Molecular Weight Distribution in Equilibrium Step-Growth Polymerizations

Step-growth polymerization is a very important process for producing different types of intermediate, commodity, and specialty polymers. For example, polyamides, polycarbonates, polyesters, and polyurethanes can all be synthesized using step-growth polymerization.
In step-growth polymerization, the functionality of the repeating units has a major role in determining the structure of the polymer. Monomers with two functional groups lead to linear polymers. The main parameters that control length and the distribution of the polymeric chains are the conversion or extent of reaction and the amount of the limiting reactant.
The weight chain length distribution in a linear step-growth polymerization (functionality = 2) can be given by:
,
where is the chain length and is the extent of reaction of the limiting reactants.
At the same time, the number chain length distribution can be calculated with:
.
Using these two equations and, as shown in the snapshots, a high degree of polymerization (determined by chain length) can be achieved only with a very high extent of reaction. At the same time the distribution will become broader as the conversion approaches 1.
Finally, values of the weight and mole average degree of polymerization are calculated.

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DETAILS

Reference
[1] A. Rudin, The Elements of Polymer Science and Engineering, San Diego: Academic Press, 1999.
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