Small-angle X-ray scattering - SAXS

SAXS spectrometers are available both as laboratory equipment and as part of large-scale facility instrumentation. The former usually make use of the Cu line with X=l.54 A, whereas synchrotron sources offer a wavelength range from 0.6 to 3 A. 

The intensity of scattering can be modeled by the same equations developed for light scattering, provided that account is taken of the different matter-radiation interaction. For visible light, scattering is a result of differences in the refractive index of the solute and the solvent, and the optical constant K (Chapter 9, Equation 9.18) is proportional to n idh/dc). For SAXS, the scattered intensity is a function of the electron density, and the molar mass is then related to the excess electron density Ap of solute over solvent. For A, = 1.54 A, the Rayleigh ratio at 0 = 0, Rq is  

Similar to light s ttering, SAXS provides a measure of A2, and the z-average radius of gyration, the main difference being the smaller size range that can 

In a traditional way, SAXS is used to investigate the correlation between synthesis parameters and the resulting gel structure, for example, the dependence of the fractal dimension of silica gels on TEOS concentration in the starter solution (Vollet et al, 2008). Time-dependent SAXS has been applied to study sol-gel transition, in terms of particle growth and change in fractal properties in the forming structure (Tamon and Ishizaka, 1998). But the method also works on dry gels and, for 

Small-angle X-ray scattering (SAXS) is a technique that is widely used to obtain microstructural information over the size range of a few nanometers to a few hundred nanometers. The main features of the technique have 

11 Small-angle X-ray scattering from unoriented polypropylene. The SAXS scattering is the dark halo of diameter at its darkest equal to about half the side of the outer square. This diameter corresponds to about 1°. (Courtesy of Dr A. P. Unwin.) 

Among all the techniques listed in this heading X-ray Scattering , the SAXS method is probably one of the most often used. The studies of phase separation and recrystallization in organic polymers or polymer mixtures very often requires SAXS experiments. In the inorganic chemistry field too, this method is used to tackle a variety of scientific purposes  

An interesting application, performed at LURE-DCl storage ring concerns the study of the swelling properties of layered minerals Pons et al. have studied the swelling of ornithine-exchanged and Li-exchanged vermiculites. The SAXS experiments allow to extract three order parameters the first moment d of the interlayer distance distribution the ratio A /(d ,) with A, the distribution variance and the ratio d Jd y with d , the most probable interlayer distance. 

The SAXS diagrams show a very intricate transition hydrated solid gel in the Li-exchanged solids. Three phases are coexisting a hydrated solid with two water layer, a gel and a very disordered solid. This study should allow to elucidate the formation process of a colloidal structure in such systems. 

Pons et al. have also followed the dessication-rehydration cycle in the montmoril-lonite clays by the SAXS method. This is an interesting study because the swelling properties of clays play an important role in the structural organization of soils. Two main conclusions arise from this work  

As in the case of LAXS measurements, the anomalous dispersion effects, arising when the energy is closed to the absorption edge, can be used with the SAXS technique. FONTAINE did ASAXS experiments, at LURE-DCl, to probe the distribution of Zn atoms in phase separated Ai—Zn alloys He measured the variation of SAXS from Guinier-Preston zones when the energy is scanned below the Zn absorption edge (Fig. 5). 

Problem 2.18 A copolymer chain consisting of Aa beads of monomer a and beads of monomer b has three single-chain structure factors Saa(k), Sab(k), and Sbb(k). They are defined as 

By definition, 5, -I- 8 = 1. Assume that the copolymer chain follows the Gaussian statistics and has a common segment length b. Find 5aa(k), ab(k), and 5 bb(k) for (1) a diblock copolymer and (2) a random copolymer in which the two monomers are placed without correlation to the neighboring monomers. Also evaluate each of 5 aa(k), 5 ab(k), and 5 bb(k) in the small k limit up to the order of k.  

Real random copolymers may have a correlation between 8/ of different i. Problem 2.19 Calcnlate the form factor for a spherical molecnle. 

Solution 2.19 Choose the polar axis along k. Then, 

Problem 2.20 Calcnlate the form factor for a rodlike molecnle. Solution 2.20 Let 9 be the angle between k and the molecnle. 

The scattered intensity I q) from globular particles is generally given by 

The real space function p(r) is directly linked to the spatial autocorrelation function (convolution square) of electron-density fluctuations inside the particle. 

In an identically diluted nonionic system ( 1 wt%), the effects of S(q) can be neglected, that is, the approximation S(q) - 1 is valid. However, S(q) should be considered for the investigated systems. S(q) is given by the Fourier transformation of the total correlation function, h(r) = g(r) — 1, as 

All measured SAXS data were analyzed by the generalized indirect Fourier transformation (GIFT) technique with the Boltzmann simplex simulated annealing (BSSA) algorithm [34, 35]. The GIFT calculation is based on the analytical or numerical solution of the Ornstein-Zernike (OZ) equation that describes the interplay between the total (h(r)) and direct (c(r)) correlation functions  

For the investigated systems, the pair potential, v r), is approximated by a hard-sphere (HS) interaction model. 

