Weight Distribution and Conversion

In the following discussion, it is assumed that polycondensation begins with equimolar quantities of bifunctional compounds (i.e. AB + AB or AA + BB), for example, the reaction of HO—R—OH with HOOC—R — COOH. Here p is the probability of forming an ester group, and it is equal 

The probability for the formation of the three ester bonds in one tetramer molecule is p. For this process, four monomeric units are necessary. The probability for the occurrence of any given number X of ester groups in a given X-mer is consequently where X is the degree of 

The probability px for the occurrence of one polymer molecule of the degree of polymerization X consists of the probability for the occurrence of ester bonds and the probability for the occurrence of nonreacted end groups, i.e., 

In a polycondensate, there are N oi molecules with different degrees of polymerization. The number of molecules with the degree of polymerization X is proportional to the total number of molecules 

According to equation (17-5), the number of molecules N, can be replaced by l moi = With equimolar initial concentrations, X can be 

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