Configurational Statistics and the Propagation Mechanism in Chain-Growth Polymerization

10 Configurational Statistics and the Propagation Mechanism in Chain-Growth Polymerization 

Analyses of polymers to determine stereosequence distributions and understand the propagation mechanism can be carried out with NMR spectroscopy aided by statistical propagation models [222, 402, 403]. A detailed discussion of the subject is beyond this book. The following is a brief explanation of the concepts. The Bernoulli, Markov, Colman-Fox, models describe propagation reactions with chain end control over monomer placement. The Bernoulli model assumes that the last monomer unit in the propagating chain end determines the stereochemistry of the polymer. No consideration is given to the penultimate unit or other units further back. In such an event, two modes of propagation are possible, meso and racemic  

The statistical probabilities, and P, which are called conditional probabilities or transitions, of forming meso or racemic dyads are defined by the following equations  

The probabilities represent the dyad tactic fractions m and r. The triad tacticity represent isotactic, syndiotactic, and heterotactic (or atactic) arrangements. They are designated as mm, rr, and nor respectively. One way to understand these definitions is by examining a representation of a section of a polymeric chain which has a total of 9 repeating units but only 8 dyads and 7 triads, as shown below  

In the above segment there are 2 racemic dyads and 6 meso dyads. In additirm, there are also 4 isotactic, 1 syndiotactic, and 2 atactic dyads. 

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