Twisting of lamellae

On the lamellar level, inside the spherulites, several different processes control the ductility of the polymer, which are sketched in Fig. 2.20 [6, 12]. Lamellae running parallel to the direction of strain can be deformed by interlamellar slip (Fig. 2.20(a)), tilted lamellae rotate into the deformation direction twisting of lamellae, Fig. 2.20(b)), and lamellae that are aligned perpendicular to the applied load (in the equatorial region) will be separated lamellar separation, Fig. 2.20(c)). 

A deformation of a lamellar block copolymer in the direction perpendicular to the lamellae orientation results in processes of kinking, breaking, and twisting of lamellae, yielding a fish-bone structure or chevron morphoiogy. 

The twisting lamellar structure of banded spherulites has been debated for decades without obtaining any satisfactory answer until recently. The nature of the isochiral (certain uniform handedness) lamellar twisting and the synchronic character of the twisting of a group of adjacent dominant lamellae both require an explanation. The permanganic etching technique provided... 

The ringed appearance (Figure 8.15) arises from twisted lamellae. The continuity of the rings through a 360 rotation suggests that the lamellae twist in phase. Spherulites contain amorphous material situated between and on the surface of lamellae. This is often polymer with low tacticity or branched polymer that does not readily crystallize and is therefore excluded from the growing crystal during the crystallization process. 

Figure 5.64 is an electron micrograph of the rephca of a fracture surface of a melt-grown polyethylene spherulite. It gives another proof that polymer sphemlites can be made of lamellae. In addition, it shows that there is a regular twist that permits an... 

It is well known that banding is the result of the cooperative twisting of the lamellae during growth. Although such twisting has been associated with internal stresses produced on the lamellae surfaces, the reason for its occurrence is still controversial (Lotz and Cheng 2005). It has also been reported in case of polymer... 

The inverse of the pitch which corresponds to the helical twist of the lamellas against each other, is plotted in Fig. 5.35 for different concentrations of formamide. The values shown in the upper part of Fig. 5.35 were determined with the Cano method, while the bottom part shows the results obtained by the direct method. The two plots in Fig. 5.35 basically show the same behavior. In both plots no clear temperature dependence of the helical twist can be found. Right after the phase transition into the lyotropic SmC analog phase, the helical structure is... 

Fig. 2.4. Sketch of the basic stractural components in HDPE geomembrane morphology - based on our understanding as of today. Folded polymer chains form extended lamellae (top left). Twisted stacks of lamellae create longitudinal fibrils (bottom). The sphere-shaped spheralite (top right) is composed of radial fibrils pointing outwards with amorphous areas in between. This stmctural model enables the interpretation of basic processes, such as stress crack formation, see Sect. 5.3.4...

When macromolecular cholesteric liquid crystals were imaged, a twisting of molecular orientation, which translated into a periodic lamellar structure in the materials, was foimd. Good agreement between afm and tern (transmission electron microscopy) was obtained in determining the widths of the lamellae. When the same polymer was processed from an isotropic solution, a homogeneous and nodular structure, lacking the periodicity of the cholesteric structure, was obtained (107). 

Wide-angle x-ray scattering (waxs) enables us to study changes in crystallinity and orientation (texture analysis) and, for instance, processes of lamellae twisting in semicrystalline polymers (12). 

Figure 37 Polarized light image of a banded spherulite of PIT. The inset shows schematics of twisted crystalline lamellae growing radially from the spherulite center. " The inset adapted with permission from Barham PJ, Keller A. J Mater Sci 1977,12,2141. Copyright Kluwer Academic/Plenum Publishers.

Figure 40 Left Schematic illustration of a PE crystalline lamella in which the stems are inclined by a significant angle in the plane perpendicular to the fast crystal growth axis (i.e., the b-axis). In terms of the symmetry operation, such lamella exhibits an inversion point when viewed along b. Right The unbalanced stresses generated on the lamellar surface result in a helicoidal twist of the crystal, which becomes symmetric about the mirror plane M perpendicular to the crystal growth direction and passing through the primary nucleus. With permission from Rosenthal, M. etal. Angewandte Chemie lot. Ed. 123 (2011) 9043-9047. ...

Figure 41 Schematics depicting the model of a twisted crystalline lamella according to Keith and Padden, where the twist is generated by surfaces stresses having opposite signs on both fold surfaces and both longitudinal halves of the lamella.

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