Pregel derivation

It has also been found that polymers possessing functional groups such as amines and pyridines are soluble in pregelled sol solutions, especially, poly (2-vinjipyridine) and poly(A/-vinylpyrrolidinone) (PVP) (49). There, materials were made as part of a study of the synthesis of nonshrinking sol—gel-derived networks (49). 

Apart from the condition defining an ideal polymerization, the equations derived in this section assume that both q and E, remain constant in the pregel stage e.g., no drift occurs. This is usually a good assumption in the pregel period due to the extremely low value of the gel conversion. However, if drift occurs, integral equations must be used (Dotson et al., 1988). 

Using the Macosko-Miller version of the tree-like model, Charlesworth analyzed his experimental results obtained for the diamine-diepoxide reaction (molecular weights, pregel composition, sol fraction). Bokare and Ghandi derived... 

To derive a specific form of the equilibrium constants bi, let us introduce a simple model for the internal structure of clusters. Clusters are assumed to take a tree structure with no internal loops (Cayley tree). Cycle formation within a cluster is neglected. This is a crude approximation on the basis of the classical theory of gelation presented in Section 3.2 [5,6,7,8], but in fact it is known to work very weU at least in the pregel regime. 

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