Non-Stoichiometric Equivalence

The relationship between number average degree of polymerization and p (Equation 5-3) only applies to polymerizations where there are exactly equal numbers of A and B functional groups. Equivalence is obtained directly in step-growth polymerizations of type I (A-B), but is more difficult to achieve for polymerizations of type II (A-A and B-B). However, if the number of functional groups is not exactly the same, we still 

We will start by defining a new quantity, r, equal to the ratio of the number of functional groups (not monomers)—Equation 5-5. 

The parameter r is defined so as to always be a fraction, so that the subscripts A and B no longer refer to a particular monomer (we ve been pretty consistent in letting A represent carboxylic acid functional groups in polyesterifications). In other words, B must always represent the functional groups that are present in excess. Keep in mind that Na and Nb represent the number of functional groups present, so that the number of monomers, Nq, is given by Equation 5-6, 

This assumes each is bifunctional. We have Nq, now all we need is N. Remember, we can count N by counting the number of end groups. Because we have unequal numbers of functional groups, we need to count all the end groups, not just those of one type, and then divide by 2. The number of chain ends, or end groups, after a fraction p have 

A and 99 moles of B, what is the maximum number average degree of polymerization  

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