USAXS and SAXS

USAXS and SAXS. Concerning USAXS and SAXS, the scattering pattern that is recorded on a 2D detector is complete if the principal axis of the sample is set normal to the direction of the incident X-ray beam (primary beam). Completeness is a result of two facts. 

The design and placement of the second beam intensity monitor demands more attention. The definition of X-ray absorption does not discriminate between primary beam, USAXS and SAXS. So the second beam intensity monitor should guide primary beam, USAXS and SAXS through its volume, whereas the WAXS should pass outside the monitor. The optimum setup for SAXS and USAXS measurements is a narrow ionization chamber directly behind the sample. For WAXS measurement a pin-diode in the beam stop is a good solution for WAXS. For USAXS and SAXS it may be acceptable, as long as the relevant part of the primary beam is caught, the optical system is in thermal equilibrium and the synchrotron beam does not jump (cf. Sect. 4.2.3.5). 

For USAXS and SAXS studies in normal-transmission geometry it is more convenient to carry out this step later - after the absorption and background correction. 

For USAXS and SAXS data the tangent-plane approximation is valid and the relation between scattering angle and the units of reciprocal space are given by Eq. (2.7). If the scattering pattern is properly aligned with the vertical direction identical to a fiber axis or the polymer chain direction, then sy = 53. In similar manner the. vx-axis of the detector is related to the actual orientation of the sample with respect to the beam. 

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 5 Combined SAS profile (USANS, USAXS, SANS, and SAXS) and WAXS profile obfained for fhe in vitro enzymatic polymerization system. The profiles were measured for the specimen reaction terminated at 24 h after onset of the polymerization. The USAXS and SAXS absolute intensities were converted to the USANS and SANS absolute intensities. The inset shows enlarged WAXS profile, where 20 is Bragg angle. From Tanaka, H. Koizumi, S. Hashimoto, T. etal. Macromolecules 2007, 40, 6304-6315. ...

Stribeck, N., Nochel, U. A method for merging of USAXS and smeared SAXS patterns of fibers. J. Appl. Cryst. 41,715-722 (2008)... 

Fig.6 SAXS, USAXS and SANS measurement son Bakken shale (geological) showing a surface fractal characteristic over six decades of I(Q)-...

Polarization is a relevant issue, because we are dealing with transversal waves (Guinier [6], p. 10-11). Polarization correction should be carried out for MAXS and WAXS data. It is less important for SAXS and USAXS patterns. In particular, if synchrotron radiation is used, the polarization correction is quite involved and based on the degree of polarization. For the purpose of reliable correction it is thus recommended to let a polarization monitor measure the actual degree of synchrotron beam polarization. 

In practice, for SAXS and USAXS experiments carried out in normal-transmission geometry the set of equations... 

In order to reduce air absorption in SAXS and USAXS setups, a vacuum tube (cf. Fig. 4.10) is mounted between sample chamber and detector. 

For SAXS and USAXS experiments it is sufficient to measure the distance R by hand or by a laser distance-meter. For MAXS and WAXS, calibration by means of samples with known sharp reflection are required. Such calibration samples are available at synchrotron beamlines. Different materials are used for application in different angular regions (isotropic crystalline materials for WAXS, Ag-behenate for MAXS, diverse biological samples3 for SAXS and USAXS). Calibration sheets are frequently published on the home pages of synchrotron beamlines. 

The measured SAXS curve of the calibration sample must have been pre-processed in the usual way (cf. Sects. 7.3 - 7.6). Therefore it is important to have calibration samples with a well-defined thickness27. Because synchrotron beamlines can be adjusted to a fairly wide range of radiation power, it is important to have thin calibration samples for a high-power adjustment (e.g., common SAXS with wide slit openings) and thick calibration samples for low-power adjustments (e.g., USAXS with microbeam). For calibration samples from synthetic polymers, thicknesses ranging between 0.2 mm and 3 mm are reasonable. It appears worth to be noted that not only polymers, but as well glassy carbon [88] can be used as a solid secondary standard for the calibration to absolute intensity. 

The experimental basis of sorption studies includes structural data (SANS, SAXS, USAXS), isopiestic vapor sorption isotherms,i and capillary isotherms, measured by the method of standard porosimetry. i 2-i44 Thermodynamic models for water uptake by vapor-equilibrated PEMs have been suggested by various groupThe models account for interfacial energies, elastic energies, and entropic contributions. They usually treat rate constants of interfacial water exchange and of bulk transport of water by diffusion and hydraulic permeation as empirical functions of temperature. 

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