Gelation and Network Formation

The aim of this chapter is to describe the process of network formation using qualitative arguments together with simple mathematical tools. The intention is to provide a first approach to the subject that should enable the reader to get acquainted with the basic concepts and definitions of the network structure. 

It is evident that the way in which the network structure is developed will depend primarily on the type of polymerization reaction that is involved stepwise or chainwise. In the former case the network growth occurs smoothly, as schematically represented in Fig. 3.1, for the paradigmatic case of an A3 homopolymerization - e.g., a molecule with three OH groups that undergoes a polyetherification reaction. 

In several types of chainwise polymerizations, species with high molar mass are generated from the beginning of the reaction. This is depicted in Fig. 3.2 for an A2 (one double bond per molecule) -I-A4 (two double bonds per molecule) free-radical polymerization - e.g., a vinyl-divinyl system. 

Living polymerizations (2.3.1, Fig. 2.2) exhibit a different type of network growth. They are classified among the chainwise polymerizations because it is always the monomer that reacts, adding to growing chains. But the growth of primary chains occurs smoothly, as in the case of stepwise polymerizations. 

For conversions lower than Xgei the average molar mass of the polymer exhibits a continuous increase. The first two moments of the molar mass distribution are the number-average molar mass, Mn, and the mass-average molar mass, M, respectively. is defined in terms of the number contribution of every species to the whole population. The weight factor used to define this average is the molar fraction. is defined in terms of the mass contribution of every species to the whole mass, so that the mass fraction is the weight factor used in its definition. 

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Branching leads in many cases to gelation and network formation. Sometimes only precursors, i.e. synthetic resins, are wanted where gelation has to be prevented. Here, of course, a theory is most efficient which contains explicitly the chemical parameters responsible for the branching reactions, which can be altered in a similar manner as in real gelling reactions. This again is warranted by the close relation of the link probability to the extent of reaction (branching). 

The classical theories of gelation and network formation are concerned in general with networks formed by point junctions. A more extensive variety of junctions and network structures can, of course, be imagined, and indeed, corresponding examples of actual gels discovered. A logical expansion from point junctions is to increase the dimensionality to produce one-, two- and three-dimensional junction zones (Fig. la). 

Stepto, R.F.T., Non-linear polymerization, gelation and network formation,... 

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