Molecular-Weight Distribution in Step-Growth Polymerization

6 MOLECULAR-WEIGHT DISTRIBUTION IN STEP-GROWTH POLYMERIZATION 

Let us consider step-growth polymerization in a batch reactor having feed of the following composition. At = 0, 

One of the ways to solve such problems is to utilize the technique of the generating function, which is described in Appendix 3.1. With the help of the generating function G s, t), the mole balance relations in Eq. (3.3.5) are combined into one partial differential equation that has a numerical solution only. However, if the feed to the batch reactor is a pure monomer or has a distribution given by Eq. (3.5.7), it is possible to obtain an analytical solution. 

Let us assume that the feed to the batch reactor is a pure monomer, which means that the initial condition is given at = 0 by the following  

If Mj is the molecular weight of the monomeric repeat unit, the weight finction, W , of a molecule of size n would be given by 

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Molecular weight distributions in step-growth polymerization described so far in this chapter are all based on the probability approach of Flory [1,15] and Stockmayer [19]. Starting with the assumptions of equal reactivity of functional groups and no intramolecular reactions, they used combinatorial arguments to derive expressions for the distribution of all species as a function of the reaction extent and then used these distributions to calculate the average properties (Mn, Mw, and PDI). For cases of practical importance these distribution functions become quite complex [19]. 

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