Fiber-diagram

The value of the angle of tilting of the texture can be determined from the analysis of x-ray fiber diagrams. As Urbanczyk noted [18], the position of layer reflexes oil and ill or the position of equatorial reflexes 010 and 100 can be analyzed. In the first case, the tilting angle of the texture (v ) can be determined from the equation ... 

Figure 8.16. Demonstration of projections in a fiber diagram. In a projection on the 5 3-axis , intensity is integrated over horizontal planes. In a projection on the 512-plane , intensity is integrated along the vertical lines... 

Thus every reflection in the fiber diagram is defined by one function fj (u, uoj, uwj) and four quadrant functions. If the model shall be fitted to a scattering pattern in which the fiber is tilted with respect to the primary beam, weighting factors are attached to each of the quadrant functions. After the fit of an experimental scattering image, the found factors quantify the tilt, and the corresponding distortion of the scattering pattern can be eliminated. 

To clarify the tacticity problem, trans-l,4-hexadiene and 5-methyl-l,4-hexadiene polymers were examined by X-ray diffraction. Fiber diagrams were obtained from samples stretched to four times their original lengths. Eight reflections from the poly(trans-1,4-hexadiene) fiber pattern may be interpreted on the0basis of a pseudo-orthorhombic unit cell with a = 20.81 + 0.05 A b =... 

Figure 6. X-ray fiber diagram of poly(5-methyl-1,4-hexadiene) prepared with a Etj,AlCl/S-TiCl, catalyst at 0°C in pentane solvent. Compression molded sample cold drawn to four times its original length.

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... 

Sisson has traced the evolution of current concepts of the crystalline part of cellulose structures. The fiber diagram obtained by X-ray diffraction is now known to be produced by a series of elementary crystals, called crystallites, which have a definite arrangement with respect to the fiber axis. It is also known that the crystallites in regenerated cellulose may be oriented to varying degrees with respect to the fiber axis and that the crystallites in regenerated cellulose and mercerized cotton differ from those in native fibers. These hydrate type crystallites appear to be more reactive chemically than the native type. 

The variations resulting from the above methods are not complete without mentioning one added complication—the differences in x-ray intensity data sets obtained by different investigators. As shown in Fig. 1, a typical x-ray fiber diagram contains many overlapping diffraction maxima whose intensities should be resolved into as many individual components as is possible, for increased precision of analysis. Because of varying methods... 

According to the expts of Andress (Ref 5) the composition of the Knecht compound after being kept under reduced press for some time should be denoted by the formula 2C6H 0Os.HNO3. He demonstrated that the compound produces a characteristic X-ray fiber diagram... 

The primary difficulty in diffractometric studies of polymeric materials in general is that the number of reflections recorded in a fiber diagram is usually less than 100 (15). This is in contrast with observation of 1000-2000 reflections in a typical study of the structure of a small... 

Figure 4. X-ray fiber diagrams of ethoxy-substituted, hexamethylene-spacer poly(ester). a, Before magnetic alignment b, after magnetic alignment and c, fiber. Sample-to-film distance, 4.7 cm.

Figure 5. Optical textures corresponding to Figures 4a and 4c fiber diagrams, a, Unaligned at 165 °C and b, fiber. Original magnification, 320 x.

There has been no report of oriented crystalline syndiotactic PMMA so far as the author knows. The author and his coworkers (39) found that oriented crystalline samples of syndiotactic PMMA can be obtained by adsorption of various solvents such as chloro-acetone and diethyl ketone. Figure 8 shows the x-ray diagrams. When the polymer is cast from chloroform solution and is stretched in hot water at 80°C, the sample is noncrystalline as shown in Figure 8. By adsorption of the solvent the fiber diagram can be... 

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. 

Crystal Volume calculated from the 010 - 100 and 105 line-breadth (5) Intensity of the S A X S diagrams, in arbitrary units, and expressed compared to the intensity R of the initial (8% shrinkage) fiber diagram. 

Single crystals for electron micrography and diffraction were obtained by dissolution of the polymer in nitrobenzene at 170°C followed by filtration. The solution was slowly cooled to 134°C and kept at this temperature for 12 h. The polymer that had crystallized was filtered and redissolved in nitrobenzene at 170°C, cooled to 139°C then very slowly to 136°C, kept at this temperature for 24 h and cooled to room temperature leaving the polymer single crystals in suspension in nitrobenzene. A total of 25 reflections could be observed on the electron dif-fractogram (hkO section) of this material. This was an improvement over the X-ray fiber diagram since only five reflections had been recorded on the equator (see Table I). 

The d-values of the electron diffractogram allowed us to fully index the X-ray fiber diagram using a triclinic unit cell. Without the electron diffraction reciprocal cell parameters (a, b, Y ) the task of indexing the fiber diagram would have been more difficult because of the paucity of hkO reflections on the equator. 

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