Statistics of Linear Step-Growth Polymerization

Consider the two equivalent linear step-growth reactions, assuming difunctional monomers and stoichiometric equivalence  

Each of the polymer molecules above contains a total of x A groups  

Considering a volume of the reaction mixture at a certain time during polymerization, we can use statistical analysis to find the polymer chain length and average molecular weight. For this analysis, we will let 

N = the total number of molecules present in the reaction mass (of all sizes) 

Ux = the number of molecules containing x A groups, both reacted and unreacted 

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As we mentioned in the introduction to this chapter, we will start by considering the statistics of linear step-growth polymerization. Remember that there are two types of such reactions in the first, each bifunctional monomer has different but complementary functional groups, an acid, A, and an alcohol, B, for example (i.e., A-B) in the second type, each monomer only has one type of functional group (i.e., A-A and B-B). In each case an A can only react with a B, ,in this example to give an ester, which we ve labeled either AB or BA in Figure 5-3 (think about it— they are equivalent and only differ in direction along the chain). 

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