Cluster number and size distributions near the gel point

The number and size distributions of finite clusters formed near the gel point, which underlie the scaling behaviors of structural and mechanical properties of developing networks, are susceptible to the degree of gelation. Flory-Stockmayer theory and percolation theory predict two distinct sets of scaling behaviors, with mean-field and critical exponents respectively. The crossover between the two behaviors was argued by de Gennes to depend on the -1/3 power of the molecular weight of the precursor chain, which was supported by earlier experimental evidence. Here, we present the cluster statistics simulated with a hybrid MC/MD model, over a wide range of molecular weights, all falling into the narrow gelation window. The cluster number distributions confirm a power law decay, with a well-defined cutoff. The cluster sizes from different precursor chains were collapsed upon proper scaling based on the critical packing arguments, which reveals a broad and gradual transition between the mean-field and critical scalings.