Effects of Cross-Linking on the Viscoelastic Functions

The effects of cross-Unking on the viscoelastic functions in the transition zone are rather small unless the cross-link density is so high that it hinders the segmental motions involved in the development of this region. In any case, cross-links shift the transition region, to larger times or lower frequencies. 

Cross-linking effects are more important in the plateau and terminal zones. For moderately cross-linked polymers, such as soft vulcanized rubbers, the equilibrium modulus is similar in magnitude to the entanglement network modulus before vulcanization. In some cases, however, the former modulus may be higher by as much as a factor of 2 than the latter one, thus 

A great number of experiments in soft cross-linked rubbers are made at substantial finite deformations. There are experimental grounds suggesting that the relaxation stress can be factored into a function of time and a function of strain (39,40), 

The unknown values of this equation can be estimated by finding the value of Eg that best fits the double logarithmic plot of [ ( ) - Ee]/Ee against t to a straight line. The values of m and mlogr can then be obtained from the slope and the intercept, respectively. By taking into account that Poisson s ratio is nearly 1/2 in this region [see Eq. (5.89)], the values of G t) are approximately equal to E t)/3. 

In the same way, the difficulty involved in obtaining the equilibrium shear compliance from the extrapolation of creep experiments to infinite time leads to the determination of by means of an expression analogous to Eq. (8.71) (42), 

---

Effects of Cross-Linking on the Viscoelastic Functions Problem Sets... 

---