Example of a chain length distribution

In a polymerization process the chain length distribution or molar mass distribution (MMD) is influenced by a large number of factors and conditions the kinetics of the reaction plays a very important role. The calculation of the resulting MMD is thus very complicated. For one of the simplest cases, a step reaction with polycondensation, a first-order approach is given here. As an example we take a hydroxy acid HO-R-COOH, which, upon condensation, forms the chain -[-O-R-CO-]n. 

With each step a -COOH and an -OH group react with each other, forming an ester group and a water molecule. If we denote the numbers of -COOH and -OH groups both by U, then at the start of the reaction U = U = the total number of hydroxy acid molecules. 

After some time t, U = U(l) the number of -COOH and -OH groups disappeared is (t/o - U), which also is the number of ester groups formed. We define the conversion grade p as the fraction of the number of groups which have reacted  

Now there are U molecules, containing together U0 basic units the number of units per chain, the average degree of polymerization P, is, therefore  

An example With a conversion grade of 0,99 P = 100. Evidently, this P is a number average degree of polymerization, Pn. 

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