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To my understanding, cationic polymerization is a type of living polymerization but my teacher's notes and Wikipedia seem to suggest they're different. I can't see the difference.

The same goes for anionic polymerization. From what I've studied so far, the difference must be subtle, if there is one.

Is there such a difference?

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This difference between living and non-living polymerizations is small in words but large in effects. In principle cationic and anionic polymerizations can be living. In practice, it is not as easy as it looks on paper. See below.

A living polymerization is any chain (or addition) polymerization that is prevented from terminating, i.e. the ends of the chains are still reactive. In a living polymerization, chain initiation has one initiation and propagation continues as long as there is monomer. Termination (almost) never happens. If your polymerization stops because your monomer runs out, adding more monomer restarts the process and the existing chains get longer. The number of chains formed matches very closely with the number of equivalents of initiator, and the length of the chains depends on the ratio of monomer to initiator.

Most chain polymerizations (radical, anionic, cationic, transition-metal insertion, and ring-opening) do not behave this way. There is a mechanism for termination that becomes increasingly kinetically favored as the concentration of free monomer decreases. Sadly, the wikipedia article for chain termination is pretty sad. Most chain polymerizations propagate and terminate quickly, with termination usually initiating the next chain. Thus, in a non-living polymerization, new chains are constantly being initiated and old chains are constantly terminating until their is no more monomer. In these cases, adding additional monomer later would not accomplish anything because the chain ends are "dead". Experimental evidence for this phenomenon includes the formations of more chains than there were equivalents of initiator. The length of the chain is more dependent on the relative rates of propagation and termination than on the initial ratio of monomer to initiator.

For radical polymerization, termination mechanisms include fragmentation by β-hydrogen abstraction or by recombination. Both of these mechanisms are inherent in the radical nature of the polymerization, and so are not preventable by exclusion of other species. Radical polymerizations are made living by the addition of species that "protect" the radical at the end of the chain to prevent it from terminating. Examples include ATRP and RAFT. The wikipedia articles for both are pretty good.

For cationic polymerization, termination mechanisms include β-hydrogen abstraction, chain transfer, and attack by nucleophiles like water. In principle, a cationic polymerization could be a living polymerization if great pains were taking to exclude all species which might induce termination. In practice this is doable, but difficult, as termination by chain transfer is always possible. See the wikipedia article on living cationic polymerization. The article is not great, but suggests that cationic polymerizations done in nonpolar solutions (not in bulk) with nonnucleophilic Brønsted or Lewis acids at low temperatures can become living polymerization.

For anionic polymerization, termination mechanisms include protonation by protic molecules, chain transfer, and reaction with electrophiles, which can include O2 in some reactions. Like cationic polymerizations, anionic polymerizations can be made living by rigorous exclusion of terminating species. Again, this is difficult, due to the possibility of chain transfer termination. However, with the correct choice of conditions, it is doable, as suggested by the wikipedia page for living anionic polymerizations. Another way to accomplish some anionic polymerizations in a living fashion is group transfer polymerization, even though it does not follow a strictly anionic mechanism.

I know that Contemporary Polymer Chemistry by Allcock, Lampe, and Mark, Prentice Hall 2003 covers this topic well, but the book is a little intense to read. In particular, the book derives the kinetic expressions for various polymerization types in the living and non-living cases. I expect other textbooks focusing of the chemistry of polymers might also cover this topic in one fashion or another.

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