Crystal structure polyethylene

The conformation of a polymer in its crystal will generally be that with the lowest energy consistent with regular placement of structural units in the unit cell. Helical conformations occur frequently in polymer crystals. Helices are characterized by a number fj where / is the number of monomer units per j number of complete turns of the helix. Thus, polyethylene could be characterized as a li helix in its unit cell with an -trans conformation. The arrangement of the molecules in the polyethylene crystal structure is illustrated in Fig. 2.8. 

Figure 9.4 Graphical diagram of polyethylene crystal structure.

The poly(ethylene terephthakte) analyzed was about 75% cr5retalline. The cr tal structure is triclinic with the moleculEu chains in an almost planar conformation. The poly(ethylene sebacate) was about 57% crystalline with a nomoclinic crystal structure with the molecular chains also in a planar conformation, in fact quite similar to the polyethylene crystal structure. The two repeating units, however, do not cocrystallize since the repeating unit lengths in the chain direction do not match. The copolymers thus show only poly(ethylene terephthalate) crystallinity. The 80/20 copolymer was about 22% crystalline, while the 60/40 copolymer was about 15% cr5retalline. 

The most widely studied crystalline polymer is polyethylene. The lowest-energy chain conformation of this macromolecule can be evaluated from considerations of the conformations of the n-butane molecule (Fig. 3.5). A series of all trans bonds produce the lowest-energy conformation in n-butane because of steric interactions and this is reflected in polyethylene where the most stable molecular conformation is the crystal with all trans bonds, i.e. the planar zig-zag. These molecules then pack into the orthorhombic unit cell given in Table 4.1. The arrangement of the molecules in the polyethylene crystal structure is illustrated in Fig. 4.5 with the polymer molecules lying parallel to the c axis. The molecules are held... 

Secondly, the ultimate properties of polymers are of continuous interest. Ultimate properties are the properties of ideal, defect free, structures. So far, for polymer crystals the ultimate elastic modulus and the ultimate tensile strength have not been calculated at an appropriate level. In particular, convergence as a function of basis set size has not been demonstrated, and most calculations have been applied to a single isolated chain rather than a three-dimensional polymer crystal. Using the Car-Parrinello method, we have been able to achieve basis set convergence for the elastic modulus of a three-dimensional infinite polyethylene crystal. These results will also be fliscussed. 

Polyethylene. The crystal structure of this polymer is essentially the same as those of linear alkanes containing 20-40 carbon atoms, and the values of Tjj and AHf j are what would be expected on the basis of an extrapolation from data on the alkanes. Since there are no chain substituents or intermolecular forces other than London forces in polyethylene, we shall compare other polymers to it as a reference substance. 

The polymers compared all have similar crystal structures but are different from polyethylene, which excludes the possibility for also including the latter in this series. Also note that the isotactic structure of these molecules permits crystallinity in the first place. With less regular microstructure, crystallization would not occur at all. 

Figure 4.10 Crystal structure of polyethylene (a) unit cell shown in relation to chains and (b) view of unit cell perpendicular to the chain axis. [Reprinted from C. W. Bunn, Fibers from Synthetic Polymers, R. Hill (Ed.), Elsevier, Amsterdam, 1953.]...

Figure 4.11 Electron micrographs of polyethylene crystals, (a) Dark-field illumination shows crystals to have a hollow pyramid structure. (Reprinted with permission from P. H. Geil, Polymer Single Crystals, Interscience, New York, 1963.) (b) Transmission micrograph in which contrast is enhanced by shadow casting [Reprinted with permission from D. H. Reneker and P. H. Geil, /. Appl. Phys. 31 1916 (I960).]...

The materials shown and described above were generally prepared from the nucleophilic phenoxide or alkoxide and the appropriate bromide. The syntheses of a variety of such compounds were detailed in a report which appeared in 1977. In the same report, complex stability and complexation kinetics are reported. Other, detailed studies, of a similar nature have recently appeared" . Vogtle and his collaborators have also demonstrated that solid complexes can be formed even from simple polyethylene glycol ethers . Crystal structures of such species are also available... 

Kashiwagi et al.10) determined the second moment anisotropy for the one-way drawn polyethylene terephthalate sheets discussed above. The three lattice sums S00, S2q and S4o were calculated from the crystal structure determination of Daubeny et al., the proton positions being calculated on the basis of known bond angles and lengths. The isotropic lattice sum S00 was adjusted to a value consistent with the measured isotropic second moment of 10.3G2. The values for P200, P220 etc. were then used to predict the optical anisotropy. The predicted refractive indices for the sheets of draw ratio 2 1 and 2.5 1 are shown in Fig. 10, together with the experimental... 

Figure 1.65 (a) Crystal structure of polyethylene unit cell shown in relation to chains, (b) View of unit cell perpendicular to chain axis. Reprinted, by permission, from Heimenz, P., Polymer Chemistry The Basic Concepts, p. 236. Copyright 1984 by Marcel Dekker, Inc. 

In semicrystalline polymers such as polyethylene, yielding involves significant disruption of the crystal structure. Slip occurs between the crystal lamellae, which slide by each other, and within the individual lamellae by a process comparable to glide in metallic crystals. The slip within the individual lamellae is the dominant process, and leads to molecular orientation, since the slip direction within the crystal is along the axis of the polymer molecule. As plastic flow continues, the slip direction rotates toward the tensile axis. Ultimately, the slip direction (molecular axis) coincides with the tensile axis, and the polymer is then oriented and resists further flow. The two slip processes continue to occur during plastic flow, but the lamellae and spherullites increasingly lose their identity and a new fibrillar structure is formed (see Figure 5.69). 

Isomorphism in copolyalkenamers was reported by Dall Asta, Motroni, and Carella (27). These copolymers may be considered as constituted by an unbranched polyethylene chain containing, at irregular intervals, fra s-intemal double bonds. It is known 28) that the crystal structure of the homo-fraws-polyalkenamers depends on the number of methylene groups existing between two subsequent double bonds the odd series crystallizes in an orthorhombic unit cell, similar to that of... 

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