Polymer single crystals dislocations

Fig. 14.—Polymer Single Crystal from Esparto-grass Xylan. (Screw dislocations and lamellar texture are typical of these crystals, which contain folded polymer-chains. The insert shows the schematic diagram of the electron diffractogram that corresponds to the dry crystal form (see Section V,l, p. 460), and confirms that the molecular axis is normal to the lamellar plane).

Figure 5-17. The termination of a dislocation in the direction of the plane of the chain at the diagonal of a polymer single crystal (after P. H. Lindenmeyer, V. F. Holland, and F. R. Anderson).

The dislocation method of stress analysis is also useful for determining craze stress fields in anisotropic (e.g., oriented) polymers . All one needs here is the stress field of a single dislocation in a single crystal with the same symmetry as the oriented polymer (the text by Hirth and Lothe provides a number of simple cases plus copious references to more complete treatments in the literature) the craze stress field can be generated by superposition of the stress fields of an array of these dislocations of density a(x). Dislocations may also be used to represent the self-stress fields of curvilinear crazes (produced by craze growth in a non-homogeneous stress field for example). Such a method has been developed by Mills... 

It is well known (66) that the a-relaxation process of crystalline polymers consists of at least two processes, referred to as ai and U2 in the order of lower temperature, respectively. The ai-process (67-77) is pronounced in melt crystallized samples and is associated with the relaxation of grain boundaries, such as dislocation of lamellae with a frictional resistance related to disordered interface layers. The magnitude of the ai-process increases with the increase in the crystal defects. The o 2-process (71,73,78-83) is pronounced in single crystal mats and is ascribed to incoherent oscillations of the chains about their equilibrium positions in the crystal lattice in which intermolecular potential suffers smearing out. The magnitude of the Q 2-process increases with the increase in the lamellar thickness and/or the degree of crystallization (39). 

It is well known [73] that plastic deformation in crystals can occur when the applied shear stress can cause one plane of atoms to slip over another plane because there is an imperfect match between these adjacent planes at a particular point in the crystal lattice. These points of imperfection are called dislocations [74] and were identified by electron diffraction techniques to relate to specific crystal defects. Dislocations are observed in polyethylene single crystals by Peterman and Gleiter [75] and give credence to the idea that yield in crystalline polymers can be understood in similar terms to those used by metallurgists for crystalline solids. 

Screw dislocations observed in single crystals of polymers may have an extraordinarily large Burgers vector, up to 10 nm or more, being equal to the total thickness of lamellar crystals [134]. Such dislocations are easily detectable by microscopes, yet they do not have hollow cores as would be required of such... 

Structurally, plastomers straddle the property range between elastomers and plastics. Plastomers inherently contain some level of crystallinity due to the predominant monomer in a crystalline sequence within the polymer chains. The most common type of this residual crystallinity is ethylene (for ethylene-predominant plastomers or E-plastomers) or isotactic propylene in meso (or m) sequences (for propylene-predominant plastomers or P-plastomers). Uninterrupted sequences of these monomers crystallize into periodic strucmres, which form crystalline lamellae. Plastomers contain in addition at least one monomer, which interrupts this sequencing of crystalline mers. This may be a monomer too large to fit into the crystal lattice. An example is the incorporation of 1-octene into a polyethylene chain. The residual hexyl side chain provides a site for the dislocation of the periodic structure required for crystals to be formed. Another example would be the incorporation of a stereo error in the insertion of propylene. Thus, a propylene insertion with an r dyad leads similarly to a dislocation in the periodic structure required for the formation of an iPP crystal. In uniformly back-mixed polymerization processes, with a single discrete polymerization catalyst, the incorporation of these intermptions is statistical and controlled by the kinetics of the polymerization process. These statistics are known as reactivity ratios. 

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... 

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