Revisiting the Master Curve Relationship for the Dimensions of Network Polymers

ABSTRACT The graph diameter correlates with the mean‐square radius of gyration and can be used to represent the 3D size of the polymer molecules. The graph diameter of the finite network polymer is investigated for both random and nonrandom architectures. By considering miniemulsion copolymerization of vinyl and divinyl monomers in Monte Carlo simulations, various types of networks are generated for investigation. The master curve relationship between the fraction d of diameter chain and cycle rank found earlier is revisited, which represents the maximum d of a randomly crosslinked homogeneous network for a given cycle rank. The relationship applies in a wide range of network maturity index NMI that is the number of cycle ranks per primary chain, approximately 3< NMI < 20. For the nonrandom inhomogeneous networks, the maximum d for a given cycle is f d times the master curve, and the calibrated d / f d curve follows the master curve. Larger NMI‐values are needed for inhomogeneous networks to reach the maximum d , however, setting NMI larger than about 5 allows d to be larger than the corresponding random networks. Although the current study focuses on microgels, the design concept can also be applied to the synthesis of macrogels.