Application of Propagation Statistics

There are alternate criteria for testing the different models [Bovey, 1972 Chujo, 1967 Inoue et al., 1971, 1984]. The Bemoullian model requires 

The term on the left is extremely sensitive, and this criterion should be used only with sufficiently accurate triad data. This is especially important if the polymer is very highly isotactic or syndiotactic, that is, with very small value of either (rr) or (mm). The term 4(mm)(rr)/ (mr)2 is considerably larger than one for the Markov and catalyst site control models. 

Having established that a particular polymerization follows Bemoullian or first-order Markov or catalyst site control behavior tells us about the mechanism by which polymer stereochemistry is determined. The Bemoullian model describes those polymerizations in which the chain end determines stereochemistry, due to interactions between either the last two units in the chain or the last unit in the chain and the entering monomer. This corresponds to the generally accepted mechanism for polymerizations proceeding in a nonco-ordinated manner to give mostly atactic polymer—ionic polymerizations in polar solvents and free-radical polymerizations. Highly isoselective and syndioselective polymerizations follow the catalyst site control model as expected. Some syndioselective polymerizations follow Markov behavior, which is indicative of a more complex form of chain end control. 

More sophisticated experimental and theoretical analysis of isoselective polymerizations have been performed by using a two-site model for propagation [Inoue et al., 1984 Wu et al., 1990]. The polymer product is fractionated into the highly isotactic, insoluble and atactic, 

Although the treatment described above has been limited to polymerizations proceeding by meso and racemic placements, the various models can also be adopted to describe the stereochemistry of 1,4-propagation in 1,3-dienes. 

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