Mechanism of Step-Growth Polymerization

The kinetics of the step-growth polymerization can be described with Flory's equal reactivity principle. Flory assumed that all steps, that is, the formation of dimers, trimers and so forth, have equal rate constants. This assumption greatly simplifies the otherwise very complicated kinetics of a condensation polymerization. Flory considered two cases:

 

Case 1: Polymerization without strong catalyst

A classic example of a step-growth polymerization is the esterification reaction between an alcohol and a carboxylic acid. The progress of the polyester-forming reaction can be easily followed by titration of the unreacted acids in the samples removed from the batch at different times. Simple esterification reactions are known to be catalyzed by acids. In the absence of a strong acid, a second acid molecule functions as catalyst (self-catalyzed polymerization). The rate of the polymerization reaction can therefore be written

-d[COOH] / dt = k · [COOH]² · [OH]

where k is the rate constant of the step-growth reaction and [X] are the mole concentrations of the monomers.
The concentrations are usually defined as mole equivalents of functional groups per unit volume. By this convention, we avoid having to write separate equations for each condensation product (dimer, trimmers etc.). However, this simplification is only valid if we assume that all reaction species have the same rate constants k regardless of size (molecular weight). If we choose equal concentrations of hydroxyl and carboxyl groups, the equation above can be rewritten as

-dc / dt = k · c³

On integration, we get an expression for a third-order reaction:

2kt = 1 / c² - 1 / c₀²

where c₀ is the initial concentration of the functional groups. The extend of the reaction is often written as the fraction of functional groups that has reacted at time t,

p = (c₀ - c) / c₀

Then c = c₀·(1 - p) and after substitution of c with this expression the rate of the polymerization equation reads

2c₀²·kt = 1 / (1 - p)² - 1

In the esterification reaction, p can be directly calculated from the carboxyl group titer. If we plot 1/(1-p)² against time, t, we find a linear relationship, which is the case for many esterification reactions of glycols and organic acids. This is usually considered proof that all mer units have similar rate constants k.

 

Case 2: Polymerization with strong catalyst

If the polymerization is carried out in the presence of a strong acid (sulfonic acids) and if the catalyst concentration is kept constant throughout the process, the polymerization follows the kinetics of a second-order reaction:

-dc / dt = k' c²

where k' = k [catalyst]. Integration of this expression yields

k' t = 1 / c - 1 / c₀

And after replacing the concentration with the extend of the reaction, p, this expression reads

c₀k' t = 1 / (1 - p) - 1

In this case, the average degree of polymerization, defined as

X_n = No. of monomers / No. of mer units = 1 / (1 - p) = c₀ / c,

increases linearly with the reaction time, which is a much more favorable situation for obtaining high average molecular weight polymers than the weak-acid catalyzed third-order reaction.

References

1. Paul L. Flory, Principles of Polymer Chemistry, Ithaca, New york, 1953

2. Paul J. Flory, Chem. Rev., Vol. 39, No. 1, 137 (1946)

3. Paul J. Flory, J. Am. Chem. Soc., 61, 12, 3334–3340 (1939)

• Summary

  Step-growth Polymerization

  The average molecular weight increases only slowly at low conversion rates and a high extents of reaction is required to reach a high molecular weight.

• A rapid loss of monomer early in the reaction is obvserved.

• All ends remain acitve throughout the reaction, i.e. no termination of the reactive end groups.

• No initiators are required.
  The reaction can be accelerated by heat and by addition of catalysts.