Journal of Statistical Physics, Vol. 38, Nos. 3/4, 1985. p. 573-587.
In 1974, Falk and Thomas did a computer simulation of Flory's Equireactive RAf Polymer model, rings forbidden and rings allowed. Asymptotically, the Rings Forbidden model tended to Stockmayer's RAf distribution (in which the sol distribution "sticks" after gelation), while the Rings Allowed model tended to the Flory version of the RAf distribution. In 1965, Whittle introduced the Tree and Pseudomultigraph models. We show that these random graphs generalize the Falk and Thomas models by incorporating first-shell substitution effects. Moreover, asymptotically the Tree model displays postgelation "sticking." Hence this phenomenon results from the absence of rings and occurs independently of equireactivity. We also show that the Pseudomultigraph model is asymptotically identical to the Branching Process model introduced by Gordon in 1962. This provides a possible basis for the Branching Process model in standard statistical mechanics.