Lamellae, electron diffraction

Electron diffraction measurements indicate that polymer chains are generally oriented normal or very nearly normal to the plane of the lamellae [13,14]. As the molecules in the polymer are at least 1000 A long and the lamellae are only about 100 A thick, the most plausible explanation is that the chains are folded [13,15], Figure 22.3 illustrates the proposed models of the fold surface in polymer lamellae [13,16],... 

An alternative hypothesis, developed from studies of the synthesis of Linde A zeolite carried out by Kerr (5) and Ciric (6), pointed to growth occurring from solution. The gel was believed to be at least partially dissolved in solution, forming active aluminosilicate species as well as silicate and aluminate ions. These species linked to form the basic building blocks of the zeolite structure and returned to the solid phase. Aiello et al. (7) followed the synthesis from a highly alkaline clear aluminosilicate solution by electron microscopy, electron diffraction, and x-ray diffraction. These authors observed the formation of thin plates (lamellae) of amorphous aluminosilicates prior to actual crystal formation. 

In addition the electron diffraction data proved to be relatively insensitive to the orientation of the -CH2OH groups. The refined values of were consistent with the preferred orientation of the lamellae with the 110 planes perpendicular to the surface. Viewed in this projection the rotation of C6-06 about C5-C6 is seen as a short linear oscillation, making it much more difficult to determine X than would be the case if full three dimensional data were available. 

The evidence that lamellae 15 nm thick can enter the hexagonal phase came from electron diffraction of specimens annealed as low as 236 °C at 0.54 GPa, 3 K lower than the maximum of the corresponding differential thermal analysis peak recorded for bulk polymer under the same conditions. At this annealing temperature lamellae were still entire, i.e. essentially of unaltered thickness although with some internal variation. No attempt was then made to anneal at lower temperatures and determine the orthorhombic/hexagonal transition temperature for this thickness. Such experiments offer, nevertheless, a direct approach by which the quantities of Eq. 9 may be determined. 

Lamellae are thin, flat platelets on the order of 100-200 A (0.01-0.02 pm) thick and several microns in lateral dimensions, while polymer molecules are generally on the order of 1,000-10,000 A long. Since the polymer chain axis is perpendicular to the plane of the lamellae, as revealed by electron diffraction, the polymer molecules must therefore be folded back and forth within the crystal. This arrangement has been shown to be sterically possible. In polyethylene, for example, the molecules can fold in such a way that only about five chain carbon atoms are required for the fold, that is, for the chain to reverse its direction. Each molecule folds up and down in a regular fashion to establish a fold plane. As illustrated in Figure 1.14a, a single fold plane may contain many polymer chains. The height of the fold plane is known as the fold period. It corresponds to the thickness of the lamellae. 

When they are grown at sufficient dilution, the crystallites approximate to lamellae with a uniform thickness of about 12 nm, the precise value depending on the temperature of growth. Electron diffraction shows that the chain axes are approximately perpendicular to the planes of the lamellae. The crystals are not exactly flat, but have a hollow-pyramidal structure, with the chain axes parallel to the pyramid axis. This pyramidal structure is seen clearly in fig. 5.5, which shows a single crystal of polyethylene floating in solution. This should be compared with fig. 5.3(b), which shows similar crystals flattened on an electron-microscope grid. The dark lines on the crystals in fig. 5.3(b) show where the pyramid has broken when the crystal flattened. 

If the stacking is regular, as is often the case, 4 can be determined by SAXS, as described in section 3.4.2. If the stacking is very irregular, elee-tron microscopy must be used to sample different regions. Electron microscopy shows that the lamellae are not always flat but may be corrugated, particularly in melt-crystallised material. Electron diffraction shows that the chain axes are then usually perpendicular to the overall plane of the lamella rather than being normal to the local thickness direction. Information about the thicknesses of the crystalline layers can be obtained from Raman spectroscopy. 

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