Relating fracture energy to entanglements at partially miscible polymer interfaces

Abstract

A new model has been developed to calculate the areal chain density of entanglements (Σeff) at partially miscible polymer-polymer interfaces. The model for Σeff is based on a stochastic approach that considers the miscibility of the system. The values agree between Σeff calculated from the model and literature values for the reinforced interfaces. Using Σeff calculated from the model, the interfacial width, and the average distance between entanglements, an equation for the fracture energy of nonreinforced polymer interfaces is proposed. This equation is used to model the transition from chain pullout to crazing. As a function of system miscibility, the model for Σeff also accurately predicts a maximum in mode I fracture energy (Gc) as a result of the transition from gradient-driven to miscibility-limited interdiffusion, which is observed experimentally. As Σeff increases, the fracture energy increases accordingly. Compared with a recent model developed by Brown, the new model correctly predicts a reduced Gc (attributed to chain pullout) when the interfacial width is less than the average distance between entanglements. Theoretical predictions of the change in fracture energy with respect to interfacial width agree with the experimental measurements. Finally, it is postulated that the use of a miscibility criterion for Gc may reveal the universal nature of the pullout to crazing transition.