General mechanical behavior of semi-crystalline polymers

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Transition between the different mechanisms

In the case of relatively short connectors, typically when N<Ne, the most common mechanism for low areal density is the chain pullout described in section For a given chain length, an increase in the areal density will result in a higher value of the stress that can be sustained at the interface without pullout occurring. The maximum stress that can be achieved will be determined either by the saturation of the interface (i.e. when no space is available at the interface for additional block copolymer) or by the plastic yield of one of the polymers, i.e. the formation of a craze. The value of the transition between simple chain pull out and crazing is designated Σ+. Experimentally, the value of this transition provides a way to estimate the monomer friction force fmono. In the following example of a PVP/PS interface (Poly(2-vinylpyridine)/Polystyrene) reinforced by a dPS-PVP block copolymer (with deuterated PS), the craze occurs on the PS side with a transition from chain scission to failure by crazing, and we get When N is further increased, the maximum force that is required to pull the chain out of the glass, i.e. fmonoN, will be higher than the force required to break a main-chain bond fb.
In this case one expects the maximum stress that can be sustained by the interface to be independent of N, and equal to fbΣ. As long as this maximum stress remains lower than the crazing stress (or, more generally, the yield stress) of both the homopolymers, the chains will break without much plastic deformation, while when fbΣ>σcraze, a craze will form and propagate at the interface ahead of the crack, causing a sharp increase in the measured fracture toughness. For a given system, fb and σcraze are fixed so that the transition should occur at the same value of Σ, defined as Σ*, provided that the connecting chain is long enough to avoid pullout. Although the jump in Gc is not always clearly seen experimentally, there is always at least a sharp increase in the slope of the measured Gc versus Σ plot.

Interdiffusion at polymeric interfaces

The early stages of polymer interdiffusion across interfaces, are inherently a non steadystate process. The studies on interdiffusion have progressed with the appearance of suitable techniques, like Neutron Reflectivity (NR) or Dynamic Secondary Ion Mass Spectroscopy DSIMS.
Stamm et al.1 and Kunz and Stamm2, studied the initial stages of polymer interdiffusion in the case of polystyrene (PS) and poly(methyl methacrylate) (PMMA) respectively. In each study, the interface between two thin films of deuterated and protonated monodisperse polymers have been investigated. The films, of thickness in the range of 50 to 100 nm, were annealed at different temperatures above the glass transition temperature for different times. Annealing times at different temperatures were reduced to a reference temperature using the WLF equation (see section equation 1.1-12). With reflectivity measurements it was possible to determine the interface profile with Ångström resolution. The authors found that the broadening of the interface, which can be taken to be representative of the motion of chain segments, across the initially quite sharp interface, was consistent with a picture given by the reptation model. In particular the power dependence of ¼ was observed in a time range corresponding to the “reptation regime”. The time regime of the broadening was found to deviate at small diffusion times from the models proposed in the case of diffusion.
However, deviations from this ideal behavior are expected to be due to the initially distorted chain conformations, the enrichment of ends at the interface, and fluctuation due to capillary waves.


Fracture toughness and interdiffusion: early studies

In one of the first systematic studies of polymer welding by Voyutskii1, and Voyutskii and Vakula2, the authors showed that the buildup of strength at the interface between two polymers involved not only full wetting, but also diffusion of the polymer chains across the interface. It is only twenty years later than the necessity to understand polymer welding motivated a series of more systematic studies on polymer interdiffusion and adhesion. This first series of experiments was typically performed with polydisperse amorphous polymers and often the studies were called crack healing experiments. A homogeneous polymer was fractured at room temperature and the two fractured pieces were then pressed together at a temperature above the Tg of the polymer for different amounts of time. In these experiments Jud et al.3 demonstrated that the measured fracture toughness of an interface between identical polymeric species increased with the square root of the time of contact above Tg. This result was taken as a proof that adhesion between two polymers involved molecular interdiffusion. Based on this idea several relatively simple models were proposed.

Adhesion between semicrystalline polymers

While, due to their well-known plastic deformation properties, glassy polymers provide excellent model systems for fracture studies, most engineering plastics are semicrystalline and have plastic deformation mechanisms and adhesion mechanisms which are much less understood.
In the case of semicrystalline polymers, the mechanical reinforcement of the interface can be achieved through either entanglements or through incorporation of polymer chains on both side of the interface in the same crystallite (co-crystallization). The microstructure of the polymer near the interface (highly dependent on thermal treatment) will strongly influence the plastic deformation properties of the polymer near the interface and therefore the measured fracture toughness.
We will first review the studies carried out on the adhesion of semicrystalline polymers. A large part of this work was performed on incompatible semicrystalline polymers, where a copolymer was formed by chemical reaction at the interface. We will then review the work on self-adhesion of semicrystalline polymers which is the topic of this thesis.

Table of contents :

1.1 Basic concepts
1.1.1 Brief introduction to polymers Introduction Types of polymers and classification A few words on polymerization Basic considerations of polymer physics A single chain Dense system of chains The amorphous state Mechanical properties of amorphous polymers
1.1.2 Semi-crystalline polymers General structure of semi-crystalline polymers Theories of crystallization kinetics General considerations Overall crystallization kinetics Molecular mechanisms of crystallization Melting General mechanical behavior of semi-crystalline polymers
1.2 Fracture behavior of polymers
1.2.1 Introduction
1.2.2 Energy balance approach
1.2.3 The stress intensity factor approach Plane strain, plane stress and different modes of fractures Basic principles of the stress intensity factor approach
1.2.4 Relationship between G and K
1.2.5 Experimental considerations
1.3 Adhesion between polymers
1.3.1 Introduction
1.3.2 Different fracture mechanisms Chain pullout Chain scission Crazing Transition between the different mechanisms
1.3.3 Interdiffusion at polymer interfaces Polymer interdiffusion Diffusion at different time scales Interdiffusion at polymeric interfaces Fracture toughness and interdiffusion : early studies
1.3.4 Polymer adhesion between amorphous polymers : the modern view Introduction Direct adhesion between amorphous polymers Reinforcement of interfaces (immiscible amorphous polymers)
1.3.5 Adhesion between semicrystalline polymers Reinforcement of incompatible semicrystalline polymers Compatibilization by formation of a copolymer Compatibilizing less immiscible semicrystalline polymers Self-adhesion of semicrystalline polymers
1.4 Conclusions and objectives of the current study


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