Phase diagram, critical properties and dimensional effects of the kinetic gelation model

The authors simulate the formation of a gel from a mixture of bifunctional and tetrafunctional monomers which may form bonds with the help of initiators on the triangular lattice. Their Monte Carlo results for the average-weight degree of polymerisation exponent, gamma , substantiate the conclusion that this model has distinct critical properties from other models of branched polymers. They observe a crossover to normal bond percolation as the concentration of initiators is increased. However, the cluster number ratio appears to be a universal quantity. They offer an explanation for the differences in phase diagrams of the two- and three-dimensional systems in terms of restricted random walkers.