Why are alkenes used to make polymers?

Well, it looks to me like since alkenes have to break one #pi# bond and make one #sigma# bond to add a monomer to the chain, that could be why they work so well. It's a thermodynamically favorable trade-off.

One popular method used to make controlled-length polymers, first introduced in 1955, is the Zeigler-Natta catalyst (which has since been updated to incorporate #"MgCl"_2# to further enhance the catalytic activity).

This is commonly used as #"TiCl"_4#, dissolved in hydrocarbon solvents in the presence of #"Al"("C"_2"H"_5)_3# (Inorganic Chemistry, Miessler et al., Ch. 14.4.1, pg. 570).

So, we have this happening to form a titanium alkyl complex first:

Next, this activated complex can react with alkenes. Let's use ethene. The ethene ligand first binds dihapto (#eta^2-#, i.e. by two atoms) to titanium.

Then, a 1,2-insertion occurs (keep your eyes peeled for this one!), changing ethene into a monohapto ligand (#eta^1-#, i.e. by one atom):

In these two steps, note that we have broken one #pi# and one #sigma# bond, and made two #sigma# bonds.

Breaking net-weaker bonds and forming net-stronger bonds is thermodynamically favorable. Hence, alkenes are a good choice for polymerization.

SIDENOTE: The above process is cyclic until it is terminated.

It allows for further polymerization by coordinating more alkenes and performing more 1,2-insertions to lengthen the alkyl chain:

and so on.

This is known as the Cossee-Arlman Mechanism, and experiments by Robert H. Grubbs have supported this mechanism as "the likely pathway for polymerization in most cases" (Inorganic Chemistry, Miessler et al., Ch. 14.4.1, pg. 571).