小角散乱

WordNet

slight or limited; especially in degree or intensity or scope; "a series of death struggles with small time in between"
a garment size for a small person
the slender part of the back
limited or below average in number or quantity or magnitude or extent; "a little dining room"; "a little house"; "a small car"; "a little (or small) group" (同)little
have fine or very small constituent particles; "a small misty rain"
on a small scale; "think small"
move or proceed at an angle; "he angled his way into the room"
the space between two lines or planes that intersect; the inclination of one line to another; measured in degrees or radians
fish with a hook
a light shower that falls in some locations and not others nearby (同)sprinkle, sprinkling
a small number (of something) dispersed haphazardly; "the first scatterings of green"; "a sprinkling of grey at his temples" (同)sprinkling
the physical process in which particles are deflected haphazardly as a result of collisions
fishing with a hook and line (and usually a pole)
a member of a Germanic people who conquered England and merged with the Saxons and Jutes to become Anglo-Saxons

PrepTutorEJDIC

(大きさが)『小さい』,小形の;(量が)『少ない』,わずかな / 『取るに足りない』,ささいな(trivial) / 《名詞の前にのみ用いて》(仕事・活動などが)『小規模の』,ささやかな / 心が狭い,利己的な / (音・声が)弱い,小さい / (文字が)小型の,小文字の / 《the~》小さいもの;(…の)細い部分《+『of』+『名』》 / 《複数形で》《英》(衣類・ハンカチなどの)小物,小間物 / 小さく,細かく / (声などが)低く,弱く / 小規模に,こぢんまりと
『かど』,すみ(corner) / 『角』,角度 / 《話》(ものを見る)角度,観点(point of view) / …'を'ある角度に動かす(向ける,曲げる) / …'を'ある角度から見る
(楽しみとして)魚釣りをする;(魚を)釣る《+『for』+『名』》
〈U〉〈C〉まき散らすこと,散布 / (また scatter)〈C〉《単数形で》分散した少数(少量)(の…)《+『of』+『名』》
魚釣り(fishing)

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2017/12/21 19:00:51」(JST)

wiki en

Small-angle scattering (SAS) is a scattering technique based on deflection of collimated radiation away from the straight trajectory after it interacts with structures that are much larger than the wavelength of the radiation. The deflection is small (0.1-10°) hence the name small-angle. SAS techniques can give information about the size, shape and orientation of structures in a sample.

Small-angle scattering (SAS) is a powerful technique for investigating large-scale structures from 10 Å up to thousands and even several tens of thousands of angstroms. The most important feature of the SAS method is its potential for analyzing the inner structure of disordered systems, and frequently the application of this method is a unique way to obtain direct structural information on systems with random arrangement of density inhomogeneities in such large-scales.

Currently, the SAS technique, with its well-developed experimental and theoretical procedures and wide range of studied objects, is a self-contained branch of the structural analysis of matter. Reflecting these situations, the international meeting on the small-angle scattering studies have been held in every three years. SAS can refer to:

Small angle neutron scattering (SANS)
Small angle X-ray scattering (SAXS)

Applications

Small-angle scattering is particularly useful because of the dramatic increase in forward scattering that occurs at phase transitions, known as critical opalescence, and because many materials, substances and biological systems possess interesting and complex features in their structure, which match the useful length scale ranges that these techniques probe. The technique provides valuable information over a wide variety of scientific and technological applications including chemical aggregation, defects in materials, surfactants, colloids, ferromagnetic correlations in magnetism, alloy segregation, polymers, proteins, biological membranes, viruses, ribosome and macromolecules. While analysis of the data can give information on size, shape, etc., without making any model assumptions a preliminary analysis of the data can only give information on the radius of gyration for a particle using Guinier's equation.^[1]