---

Section 2 of this chapter describes the characterization of carbonaceous materials by powder X-ray diffraction, small-angle-X-ray scattering (SAXS), measurements of surface area, and by the carbon-hydrogen-nitrogen (CHN) test, a chemical analysis of composition. In this section, we also describe the electrochemical methods used to study carbonaceous materials. 

Small-angle X-ray scattering (SAXS) [19] has been widely used to investigate the inhomogeneous electron density in materials [20]. In carbonaceous materials, porosity is commonly encountered. The pores form and provide escape routes for gases produced during the pyrolysis process. 

Small-angle X-ray scattering (SAXS), circular dichroism (CD), and UV spectroscopy at different temperatures were used to investigate the nature of calf-thymus DNA in aqueous solution, in the presence of [Me Sn] " (n = 1-3) species. The results demonstrate that the [MeSn(IV)] moiety does not influence the structure and conformation of the DNA double helix, and does not degrade DNA, as indicated by agarose gel electrophoresis. Inter alia, the radii of gyration, Rg, of the cross section of native calf-thymus DNA, determined by SAXS in aqueous solution in the presence of [Me Sn] " (n = 1-3) species are constant and independent of the nature and concentration of the [Me Sn] species. 

Tsou and Measmer examined the dispersion of organosUicates on two different butyl mbbers, namely BIMS and brominated poly(isobutylene-co-isoprene) (BIIR) with the help of small angle X-ray scattering (SAXS), wide angle X-ray scattering (WAXS), atomic force microscopy (AFM), and TEM [91]. There is also a patent on BIMS nanocomposites for low permeability and their uses in tire inner tubes [92]. 

Small-angle X-ray scattering (SAXS) data have made it possible to deduce the localisation of organic additives (pigments) in the bulk of isotactic polypropylene (iPP) [344]. This work has confirmed that the additives are located in the amorphous phase, in spite of their crucial influence on the formation of the crystalline phase of iPP. SAXS has also been used to study the 3D structure of different carbon-black aggregates, and silica-filled SBR rubber compounds [345]. 

A Siemens Kratky camera system was utilized for small angle x-ray scattering (SAXS) measurements in conjunction with an M. Braun position sensitive detector from Innovative Technology Inc.. Wide angle x-ray diffraction was obtained utilizing a Philips table-top x-ray generator. 

Generally, it is most likely that metal NPs are stabilized by the aggregates of the non-functionalized imidazolium ILs rather than by the isolated ions. In addition, the interaction between ILs and the metal NPs have been evidenced by X-ray photoelectron spectroscopy (XPS), small-angle X-ray scattering (SAXS), isotope labeling, and surface-enhanced Raman spectroscopy (SERS) techniques. 

Some small-angle X-ray scattering (SAXS) techniques have also been applied to elastomers. Examples are the characterization of fillers precipitated into elastomers, and the corresponding incorporation of elastomers into ceramic matrices, in both cases to improve mechanical properties [4,85,213]. 

In the small-angle X-ray scattering (SAXS) regime the typical nanostructures (in semicrystalline materials, thermoplastic elastomers) are observed. Because of the long distance between sample and detector time-resolved measurements can only be carried out at synchrotron radiation sources (Sect. 4.2.1.2). 

Sliding diffusion Small angle X-ray scattering (SAXS) Topology... 

The former problem is a general problem not only for polymers but also for any other materials (atomic or low molecular weight systems). Although nucleation is a well-known concept, it has never been confirmed by direct observation due to the low number density of the nuclei to be detected with present experimental techniques, such as small angle X-ray scattering (SAXS). Therefore, one of the most important unresolved problems for basic science is to obtain direct evidence to solve the nucleation mechanism of any material. 

The purpose of this section is to present direct evidence of nucleation during the induction period by means of synchrotron small angle X-ray scattering (SAXS). In the classical nucleation theory (CNT), the number density distribution function of nuclei of size N at time t, f(N, t), is expected to increase with an increase of t during the induction period and saturates to a steady f(N, t),fst(N) in the steady period. The change off(N, t) should correspond to that of the scattering intensity of SAXS. 

Brenner, A.M., Adkins, B.D., Spooner, S., and Davis, B.H. 1995. Porosity by small-angle x-ray scattering (SAXS) Comparison with results from mercury penetration and nitrogen adsorption. J. Non-crystal. Solids 185 73-77. 

In the third part of the chapter the solid state properties of our block copolymer are examined. The surface energies of these materials are characterized by contact angle measurements. The organization of the polymer chains in the solid state phase is investigated by small-angle X-ray scattering (SAXS) and the gas selectivity of porous membranes coated with these block copolymers is characterized by some preliminary permeation measurements. 

Small-angle neutron scattering (SANS), 14 710, 19 568, 20 339 Small-angle X-ray scattering (saxs), 20 339, 341-342, 26 432 of amorphous silica, 22 474 Small beer, 26 471 Small Business Innovation Research (SBIR) program, 24 395, 399 Small Business Technology Transfer (STTR) program, 24 395 Small communities... 

---