AGGREGATION BEYOND THE GEL POINT - A NEW CLASS OF EXACTLY SOLVABLE MODELS

The existing models describing the kinetics of aggregation in the pres ence of an infinite cluster, or gel, are reviewed, and a new class of post-gel models is proposed. In this new class of models, clusters are assumed to be acyclic and the rate constant for reactions involving t he gel call be varied. The model is called the generalized acyclic mod el (GAM) since it generalizes Stockmayer's model and Ziff's third mode l. It is shown that the GAM can be solved exactly in terms of standard (hypergeometric) functions. The solutions are analyzed in detail, bot h asymptotically in various limits and numerically.