Complex network analysis of completely extended chains in rubber elasticity

Rubber elastic theory describes the relationship between the microscopic chain structure and macroscopic mechanical properties of soft network polymers, such as elastomers and gels. When the deformation exceeds a certain threshold, the formation of extended chains induces hardening and failure of the materials, which has been tackled by experiments involving measurement techniques and mechanochemistry. However, the relationship between the network structure as concerns connectivity and the formation behavior of extended chains has hardly been described. Herein, we demonstrate the quantification of chain connectivity based on complex network science to investigate the formation mechanism of completely extended chains in rubber elasticity. Polymer chains in the central position of the network tended to persist in the extended chains as concerns connectivity. Furthermore, the formation of extended chains induces neighboring polymer chains to become extended chains, causing stress concentration at the network scale. Our approach, based on complex network theory, is useful as a bridge between conventional theory and experiments for describing complicated rubber elasticity at the mesoscale.