Time to gelation

Suppose, for example, that capping protein is in excess and that capping is irreversible. Then, by Equations 7 and 18, we readily find that the time to gelation is given as... 

Figure 9 illustrates the dynamic moduli and complex viscosity results for the cycloaliphatic epoxy/anhydride resin. The tgei value denotes the time to gelation based on the dynamic moduli crossover (G = G") and is estimated at... 

This equation can be used to solve for the time to gelation... 

Fig. 11. TIT cure diagram temperature of cure vs. the times to gelation, vitrification and degradation, including TBA and gel fraction data , gelation (TBA) O. vitrification , devitrification O, char formation A, gelation (gel fraction). T, an estimate of and the hypothetical value of T, are included. The system studied was XD7342/DDS (see Fig. 9 caption)...

A comparison of Figs. 11 and 12 also serves to highlight the effect of functionality on cure and properties. The system of Fig. 11 is a trifunctional epoxy cured with a tetrafunctional aromatic amine, whereas the system of Fig. 12 is a difunctional epoxy cured with the same amine. As expected, the more highly functional system has the higher Tg, and shorter times to gelation the times to vitrification are also shorter. The difference in these transformation times arises from two factors ... 

The calculation of the time to gelation is straightforward if gelation is assumed to be an isoconversion state and if the kinetics of the reaction are known. The rate of reaction in general is ... 

Whereas the calculation of the time to gelation is relatively simple, the calculation of the time to vitrification (tyu) is not so elementary. The critical point is to obtain a relationship between T, and the extent of conversion at T, (Pvu)- Once the conversion at Tg is known, then the time to vitrification can be calculated from the kinetics of the reaction. Two approaches have been examined one calculates tyu based on a relationship between T, and Pyj, in conjunction with experimental values of Pvit the other approach formulates the Tg vs. pyj, relationship from equations in the literature relating Tg to molecular weight and molecular weight to extent of reaction... 

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... 

Fig. 15. TTT cure diagram TJT vs. times to gelation and vitrification. Theoretical (solid lines) First-order kinetics using the following parameters T = —19 °C T, = 166 °C Ej/Em = 0.34 FJPft = 0-19 E, = 12.6 kcal/mole A = 4.5x 10 min" pgy, = 0.75 g,Tg = 49 °C. Experimental , pregel (TBA) , gelation (TBA) Q, vitrification (TBA) , diffusion control (infra spectroscopy) A, gelation (gel fraction). The system studied was Epon 828/PACM-20 (see Fig. 4 caption)...

The model was also applied to the reaction of a tetrafunctional amine with a trifunctional epoxy, denoted A4 + 4/3Bj, and was compared with available data (Fig. 18). An approximate value of k was obtained from the times to gelation. This model appears to provide a reasonable framework within which the vitrification process for nonlinear systems can be discussed. 

Identical morphologies were obtained from two samples of the same resin system with significantly different cure conditions - sample 4 200C/0.5h, sample 5 170C/4h (Table IX). Solvent absorption and torsion pendulum results were used to determine that sample 5 did not achieve full cure until 4 hours. The times to gelation differ by a factor of three, yet the final morphologies are nearly identical. 

The curing of thermoset polymeric materials can be represented in terms of a time/temperature/transformation cure diagram, as schematically represented in Figure 5.1. In the cure diagram the times to gelations, induction time, maximum polymerisation degree and vitrification are plotted versus cure temperature [22, 23]. 

Fig. 3. Generalized time-temperature-transformation (TTT) cure diagram. A plot of the times to gelation and vitrification during isothermal cure versus temperature delineates the regions of four distinct states of matter liquid, gelled rubber, gelled glass, and ungelled glass. From Ref. 12.

Microstructural features such as volume fraction of rubbery particles and the particle size distribution will depend on the initial resin/modifier compatibility and the cure scheme. From the processor s standpoint, the blend needs to be stable and produce the desired morphology upon cure consistently. Ideally, one would like the liquid rubber modifier and the unreacted resin to form a miscible blend at room temperature. Cure conditions will then control rubbery particle formation. Factors that affect phase separation include cure temperature and time to gelation, which is a function of temperature and catalyst system. 

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