Random Branching Without Network Formation

To complete our discussion of branching, we are going to consider two special cases. The first of these involves random branching without network formation. There is presently (circa. 2007) considerable interest in the potential uses of hyperbranched polymers, and this is what you get if you perform a polycondensation on an A-R-B, molecule, where, again, an A can only react with a B. 

The magnitude of a must always be less than ae, becausepA 1. Thus gelation cannot occur. At high degrees of conversion, very large hyperbranched molecules may be produced, but not a network. 

Flory also derived equations for the number and weight average degree of polymerization, the equations for which, along with that for the polydispersity, we have reproduced in Equations 5-31. 

take these chains at random and attach them to R-A molecules until they all have attached chains. Because large, small and intermediate size chains are combined into larger molecules at random, the molecular weight distribution narrows. This can 

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From Eq. (4) it can be seen that as the conversion is driven towards completion, i.e.,p is close to unity, the molecular weight distribution increases dramatically. Theoretically, polycondensation of A2B monomers should form an infinite molecule at extremely high conversions, though in practice this is seldom observed. Flory concluded that condensation of A B monomers would give randomly branched molecules without network formation [1]. However, the occurrence of unwanted reactions (an A group reacts with an A group, for instance) will eventually give rise to an infinite network. Therefore, side-reactions have to... 

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