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. 

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... 

If the monomers are bifunctional, as in the above example, then a linear polymer is formed. Terminating monofunctional groups will reduce the average degree of polymerisation. Polyfunctional monomers, such as glycerol and phthalic acid, are able to form branching points, which readily leads to irreversible network formation (see Chapter 9). Bakelite, a condensation product of phenol and formaldehyde, is an example of such a space-network polymer. Linear polymers are usually soluble in suitable solvents and are thermoplastic - i.e. they can be softened by heat without decomposition. In contrast, highly condensed network polymers are usually hard, are almost completely insoluble and thermoset - i.e. they cannot be softened by heat without decomposition. 

The percolation processes were first developed by Flory [235] and Stockmayer [236] to describe polymerization process, which result in gelation, that is, the formation of very large networks of molecules connected by chemical bonds. But, their theory was developed only for a special kind of network, namely, the Bethe lattice, an infinite branching structure without any closed loops. Broadbent and Hammersley have developed a more general theory and have introduced it into the... 

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