Small angle scattering X-rays

SAXS is a powerful tool to study the morphology of semicrystalline systems. The application of this technique is based on the electron density difference between the crystalline and amorphous phases (lamellar structure) in polymer systems. The crystalline (l ) and amorphous (IJ thicknesses can be obtained using this technique. Besides, the distance from one crystalline region to the next provides the size of a lamellar structure, also known as the long period (L). Other morphological features are the interface 

The long period L is the distance between phases of the same type. Each of these thicknesses has a size distribution, typically Gaussian. The interface thickness E is the distance when the interface is not sharp, that is, the interface is finite. The lamellar stacking size can be finite or infinite. 

SAXS is determined by interference phenomena, where the waves are coherent and therefore their amplitudes can be added even if the emerging waves are not in phase as in the case of WAXS [10]. SAXS intensity is given by the absolute square of the resulting amplitude, which is obtained by summing all secondary waves. All amplitudes have the 

Electron density function is defined as the number of electrons per unit volume and it is denoted as p r). Electron density function of a semicrystalline polymer consists of a series of alternating steps, positive Pi and negative P2, which represent phases, and flucmate around an average value p. If, for example, an r vector is passed along the semicrystalline structure (Fig. 19.5), it can be seen that p r) = /Oj if p r) Pm-On the other hand, p(r) = P2 if p f) Pm where p is a high density region (crystalline) and P2 is a low density region (amorphous). 

Because of the inverse relation existing between the size of the scatterer and the distance of incidence of the source, experimental effects are observed in reciprocal space. Therefore, in order to obtain estimates in the reciprocal space, the geometry of a system with two dispersion centers which is impacted by X-ray beam is defined, determining a scattering vector in the reciprocal space, q. 

SMALL-ANGLE X-RAY SCATTERING, NEUTRON SCATTERING, AND LASER LIGHT SCATTERING 

Physical Chemistry of Macromolecules Basic Principles and Issues, Secorul Edition. By S. F. Sun ISBN 0-471-28138-7 Copyright 2004 John Wiley Sons, Inc. 

To demonstrate their similarity, small-angle x-ray scattering data may be treated as light-scattering data. In parallel to light scattering, we have 

As may be easily assessed by applying Bragg law, the analysis of aggregates of size over the tens of A requires that the investigation be focused in an angular range 

Theoretical I(q) and p(r) have been derived for a number of different geometries, so a fitting based on these models helps in obtaining a good picture of the morphology of the system. More complex shapes can be approximated by a collection of primary particles, such as spheres. 

What has been said so far applies to dilute systems, but densely packed colloidal particles, such as highly filled nanocomposites, require to take into account the interparticle interference effects. Another assumption that is not always valid is that the particles are homogeneous and monodisperse in size. Particle anisotropy and polydispersity are very common factors that bring about severe deviations of the system from ideality. A distribution of sizes must therefore usually be included in the theoretical models used to reproduce the experimental SAXS patterns. 

As said earlier, many intensity functions have been calculated for a number of different shapes, for example, spheres, ellipsoids, parallelepipedons, and cylinders, which are all similar in the central range. A universal approximation exists for the central part of SAXS traces. Guinier [97] proposed an exponential function only dependent on the radius of gyration R  

Another model-independent parameter can be found in the final slope of the SAXS pattern. In this region, which depends mainly on the fine structure of the particle and not on the mutual arrangement of particles, the intensity I q) can be approximated by the so-called Porod s law [98,99], I(q) ((A/o) 2jrS)/q, where S 

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Brumberger H (ed) 1967 Small-Angle X-ray Scattering (New York Gordon and Breach)... 

Figure C2.17.12. Exciton energy shift witli particle size. The lowest exciton energy is measured by optical absorjDtion for a number of different CdSe nanocrystal samples, and plotted against tire mean nanocrystal radius. The mean particle radii have been detennined using eitlier small-angle x-ray scattering (open circles) or TEM (squares). The solid curve is tire predicted exciton energy from tire Bms fonnula.

Mattoussi H efa/1996 Characterization of CdSe nanocrystalline dispersions by small angle x-ray scattering J. Chem. Phys. 105 9890... 

O. Kiathy, in O. Glatter, O. Kiathy, eds., Small-Angle X-Ray Scattering, Academic Press, Inc., New York, 1982. 

Cazorla-Amords, D., dc Lecea, C. S. M., Alcaniz-Monge, J., Gardner, M., North, A. and Dore, J., Characterization of activated carbon fibers by small-angle x-ray scattering. Carbon, 1998, 36(3), 309 312. 

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. 

There are many ways to eharaeterize the strueture and properties of carbonaceous materials. Among these methods, powder X-ray diffraetion, small angle X-ray scattering, the BET surfaee area measurement, and the CHN test are most useful and are deseribed briefly here. To study lithium insertion in carbonaeeous materials, the eleetroehemieal lithium/earbon eoin eell is the most eonvenient test vehicle. 

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. 

In this case, the elements of the crosslinked structure exhibit higher mobility, the permeability of the crosslinked structure depends on the degree of hydration. It should be noted that the pore size in hydrated crosslinked copolymers is determined by small-angle X-ray scattering or with the aid of electron microscopy using special methods of preparation for the CP samples [15],... 

Glatter D, Kratky O (1982) Small angle X-ray scattering, Academic, London... 

Small angle X-ray scattering Rg, chain contour length, L solution conformation and flexibility If M is also known, can provide mass per unit length Ml [5]... 

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]. 

Fujimura M., Hashimoto T., and Kawai H., Small-angle x-ray scattering study of perfluorinated ionomer membranes. 2. Models for ionic scattering maximum. Macromolecules, 15, 136, 1982. 

Porod, G., Small-Angle X-Ray Scattering, Academic Press London, 1982. 

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