Dislocations, polymer crystals

Although polymer crystal structures are known, and some slip mechanisms (slip plane and slip direction) determined, these are less important than for metals. Firstly, the amorphous phase plays an important part in the mechanical properties. Secondly, polymer yield strengths are not determined by obstacles to dislocation movement. However, it is possible to fabricate highly anisotropic forms of semi-crystalline polymers, so crystal characterization and orientation are important. 

In addition, conformational disorder in polymer crystals may give rise to point and line defects which are tolerated in the crystal lattice at a low cost of free energy as kinks [104,105], jogs [106,107] and dislocations [108,109]. Such crystallographic defects arise whenever portions of chain adopt conformations different from the conformation assiuned by the chains in the crystal state [99], and have been widely discussed in the literature, in the case of polyethylene [108,109] and some aliphatic polyamides [99,106]. Point and... 

Two final points need to be made about secondary nucleation. First, that screw-dislocation defects, described in more detail in Sect. 5.3, prodnce indesttnctible secondary nuclei for growth on top of the fold surfaces of polymer lamellae. This surface would otherwise be inactive for further growth and restrict polymer crystals to single lamellae (see Chap. 5). An example of a series of screw dislocations is shown in Fig. 3.72 on the example of poly(oxyethylene) of 6,000 molar mass grown... 

All the aspects and processes discussed above apply also to the crystallisation of polymers [18-31]. However, in addition, the connectivity of the monomers causes several restrictions. One of the most obvious ones is represented by the quasi-two-dimensional lamellar shape of polymer crystals. A lamella is formed by crystalline segments of the chain (the stems) arranged vertically and limited (on top and below) by amorphous (fold) surfaces. Therefore, polymer crystals grow essentially only in two dimensions. Growth in the third dimension is rather difficult, in particular when the polymer contains non-crystallisable units which will segregate to the surfaces of the crystals. Growth in the third dimension necessitates deviations from the perfect lamellar structure, e.g. screw dislocations. The topic of polymer crystallisation has been the subject of a tremendous amount of studies over the last 60 years [5-8,10-65],... 

Fig. 4. Melt-crystallized polyethylene lamellae (a) linear polymer crystallized at 130°C as a planar crystal in which successive layers spiraling around the central (etched-out) giant screw dislocation are not in contact (b) ridging along 6 in a 17,000 mass fraction of linear poljrmer crystallized at 129°C (c) an ethyl-branched copolymer crystallized at 123°C showing a central S-profile, asymmetrically placed screw dislocations and new layers diverging therefrom. From Ref. 66.

Figure 1. Synchrotron X-ray topograph of a PTS polymer crystal showing growth dislocations D, mechanically induced dislocations M and a planar twin boundary P (g 112, A= 1a (crystal plane (100))...

These defects existed in the same geometry in the monomer and polymer crystal and hence are frozen in during the radiopolymerization process. There was no visual evidence of enhanced polymerization in the vicinity of these defects or of dislocation multiplication. This apparent lack of enhanced reactivity at dislocations to high energy radiation was confirmed in kinetic studies of the y-ray induced process. 

Figure 2.24 Hierarchy of structures observed when a polymer crystallizes. Molecules adopt an extended conformation, or fold. The crystallized molecules are organized into lamellae. Crystalline layers and amorphous layers form a lamellar stack. Radial growth of lamellae leads to spherulitic supermolecular structures. The spokes of the spherulite result from defects in lamellar organization, such as giant screw dislocations...

The model of thermal nucleation of screw dislocations by Peterson [143, 144] and Young [150,151] has been shown to account fairly well for the plastic behavior of PE [152,153] and PP [154] and for the yield stress dependency on crystal thickness. Elastic line energy calculations indicate that nucleation of screw dislocations is more favorable than that of edge dislocations [155,156]. Glide is also easier for the former [157]. It has been shown that screw dislocations pai-allel to the chain stems may be nucleated firom the lateral surface of thin polymer crystal platelets upon coupled thermal and stress activation [143,144,158]. 

Peterson J M (1966) Thermal initiation of screw dislocations in polymer crystal platelets, J Appl Phys 37 4047-4050. 

It is clear that crystalline polymers are by no means perfect from a structural viewpoint. They contain crystalline and amorphous regions and probably also areas which are partially disordered. It has been recognized for many years that crystals of any material contain imperfections such as dislocations or point-defects and there is no fundamental reason why even the relatively well-ordered crystalline regions of crystalline polymers should not also contain such defects. In fact, it is now known that polymer crystals contain defects which are similar to those found in other crystalline solids, but in considering such imperfections it is essential to take into account the macromolecular structure of the crystals. 

The possibility of dislocations being involved in the deformation of polymer crystals has received considerable attention over recent years. This will be considered later (Section 5.5.5) and this section will be concerned with dislocations that may be present in undeformed crystals. The most obvious example of the occurrence of dislocations in polymer crystals is seen in Fig. 4.13 where the crystals contain growth spirals. It is thought that there is a screw dislocation with a Burgers vector of the size of the fold length (—100 A) at the centre of the spiral. Such a dislocation is illustrated schematically in Fig. 4.24 and the Burgers vector and dislocation line are parallel to each other and the chain direction. 

With recent advances and improvements in the instrumentation of electron microscopy there have been numerous reports of the observation of dislocations in atomic, ionic and molecular crystals through direct imaging of the crystal lattice. Although this technique is difficult to apply to polymer crystals because of radiation damage, recently dislocations have been imaged directly in polymer crystals. 

Fig. 4.24 Schematic representation of screw dislocations with Burgers vectors parallel to the chain direction in lamellar polymer crystals, (a) Illustration of relation between the dislocation line and the chain direction (indicated by striations). (b) Screw dislocation leading to growth spiral.

In general, it is found that the tensile strengths of materials are very much lower than E/10 because brittle materials fracture prematurely due to the presence of flaws (Section 5.6.2) and ductile materials undergo plastic deformation through the motion of dislocations. However, fine whiskers of glass, silica and certain polymer crystals which do not contain any flaws and are not capable of plastic deformation have values of fracture strength which are close to the theoretically predicted ones. 

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