Distribution Cutoff for Clusters near the Gel Point

The mechanical and dynamic properties of developing networks near the gel point are susceptible to the distribution of dusters coexisting with percolating networks. The distribution of duster numbers follows a broad power law, wrapped by a cutoff function that rapidly decays at a characteristic size. The form of the cutoff function has been speculated based on known results from lattice percolation and, in certain cases, solved. We obtained this cutoff function from simulated dynamic dusters of polymeric precursor chains using a hybrid Monte Carlo algorithm. The results obtained from three different precursor chain lengths are consistent with each other and are consistent with the expectation from lattice percolation.