In three-dimensional polymerizations, gelation is due to the formation of network structures of indefinite extent. These giant structures make their appearance when the degree of branching or cross-linking of the polymer chains exceeds a critical value. Gelation may be considered analogous to explosion in gas-phase reactions propagated by chains which undergo branching. After gelation has occurred, the sharp distinction between gel and sol is analogous to the demarcation between a liquid and its saturated vapor. Observed average molecular weights of three-dimensional polymers must be interpreted with extreme caution, owing to the peculiarity of the distribution of species in the vicinity of the gel point. Applications of the theory to raw rubber, protein gels, and inorganic gels have been discussed.

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