Branching, non-linear polymers

The units which constitute the polymer may have, by accident or on purpose, a functionality larger than two. Thus, it is possible to obtain branched or reticulated structures whose elements are linear polymer segments. Two classes of structures can roughly be distinguished. 

The reticulated structures are made up of clusters. If all the clusters have a finite size, the system is soluble and the solution is called sol. On the other hand, if the structure contains a cluster of infinite size, the system is a gel which is not soluble but which may swell in a solvent. The same reaction may lead either to sols or to gels according to the final branching rate. The sol-gel transition may be considered as a percolation transition. Note that an infinite cluster can be made either by chemical binding or (partially) by topological trapping [see Fig. 1.8]. From a mechanical point of view, a sol is viscous, a gel is elastic. Thus a piece of vulcanized rubber can be considered as a gel. 

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