thermosetting resins such as epoxy and unsaturated polyester, and as reflected in a TTT-diagram, is a diffusion modified Kamal-Sourour reaction model [9, 14, 13]. To model autocatalytic cure kinetics, the model can be applied as... 

Figure 2.3 Reaction rate versus degree of cure for an autocatalytic model—curves a and b, at temperatures Ta and Tb, respectively, have an initial reaction rate equal to zero, and curve c has an initial reaction rate different from zero...

Figure 2.5 Degree of cure time versus time for an autocatalytic model—curves a, b, and c have temperatures Ta, Tb, and Tc, respectively, where Tc > Tb > Ta...

Han et al. [191] found that the rate of cure of a resin is greatly influenced by the presence of fibers and the type of fibers employed. The rate of reaction for resin-fiber system can be 60 percent different from that of neat resin, after a 10-min cure. A similar conclusion was presented by Mijovic and Wang [192] for graphite-epoxy composites based on TGDDM/DDS (33phr). They verified large differences (see Table 2.5) in the kinetic parameters when considering an autocatalytic model. 

Because of all these minor components (e.g., catalysts and inhibitors, added to major ones) the cure of vinyl ester resins is very complex, involving many competitive reactions. There are some new variables to account for, such as the inhibitor and initiator concentrations and induction time. Several papers [81,96,200,201] use the mechanistic approach, claiming that the phenomenological models do not explicitly include these facts, resulting in a new parameter characterization after each change in resin formulation [96]. Despite these arguments, the phenomenological approach is the most widely used and is based on an autocatalytic model which has been successfully applied to epoxy resins. Many authors [30,34,74,199,202,203] proposed the Equation 2.30 to describe the cure kinetic of unsaturated polyesters ... 

Equation 8.5 is an implicit integral equation because the rate of cine depends upon the current degree of cure. Whereas closed form solutions exist for the nth order and autocatalytic reaction models, a numerical integration technique, such as Runga-Kutta, is often used to solve Equation 8.5. 

The epoxy-oligomer curing with amines has an autocatalytic character due to the accumulation of hydroxyl groups during the reaction [cf. Scheme (1)]. 

The delay period exhibited with sulfenamide cures is explained in terms of the formation of intermediates by reaction with activated sulfur (Scheme 5) (80MI11508). The 2-mercap-tobenzothiazole (31) produced reacts rapidly with the sulfenamide providing a more facile pathway for vulcanization (equation 11). The amine (38) produced also acts as a catalyst, so that the cure, once started, becomes autocatalytic (64MI11503). 

As a result of reaction (3-2), the concentration of hydroxyl will increase and this can produce an autocatalytic effect. In practice basic or acidic catalysts are often added to accelerate the cure, and tertiary amines are frequently used for this purpose. 

The results of DSC studies on the anhydride cure of epoxy resins are summarised in Table 2. These studies have confirmed that the cure mechanism is complex. The early stages show autocatalytic features while the later stages are complicated by the effects of diffusion control. Intermediate stages of cure can show an approximation to overall kinetic orders of 1 or 2. In general the isothermal DSC data are easier to... 

Isothermal kinetic runs for the same system were also analyzed by Mauri et al. (1997) and Galante et al. (1999). An excellent fit of a first-order kinetics after an induction period was reported, with E lying in the range of 70-75 kJ mol-1. Obviously, the overall behavior, including the induction period, is autocatalytic. However, for conversions higher than about 0.15, a first-order kinetics provided an excellent agreement, particularly at low cure temperatures and up to vitrification. This behavior is partially explained by Eq. (5.29) the function f(x) exhibits a behavior close to (1 — x) in the 0.4—0.8 conversion range. 

Pichaud et al. (1999) highlight the chemorheology and dielectrics of the cure of DGEBA with isophorone diamine (IPD). The kinetics are well described by an autocatalytic model and the chemorheology is well described by the Macosko model... 

Other researchers have also successfully applied the autocatalytic model [122, 134]. For fitting the conversion-time curves in this context, the conversion can be indirectly obtained from the Tg of the partly cured matrix. Georjon et al. [122] studied the evolution of Tg with cyanate conversion in the isothermal cure of un-... 

Assuming co-reaction, the cure reaction of a mixture of bis(4-maleimido phenyl) methane and BACY was followed by FTIR [221]. The reaction kinetics, studied by DSC, suggested dependency of cure mechanism on blend composition. The apparent activation energy computed by the Prime method increased with BMI content. The rate maximum at a fractional conversion range of 0.32-0.33 indicated an autocatalytic nature of the reaction. The different pattern of activation energy with fractional conversion for two different blend compositions indicated non-identical cure mechanisms for the two compositions. The cyclot-rimerization of BACY occurred during the cure of a 1 2 molar ratio of BMI and BACY. Since activation parameters derived from DSC method are generally not consistent, and since the cyanate cure can be catalyzed by impurities present in BMI, which was not taken into consideration, the authors conclusions on the cure mechanism based on DSC kinetics can be erroneous. 

The autocatalytic model has been shown to predict the cure of thermoset resins accurately [92] some of the more recent studies in this area are cited in a number of references [90, 91, 93-%]. 

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