Fractal dimensionality for kinetic gelation with conserved initiators

A kinetic gelation model is developed for which the number of active initiator molecules is conserved. For this reason this model exhibits a gelation threshold even for very small values of c_I, the concentration of initiator molecules, in contrast to the conventional model of kinetic gelation with non-conserved initiators. This model is studied by Monte Carlo analysis for a two-dimensional triangular lattice with a sequence of lattice sizes up to 900*900 sites. The authors use finite-size scaling to study the dependence of y_h (the fractal dimension) and y_T (=1/ nu ) upon c_I. They find that y_T depends weakly on c_I, but that the fractal dimension y_h is independent of c_I. This is in accord with the most recent work for the conventional kinetic gelation model with non-conserved initiators.