Chem 421: Introduction to Polymer Chemistry

Molecular Weight in Step Polymerization

The Carothers Equation

In an ideal case, there is a simple relationship between the conversion in a step polymerization and the MW obtained. It was first described by W. Carothers in the 1930s, and expanded by P. Flory.

The most important result of this equation is that real polymer does not form except at very high conversions in step polymerization. Therefore, one requires very pure ingredients, absolutely clean reaction chemistry (i.e., no side reactions), well-balanced stoichiometry (for AA-BB reactions), and often prolonged reaction times.

Note also if you divide out the two MW equations above, the polydispersity (M_w / M_n) is simply given by p + 1. Therefore, for typical step polymerizations, PD equals approximately 2.0.

MW Control in Step Polymerization

There are two ways to purposefully reduce the MW in a step polymerization: add a monofunctional component, or unbalance the stoichiometry (for AA-BB). Modifications of the Carothers equation have been derived to predict the MW in these situations:

The question you might be asking at this point is "Why would one want to do this?" Actually, there are many reasons:

• Many useful polymer properties level off at moderately high MW. Very high MW doesn't have any benefit in most cases.
• Polymer melt and solution viscosity increase monotonically with MW. Very high MW polymer is more difficult to process.
• For step polymers, the properties can change during processing unless the MW is deliberately capped.
• Example for a sample of Nylon 66 held in melt at 218 °C for 5.5 h:
  • - initial melt viscosity=480 poise
  • - unmodified=2290 poise
  • - 2.5% excess diacid used=515 poise

Step Polymerization - What Can Go Wrong

• Impurities containing only one functional group.
• Impurities that poison the catalyst (if used).
• Decomposition of monomer.
• Unwanted side reactions.
• Physical loss of monomer during reaction.
• Reversibility (unfavorable equilibrium).
• Stoichiometric imbalance (for syndioregic mode).

What's needed:

• Extremely pure ingredients.
• Clean, very high yield reactions.
• At least moderate reaction rates.
• Precise balance of functional groups.

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