Orthorhombic unit cells

Table 3. X-ray powder data for Rhp4 (Debye-Scherrer data, CuK radiation from a graphite monochromator. Unit cell orthorhombic a, 9 71(2) b, 9-05(2) c, 5-63(1) (A) V, 495 (A ), Z = 8, S.G.

The tetragonal system can also have species in the center of the unit cell. Orthorhombic crystals can have species in the center (body-centered), in all faces (face-centered), only in opposing faces (end-centered), or only at the corners (primitive). Monoclinic unit cells can be either primitive or end-centered, with species in one set of opposing faces. Triclinic, hexagonal, and trigonal unit cells are just primitive. 

Polyethylene exhibits three types of unit cells—orthorhombic, monoclinic, and hexagonal—all of which are relatively simple compared to other polyolefins and to polymers in general. The orthorhombic unit cell is by far the most common for all practical purposes it may be considered to be the only one present in eommereial samples. 

Fig. 4. Structure of orthorhombic polyethylene unit cell projected on the ab plane. The right-hand pictures define the setting angle .

The many commercially attractive properties of acetal resins are due in large part to the inherent high crystallinity of the base polymers. Values reported for percentage crystallinity (x ray, density) range from 60 to 77%. The lower values are typical of copolymer. Poly oxymethylene most commonly crystallizes in a hexagonal unit cell (9) with the polymer chains in a 9/5 helix (10,11). An orthorhombic unit cell has also been reported (9). The oxyethylene units in copolymers of trioxane and ethylene oxide can be incorporated in the crystal lattice (12). The nominal value of the melting point of homopolymer is 175°C, that of the copolymer is 165°C. Other thermal properties, which depend substantially on the crystallization or melting of the polymer, are Hsted in Table 1. See also reference 13. 

The equimolar copolymer of ethylene and tetrafluoroethylene is isomeric with poly(vinyhdene fluoride) but has a higher melting point (16,17) and a lower dielectric loss (18,19) (see Fluorine compounds, organic-poly(VINYLIDENE fluoride)). A copolymer with the degree of alternation of about 0.88 was used to study the stmcture (20). Its unit cell was determined by x-ray diffraction. Despite irregularities in the chain stmcture and low crystallinity, a unit cell and stmcture was derived that gave a calculated crystalline density of 1.9 g/cm. The unit cell is befleved to be orthorhombic or monoclinic (a = 0.96 nm, b = 0.925 nm, c = 0.50 nm 7 = 96%. 

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). 

The crystal stmcture of PPT is pseudo-orthorhombic (essentially monoclinic) with a = 0.785/nm b = 0.515/nm c (fiber axis) = 1.28/nm and d = 90°. The molecules are arranged in parallel hydrogen-bonded sheets. There are two chains in a unit cell and the theoretical crystal density is 1.48 g/cm. The observed fiber density is 1.45 g/cm. An interesting property of the dry jet-wet spun fibers is the lateral crystalline order. Based on electron microscopy studies of peeled sections of Kevlar-49, the supramolecular stmcture consists of radially oriented crystaUites. The fiber contains a pleated stmcture along the fiber axis, with a periodicity of 500—600 nm. 

Physical Properties. The absorption of x-rays by iodine has been studied and the iodine crystal stmcture deterrnined (12,13). Iodine crystallizes in the orthorhombic system and has a unit cell of eight atoms arranged as a symmetrical bipyramid. The cell constants at 18°C (14) are given in Table 1, along with other physical properties. Prom the interatomic distances of many iodine compounds, the calculated effective radius of the covalently bound iodine atom is 184 pm (15). 

Syndiotactic polypropylene also forms hehcal molecules however, each chain unit consists of four monomer units having a spacing of 0.74 nm. The unit cell is orthorhombic and contains 48 monomer units having a crystaHographic density of 0.91 g/cm (27). 

Aminophenol. This compound forms white plates when crystallized from water. The base is difficult to maintain in the free state and deteriorates rapidly under the influence of air to pink-purple oxidation products. The crystals exist in two forms. The a-form (from alcohol, water, or ethyl acetate) is the more stable and has an orthorhombic pyramidal stmcture containing four molecules per unit cell. It has a density of 1.290 g/cm (1.305 also quoted). The less stable P-form (from acetone) exists as acicular crystals that turn into the a-form on standing they are orthorhombic bipyramidal or pyramidal and have a hexamolecular unit (15,16,24) (see Tables 3—5). 

The PVC crystaUites are smaU, average 0.7 nm (3 monomer units), in the PVC chain direction, and are packed lateraUy to a somewhat greater extent (4.1 nm) (21,33). A model of the crystaUite is shown in Figure 6. The crystalline stmcture of PVC is found to be an orthorhombic system, made of syndiotactic stmctures, having two monomer units per unit cell and 1.44—1.53 specific gravity (34—37). 

For instance, in the three crystalline forms (a, 3, y) of i-PP the chains are always in the conformation of threefold helix (s(3/l)l symmetry) but are packed in different ways in monoclinic [24], hexagonal [25], and orthorhombic [26] unit cells, respectively. The X-ray diffraction spectra of unoriented samples in the crystalline forms a, P, y are reported in Fig. 6. 

This is, for instance, the case of the a and 5 forms of PVDF (also called form II and form lip, that is form II polarized), both contain chains with a TG+TG" conformation and have an orthorhombic unit cell with substantially identical dimensions [30, 31]. Detailed X-ray diffraction analyses have shown that the two chains in the unit cells are with the dipole vectors pointing in opposite directions in the a form, while they are in the same direction in the 8 form [32],... 

Two helices are packed antiparallel in the orthorhombic unit cell. Association of the helices occurs through a series of periodic carboxylate potassium water - carboxylate interactions. An axial projection of the unit-cell contents (Fig. 23b) shows that the helices and guest molecules are closely packed. This is the first crystal structure of a polysaccharide in which all the guest molecules in the unit cell, consistent with the measured fiber density, have been experimentally located from difference electron-density maps. The final / -value is 0.26 for 54 reflections, of which 43 are observed, and it is based on normal scattering factors.15... 

Two antiparallel helices, related by space group symmetry, are packed in an orthorhombic unit cell (Fig. 39b). There is substantial interdigitation between the helices so that side chains and main chains are linked by hydrogen bonds, such as 0-4E-0-4D (2,73 A) and 0-4D-0-3F (2.84 A) involving parallel and antiparallel strands, respectively. Plausible sites for sodium ions are near the... 

Fig. 39. (continued)—antiparallel packing arrangement of helices in the orthorhombic unit cell viewed down the c-axis shows considerable interdigitation. Hydrogen bonds (not shown) connect adjacent chains. 

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