Small-angle X-ray scattering intensity

Fig. 24 Small-angle X-ray scattering intensity in a s4/(s)-s-plot (circles). The solid line represents the best fit according to Porod s law at scattering vectors in the range of 0.4 to 0.8 nm-1. The insert shows an idealized model of smectic A-like PEI retinoate structures, consisting of well-separated supramolecular lamellar sheets (a) ionic layers with thicknesses of 0.6 nm (PEI-600), 0.7 nm (PEI-2000 and PEI-25000) and 0.8 nm (PEI 750000) (b) nonionic layers with thicknesses of 2.7 nm (PEI-600, PEI-2000, PEI-25000 and PEI-750000). Reprinted with permission from [179]. Copyright 2000 American Chemical Society...

Figure 3. Small-angle x-ray scattering intensity curves demonstrating the effect of soft-segment molecular weight for three polycaprolactone polyurethanes (MDI/BD) of approximately equal hard-segment content. (A) 57% by wt, FCL 2000-178 (S) (B) 53% by wt FCL 830-123 (S) and (C) 61% by wt, FCL 830-134 (S).

Fig. 9. Small angle X-ray scattered intensity from craze fibrils of air crazes in PS...

Fig. 19. The stress-strain curves recorded for the two triblock copolymer samples during cold drawing of films with a constant rate of 1 mm/min. ABA-isolated clean pnBA central block Mn=65,200 pMMA outer blocks, Mn=13,150, overall Mw/Mn=1.34. ABA-sequential clean pnBA central block, Mn=67,500 pMMA-grad-pnBA outer blocks 13mol% nBA and 87 mol% MMA, Mn=10,600, overall Mw/Mn=1.24. Inset small angle X-ray scattering intensities for these samples. Reprinted with permission from [94]. Copyright (2000) John Wiley Sons, Inc.

Figure 5.18 Small-angle x-ray scattering intensity for a lignite coal. (From Bale and Schmidt.33)...

The ABA-sequential copolymer contained a clean central block of nBA ofM = 67,500, and two gradient end block copolymers containing 13 mol% nBA and 87 mol% MMA, with an = 10,600, and an overall Mw/Mn = 1.24 (120). The insert shows the small-angle X-ray scattering intensities for these samples, which correspond to cylindrical morphology of pMMA hard segments. Since both types... 

The insert shows the small angle X-ray scattering intensities for these samples. 

The basic concept of 2D IR spectroscopy based on the correlation analysis of perturbation-induced time-dependent fluctuations of IR intensities could be readily extended to other areas of polymers spectroscopy. The 2D correlation analysis has been successfully applied to the time-dependent variations of small angle X-ray scattering intensity measurement [4], In this study, a small amplitude dynamic strain is applied a sheet of microphase-separated styrene-butadiene-styrene triblock copolymer sample. Intensity variation of scattered X-ray beam due to the strain-induced changes in the interdomain Bragg distances coupled with the reorientation of microdomain structures is analyzed by using the 2D correlation map. Similarly, the formal approach of 2D correlation analysis to time-dependent spectral intensity fluctuations has been extended to UV, Raman [63], and near-IR spectroscopy [64], There seems no intrinsic limitation to the application of this versatile technique in polymer spectroscopy. 

Fig. 17. Desmeared small-angle X-ray scattering intensities for a styrene/isoprene diblock copolymer (78% styrene, M 320000) and its mixtures with polystyrene (M 81000) (the weight fraction of the latter in the mixture is indicated on the plot). The dotted curves are best fitting curves calculated for scattering from isolated spheres. (From Hashimoto, Fujimura, Hashimoto, and Kawai >)...

Tomsic, M., Fritz-Popovski, G., Vloek, L., and Jamnik, A. (2007). Calculating small-angle x-ray scattering intensities from Monte Carlo results Exploring different approaches on the example of primary alcohols. Acta Chim. Slov., 54,484—491. 

Matsuo M and Sawatari C (1990) Morphological and mechanical properties of poly(ethyleue terephthalate) gel and melt films in terms of the crystal lattice modulus, molecular orientation, and small angle X-ray scattering intensity distribution, Polym J 22 518-538. 

B. (2010) Condensation-induced decrease of small-angle X-ray scattering intensity in gelling silica solutions. /. Phys. Chem. 

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 ... 

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. 

At very early times of crystallization, there is considerable experimental evidence [9-15] for density fluctuations before the full crystallographic features can be detected. The major evidence is the appearance of a peak (at max) in intensity, of the small-angle X-ray scattering versus scattering... 

A determination of the molecular weight by small-angle x-ray scattering requires, therefore, knowledge of the scattering intensity as a function of protein concentration and angle of observation, as well as of the electron density increment, ( — ), which replaces the refractive index... 

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