Free Radical Polymerization - Dienes
Free Radical Polymerization - Dienes
Isolated Dienes - Crosslinking
Many monomers have multiple vinyl groups capable of polymerizing independently. Therefore, these monomers are capable of forming four or more bonds to other molecules, leading to crosslinked systems. Here are some common examples, among many commercial varients:

The example at the top left (divinyl benzene) is sold commercially as a mixture of the para and meta isomers. It is used in varying amounts as a comonomer with styrene to create insoluble beads (by suspension polymerization) for chromatography packings, catalyst carriers, ion-exchange resins, substrates for combinatorial synthesis, etc.
Conjugated Dienes - Important Commodity Monomers
There are several important monomers with conjugated (1,3) vinyl groups.

The two double bonds can react separately or together. In actual practice, both processes occur, leading to a copolymer with different repeat units. The resulting chains contain double bonds, important for subsequent crosslinking reactions (i.e., vulcanization of rubber).
If the double bonds react separately, the process is called 1,2-propagation. The second double bond in the monomer ends up as a pendant group.

Resonance can transmit the radical to the other end of the monomer, leading to 1,4-propagation. The double bond ends up within the polymer chain, so there are cis and trans isomers possible.

Of course, the physical properties of the polymer depends strongly on the amount of each isomer formed. Generally, polymerization of 1,3-dienes leads to low Tg materials that are useful as rubbers. Natural rubber, for example, consists of >90% cis polyisoprene. Polychloroprene was developed by DuPont in the 1930's (led by Wallace Carothers, famous for step polymerization), to produce a rubber that resisted solvents very well. It is best known by the trade name, Neoprene, and is used for hoses and diver's wetsuits.
Nearby Dienes - Cyclopolymerization
When unconjugated dienes are in close proximity of the same monomer, an interesting variation occurs. Instead of the expected crosslinked systems, these monomers generate linear, soluble polymers by a kind of alternating intermolecular-intramolecular propagation. The rationale for this behavior is as follows: once the first double bond in the molecule reacts, the resulting radical finds the second double bond close by. The most kinetically available position on the second double bond gets attacked, closing a ring. A new radical is produced that can attack another separate molecule to continue the process.
The example illustrates an important commercial polymer made by the Calgon company (based on a diallyl ammonium salt as monomer) and used for waste water treatment. Historically, this was the first cyclopolymerization discovered (work of G. Butler, Florida).

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