Sol-gel transition behavior near critical concentration and connectivity

A polymer cross-linking system undergoes a phase transition from liquid to solid at a critical point, which is called the sol-gel transition. The sol-gel transition is often understood in the context of the lattice-based percolation model. Two parameters govern the sol-gel transition including the connectivity and polymer concentration. In this study, we independently tuned these parameters and experimentally accessed the sol-gel transition point as a function of connectivity and concentration using a model gel system (tetra-polyethylene glycol gel). The connectivity required to percolate the system continuously increased as the polymer concentration decreased, which is completely different from that predicted by the site-bond percolation model. The viscoelastic behavior at the critical points indicates that the fractal dimension of the percolation clusters deviated from the prediction of the lattice-based percolation model as the polymer concentration decreased. These results indicate that the lattice assumption cannot be applied for a gelling system prepared far below the overlapping concentration.