Molecular Weight Control in Step Growth Polymerization

Molecular Weight determines the mechanical properties of polymers as well as it affects their viscosity, therefore it is the key parameter to control in order to obtain the desired characteristics. In step growth polymerization,  the chemical equation can be described as follows:

The polymer results of the addition of  two bifunctional monomers, a monomer plus a dimer, a dimer plus a trimer and so on. Thus,  the molecular weight distribution is statistically determined and depends only  on the conversion of functional groups. Typical  Step Growth polymers are shown in the table below:

If fav is defined as the average number of functional groups per monomer molecule and p is the conversion of functional groups,  the amount of functional groups used would be twice the number of monomers consumed. Then, the conversion can be expressed as:

The number average degree of polymerization  Xn is the ratio between the initial number of monomer molecules and the remaining molecules at conversion p. The number average molecular weight of the polymer is obtained by multiplying Xn with the monomer residue molecular weight. The equation is known as the Carothers equation. For a stoichiometric case of both bifunctional monomers (average functionality 2), the Carothers equation results in:

It can be seen from the figure that a molecular weight control with conversion would prove very unreliable, since slight changes in conversion leads to very different number average degrees of polymerization. For a Xn= 100, p=0.99;  while for a polymer with Xn= 200, a p=0.995 is required. Therefore a large molecular weight increase is reached for a very small conversion interval. Several more effective control strategies are used:

Control via Reaction Stoichiometry

If one of the monomers is used in excess, there is a limiting molecular weight at p=1. The average number of functional groups per monomer is affected (if we suppose B in excess, Ni0 the number of initial monomer i molecules and r = Na0/Nb0):

Consequently the Carothers equation is transformed to

Control Via Chain Stoppers

This strategy consists of the addition of mono-functional molecules that impede further polymer chain growth. To illustrate this, let’s use as an example [1] of a polyamide obtained from adipic acid and hexamethylene diamide, with acetic acid as a chain stopper. It is to be determined how much acetic acid must be added to the reaction to obtain an average number degree of polymerization of say, 500. From the Carothers equation, fav can be calculated at p=1:

That is, a moles of acetic should be added to reach the desired molecular weight.

[1]  The Elements of Polymer Science and Engineering. A.Rudin 2012.