Graph Theoretical Approach to the Mechanical Strength of Polymers

Abstract

In this research work, a graph theoretical approach has been introduced to find a mathematical model for the change of hardness of weakly cross-linked polymer network systems with the change of configurations. The polymers studied are (i) poly(methyl methacrylate), (ii) styrene–acrylonitrile copolymer and (iii) polystyrene. In very weakly cross-linked polymer network systems, both the chain entanglement and the network rigidity competitively contribute to the hardness of polymer network. The average length (i.e. molecular weight), and length distribution of chains between the cross-linking sites both play important roles in network rigidity. The former can be changed by the mole fraction of the cross-linker, and the latter by the molecular weight of the prepolymer formed, which can be controlled by the late addition of the cross-linker. Graph theoretical approach introduces simplifications to the dynamics of polymer chains and polymer network, and thus can explain the change of hardness with the change of chain statistics. It was shown that there was a very good agreement between the theoretical equations and the experimental hardness values of polymer network systems studied. It was also found that there were scaling relations between the parameters used in the theoretical equation.