The Unit Cell of Crystalline Polymers

When polymers are crystallized in the bulk state, the individual crystallites are microscopic or even submicroscopic in size. They are an integral part of the solids and cannot be isolated. Hence studies on crystalline polymers in the 

It was only in 1957 that Keller (19) and others discovered a method of preparing single crystals from very dilute solutions by slow precipitation. These too were microscopic in size (see Section 6.4). However, X-ray studies could now be carried out on single crystals, with concomitant increases in detail obtainable. 

Of course a major difference between polymers and low-molecular-weight compounds relates to the very existence of the macromolecule s long chains. These long chains traverse many unit cells. Their initial entangled nature impedes their motion, however, and leaves regions that are amorphous. Even the crystalline portions may be less than perfectly ordered. 

This section describes the structure of the unit cell in polymers, principally as determined by X-ray analysis. The following sections describe the structure and morphology of single crystals, bulk crystallized crystallites, and spherulites and develops the kinetics and thermodynamics of crystallization. 

One of the most important polymers to be studied is polyethylene. It is the simplest of the polyolefins, those polymers consisting only of carbon and hydrogen, and polymerized through a double bond. Because of its simple structure, it has served as a model polymer in many laboratories. Also polyethylene s great commercial importance as a crystalline plastic has made the results immediately usable. It has been investigated both in the bulk and in the single-crystal state. 

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Crystallinity in polymers was first observed by X-Ray Diffraction even before these materials were understood to be polymers. Prominent examples were polysaccharides, especially cellulose (Herzog et al. 1920) and stretched natural rubber (Katz 1925). This was before Staudinger s macromolecular concept was widely accepted (Morawetz 1995). By the time synthetic crystalline polymers such as polyethylene (in 1933) and nylons (in 1935) were developed, it was generally acknowledged that the unit cell of a polymer crystal was based on repeating monomer units, rather than on the whole molecules. 

Polymers invariably form helical structures, and the helix symmetry is denoted by u, indicating that there are u repeat units in V turns of the helix. The helix pitch is denoted by P and the molecular repeat distance is c = vP. X-ray diffraction patterns from non-crystalline specimens contain diffracted intensities restricted to layer lines that are spaced by 1/c. On a diffraction pattern from a polycrystalline specimen, diffraction signals, or Bragg reflections, occur only at discrete positions on the layer lines, the positions being related to the lateral dimensions of the unit cell of the crystal. The meridian (vertical axis) of the diffraction pattern is devoid of diffracted intensity unless the layer line number J, is a multiple of u, so that u can be determined straightforwardly. The diffracted intensities can be calculated using standard expressions (2), for model structures (i.e. given the atomic coordinates). 

In fibres of some polymers, made under certain conditions, the crystalline regions are found to be tilted with respect to the fibre axis in a well-defined crystallographic direction. This is a very valuable feature, because the diffraction patterns of specimens in which this type of orientation occurs are of precisely the same form as tilted crystal diffraction patterns of single crystals rotated round a direction inclined to a principal axis. The unit cell cannot be obtained directly, for 90° oscillation tilted crystal photographs are required for direct interpretation, but unit cells obtained by trial can be checked by the displacements of diffraction spots from the layer lines this is a severe check, and consistent displacements would leave no doubt of the correctness of a unit cell. This procedure played an effective part in the determination of the unit cell of polyethylene terephthalate (Daubeny, Bunn, and Brown, 1954). 

Polymers can be either amorphous or semicrystalline in structure. The structure of amorphous materials cannot be described in terms of repeating unit cells such as that of crystalline materials because of nonperiodicity, the unit cell of an amorphous material would comprise all atoms. The physics and chemistry of the amorphous state remain poorly understood in many aspects. Although numerous experiments and theoretical studies have been performed, many of the amorphous-state features remain unexplained and others are controversial. One such controversial problem is the nature of glass-liquid transition. 

PVF, exhibits four crystalline forms, denoted a, jS, y, and 6 [89]. In each ca.se the unit cell contains two polymer chain segments, but the molecular conformations differ. The (3 phase is the one of greatest interest, as it is ferroelectric. The strong dipole of the unit cell is a consequence of the all-trans conformation (Fig. 38) of... 

When the structural features of crystalline polymers are examined beyond the level of the unit cell, it is very important that their semi-crystalline character... 

Let us now briefly mention the important applications of WAXS in polymer physics. We have already presented a whole range of applications in Chapters 6, 7 and 9. First of all, WAXS provides direct evidence of the physical structure. The polymer can be considered as semicrystalline provided that sharp Bragg reflections are observed. A diffuse scattering pattern indicates that only short-range order is present. The polymer is probably fully amorphous. However, it is possible that it is liquid-crystalline with a nematic mesomorphism (see Chapter 6). WAXS is the standard method for the assessment of crystallinity. Details of the different X-ray methods used to determine crystallinity are presented in Chapter 7. X-ray diffraction is the major tool used in crystallographic work. The assessment of the unit cell of polymers with unknown crystal structure, and... 

Commercial ETFE is an equimolar copolymer of ethylene and tetrafluoroethylene (1 1 ratio) and is isomeric with polyvinylidene fluoride. ETFE has a higher melting point than PVDF and a lower dissipation fac-torl l because of its special chain conformation. Crystalline density was 1.9 g/cm for a polymer containing 12% head-to-head defect, The unit cell of the crystal is expected to be orthorhombic or monoclinic with cell dimensions of a = 0.96 nm, b = 0.925 nm, c = 0.50 nm and 7= 96°. 

For theoretical purposes, just as with any other substances, the vibrational modes of crystalline polymers may be considered in terms of their unit cell and the symmetry associated with this cell. The number of atoms in the unit cell determines the maximum number of fundamental vibrations that may occur,... 

Polyethylene is by far the most studied linear high polymer. Its repeating unit is CHg, so that all subsequent data on heat capacities refer to 14.03 g of the polymer. In the crystalline state, planar zig-zag chains of polyethylene extend through the whole crystal. The unit cell of the CHg repeating units is orthorhombic with the 30 C parameters ... 

Poly(vinyl fluoride) [24981-14-4] (PVF) is a semicrystaltiae polymer with a planar, zig-zag configuration (50). The degree of crystallinity can vary significantly from 20—60% (51) and is thought to be primarily a function of defect stmctures. Wide-line nmr and x-ray diffraction studies show the unit cell to contain two monomer units and have the dimensions of a = 0.857 nm, b = 0.495 nm, and c = 0.252 nm (52). Similarity to the phase I crystal form of poly (vinytidene fluoride) suggests an orthorhombic crystal (53). 

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