Effect of Cross-Linking on Tg

The effect of cross-linking on Tg can be treated along similar lines to the effects of molecular weight and branching. When two polymer chains are connected by introducing a crosslink at intermediate points, the chains are pulled closer together at these points and the free volume is decreased. This reduction in the free volume raises Tg. 

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Noting the instruments mentioned in Section 8.3, what instrument would you most like to have in your laboratory if you were testing (a) each of the three theories of Tg, (b) the molecular weight dependence of Tg, (c) the effect of cross-linking on Tg. Defend your choice. 

Pig. 45. Schematic diagram showing the effects of cross-linking on modulus and damping (loss tangent) vs temperature behavior at Tg. 

Gel Tg. the temperature at which gelation and vitrification occm simultaneously Tgo. the Tg of the mixed reactants, corresponding to a minimiun cure In isothermal cures, at temperatures between the gel Tg and Tgo, the resin undergoes gelation followed by vitrification. Since Tg is a function of both the degree of cure and the cross-link density, it increases to a point at which aU polymer reaction sites have been consumed. At that point, the Tg reaches a plateau and does not increase further with temperature until the decomposition temperature where a char region occurs (Fig. 2.17). An example of the effect of cure conditions on Tg and CTE values was shown by Konarski " who varied the cure cycles of an anhydride-cured epoxy from 130 to 175 °C as shown in Table 2.10. The value of Tg continued to... 

B.6.3.2 Effect of Cross-link Density on Tg The criterion of the second-order transition temperature is that the temperature-dependent conformational entropy, becomes zero. If So is the conformational entropy for the un-cross-linked system, and ASr is the change in conformational entropy due to adding cross-links (99),... 

A unified approach to the glass transition, viscoelastic response and yield behavior of crosslinking systems is presented by extending our statistical mechanical theory of physical aging. We have (1) explained the transition of a WLF dependence to an Arrhenius temperature dependence of the relaxation time in the vicinity of Tg, (2) derived the empirical Nielson equation for Tg, and (3) determined the Chasset and Thirion exponent (m) as a function of cross-link density instead of as a constant reported by others. In addition, the effect of crosslinks on yield stress is analyzed and compared with other kinetic effects — physical aging and strain rate. 

Higher degrees of cross-linking have a a significant effect for an unsaturated polyester resin with short and stiff cross-links, Tg appeared to be increased by 21 °C when the number of atoms between cross-links amounted to 50, while with 24 atoms between cross-links the increase was 93 °C. So, with thermosets the cross-link density has a large effect on Tg, and, consequently, on the usability at higher temperatures. 

Figure 31.8 shows the effect of the cross-linker (CLfs) concentration on the ionic conductivity and the Tg for the IL-type network polymer Pic TFSI-CLfs). After cross-linking, the Tg of the network was increased about 5°C, compared to that of the linear polymer, and the ionic conductivity decreased by about one-third. 

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