Summary of branching and gelation

A wide variety of linking processes can lead to the transformation from a liquid to a solid known as gelation. This transition occurs at a particular extent of reaction, p, called the gel point. A rough estimate of the gel point for linking precursor molecules (or monomers) with functionality / is 

This molar mass distribution applies to all polymers below the gel point and above the gel point it applies to the sol fraction. The weight-average molar 

The number-average molar mass stays finite at the gel point and therefore the polydispersity index of the sol diverges at the gel point proportional to Ww. 

At the gel point, the distribution of molar masses is a power law, since M diverges. Above the gel point the system consists of a macroscopic gel, permeated by a polydisperse soup of microscopic molecules (the sol) described by the same self-similar distribution of molar masses. The distribution of molar masses in the sol gets progressively narrower as the reaction proceeds further beyond the gel point, since the characteristic molar mass M decreases. The fraction of the material that is a part of the gel, called the gel fraction Pgd, grows steadily above the gel point  

Once the extent of reaction reaches approximately twice the gel point, nearly all monomers are attached to the gel and there is essentially no sol fraction remaining. Such well-developed networks are the subject of Chapter 7. 

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