for strong interfaces where Gc > 50 J/m2. has the physical meaning of an opening displacement and is characteristic of the elastic and geometric parameters of the craze itself. It does not vary much from one polymer to another. mδ It should be noted that σcraze and hf are directly analogous to the parameters σˆ and used in cohesive zone models[9]. δˆ The dependence of Gc on σint 2 has been mainly tested for two experimental systems: diblock copolymers of polystyrene-poly2-vinylpyridine (PS-PVP) at the interface between PS and PVP[4] and for diblock copolymers of PS-polymethylmethacrylate (PS-PMMA) at the interface between poly(oxyphenylene) (PPO) and PMMA[10]. The agreement between the model is qualitatively and quantitatively very good. REINFORCEMENT BY BROADENING OF THE INTERFACE While in the case of connector molecules at the interface of very immiscible polymers, the value of σint is unambiguously given by equation 1, if the two polymers are less immiscible and the interfacial width becomes of the order of the average distance between entanglement points, a significant stress can be transferred by the entanglements formed at the interface. In this case experiments have shown that Gc is a unique function of the width of the interface ai, provided that the molecular weight of the polymers is well above the average molecular weight between entanglements[11]. As shown on figure 3, however the increase in Gc with ai shows clear transitions between different regimes: for thin interfaces one can argue that σint < σcraze and no plastic zone is formed at the interface; above a certain value of ai, Gc increases dramatically implying that the crack is preceded by a craze. Finally at high values of ai , Gc saturates and bulk toughness is retrieved. Although the exact value of ai at the transition point varies somewhat from a system to another, it is always of the order of 10 nm. Therefore if a random copolymer is able to sufficiently reduce the immiscibility and broaden the interface to 10 nm, one expects to see a very large effect on the adhesive properties. This result has been confirmed experimentally for PS-r-PMMA random copolymers[12] and PS-r-PVP random copolymers at interfaces between their respective homopolymers[13,14]. 600 500 400 300 200 100 0 G c (J/m2) 20 15 10 5 0 aI (nm) regime I regime II regime III Figure 3: Fracture toughness Gc of interfaces between glassy homopolymers as a function of their width ai. Data from [15]. GENERALIZATION OF THE MODEL The craze growth model developed in the preceding sections is very attractive since it directly relates a macroscopic value Gc with molecular parameters and material parameters such as σcraze which can be independently measured. While the original model was developed for glassy polymers which readily craze, subsequent studies have shown that the main features of the model (summarized in equations 3 and 4) may be much more robust. Fracture experiments of interfaces between semi-crystalline polymers, reinforced with
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