Cluster growth from a dilute system in a percolation process

Abstract: The gelation process has been explained in the framework of percolation models. Although the percolation models accurately predict the gelation behaviors above the overlap concentration of prepolymers (c*₀), they do not predict the gelation behaviors below c*₀. We measured the osmotic pressure during the gelation of a series of model polymer gels, namely, tetra-polyethylene glycol (PEG) gels. The osmotic pressure decreased during the gelation reaction and was constant after the sol–gel transition. These results suggest that the clusters grow and fill the system at the sol–gel transition point. As a result, the gels behaved as semidilute systems regardless of the initial polymer concentration. This representation of the sol–gel transition at the overlap condition of the critical clusters corresponds well to the aggregation process predictrion. These results will help better understanding of general percolation problems in the dilute regime.