Die Beugung von Röntgenstrahlen in Flüssigkeiten als Effekt der Molekülanordnung

Two di erent levels of the free-volume approximation for describing one-dimensional mixtures of hard rods of two di erent lengths are analysed and tested against the exact solution. The mean-ÿeld level free-volume approach, where only the statistically pre-averaged free volume of the larger rods is accounted for, yields a spurious phase transition. Taking correlations into account not only gives better quantitative results, it also shows qualitative right physics, i.e., no phase transition.

show abstract

“…The number density distribution has been derived by Zernike and Prins [27], and reads between a and 2a as…”

Section: Mean-ÿeld Free-volume Approximationmentioning

confidence: 99%

The importance of correlations in free-volume models for depletion phenomena

Oversteegen

Lekkerkerker

2002

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

show abstract

“…In the case of discrete scattering arising from a system of stacked, flat and extended lamellae, Stribeck (1996) has extended the treatments of Zernike & Prins (1927) and Blundell (1978) to develop an analytical expansion of the 'ID slit-smeared scattering intensity'…”

Section: Detecting Void Scatteringmentioning

confidence: 99%

Studying the Microstructure of Unaged and Aged PVDF by Small- and Wide-Angle X-ray Scattering

Stribeck¹,

Buchner²

1997

J Appl Cryst

View full text Add to dashboard Cite

A layer from plasticized poly(vinylidene fluoride) (PVDF) was aged by exposing one of its faces to an aggressive fluid at elevated temperature and pressure. From visual inspection the aged material appeared not to be homogeneous. Therefore, samples from three distinguishable regions were compared with a sample cut from the virgin material by studying their small-and wide-angle X-ray scattering (SAXS and WAXS). The results show that plasticizer has vanished from the aged material, the crystalline layer thickness distribution has narrowed, amorphous lamellae are collapsed and voids have been created. Within the aged material the number of voids varies: there are more at the inner surface and fewer at the outer surface beneath the rods of a supporting metal grid. Based on the results of this study and theoretical considerations, a method for the quantitative description of the ageing process is proposed, which only requires a simple kind of SAXS measurement.

show abstract

“…The normalized intensity of scattering by such a twodimensional system (cf. Zernike & Prins (1927) for the equivalent three-dimensional case) is…”

Section: Non-independent Particles With Arbitrary Locationmentioning

confidence: 99%

Scattering from cylindrically symmetric systems

Oster¹,

Riley²

1952

Acta Cryst

187

124

View full text Add to dashboard Cite

Expressions for the intensity of scattering by systems composed of infinitely long cylindrical particles are derived. Four types of independent scattering regions are considered: (1) isolated cylindrical rods, with and without internal radial structure; (2) aggregates of parallel rods with fixed locations; (3) systems of parallel rods with variable locations; (4) two-dimensional crystals. The effect of random and specific orientation of independent scattering regions in discussed. The results are applicable to low-angle X-ray scattering from fibres and from macromolecular or micellar solutions.In a previous paper (Oster & Riley, 1952) we considered the scattering of X-rays and visible light by isotropic systems and confined our treatment to those cases which possess spherical symmetry. We shall now extend our examination to assemblies which possess cylindrical symmetry and in which the fundamental particles are very long compared with the wavelength ), of the radiation used. On the macroscopic scale such systems may be isotropic or anisotropic. In the former case they are collections of cylindrically-symmetric domains in random orientation; in the latter, the domains themselves have preferred orientation. Micellar solutions are an example of the first type and completely oriented fibres of the second. We shall show that there is a close analogy between the expressions for the intensity of scattering by cylindrically symmetric systems and those for the equivalent spherically symmetric cases discussed in our first paper. The results obtained in the present paper are not only applicable to X-ray scattering and diffraction by certain macromolecular and colloidal systems but also to visible-light scattering and diffraction by macroscopic systems having cylindrical symmetry.A peculiar feature of systems of long rod-shaped particles is the correlation in orientation which sets in if the concentration exceeds a certain critical value, depending on the particle length and the forces of interaction (Onsager, 1949; 0ster, 1949). Very long particles will, even in fairly dilute solution, show correlation in orientation, the rods being nearly parallel over rather large domains. Fibres in bundles can usually be rendered parallel, at least in local regions, by stretching and rolling the sample. These properties of elongated particles considerably simplify the mathematics of the problem as it then reduces to a two-dimensional calculation.In this paper we shall calculate the angular distribution of scattered intensity for (1) isolated * Present address: Polytechnic Institute of Brooklyn, Brooklyn 2, New York, U.S.A. cylindrical rods, with and without internal radial structure, (2) aggregates of parallel rods with fixed locations, (3) systems of parallel rods with variable locations as expressed generally by a radial distribution function, and (4) two-dimensional crystals consisting of an infinite periodic array of parallel rods. As in the previous paper, we shall eliminate the scale factor by writing all expressions in terms of ...

show abstract

Die Beugung von Röntgenstrahlen in Flüssigkeiten als Effekt der Molekülanordnung

Cited by 609 publications

References 0 publications

The importance of correlations in free-volume models for depletion phenomena

The importance of correlations in free-volume models for depletion phenomena

Studying the Microstructure of Unaged and Aged PVDF by Small- and Wide-Angle X-ray Scattering

Scattering from cylindrically symmetric systems

Contact Info

Product

Resources

About