Melting temperature of networks formed from random chains

3 Melting temperature of networks formed from random chains 

Wide-angle x-ray diffraction studies of crystalline networks of both polyethylene and natural rubber show that with increasing cross-linking density there is a progressive broadening of the reflections from various crystalline planes.( 13,14,23) This broadening can be attributed to either a decrease in crystallite size, the development of ftuther imperfections in the crystals, or to strain. Irrespective of which of these 

Units that neighbor those cross-linked may also be prevented from crystallizing. Hence the longitudinal development of crystallinity is restricted to an extent greater than would be expected solely by the concentration of cross-linked units themselves. To account for this effect, empirical modifications have been made to Eq. (7.7).(15,20) The fraction of cross-linked units p is replaced by the quantity Kp, where K represents the number of chain units per cross-link unit that are excluded from the crystallization process. Thus Eq. (7.7) can be rewritten as 

The fractions of the chain units that are cross-linked can be expressed in terms of Me, the molecular weight between points of cross-links as 

It follows from Eq. (7.1) that only a small fraction of intermolecular cross-linked units are required for network formation at the gel point. For example, for a 

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