Polymerisation processes with intrapolymer bonding. I. one type of unit

Abstract

We study clustering (‘polymerisation’) processes under the assumptions that new bonds may or may not form within an existing cluster. We show that both models exhibit criticality (‘gelation’) at the same point, and investigate statistics of polymer size and structure beyond criticality in the first case. Gelation may or may not be accompanied by critical effects at unit level; we examine a prototype of each case: the cosh model and the Poisson model.