Peaks in SAXS Patterns

Peaks in SAXS patterns rest on a rapidly decaying background. Figure 8.7 shows an example for a typical isotropic bulk semicrystalline polymeric material. The long period of such data should never be determined from the peak maximum found in the... 

The indexing and relative peak intensities in SAXS patterns from Ae cubic phase are fit well by the I-WP model, but not by alternative models (161 ... 

Figure4.11 presents the macroscopic and nanoscopic strains in the irradiated volume of the samples as a function of elapsed time, s is the macroscopic strain as computed from the strain of the grid of fiducial marks on the samples. ,/( ) is a nanoscopic strain that is computed from the movement of the maximum position of the SAXS peak in the pattern 7(s). s ,cdf is a nanoscopic strain parameter computed from the movement of the maximum position of the long period peak in the CDF. Choosing this parameter we take the most probable long period for the average long period.

N2 adsorption-desorption isotherms revealed that MCs had hi surface area (>1200 m /g) and large pore volume (>1.0 cm /g). From SAXS patterns of the prepared materials, it was confirmed that pores of SBA-15 and CMK-3 retained highly ordered 2-dimensional hexagonal type arrangement [5], while MCM-48 had 3-dimensional cubic type pore structure. It should be noted that a new scattering peak of (110) appeared in the CMK-1 after the removal of MCM-48 template. Furthermore, the pore size of CMK-1 and the wall thickness of MCM-48 were found to be 2.4 nm and 1.3 nm, respectively. This result demonstrates that a systematic transformation of pore structure occurred during the replication process from MCM-48 to CMK-1 [6]. 

What is a peak Local intensity maxima or shoulders in scattering patterns are called peaks or reflections, in particular when they are sharp. In USAXS and SAXS even a broad shoulder is called a peak. The set of all peaks is named discrete scattering. 

Figure 8.36. SAXS pattern of a thermoplastic elastomer during straining. The thin horizontal line in the center is called an equatorial streak. In this case it is well-separated from the long-period peaks above and below... 

A comparison of the calculated relative peak heights using the very simplified electron density profiles of Figs. 23b and 23d with the SAXS pattern of the sample, Fig. 24, unequivocally indicates the presence of the non-centrosysmmetric lamellae structure depicted in Fig. 23a. In agreement with SCMF calculations [90], the centrosymmetric two-way arrangement (Fig. 23c) of A-B-C-A-C-B pattern was not observed. 

Fig. 2.16 Results obtained from an oscillatory shear experiment on an/ps = 0.103 PS-PEP diblock (Okamoto et al. 1994a). (a) SAXS patterns obtained at four representative strain phases as shown in (b) (c) a model showing (110) and (110) planes that give rise to the four diffraction peaks in (a). The pattern at each phase was obtained by integrating over [ A + 0 A + 0,-], where 0 = 0, id2, ittH and A = 0.194tt. Each pattern represents an average over 80 strain cycles.

Fig. 5.17 SAXS patterns for PEQwPBO.w showing (a) the ordered melt structure (T = 90 °C) (b) a metastable structure at T = 42 °C (c) the equilibrium once-folded structure grown at T - 50°C by a self-seeding process (Ryan et al. 1997). Numbers indicate the order of reflection from a lamellar structure and the arrow indicates the position of the peak in the ordered melt. The calculated repeat lengths for possible molecular conformations are indicated.

Rothwell, Martinson and Gorman have studied the formation of stress induced crazes in polymethyl methacrylate. The sample was initially stressed and held at a strain of 3.5 %. Upon relaxation, SAXS-patterns of 1.5 s were recorded using a linear photodiode detector array. A sequence of selected curves recorded in a plane parallel to the strain direction is shown in Fig. 49. The peak at h = 0.014 is probably due to an... 

Clearly, the structure factor dominates the SAXS patterns. It is relevant to ask whether the cylinder form factor, depending on the pore radius, also plays a significant role in the scattering distribution. The calculated cylinder form factor is defined by a Bessel function [12,15,17] which has zeroes at specific k-values. As shown in Fig 4, the experimental profiles for 40 V membranes (pore diameter 48nm) do not display a clear link to this pattern. The predicted first minimum is close to the broad third-order structure factor peak. It is consequently impossible to derive a value for the pore radius directly from the resuhs without a more detailed analytic treatment. This is disappointing, as the pore size is fundamentally important in the use of AAO membranes in filtration or as templates. Electron microscopy studies show that for the synthetic conditions employed, pore diameters above 12mn are linearly related to anode voltage (1.2 nnW) and so are approximately half the mean pore separation [7,15]. 

Fig. 4 illustrates the general features of the SAXS patterns obtained from AAO membranes containing cobalt nanowires. The intensity profile from a 40V cobalt-fified AAO membrane (pore diameter 48 nm) in the face-on position is compared with that from an empty 40V membrane. There is a much more substantial modification of the SAXS pattern than expected. The peaks from the cobalt-filled membrane are displaced to slightly higher k-values the oscillatory amplitude is reduced and there is an additional broad subsidiary peak at lower k-values (k=0.033 nm ). 

The orientation of crystalline stems with respect to the interface of the microstructure in block copolymers depends on both morphology and the speed of chain diffusion, which is controlled by block copolymer molecular weight and the crystallization protocol (i.e. cooling rate). In contrast to homopolymers, where folding of chains occurs such that stems are always perpendicular to the lamellar interface, a parallel orientation was observed for block copolymers crystallized from a lamellar melt phase perpendicular folding was observed in a cylindrical microstructure. Both orientations are shown in Fig. 8. Chain orientation can be probed via combined SAXS and WAXS on specimens oriented by shear or compression. In PE, for example, the orientation of (110) and (200) WAXS reflections with respect to Bragg peaks from the microstructure in the SAXS pattern enables the unit cell orientation to be deduced. Since PE stems are known to be oriented along the c axis, the chain orientation with respect to the microstructure can be determined. 

SAXS results have been of central Importance in the Interpretation of the structure of lonomers. A peak is typically observed in the scattering pattern of most lonomers at a scattering vector, k, of 1 to 3 nm. Examples of the SAXS patterns for a series of SPS lonomers with varying sulfonate concentration and different cations are shown in Fig. 8. Although the "ionic peak"... 

As for ASAXS, we are currently using this technique to separate the crystallite and ionic "peak" scattering in the semicrystalline ionomers Nafion and Surlyn. Since these two scattering sources overlap in q-space, it has in the past proved difficult to separate and model these scattering sources, but with ASAXS this task becomes possible. Also, we are investigating the hlgh-q shoulder we have observed in the SAXS patterns of sulfonated polyurethane ionomers[45], which may be evidence of structural order within the ionic aggregates. 

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