Average Molecular Weights for the Most Probable Distribution

For a polymer possessing the most probable distribution, the mole fraction Na is given by Eq. (1) hence 

The weight average degree of polymerization (see Eq. VII-27) is similarly obtained  

The root-mean-square degree of polymerization for the most probable distribution is found to be 

When the molecular weight is large, p may be replaced by unity with small error, and the above ratios become l /2 2, i.e., the ratios of the various averages are practically independent of the degree of polymerization. 

Cyclic Condensation Polymers.—The foregoing discussion has proceeded under the assumption that the only products of bifunctional condensation are open chain polymer molecules—an assumption which obviously will not be exactly valid since cyclic polymers must always occur to some extent. The nature of the error introduced by this assumption will be examined in the course of the following discussion of cyclic polymer components. 

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