Computer simulation of a model for irreversible gelation

Abstract

A random mixture of bifunctional and tetrafunctional units is placed on a simple cubic lattice. Permanent bonds between these units are then formed by the random motion of active centres (radicals) resulting in a model for the gelation of polyacrylamide and similar processes. The largest of the clusters formed by this kinetic percolation process is identified with the gel fraction, the 'mean cluster size' with the weight-average degree of polymerisation. The critical exponent gamma of the mean cluster size is roughly the same as for random percolation, that is, different from that of the 'classical' theory of Flory (1941) and Stockmayer (1943), but the corresponding amplitude ratio, that is, the ratio of average molecular weight on both sides of the gel point, differs strongly from its value in random percolation. Thus, this kinetic gelation model seems to belong to a universality class of its own, different from both that of random percolation and that of classical gelation theories.