Statistical treatment of polycondensation reactions

In the statistical analysis of polycondensation the extent of reaction, p, is defined as the probability that a functional group has reacted at time t. (In kinetic treatments p is often used as the equivalent expression, the fraction of functional groups which has reacted.) It follows that (1—p) is the probability of finding a functional group unreacted. 

If the total number of units (in this case, carboxyls) is Nq, then the number of polymer molecules (N) is 

This last equation is the statistical number-distribution function for a linear polycondensation reaction at the extent of reaction p. 

This is the statistical weight-distribution function for a linear polycondensation reaction at the extent of reaction p. The number-distribution and weight-distribution functions are illustrated in Figs. 1 and 2 for values of p. 

The equations for the weight- and number-average distribution functions can be used to calculate the different average depees of polymerization. The number-average depee of polymerization (x ) is 

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