Alternate Approaches for Molecular-Weight Distribution

The expected masses of polymers which contain a randomly selected A, B, or B group in the system are denoted by wa, wb. and ww In order to obtain these quantities it is convenient to introduce the quantities wA, w H, w B, and W A, wB, wB,. Here w A represents the expected mass attached to a randomly selected A group in the system looking inward toward the other A group of the A—A structural unit of which it is a part and w°A represents the expected mass attached looking outward from the randomly selected A group as shown in XII. Similarly, w B, vt g, Wg, and Wg, represent the expected inward and outward masses attached to B and B groups. 

Equations 2-102 through 2-108 can be solved and their results combined with Eqs. 2-99 through 2-101 to yield 

The weight-average molecular weight, obtained hy a weight averaging of wa, wg, and wbs is given by 

It is useful to introduce the fractions of unreacted A, B, and B functional groups 

For the case where B and B groups have the same reactivity  

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