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projection to 90o, labeled a*. The chain consists of a 3*7/2 helix. Again, the growth in direction c was possible via growth spirals or screw dislocations as shown in Fig. 3.72. The growth spirals in Fig. 5.55 are visible in the center in form of a terrace, a combination of two growth spirals of opposite handedness as described in Sect. 5.3, and at the lower edge as a standard left-handed spiral.

5.2.5. Dendrites and Spherulites

Only on relatively slow crystallization do folded-chain single crystals grow. As the crystallization speeds up, problems arise in solution with the diffusion of molecules to the growth front, and in the melt with conduction of the heat of crystallization away from the growth front, as is discussed in Sect. 3.6. Instead of large, flat crystal surfaces, skeletonized, serrated surfaces are produced by a decrease of the polymer concentration in front of large, flat growth faces, as illustrated in Figs. 3.80–82. Wellknown dendrites are the snowflakes illustrated in Fig. 5.1. Similar looking dendrites of polyethylene are illustrated in Fig. 5.56. The picture is an interference micrograph, so that the dark interference fringes signify the increasing thickness of the dendrite towards the center. The increase in thickness between two interference fringes is about 1 m or the thickness of 100 lamellar crystals. Screw dislocations allow the

Fig. 5.56

thickening in the c-direction which is normal to the plane of the paper. Figure 5.57 gives the molecular mass and supercooling-dependence of dendritic and single crystal growth. At the boundary between single-crystal lamellae and dendrites, one can find intermediate morphologies, such as single crystals or growth spirals with sharpened edges as shown in Fig. 3.81. On entering the area of dendritic growth, branches develop which ultimately change to dendrites as seen in Fig. 3.82.

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Fig. 5.57

Fig. 5.58

Figure 5.58 represents a polyethylene dendrite still floating in the solvent out of which it was grown (causing the reduced contrast). It reveals that dendrites do not grow flat, as the snow flakes of Fig. 5.1, but splay apart from a common center, the crystal nucleus. Only on settling on the microscope slide is the regular nature of the dendrite shown as seen in Fig. 5.56. Similar three-dimensional shapes are also found

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in single crystals with growth spirals due to the tent-like structure, illustrated in Fig. 5.53. Continued twinning is the ultimate cause of the growth of a dendrite, coupled with the creation of many growth spirals to thicken the crystal.

Hedgehog dendrites as shown in Fig. 5.59 are a special class of dendrites. They lack the special symmetry between the branches of the dendrites in Fig. 5.56. An explanation is their start from heterogeneous nuclei, described Sect. 3.5. Indeed, nucleating material added to the solution was found to reside in the center of the hedgehog dendrites. The regular dendrites of Fig. 5.56 grow from an initial, small single crystal that cannot keep straight growth surfaces because of the fast crystal growth. Observing crystal morphology may thus reveal the type of nucleation.

Fig. 5.59

Fast growth of crystals from the melt produces spherulites, as shown schematically in Figs. 3.55–57 and illustrated by the micrograph in Fig. 5.60. In most of these spherulites one expects also a dendritic morphology. The high polymer concentration in the melt, however, hinders the separation of the branches. The birefringence of the polymer crystals gives the spherulites their characteristic appearance under the polarizing microscope illustrated in Fig. 5.60. The birefringence and polarizing microscopy are discussed in Appendix 15. Although the spherulites look like solid spheres that grow from a nucleus in the center, one finds that the polymer molecules within and between the spherulites are only partially crystalline. The link to nucleation kinetics is given by the shape of the interfaces between adjacent spherulites as they grow. Details of spherulitic crystallization kinetics are discussed in Sect. 3.6.5 using the Avrami treatment.

The two sketches in Fig. 5.61 illustrate different paths to a spherulitic crystal morphology. These paths create a spherical overall appearance, despite the fact that the basic crystals are polyhedra, i.e., the spherulites are aggregates of polyhedral

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Fig. 5.60

Fig. 5.61

crystals or dendrites growing out of a common nucleus. Hedgehog spherulites are found, for example, in crystalline selenium as shown in the electron micrograph of Fig. 5.62. The crystal structure is shown in Fig. 5.20.

