Aggregation beyond the gel point: A new class of exactly solvable models

The existing models describing the kinetics of aggregation in the presence of an infinite cluster, orgel, 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 the gel can be varied. The model is called thegeneralized acyclic model (GAM) since it generalizes Stockmayer's model and Ziff's third model. It is shown that the GAM can be solved exactly in terms of standard (hypergeometric) functions. The solutions are analyzed in detail, both asymptotically in various limits and numerically.Dedicated to Matthieu Ernst, on the occasion of his 60th birthday.