Fold plane

The most stable state minimizes the free energy, that is G is most negative there. If the surface area of the fold plane is very large we may neglect the first term of Eq. (2.1) compared with the remaining terms leading to ... 

Fig. 3.5a, b. Growth on the surface of lamellae, viewed looking onto the fold plane, showing two different types of growth. In a a single strip spreads across the surface before another patch can nucleate, b shows several patches in the same layer, which may in turn support further nucleation events... 

Note A lamellar crystal is usually of a thickness in the 5-50 nm range, and it may be found individually or in aggregates. The parallel-chain stems intersect the lamellar plane at an angle between 45° and 90°. The lamellae often have pyramidal shape owing to differences in the fold domains, as a result, one can deduce different fold planes and fold surfaces from the lamellar morphology. 

Portion of a polymer crystal wherein the fold planes have the same orientation. 

Fig. 2.101 Micro-twinning operation to UjOg-type structure. The structures are represented by a chain of pentagonal bipyramids for simplicity. The structures with a (/, /)ij,OB typc twinning operation are shown, where I is the number of pentagonal bipyramids between the twin planes (hatched ones), (a) UjOg-type structure (mother structure) (b) / = 0 (same as the mother structure) (c) I = 1 (d) I = 2 (e) / = 3 (f) Z = 4. The chain lines indicate the folding planes.

Fig. 2.105 Model structure with iw = 11 = 11 x 1 (see Fig. 2.102(c)).5 Anion packing distortion, shown by gaps between adjacent pentagonal bipyramids, is evident near the folding plane.

It is evident from the ductility and strength of polymers that the ties between lamellae must be stronger than the van der Waal s forces holding neighboring, parallel fold planes together. Evidently some molecules (tie molecules) must participate in the growth of two or more adjacent lamellae, thereby providing relatively short molecular links between the lamellae. 

Figure 2.20 (a) Model of a lamellar crystal showing regular, adjacent re-entry folds, (b) Model of fold plane illustrating chain folding with imperfections which may occur in the structure. (From Ref. 21.)... 

Fig. 21. Schematic representation of a subsonic C02 laser with purely chemical excitation (after Cool82)). A He and Fg injectors, H CO2 and NO inlet, C construction detail shown in B, L D2 mixing array, K part of the D2 inlet system which is shown in detail in J, D sodium chloride window, E totally reflecting cavity mirror with long focal length, M, F beam-folding (plane) mirrors, O partially reflecting cavity mirror for output coupling, N laser beam, G resonator housing flushed with nitrogen...

The alternating parallel orientation of the planes of zigzag indicates that the chains twist in addition to folding within their fold plane. 

The crystal is divided into fonr qnadrants (broken hnes) and, as we shall see shortly, each sector slopes away from the apex of the pyramidal structure. The fold planes in each quadrant are parallel to the outside edge of that quadrant. It follows that the entire crystal is composed of four triangular quadrants that contain rows of fold planes. 

The hollow pyramidal structure is due to the packing of the folded chains in which successive planes of folded molecules are displaced from their neighbors by an integral of repeat distances. In some cases, the fold and fold period are regular, and the displacement of adjacent fold planes is uniform. This results in the formation of a planar pyramid. In other cases, however, the direction of displacement is reversed periodically. In this case, corrugated pyramids are formed. 

FIGURE 1.14 Schematic representation of (a) fold plane showing regular chain folding, (b) ideal stacking of lamellar crystals, (c) interlamellar amorphous model, and (d) fringed micelle model of randomly distributed crystallites. 

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. 

Crystallization in miscible blends can occur with rejection of the noncrystallizing component, so that its concentration in the amorphous phase increases. Alternatively, if it can be accommodated in the unit cell, it may be entrapped, with consequent alteration in the mean unit cell volume (Tomlin and Roland, 1993). In NR, there is also a shift to formation from a-lamellae to the )3-lamellar form (Zemel and Roland, 1992b) (Figure 3.25). These crystal structures have the same unit cell, but the latter has a greater fold-surface free energy. Thus, the noncrystallizing blend component is more readily accommodated into the fold plane at the crystal surface. 

Each line represents one fold-plane (growth plane)... 

Originally hard-elastic PP was made from crystalline lamellar materials and was processed via melt spinning and crystallization under stress, followed by annealing under tension. The structure of the material consists of stacked crystalline lamellae (5-40 nm thick) with fold planes normal to the fiber direction. Between the lamellae, microfibrils oriented parallel to the draw direction are located. Under load, the lamellae tend to separate and voids bridged by fibrils appear. The void volume is initially about 18% at zero strain which increases to about 65% at 15% strain. No further increase in void volume was observed above 15% deformation. 

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