During the preparation for electron microscopy the heterogeneous (?) nucleus in the center was not replicated and is missing from the fracture surface. The molecules

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subsequent thickening due to the growth spirals splays the lamellae apart, so that ultimately a spherical crystal growth front results. Compare the length scale to that of Fig. 5.60 to judge that the eyes in the center of the spherulite cannot be visible by optical microscopy. They will, in time, fill with less-well arranged lamellae.

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

Fig. 5.64

alternation of circular interference rings inside the spherulite, as can also be seen in optical micrographs such as Fig. 5.60. One can see from the lamellar orientation that the molecular chains are aligned tangentially to the spherulite surface. Observation of the birefringence of the spherulites under the optical microscope can similarly establish the orientation of the molecules within the spherulites.

The analysis of melt-grown crystals is often difficult because a large part of the semicrystalline polymers is made up of the amorphous material that does not show any structure under the polarizing microscope (see Appendix 15). Poly(ethylene terephthalate) is a typical example. Its crystal morphology becomes visible only after the amorphous phase is etched away by hydrolysis as described in Sect. 3.4.5 and Fig. 3.52. The crystals hydrolyze more slowly and, thus, remain for analysis when most or all of the amorphous polymer segments are etched away. The morphology of the remaining debris from melt-crystallized poly(ethylene terephthalate) is shown in Fig. 5.65. Another method of analysis involves the staining of the noncrystalline molecules. Above the glass transition temperature, heavy metal compounds, such as involving of Os, Ru, can still diffuse into the amorphous areas of the polymer and make them opaque to electrons and outline the crystals which are more transparent to the electrons.

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Fig. 5.65

5.2.6 Fibers

A different, frequent crystal morphology of flexible, linear macromolecules is that found in fibrils, as shown in Fig. 5.41. The fibers are usually drawn from prior crystallized lamellae, or from the amorphous state in form of a melt, gel, or solution. Most progress has been made in the analysis of fibers grown from solution in a flowfield that continuously stretches the long molecules by extensive flow as described in Sect. 5.6. Figure 5.66 shows, as an example, polyethylene fibers grown by stirring a solution of the polymer. The fibers have a so-called shish-kebab, double morphology. The name originates from the Turkish, sis = skewer, and kebab = mutton. The fibers consist of two components, fibrillar, extended-chain (defect) crystals are coupled with an overgrowth of lamellae. The shish of the structure is made up of the fraction of the polymer of the highest molar mass which is most susceptible to extension, as is discussed further in Sect. 5.6. The kebabs are lamellae that nucleate subsequently on the shish at more or less regular distances and grow into the double morphology. Both parts are joint to an integral structure and can change in proportion, depending on the amount of flow, the molar-mass distribution, concentration, and the temperature of crystallization.

Figure 5.67 illustrates that the ends of the fibers are often tapered. This special structure is an indication that growth in the fiber direction seems to occur by long molecules caught on the fiber surface which are then smoothed by the flow past the fiber and give rise to the longitudinal growth.

Fibers drawn from prior grown lamellar crystals must undergo a major rearrangement of the morphology on drawing. This mechanism is discussed with the properties of the defects in crystals in Sect. 5.3.

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Fig. 5.66

Fig. 5.67

Details of the structure of fibers grown from the melt have been derived from an X-ray fiber analysis for the example of poly(ethylene terephthalate) [23–25]. The basic X-ray scattering technique is summarized in Appendix 16. The full-pattern fiber analysis used in this analysis, the Rietveld method, is given in [26]. The triclinic crystal structure of poly(ethylene terephthalate) is illustrated in Fig. 5.68. The unit cell

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Fig. 5.70

Fig. 5.71

The crystal diffraction-pattern in Fig. 5.70 was computed from the observed pattern in Fig. 5.69 by fitting the structure of the crystal in Fig. 5.68 considering all possible defects. An additional, third phase must be present as shown by Fig. 5.72. The third phase has the character of a liquid-crystalline mesophase and determines much of the fiber properties, as discussed in Sect. 5.3.6 with Figs. 5.113–115.