X-ray scattering function

H. L. Friedman, D. M. Zebolsky, and E. Kalman, Calculated X-ray scattering functions for models for aqueous PI14ASQ which fit the osmotic coefficient data, J. Solution Chem. 5, (1976). 

Fig. 9. X-ray scattering function H(k) [60] of iPP (N = 48 CHx sites, p = 0.03282 A , T = 453K) computed from SC/PRISM theory dashed curve) and MD simulations solid curve). SC/PRISM theory used repulsive Lennard-Jones nonbond potentials, and the MD used the full Lennard-Jones potential with a 12 A cutoff. The experimental data of Londono et al. [110] is shown as points...

Stribeck N (1996) Small-angle X-ray scattering functions in the vicinity of zero scattering angle with an application to polymer blends, Macromolecides 29 7217-7220. 

The structural analysis described above and in more detail elsewhere, shows the x-ray scattering functions to be sensitive to intrachain correlations. In fact, a more "random chain model (with a delocalized rotation state for one bond) than the "random coil" chain model is required to give a satisfactory match between the experimental and model si (s) functions. A model in which the interchain correlations are minimal with no orientational correlations provides a scattering function which is in good agreement with the observed scattering. Thus there seems to be no evidence to require more local order than inherent in a dense molecular system. This is perhaps not suprising. The polyisoprene molecule has a compact cross section, almost cylindrical in nature and corresponds to the "typical molecule drawn in schematic views of the noncrystalline state. 

This is the result we have sought, although it needs a bit of additional manipulation to make its usefulness evident. The derivation we have followed in this section was developed by Debye in the context of x-ray scattering by the individual atoms of small molecules. Since s o , this function again empha-... 

Figure 4.4. X-rays scattered by atoms in an ordered lattice interfere constructively in directions given by Bragg s law. The angles of maximum intensity enable one to calculate the spacings between the lattice planes and allow furthermore for phase identification. Diffractograms are measured as a function of the angle 26. When the sample is a...

In this contribution we will deal with electron-electron correlation in solids and how to learn about these by means of inelastic X-ray scattering both in the regime of small and large momentum transfer. We will compare the predictions of simple models (free electron gas, jellium model) and more sophisticated ones (calculations using the self-energy influenced spectral weight function) to experimental results. In a last step, lattice effects will be included in the theoretical treatment. 

As will be shown in Section 3, inelastic X-ray scattering experiments can help to decide which theoretical approach is appropriate. One must keep in mind that this static correction is far from an appropriate description of electron correlations. A more accurate way is to account for dynamical screening by writing %(q, co) in terms of the one-particle Greens function G(p, e) corrected for many-particle effects by a... 

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. 

X-ray scattering intensities calculated from these models showed little variation as a function of concentration of EN, indicating that X-ray scattering will not be able to distinguish between PEBB crystalline domains with EN excluded from the domains and the situation where uniform inclusion in the crystalline domains takes place. 

Options of data analysis can be deduced from the magic square and our notions concerning the structure. As an example let us consider the case of small-angle X-ray scattering. Here it is, in general, assumed that the structure is described by a continuous density function. Although there is no9 way back from intensity to density, there are several options for data analysis ... 

Stribeck N (1980) Computation of the Lamellar Nanostructure of Polymers by Computation and Analysis of the Interface Distribution Function from the Small-Angle X-ray Scattering. Ph.D. thesis, Phys. Chem. Dept., University of Marburg, Germany... 

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. 

The ordering of the anions in bmimX ionic liquids has also been suggested by our recent large-angle x-ray scattering experiment on liquid bmimi [23]. Figure 13 shows a differential radial distribution function obtained for liquid bmimi at room temperature. Clear peaks in the radial distribution curve are... 

Figure 13. Differential radial distribution function of liquid bmimi by large-angle x-ray scattering [23].

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