Thermal Analysis of Polymeric Materials

508 5 Structure and Properties of Materials

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5.2.7 Isometric Crystals

To obtain isometric crystals as described in Fig. 5.41, one must restrict the width of the thin lamellae. This is illustrated in Fig. 5.74 with single-molecule single crystals grown from droplets of a very dilute solution of poly(oxyethylene) in benzene. Each of the crystals contains only one molecule [27]. The poly(oxyethylene) was of a broad

Fig. 5.74

molar-mass distribution with a viscosity average of 2.2×106 Da. The mass-estimates of the crystal shapes in Fig. 5.74 agree well with the molar-mass distribution and the electron-diffraction pattern of a single crystal in the upper left of Fig. 5.74 proves the single-crystal structure. Details of the crystal morphology correspond to the description of Fig. 5.55 [28].

On fast cooling of melts, one approaches isometric crystals of nanophase dimensions with the fringed-micellar macroconformations displayed Fig. 5.42. Similar structures are also obtained in poorly crystallized fibers. Figure 5.75 illustrates the close-to-isometric, but small fringed-micellar crystals for cellulose from rayon fibers. This figure is in contrast to the crystals of the native cotton fibers of Fig. 5.73 which are much larger and show for their larger crystals an acicular rather than an isometric morphology (see Fig. 5.41).

Extended-chain crystals of large size are seen in Fig. 5.76, an electron micrograph of a surface replica of polyethylene [29–31] Their morphology is still lamellar, or better called platy when using the nomenclature of Fig. 5.41. The plates and lamellae have a broad distribution of thickness. The chains run parallel to the major striations seen. In the largest lamella, the chain extension is macroscopic, almost 2 m, which equals a molar mass of 225,000 Da. Crystals of such magnitude are large enough to be considered equilibrium crystals. The smaller lamellae grew at a later time. To

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Fig. 5.75

Fig. 5.76

some degree they have a lower molecular mass, as will be discussed in Sect. 7.1. Intersections between two extended-chain lamellae are shown in Fig. 5.77. They are common features. From the narrowing at the center of such intersections it was concluded that the plates grew first as thin lamellae and then extended on annealing, as discussed in Sect. 5.2.3. The conditions of growth of these extended-chain crystals

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it was grown from a monomeric single crystal without ever leaving the crystal constraint in a topotactic polymerization, a crystallization during polymerization (see also Sect. 3.6.7, Fig. 3.104 and Sect. 5.2.2). One can see from the chemical structure that the monomer has most of its bulk in the side chains, so that the crystals of monomer and polymer change little in volume on polymerization and can be isomorphous (see Sect. 5.4.10). Of special interest in this crystal are its optical and electrical properties.

Large domains of macroscopic order can also be produced by amorphous liquids, as is illustrated in Fig. 5.79 for an amphiphilic block copolymer. Such large-domain structures are illustrated in Figs. 5.38–40, and are discussed in Sect. 7.1.6. The driving force to produce this liquid-crystalline-like structure is the need to collect the junction points between the blocks in well-defined surfaces of minimal area.

Fig. 5.79

5.3 Defects in Polymer Crystals

In this section it will be shown that many properties of crystalline materials do not have a simple correlation to the ideal crystal structure, as described in Sect. 5.1. Rather, minor microscopic defects may have a major influence on the material’s properties. For example, if one calculates the strength of a crystal by assuming that failure occurs when all bonds across a chosen surface break, one is usually wrong by a factor of 100 to 1,000. For crystals other than macromolecules, the knowledge about the importance of the defect structure and the details of the mechanisms involving microscopic defects was developed starting in the 1930s. For polymer crystals, this understanding is still in its beginning.

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5.3.1 Materials Properties

To understand the importance of defects in polymer crystals, one must distinguish structure-insensitive properties from structure-sensitive properties. For crystals of small molecules and rigid macromolecules (see Fig. 1.6), the structure-insensitive properties often can be derived directly from the ideal crystal structure as summarized in Fig. 5.80. The density, for example, can be calculated from the unit cell dimensions (see Sect. 5.1). The polymeric materials in form of flexible macromolecules are, in

Fig. 5.80

contrast, usually semicrystalline and their structure-insensitive properties are given by the sum of contributions from the crystalline and amorphous phases, using an appropriate crystallinity parameter. Figure 5.80 illustrates how to calculate the weight fraction crystallinity, wc, from the volumes of the assumed two phases. The corresponding volume fraction crystallinity, vc, is derived in Fig. 3.84. The correlation between both can easily be derived to be wc = ( c/ )vc. Many structure-insensitive properties can, in turn, serve to find the weight-fraction or volume-fraction crystallinity, as is shown in Sect. 5.3.2.

Several structure-sensitive properties are listed at the bottom of Fig. 5.80. They need, in contrast to structure-insensitive properties, a detailed defect mechanism to be understood, as is discussed in Sects. 5.3.3 6. The structure-sensitive properties are at the center of most of the important material properties.

5.3.2 Crystallinity Analysis

To determine the crystallinity of a sample, many structure-insensitive properties can be used, since they can be separated into contributions from the amorphous and the crystalline phase. Three examples are given in this section: X-ray, infrared, and

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calorimetric analyses. The calculation of crystallinity from dilatometry (see Sect. 4.1) is already given in Fig. 5.80.

Figure 5.81 shows an X-ray diffraction pattern for polyethylene. The separate contributions from the amorphous and crystalline parts of the fiber are clearly visible and have to be quantitatively separated. The equation given in Fig. 5.81 is the Bragg equation that links diffraction angle and wavelength of the X-rays to the crystal-plane

Fig. 5.81

separations, as described in Appendix 16. To separate the amorphous scattering from the crystalline, the properly integrated intensities must be compared. The total diffraction intensity of a given sample mass is constant, but not so easy to assess because diffraction into all angles must be considered. An often used approximate technique is illustrated in Fig. 5.82 for polypropylene crystallized from the melt. The separation of the amorphous and crystalline X-ray scattering over a limited diffractionangle range is chosen as indicated. Although only a part of the range of scattering angles is used for the analysis, a crystallinity can be deduced, once the calibration constant k in the boxed equation is evaluated. A plot of areas in the diffraction diagram versus specific volumes for different polyethylenes is given in Fig. 5.83. It yields proper crystalline and amorphous specific volumes at 100% and zero crystallinity, indicating the validity of the analysis. The density of the crystal is known from its structure, as discussed in Sect. 5.1, and the amorphous density is available by extrapolation of dilatometric data from the melt at temperatures above the glass transition. For oriented samples this process is not as easy to carry out because of difficulties in the accounting for all scattering intensities. Similarly, when a third, an intermediate phase is present, one needs to introduce different techniques to explain even the structure-insensitive properties. The Figs. 5.69–72 show such a three-phase separation for fibers of poly(ethylene terephthalate).

514 5 Structure and Properties of Materials

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Fig. 5.82

Fig. 5.83

A technique that leads to quantitative data for the determination of the volumefraction crystallinity is the infrared analysis. As an example, in Fig. 5.84 one can see the two areas in the IR spectrum of polyethylene where amorphous and crystalline samples are largely different (frequencies A and C). The equation in the upper righthand corner permits now a quantitative evaluation, as is documented in Fig. 5.85 for

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Fig. 5.84

Fig. 5.85

a number of bulk samples of different crystallization history. By plotting the ratio I/Io versus the density, a straight line results. Again, the extrapolation to fully crystalline and amorphous samples yields the expected densities, suggesting an internal consistency of the two-phase or crystallinity model for the structure-insensitive properties of bulk polyethylene.