USAXS Measurements

The USAXS measurements in the q-range 0.0002 A q 0.3 A were carried out at the Advanced Photon Source at Argonne National Laboratory, where the USAXS instrument [34,35] is installed at undulator beamline 33-ID. Monochromatic (12 keV) X-ray flux of 10 photons/second was obtained using a double crystal monochromator equipped with Si (111) crystals, and a pair of mirrors after the monochromator was used to suppress the harmonic content of the beam. 

The USAXS instrument uses a 6-reflection symmetric Si (111) channel cut crystal before and another 6-reflection channel cut after the sample to 

The USAXS data were reduced, absolute calibrated, and corrected for instrumental curve using software Indra  

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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). 

We investigated foe process by a time-resolved USAXS measurement during OOT from hex-cylinder to bcc-sphoe. The change in foe USAXS profile around the first-order scattering maximum was obtained as a function of time after T-jump from hex-cylinder to bcc-sphere and foe transition is found to be classified into 3 stages. 

The USAXS measurements were performed for KE-PlOW dispersions at several C s and era s. Figure 2 shows the scattering intensity as a function of scattering vector (q) at Cs = 10 M and at two which corresponded to the order and disorder regions. In the disorder region (ffa = 0.1 X 10" Cem" ), a broad peak and a shoulder caused by interparticle interference from a Uquid-type spatial arrangement of particles were observed in addition to the broad peaks from the form factor of isolated particles. We note that these interference peak and shoulder disap-... 

The ultra small-angle X-ray scattering (USAXS) extends the accessible structure towards the micrometer range. Time-resolved measurements require a synchrotron beam that is intensified by an insertion device (Sect. 4.2.2). 

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. 

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. 

Even when looking at samples with rather good contrast, such as mineral oxides in water, much longer exposure times (of the order of minutes) must be used with X-ray scattering than with light (of the order of seconds) and samples must, in general, be much more concentrated. Berthon et al. [45] used USAXS to measure fractal structure in resorcinol-formaldehyde gels. 

The role of cavity formation in the creep process has been elucidated by a number of experimental techniques, including density measurements (23, 43], measurements of ultrasonic velocities [34, 35], determination of elastic moduli by instmmented indentation [31], and anomalous ultra-small angle X-ray scattering (A-USAXS) [23, 46]. The results of density measurements are illustrated in Figure 13.13. The vertical axis of this figure was calculated from measured density changes in tensile or... 

The SALS instrument used for this work was developed with National Science Foundation support under NSF DMR-0108976. Simultaneous SAXS and WAXS experiments were carried out at National Synchrotron Light Source, Brookhaven National Laboratory, which is supported by Department of Energy, Division of Materials Sciences and Chemical Sciences. The authors thank NIST for support of the use of beamline X27C. USAXS data was measured at beamline 33-ID at the Advanced Photon Source, Argonne National Laboratory. Use of the Advanced Photon Source is supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. W-31-109-Eng-38. We would also thank Dr. D. J. Lohse (ExxonMobil) for providing the copolymers. 

For latex dispersions, the two-state structure has been confirmed by microscopy. In polyelectrolyte solutions it has been inferred from the fact that 2D xp < 2Do as described in Sect. 2. However, the size of the ordered duster was not estimated. For polyelectrolyte solutions, the intermoleculm- distmice calculated from the Bragg peak position was of the order of 100 A. Hence, it may be a reasonable estimate that the size of the polyel arolyte cluster would be of the order of several thousand A to several micrometers. Because the USAXS intensity was not sufficiently high enough for solutions of ionic polymers such as NaPSS, we determined the size of the duster by using neutron scattering [65]. In the following the SANS measurements for NaPSS-D20 solutions are described. 

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

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. ...

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