Long chain branches and covalent cross-links

5 Long chain branches and covalent cross-links 

When analyzing cross-linked systems a distinction must be made between the whole polymer and the sol-gel fractions. The concentration and distribution of the cross-links will be different in each fraction. The particular method by which the cross-links are introduced could also influence the kinetics. They can be introduced by specific chemical reactions or in special cases by the action of high energy ionizing radiation. Ultimately, all these factors have to be sorted out. Most of the studies of the crystallization of cross-linked polymers have involved either natural rubber, poly(cis-l,4-isoprene), or polyethylenes with different molecular architecture. 

The above examples point out that the formal aspects of the overall crystallization kinetics are unaffected by the introduction of intermolecular cross-links, when the cross-links are introduced in the amorphous state. The fanning out of the isotherms. 

The overall crystallization kinetics of an unfractionated linear polyethylene, cross-linked by a peroxide reaction has also been studied. (95,96) A special feature of this work was the study of the separated sol and gel portions at different levels of cross-linking. The overall crystallization rates, in terms of the reciprocal of the half-time, l/ti/2, are plotted against the crystallization temperamre in Figs. 10.41 and 10.42 for a set of sol and gel fractions respectively. The gel fractions are characterized by the molecular weight between cross-links. Me, assuming ideal network formation. The sol portions are defined by their number average molecular 

Mandelkern, L. in Growth and Perfection of Crystals, R. H. Doremus, B. W. Roberts and D. Turnbull eds, John Wiley (1958) p. 467. 

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Secondary bonds are considerably weaker than the primary covalent bonds. When a linear or branched polymer is heated, the dissociation energies of the secondary bonds are exceeded long before the primary covalent bonds are broken, freeing up the individual chains to flow under stress. When the material is cooled, the secondary bonds reform. Thus, linear and branched polymers are generally thermoplastic. On the other hand, cross-links contain primary covalent bonds like those that bond the atoms in the main chains. When a cross-linked polymer is heated sufficiently, these primary covalent bonds fail randomly, and the material degrades. Therefore, cross-linked polymers are thermosets. There are a few exceptions such as cellulose and polyacrylonitrile. Though linear, these polymers are not thermoplastic because the extensive secondary bonds make up for in quantity what they lack in quahty. 

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