Master Curve for the Dimensions of Statistical Network Polymers

The graph diameter D is correlated with the mean-square radius of gyration Rg² and is a useful measure to design and control the network architecture. The fraction d of segments located in the diameter chain, defined by d = D/n_s, where n_s is the total number of segments in the polymer, is investigated for various statistical network polymers. It is found that the relationship between d and the cycle rank r of the well-developed statistical networks follows a master curve. As a convenient measure to define the well-developed networks, the network maturity index (NMI) is proposed. The random crosslinked networks with NMI > 3 are considered well-developed, but a larger value of NMI is required for the nonrandom, heterogeneous networks. With the help of prior knowledge of the relationship between Rg² and D, the master curve for the relationship between the contraction factor g and r can also be determined.