Equatorial scattering

This equation is the Porod law for the large-angle tail of the scattering curve along the equatorial direction, which indicates that the equatorial scattered intensity I q is proportional to in the Porod... 

Celia, Lee and Hughes ( ) have studied the Lorentz correction for fibres in some detail they consider that the correction 2 sin 8cos0 is most appropriate for the equatorial scatter from a parallel bundle of fibres. 

When the direction of the external field is reversed, the scattering contours dis-fday a striking time dependent change accompanying the turn around of the molecular clusters. New equatorial scattering rqipears in both the Vh and the H, patterns. The intensity of the Vh transmission varies with time having two maxima (and one minimum), and these three limited intensities occur while the infra-red dichroic ratio at 3300 cm decreases and stays around its minimum value of about one in the cluster reversal process. It is true to say that when the direction of the molecular... 

SAXS pattern of radiation-polymerized PTOX in Figure 3A shows only a sharp equatorial scattering, but no meridional scattering. Those for PTOX obtained by plasma initiated polymerization (samples PTOX-20-1P and PTOX-40P shown in Figures 3B and 3C) are similar. In the case of PTEOX, those polymerized through radiation initiation but post-polymerized below 80°C (sample PTEOX-12)... 

Typical X-ray diffraction patterns of the equatorial scattering areas for spin-drawn fibers spun at draw ratios of 4 and 7 are shown in Fig. 6a and b. 

The diffuse scattering from oriented polymers exhibits dependence upon the equatorial scattering angle that principally reflects the orientation of the microvoids. Formally, these may be treated in terms of direction dependent correlation functions as discussed in Section 3.3.2. 

To get simultaneous SAXS and WAXS patterns, the WAXS could be monitored only in a limited range using a tilted detector. By using a horizontal tensile direction the vertically arranged WAXS detector monitors mainly the equatorial scattering of the sample. To follow also quick changes exclusively in the crystalline phase WAXS measurements were performed alternatively with the WAXS detector directly in the beam behind the sample and a sampling rate of 1 s. 

Fig. 5. Equatorial scattering intensity of undeformed iPP at room temperature and during strain hardening at elevated temperatures. The curves always show a projection of the angular range of 2 ° around the equatorial direction. Right WAXS-pattems, azimuthal angle vs. scattering angle 20 at three characteristic points imdeformed as well as immediately before failure at room temperature and 150 °C.

Fiber diagrams for three copolymer compositions are shown in fig. 1, and meridional 0/29 diffractometer scans for all five are shown in fig. 2. The data indicate that there is a high degree of axial orientation of the molecules in the fibers. The fiber diagrams show intense equatorial scatter at d-5.0-2.5A which contains some very sharp maxima equatorials at d=4.6 and 2.6A and an off-equatorial at d=3.3A. These data indicate that there is some three-dimensional order, but the diffuse equatorial scatter shows that much of the lateral packing is irregular. The question of the chain packing can only be addressed when we have a model for the chains themselves, which will be derived from the meridional data (fig. 2). 

The S AXS pattern of uniaxial extruded PBT films revealed a network of oriented fibrils with irregular cross sections, very similar to the structure found in fibers of the aramids [131], The diffuse equatorial scattering, also observed for example in cellulose fibers, is typical of fibers manufactured by wet-spinning and air-gap spinning processes. 

Figure 5.5 Calculated equatorial scatterings from an assembly of hard rods. Y axis is the intensity while X axis is the scattering vector 2qa. (a) Without structure factor and (b) with structure factor.

It is noteworthy that, for an oriented nematic liquid crystalline polymer, the equatorial scattering provides important information regarding the interchain correlation, while the meridional scattering represents the correlation along the chains, which in general is featureless in the experimental X-ray diffraction patterns. 

For the two-dimensional liquid, the scattering signature is similar to that of the nematic liquid crystalline polymers discussed in the previous section. It should have a diffuse equatorial scattering whose intensity is significantly lower than that of the meridional scatterings from the one-dimensional crystal. 

The second example is an alternative copolymer. It has a regular chain structure rather than being a random copolymer. The chemical structure of the second polymer is shown in Figure 5.19. The fiber pattern of this polymer is shown in Figure 5.20. Similar to the first polymer, the pattern shows a strong but diffuse equatorial scattering, which, as discussed previously, arises from the correlation... 

A remarkable study of the deformation behaviour of segmented PUs was conducted by Yeh and coworkers [51]. Yeh et al. concluded that disrupted hard domain lamellae and strain-induced aligned SS contribute to equatorial scattering in the low hard segmented (12 wt%) PUs, but the intensity may be decreased due to the lack of electron density contrast between the HS fibrils and the aligned SS chains and/or the decrease in coherent scattering due to the small size of the broken down lamellae [51, 284]. The contribution of various orientations (perpendicular, parallel, and at angle) of hard domain lamellae orientation was also probed by Lee et al, on the... 

Figure 3.18 shows a schematic representation of double-oriented-kebab strac-ture. Stacks of parent lamellae is responsible for meridional scattering the SAXS patterns, whereas stacks of daughter lamellae exhibited equatorial scattering. The equatorial scattering is attributed to the overlap of scattering from daughter lamellae and shish. 

The equatorial scattering spots in the SAXS pattern can be attributed to the growth of the kebab-like lamellar stractrrres normal to the flow direction, and the meridianal scattering streaks can be ascribed to the formation of shish parallel to the flow directiorr. ... 

Figure 2.1 shows SAXS patterns of PTeOX and PTOX. PT OX post-polymerized at a temperature below 70 °C indicates no meridional scattering, which is rimilar to that of PTOX obtained at 55 °C. On the otha- hand, PTgOX obtained over 80 °C shows clear meridional as well as equatorial scattering, and the spot-like scatterings also are observed outside the broad meridional scattering. 

Since it was reportedthat the diffuse equatorial scattering in SAXS is caused by the microvoids between the fibrillar crystals, the lamellar crystal formed from the partial melt may fill up the microvoids so that the diffuse scattering in the equatorial direction decreases. 

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