Fiber period

Typical snapshots and the structure functions at 350 K are shown in Fig. 39. In the initial state at 0.1 ns, we see two intense peaks on the meridian at q = 52 nm-1 and on the equator q = 14 nm-1, where the peaks correspond to half the fiber period of PE and the nearest neighbor inter-chain... 

Senti and Witnauer206 have reported studies on the fiber diagrams from various alkali-amyloses. Specimens were obtained by deacetylating clamped specimens of amylose acetate with the appropriate alkali. The positions of the alkali ions and the lateral packing of the amylose chains were determined with the aid of Patterson projections. In the A - and B -modifica-tions, the fiber period was 22.6 A. (extension of 6 D-glucose units), whilst in the V -modification it was 8.0 A. These authors have also studied in detail the addition compounds of amylose and inorganic salts with special reference to the structure of the potassium bromide-amylose compound.206 Oriented alkali fibers were treated with the appropriate salt solution. Stoichiometric compounds were formed. The x-ray patterns from these showed that the addition compounds with potassium salts crystallized in... 

The crystal structures of C2Ht—CO copolymers with QH4/CO ratios of 1, 1.3, 2.2 and 3.5 have been determined49,50). For the 1 1 copolymer an orthorhombic unit cell of dimensions a = 7.97, b = 4.76, c (fiber axis) = 7.57 A was observed 49). The main chain had a planar zigzag form. For copolymers with higher C2Ht contents, the fiber periods were essentially identical with that of polyethylene (c 2.54 A) 50). Also, the higher the C2H content, the shorter the a axis and longer the b axis. 

Figure 4. Three-dimensional closed surface for possible conformations of the skeletal chain of polyfethylene oxybenzoate) with the (2/1) helical symmetry and a fiber period of 15.60 A (4)...

In the fiber diagram, spots corresponding to a long fiber period (35 A) were observed, in addition to the lines corresponding to 8.8 A. The structure analysis is in progress but a very complicated molecular and a crystal structure is anticipated. 

The fiber period of 5.79 A for (C) together with the results of a conformational study and the values of its intensity pointed to a triple-stranded 6/1 helical structure with P63 symmetry... 

Fig. 5.7 Macroscopic damage modes that occur during the tensile and flexural creep of fiber-reinforced ceramics. It is assumed that matrix or fiber damage is avoided during initial application of the creep load (see discussion of loading rate effects in the next section). Periodic fiber fracture can occur if the creep rate of the matrix exceeds that of the fibers. Periodic matrix fracture is common when the matrix has a higher creep resistance than the fibers. In this figure, it is assumed that initial microstructural damage is avoided during application of the creep load.

Some special attention should be placed on the p (bulk) phase as well. Although this form is often reported as being non-crystalline, it gives rise to sharp Bragg reflections commensurate with lamellar order with a long period of 12.3 A [74] and fiber periodicity of 16.6 A (which corresponds to two monomer units) [67]. Thus, it differs from real crystals in the sense that it is mesomorphic. This phase also includes the presence of absorbed solvent and may be obtained by extended exposure to solvent vapor or solvent (cf., the solvent section). In particular, it has been found to appear as an intermediate step in the transformation from the solvent induced clathrate-like structure to the solvent-free well-ordered a phase [74], The a and fi (bulk) phases may coexist and are closed related to one another but are still structurally incompatible. 

Kakudo and Kasai have summarized the central problem well ( ) "There are generally less than 100 independently observable diffractions for all layer lines in the x-ray diagram of a fibrous polymer. This clearly imposes limitations on the precision which can be achieved in polymer structure analysis, especially in comparison with the 2000 or more diffractions observable for ordinary single crystals. However, the molecular chains of the high polymer usually possess some symmetry of their own, and it is often possible to devise a structural model of the molecular chain to interpret the fiber period in terms of the chemical composition by comparison with similar or homologous substances of known structure. Structural information from methods other than x-ray diffraction (e.g., infrared and NMR spectroscopy) are also sometimes helpful in devising a structural model of the molecular chain. The majority of the structural analyses which have so far been performed are based on models derived in this way. This is, of course, a trial and error method". Similar perspectives have been presented by Arnott ( ), Atkins ( ), and Tadokoro... 

X-Ray diffraction observations of E-V powders and fibers showed an expansion of the unit-cell basal plane, mainly in the a-direction, and a constant fiber period, respectively, as their chlorine content increased. Together these observations indicate that at least some V units, with their attendant Cl atoms, are incorporated into the crystals, resulting in an increase in interchain separation, but no alteration in the M-trans, planar zigzag conformation found for crystalline PE. 

Here only the results of the structure analyses are presented. Table II shows the crystal data of the two hydrates. Both phases crystallize into the monoclinic system of space group C2/c. There are eight monomeric units and twelve water molecules (the mole ratio is 1/1.5) in the sesquihydrate unit cell, and four monomeric units and eight water molecules (the mole ratio is 1/2) in the dihydrate unit cell. The theoretical values of water content of the crystal lattices are 38.6 wt. for the sesquihydrate and 5-5 wt. for the dihydrate, and these values are accordance well with the observed water contents for a whole sample, ca. i+0 wt.% and more than 5 wt., respectively (Table l). The fiber period is 7.36 A in both hydrates, which corresponds to the length of two monomeric units taking the planar zigzag conformation. 

It has been shown (46) that PTT has a very low theoretical crystal modulus, 2.59 GPa (375, 550 psi), compared to 107 GPa (1.55 x 10 psi) of PET (47) because of PTT s highly contracted helical-like conformation, whereas PET chain is fully extended with trans conformation. When a PTT fiber is stretched in situ in a waxd, the fiber period, measured from the Bragg d-spacing, increases immediately and is proportional to the applied strain up to 4% strain before deviating from affine deformation (48). Up to this critical strain the crystal deformation is reversible. The response of microscopic crystalline chains to macroscopic deformation explains why PTT has the best elastic recovery among the three aromatic polyesters. Further, PTT s elastic recovery and permanent set are nearly the same as nylon-6,6 up to 30% strain (25). 

In most cases, structural analysis of polymer crystals is carried out using uniaxially oriented samples (fibers or films). The basic procedures include (1) determination of the fiber period (2) indexing (hkl) diffractions and determining the unit cell parameters (5) determination of the space group symmetry (4) structural analysis and (5) Fourier transforms and syntheses and Patterson functions. The first three aspects of the procedure are discussed here, and the last two aspects are left for further references. 

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