Repeating units between cross-links

Figure 2 Equilibrium swelling degree of gels as predicted by Eq. (9). Z is the average number of repeat units between cross-links (Z lpxVm)-...

Fig. 8. Illustration of simple quantitative structure-property relationship given by equation (4) for the dependence of Tg on cross-linking. Tg(oo) is the Tg of the uncross-linked limit (n->-oo, where n is the number of repeat units between cross-links). Alrot is a number of rotational degrees of freedom per repeat unit parameter. Each curve is labeled by the value of Alrot-...

The analysis of a large amount of experimental data collected from the literature ((1), for a more detailed discussion see (55)), led to the simple quantitative structure-property relationship given by equation 4 (illustrated in Figure 8), where n (defined by equation 5) is the average number of repeat units between cross-links. is the average molecular weight between cross-links. M is the... 

Ne Number of repeating units between cross-links... 

The Tg values of cross-linked polymers are similar to those of comparable linear polymers providing the cross-linked polymer has a low cross-linked density, i.e., 30 to 50 repeating units between the cross-links. The Tg values increase as the cross-link density increases. Thus the Tg of hard rubber which is more highly cross-linked is higher than that of soft vulcanized rubber. 

Extrapolated melting temperatures as a function of extension ratio, 110 repeating units between successive cross-links, the melting temperature at extension ratio 1.0 is 333.5 K, heat of fusion 8.37 kJ/mol. Data by W. R. Krigbaum, J. V. Dawkins, G. H. Via, and Y. I. Balta,/. Polymer ScL, Part A-2, 4, 475 (1966). 

In these equations Va, Vb, and vq are the molar volumes of the network repeating unit, Nc is the number of repeating units in the network between cross-links, x is the Flory-Huggins parameter, (p is the volume fraction of the network, (p is the network volume fraction in relaxed state, usually taken to be the value at which the network was formed and Nb is the number of repeat units in the linear chain. Constants A and B follow from the rubber elasticity theory, usually A = 1 and B = 2//c, where/c is the functionality of the crosslinks, kn is the constant that determines the amount of contrast between the two components and the radiation type, and S(0) is the zero-angle scattering intensity. 

---