Repeat distance

The c axis corresponds to both the short axis of the crystal and the axis along the molecular chain. The observed repeat distance in the c direction is what would be expected between successive substituents on a fully extended hydrocarbon chain with normal bond lengths and angles (see Sec. 1.2). 

Fig. 2. The steric protection of the carbon backbone by fluorine of a polytetrafluoroethylene chain. The hehcal configuration with a repeat distance of 1.68...

Crystal Structure. The crystal stmcture of PVDC is fairly well estabhshed. Several unit cells have been proposed (63). The unit cell contains four monomer units with two monomer units per repeat distance. The calculated density, 1.96 g/cm, is higher than the experimental values, which are 1.80—1.94 g/cm at 25°C, depending on the sample. This is usually the case with crystalline polymers because samples of 100% crystallinity usually cannot be obtained. A dkect calculation of the polymer density from volume changes during polymerization yields a value of 1.97 g/cm (64). If this value is correct, the unit cell densities may be low. 

The repeat distance along the chain axis (0.468 nm) is significantly less than that calculated for a planar zigzag stmcture. Therefore, the polymer must be in some other conformation (65—67). Based on k and Raman studies of PVDC single crystals and normal vibration analysis, the best conformation appears to be where the skeletal angle, is 120°, and the torsional of opposite sign) is 32.5°. This conformation is in... 

Unit cells of pure cellulose fall into five different classes, I—IV and x. This organization, with recent subclasses, is used here, but Cellulose x is not discussed because there has been no recent work on it. Crystalline complexes with alkaU (50), water (51), or amines (ethylenediamine, diaminopropane, and hydrazine) (52), and crystalline cellulose derivatives also exist. Those stmctures provide models for the interactions of various agents with cellulose, as well as additional information on the cellulose backbone itself. Usually, as shown in Eigure la, there are two residues in the repeated distance. However, in one of the alkah complexes (53), the backbone takes a three-fold hehcal shape. Nitrocellulose [9004-70-0] heUces have 2.5 residues per turn, with the repeat observed after two turns (54). 

X-ray studies indicate that the vinyl chloride polymer as normally prepared in commercial processes is substantially amorphous although some small amount of crystallinity (about 5% as measured by X-ray diffraction methods) is present. It has been reported by Fuller d in 1940 and Natta and Carradini in 1956 that examination of the crystalline zones indicates a repeat distance of 5.1 A which is consistent with a syndiotactic (i.e. alternating) structure. Later studies using NMR techniques indicate that conventional PVC is about 55% syndiotactic and the rest largely atactic in structure. 

FIGURE 17.14 The helical arrangement of actin monomers in F-actin. The F-actin helix has a pitch of 72 nm and a repeat distance of... 

Figure 8.16 Layer-plane sequence along the c-axis for graphite in various stage I -5 of alkali-metal graphite intercalation compounds. Comparison with Fig. 8.15 shows that the horizontal planes are being viewed diagonally across the figure. /,. is the interlayer repeat distance along the c-axis.

Chain metasilicates Si03 formed by comersharing of Si04 tetrahedra arc particularly prevalent in nature and many important minerals have this basic structural unit (cf, polyphosphates, p, 528), Despite the apparent simplieily of their structure motif and stoichiometry considerable structural diversity is encountered because of the differing conformations that can be adopted by the linked tetrahedra. As a result, the repeat distance along the c -axis can be (1). 

Figure 9.6 Schematic representation and exampies of various chain metasilicates (SiO with repeat distances (in pm) after i, 2,. 7. 9 or 12 tetrahedra (T), ((ht) high-temperature form (hp) high-pressure form].

Therefore, these synchrotron experiments show that the repeat distance for the smectic layer lies very close to, but is distinct from, that of the crystal. Moreover, the smectic peak disappears totally when the transformation is complete, indicating that the mesophase has been destroyed in the semicrystalline sample. 

Fig. 17.9 Sections of the V4O10 layers in Co(pyz)V40,o (a) and (Me4N)V40,o (b). Repeat distances of the apical oxygen atoms are labeled as dashed lines, which are a...

Figure 4.10 With increasing oxygen exposure at 295 K, the Mg(0001) surface consists of both hexagonal and square lattice structures the line profiles indicate repeat distances of 0.321 and 0.56 nm in the atom resolved hexagonal and square structures, respectively, the former being the most prevalent structure present. (Reproduced from Ref. 41).

Measurements of the streak separations yield the repeat distances of the guest molecules along the canal. These measurements have been made5), and the results generally correspond with the known length of the guest molecule in extended conformation. See also Section 6. 

Figure 25 Schematic dispersion relationships of the bands of an infinite linear Te chain (a) for an equidistant chain, (b) for an alternating chain with the repeating distance a and (c) for an alternating chain with a much smaller repeating distance a. The dotted line at EF represents the Fermi level...

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