Theory

Continuum description

SAXS patterns are typically represented as scattered intensity as a function of the magnitude of the scattering vector $q=4\pi \sin(\theta )/\lambda$ . Here $2\theta$ is the angle between the incident X-ray beam and the detector measuring the scattered intensity, and $\lambda$ is the wavelength of the X-rays. One interpretation of the scattering vector is that it is the resolution or yardstick with which the sample is observed. In the case of a two-phase sample, e.g. small particles in liquid suspension, the only contrast leading to scattering in the typical range of resolution of the SAXS is simply Δρ, the difference in average electron density between the particle and the surrounding liquid, because variations in ρ due to the atomic structure only become visible at higher angles in the WAXS regime. This means that the total integrated intensity of the SAXS pattern (in 3D) is an invariant quantity proportional to the square Δρ². In 1-dimensional projection, as usually recorded for an isotropic pattern this invariant quantity becomes $\int I(q)q^{2}\,dx$ , where the integral runs from q=0 to wherever the SAXS pattern is assumed to end and the WAXS pattern starts. It is also assumed that the density does not vary in the liquid or inside the particles, i.e. there is binary contrast.

SANS is described in terms of a neutron scattering length density.

Porod's law

At wave numbers that are relatively large on the scale of SAS, but still small when compared to wide-angle Bragg diffraction, local interface intercorrelations are probed, whereas correlations between opposite interface segments are averaged out. For smooth interfaces, one obtains Porod's law:

I(q)\sim Sq^{-4}

This allows the surface area S of the particles to be determined with SAS. This needs to be modified if the interface is rough on the scale q⁻¹. If the roughness can be described by a fractal dimension d between 2-3 then Porod's law becomes:

I(q)\sim S'q^{-(6-d)}

Scattering from particles

Small-angle scattering from particles can be used to determine the particle shape or their size distribution. A small-angle scattering pattern can be fitted with intensities calculated from different model shapes when the size distribution is known. If the shape is known, a size distribution may be fitted to the intensity. Typically one assumes the particles to be spherical in the latter case.

If the particles are in solution and known to have uniform size dispersity, then a typical strategy is to measure different concentrations of particles in the solution. From the obtained SAXS patterns one can extrapolate to the intensity pattern one would get for a single particle. This is a necessary procedure that eliminates the concentration effect, which is a small shoulder that appears in the intensity patterns due to the proximity of neighbouring particles. The average distance between particles is then roughly the distance 2π/q*, where q* is the position of the shoulder on the scattering vector range q. The shoulder thus comes from the structure of the solution and this contribution is called the structure factor. One can write for the small-angle X-ray scattering intensity:

I(q)=P(q)S(q),

where

$I(q)$ is the intensity as a function of the magnitude $q$ of the scattering vector
$P(q)$ is the form factor
and $S(q)$ is the structure factor.

When the intensities from low concentrations of particles are extrapolated to infinite dilution, the structure factor is equal to 1 and no longer disturbs the determination of the particle shape from the form factor $P(q)$ . One can then easily apply the Guinier approximation (also called Guinier law, after André Guinier), which applies only at the very beginning of the scattering curve, at small q-values. According to the Guinier approximation the intensity at small q depends on the radius of gyration of the particle.^[2]

An important part of the particle shape determination is usually the distance distribution function $p(r)$ , which may be calculated from the intensity using a Fourier transform^[3]

p(r)={\frac {r^{2}}{2\pi ^{2}}}\int _{0}^{\infty }I(q){\frac {\sin qr}{qr}}q^{2}dq.

The distance distribution function $p(r)$ is related to the frequency of certain distances $r$ within the particle. Therefore it goes to zero at the largest diameter of the particle. It starts from zero at $r=0$ due to the multiplication by $r^{2}$ . The shape of the $p(r)$ -function already tells something about the shape of the particle. If the function is very symmetric, the particle is also highly symmetric, like a sphere.^[2] The distance distribution function should not be confused with the size distribution.

The particle shape analysis is especially popular in biological small-angle X-ray scattering, where one determines the shapes of proteins and other natural colloidal polymers.

History

Small-angle scattering studies were initiated by André Guinier (1937).^[4] Subsequently, Peter Debye,^[5] Otto Kratky,^[6] Günther Porod,^[7] R. Hosemann^[8] and others developed the theoretical and experimental fundamentals of the method and they were established until around 1960. Later on, new progress in refining the method began in the 1970s and is continuing today.

