Diffraction from uniaxially oriented specimen

Figure 5. Diffraction from an uniaxially oriented specimen of stretched calf thymus DNA (courtesy M. H. F. Wilkins). The molecules are approximately 14, helices with c = 10.6 nm. The Bragg reflections on the equator can be indexed on the basis of a rhombic net with a = b = 2.30 nm.

Figure 4.29. Diffraction from a uniaxially oriented specimen.

Therefore, uniaxially oriented samples should be prepared for this purpose, which give so-called fiber pattern in X-ray diffraction. The diffraction intensities from the PPX specimen of P-form, which had been elongated 6 times at 285°C, were measured by an ordinary photographic method. The reflections were indexed on the basis of the lattice constants a=ft=2.052nm, c(chain axis)=0.655nm, a=P=90°, and y=120°. Inseparable reflections were used in the lump in the computation by the least square method. 

The structure of the crystalline regions of polymers can be deduced from wide-angle X-ray diffraction patterns of highly stretched specimens. When the stretching is uniaxial the patterns are related to those obtained from fully oriented single crystals. The crystal structure of polyethylene was determined by Bunn [7] as long ago as 1939 (Figure 1.10). 

Figure 9 shows the uniaxial orientation distribution functions qjiCp 0), determined from X-ray diffraction measurement, for a high-density polyethylene specimen stretched to an extension ratio of 1.4. Twelve different 7th reciprocal lattice vectors were observed. With qjiCp 0) for7 = 1 to 12, the coefficients Qj were calculated from equation (9) for any higher orders of I, and then the coefficients Wion were calculated from the simultaneous equations of equation (11) with respect to 7 by the weighted least-square method up to /= 18. 

---