Journal of Polymer Science Part B: Polymer Physics, Vol.40, No.19, 2292-2302, 2002
Relating fracture energy to entanglements at partially miscible polymer interfaces
A new model has been developed to calculate the areal chain density of entanglements (Sigma(eff)) at partially miscible polymer-polymer interfaces. The model for Sigma(eff) is based on a stochastic approach that considers the miscibility of the system. The values agree between Sigma(eff) calculated from the model and literature values for the reinforced interfaces. Using Sigma(eff) 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 Sigma(eff) also accurately predicts a maximum in mode I fracture energy (G(c)) as a result of the transition from gradient-driven to miscibility-limited interdiffusion, which is observed experimentally. As Sigma(eff) increases, the fracture energy increases accordingly. Compared with a recent model developed by Brown, the new model correctly predicts a reduced G(c) (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 G(c) may reveal the universal nature of the pullout to crazing transition.
Keywords:fracture energy;chain pullout;miscibility;interfaces;crazing;stochastic modeling;packing length