Vitrification time-temperature-transformation

Gelation, vitrification and phase-separation transitions in curing systems are very well described in the work of GilUiam (1986) via the use of time-temperature-transformation diagrams. 

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]. 

The curing of a thermoset epoxy resin can be expressed in terms of a time-temperature-transformation (TTT) diagram (Fig. 10) (149,150). Later, a CTP (cure-temperature-property) diagram was proposed as a modification of the TTT diagram (151). For nonisothermal cure, the conversion-temperature-transformation (CTT) diagram has been shown to be quite useful (152). In the TTT diagram, the time to gellation and vitrification is plotted as a function of... 

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.

As opposed to the liquid-crystal transformation, the liquid-glass transformation is not a phase transition and therefore it can not be characterized by a certain transition temperature. Nevertheless, the term "the vitrification temperature , Tv, is widely used. It has the following physical meaning. As opposed to crystallization, vitrification occurs when the temperature changes continuously, i.e. over some temperature interval, rather than jump-wise. Inside this interval, the sample behaves as a liquid relative to some of the processes occurring in it, and as a solid relative to other processes occurring in it. The character of this behaviour is determined by the ratio between the characteristic time of the process, t, and the characteristic relaxation time of the matrix, x = t//G, where tj is the macroscopic viscosity and G is the matrix elasticity module. If t x, then the matrix should be considered as a solid relative to the process, and if t > x it should be considered as a liquid. The relation tjx = 1 can be considered as the condition of the matrix transition from the liquid to the solid (vitreous) state, and the temperature Tv at which this condition is realized as the temperature of vitrification. Evidently, Tv determined by such means will be somewhat different for the processes with different characteristic times t. However, due to the rapid (exponential) dependence of the viscosity rj on T, the dependence of Tw on t (i.e. on the kind of process) will be comparatively weak (logarith-... 

At hi temperatures thermal degradation becomes important, and may prevent full cure from being achieved Two degradation events have been noted in relation to the TTT diagram devitrification followed by elastomer formation and vitrification followed by char formation. The devitrification event corresponds to a decrease in Tg from above to below the isothermal cure temperature the time to this event may be considered to be the lifetime of the material since it marks the limit in time for the material to support a substantial load. The second event is an elastomer-to-glass transformation, accompanied by an increase in Tg and rigidity, and is presumably due to the onset of char formation... 

The other independent transformation that can take place during network formation is vitrification. This transition occurs at the particular conversion where the increasing glass-transition temperature (Tg) of the reacting system equals the instantaneous value of the cure temperature. At this time, the macroscopic behavior of the system changes from a liquid or rubber to a glass. This means an increase of several decades in the value of the storage modulus. 

Gelation and vitrification curves are usually presented together in transformation diagrams relating temperature vs time or conversion vs temperature. Examples will be presented in the next section, including the miscibility curve for modified-thermosetting polymers. 

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