Organisations

As a 'low resolution' diffraction technique, the worldwide interests of the small-angle scattering community are promoted and coordinated by the Commission on Small-Angle Scattering of the International Union of Crystallography. There are also a number of community-led networks and projects. One such network, CanSAS - the acronym stands for Collective Action for Nomadic Small-Angle Scatterers, emphasising the global nature of the technique, champions the development of instrumental calibration standards and data file formats. It has also created a Web Portal to a variety of SAS-related resources.

References

^ Guinier/Fournet, chapter 4
^ ^a ^b Svergun DI; Koch MHJ (2003). "Small-angle scattering studies of biological macromolecules in solution". Rep. Progr. Phys. 66 (10): 1735–1782. Bibcode:2003RPPh...66.1735S. doi:10.1088/0034-4885/66/10/R05.
^ Feigin LA; Svergun DI (1987). Structure Analysis by Small-Angle X-Ray and Neutron Scattering (PDF). New York: Plenum Press. p. 40. ISBN 0-306-42629-3.
^ A. Guinier, C.R. Hebd: Séances Acad. Sci. 2o4, 1115 (1937)
^ P.Debye, A.Bueche J. Appl. Phys. 28,679 (1949)
^ O. Kratky: Naturwiss.26,94 (1938)
^ Kolloid-Z. 124,83 (1951)
^ R. Hosemann: Kolloid-Z.177,13 (1950)

Textbooks

André Guinier, Gerard Fournet: Small-angle scattering of x-rays. New York: John Wiley & Sons (1955)
O. Glatter, Otto Kratky (eds.): Small Angle X-ray Scattering. London: Academic Press (1982). Out of print.

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English Journal

Analytically monitored digestion of silver nanoparticles and their toxicity on human intestinal cells.

Böhmert L, Girod M, Hansen U, Maul R, Knappe P, Niemann B, Weidner SM, Thünemann AF, Lampen A.Author information BfR Federal Institute for Risk Assessment , Berlin , Germany.AbstractAbstract Orally ingested nanoparticles may overcome the gastrointestinal barrier, reach the circulatory system, be distributed in the organism and cause adverse health effects. However, ingested nanoparticles have to pass through different physicochemical environments, which may alter their properties before they reach the intestinal cells. In this study, silver nanoparticles are characterised physicochemically during the course of artificial digestion to simulate the biochemical processes occurring during digestion. Their cytotoxicity on intestinal cells was investigated using the Caco-2 cell model. Using field-flow fractionation combined with dynamic light scattering and small-angle X-ray scattering, the authors found that particles only partially aggregate as a result of the digestive process. Cell viabilities were determined by means of CellTiter-Blue® assay, 4',6-diamidino-2-phenylindole-staining and real-time impedance. These measurements reveal small differences between digested and undigested particles (1-100 µg/ml or 1-69 particles/cell). The findings suggest that silver nanoparticles may indeed overcome the gastrointestinal juices in their particulate form without forming large quantities of aggregates. Consequently, the authors presume that the particles can reach the intestinal epithelial cells after ingestion with only a slight reduction in their cytotoxic potential. The study indicates that it is important to determine the impact of body fluids on the nanoparticles of interest to provide a reliable interpretation of their nano-specific cytotoxicity testing in vivo and in vitro.
Nanotoxicology.Nanotoxicology.2014 Sep;8:631-42. doi: 10.3109/17435390.2013.815284.
Abstract Orally ingested nanoparticles may overcome the gastrointestinal barrier, reach the circulatory system, be distributed in the organism and cause adverse health effects. However, ingested nanoparticles have to pass through different physicochemical environments, which may alter their properti
PMID 23763544

Structural and functional properties of alkali-treated high-amylose rice starch.

