eg. H-CH2-CH2-Br + OH- → CH2=CH2 + H2O + Br-
In this case, a strong base (OH-) removes the hydrogen to form water, resulting in the the elimination of a bromide ion and the formation of the double bond.
Polymerization used to be principally classfied via reaction type, either addition or elimination\\condensation reaction. This is now no longer as much in favour, since it obscures a far more important aspect of polymerization, namely the kinetics. These days polymerization is usually categorised as being either step growth or chain growth, with side excursions into living/controlled polymerization.
An elimination reaction (in polymer chemistry) results in the spitting out of a small molecule during the reaction, hence the name. The formation of nylon is called an elimination reaction, since it occurs via the reaction between a carboxylic acid and an amine, generating the amide bond and eliminating water, and the crosslinking reaction that occurs during the thermosetting of a phenol formaldehyde resin is also considered to be an example of an elimination reaction. Within classical organic chemistry however, these reactions could be classed more formally as substitution reactions. This doesn't work very well either however; there isn't really, as such, the exchange of one functional group for another. The whole point of classifying a reaction by its type is that it should tell you something about how the reaction proceeds and the conditions under which it would work best. And here we have reached the point at which the definitions obscure, rather than illuminate, the underlying principles in which we are interested.
Elimination polymerization
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