Statistical models and polymer propagation

The statistical models discussed above were developed essentially as a means of describing polymer microstructure as observed by NMR spectroscopy. However, it is certainly no coincidence that these models are intimately 

It is worth while examining here the links between these two formalisms for polymer propagation (i.e. probabilistic and kinetic) because, under appropriate conditions, NMR-derived sequence distributions can be used to determine the relative reactivities of pairs of comonomers. Whilst more traditional techniques are available to do this, they prove to be very laborious and rather insensitive. In addition, of course, the NMR method can also provide insight into the mechanism of copolymer propagation often not available using traditional methods. 

Since the terminal model is the one most frequently used to describe copolymerisation, its relationship with the corresponding first-order Markov model is examined in some detail. 

In general, during copolymerisation, the two reacting monomers are not incorporated into the polymer chain in the same proportion as in the initial comonomer mixture. The reason for this is that the two monomers generally have different reactivities towards the growing chain ends. In the terminal model, it is assumed that the nature of the monomer at the growing chain end determines relative comonomer reactivity. In other words, there are four types of propagating step, each defined by a different rate constant  

These propagation steps are entirely analogous to those given for the first-order Markov model, except that addition probabilities have been replaced by rate constants. Mayo and Lewis derived the following differential equation to describe terminal model copolymerisation [8]  

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