Cai J, Yang Y, Man J, Huang J, Wang Z, Zhang C, Gu M, Liu Q, Wei C.Author information Key Laboratories of Crop Genetics and Physiology of the Jiangsu Province, Plant Functional Genomics of the Ministry of Education, Yangzhou University, Yangzhou 225009, China.AbstractNative starches were isolated from mature grains of high-amylose transgenic rice TRS and its wild-type rice TQ and treated with 0.1% and 0.4% NaOH for 7 and 14 days at 35 °C. Alkali-treated starches were characterised for structural and functional properties using various physical methods. The 0.1% NaOH treatment had no significant effect on structural and functional properties of starches except that it markedly increased the hydrolysis of starch by amylolytic enzymes. The 0.4% NaOH treatment resulted in some changes in structural and functional properties of starches. The alkali treatment affected granule morphology and decreased the electron density between crystalline and amorphous lamellae of starch. The effect of alkali on the crystalline structure including long- and short-range ordered structure was not pronounced. Compared with control starch, alkali-treated TRS starches had lower amylose content, higher onset and peak gelatinisation temperatures, and faster hydrolysis of starch by HCl and amylolytic enzymes.
Food chemistry.Food Chem.2014 Feb 15;145:245-53. doi: 10.1016/j.foodchem.2013.08.059. Epub 2013 Aug 27.
Native starches were isolated from mature grains of high-amylose transgenic rice TRS and its wild-type rice TQ and treated with 0.1% and 0.4% NaOH for 7 and 14 days at 35 °C. Alkali-treated starches were characterised for structural and functional properties using various physical methods. The 0.1%
PMID 24128474

Chitosan-decorated polystyrene-b-poly(acrylic acid) polymersomes as novel carriers for topical delivery of finasteride.

Caon T1, Porto LC2, Granada A1, Tagliari MP1, Silva MA1, Simões CM1, Borsali R3, Soldi V4.Author information 1Programa de Pós-Graduação em Farmácia (PGFAR), Departamento de Ciências Farmacêuticas, Universidade Federal de Santa Catarina, Campus Universitário, Trindade, 88040-900 Florianópolis, SC, Brazil.2Programa de Pós-Graduação em Química, Departamento de Química, Universidade Federal de Santa Catarina, Campus Universitário, Trindade, 88040-900 Florianópolis, SC, Brazil.3Centre de Recherches sur les Macromolécules Végétales (CERMAV-CNRS), Affiliated with Grenoble University and ICMG FR 2607, BP53, 38041 Grenoble Cedex 9, France.4Programa de Pós-Graduação em Química, Departamento de Química, Universidade Federal de Santa Catarina, Campus Universitário, Trindade, 88040-900 Florianópolis, SC, Brazil. Electronic address: soldi.valdir@gmail.com.AbstractIn view of the fact that the oral administration of finasteride (FIN) has resulted in various undesirable systemic side effects, the topical application of polystyrene and poly(acrylic acid)-based polymersomes (underexplored system) was investigated. Undecorated PS139-b-PAA17 and PS404-b-PAA63 vesicles (C3 and C7, respectively) or vesicles decorated with chitosan samples of different molecular weight (C3/CS-oligo, C7/CS-oligo, C3/CS-37 and C7/CS-37) were prepared by the co-solvent self-assembly method and characterized by small-angle X-ray scattering,transmission electron microscopy and dynamic light scattering techniques. In vitro release experiments and ex vivo permeation using Franz diffusion cells were carried out (through comparison with hydroethanolic finasteride solution). The ideal system should provide high finasteride retention in the dermis and epidermis while allowing some control of the drug release. The particle size and in vitro release were negatively correlated with the permeation coefficient and skin retention in both the epidermis and dermis. The findings that the longest lag time was obtained for the hydroethanolic drug solution and lowest permeation for the systems able to release the drug faster support the hypothesis that nanostructured systems may be required to enhance the penetration and permeation of the drug. Chitosan-decorated polymersomes interacted more strongly with the skin components than non-decorated samples, probably due to the positive surface charge, which increased the FIN retention and reduced the lag time. C7 polymersomes decorated with chitosan were more appropriate for topical applications (high retention in the dermis and epidermis and controlled drug delivery).
European journal of pharmaceutical sciences : official journal of the European Federation for Pharmaceutical Sciences.Eur J Pharm Sci.2014 Feb 14;52:165-72. doi: 10.1016/j.ejps.2013.11.008. Epub 2013 Nov 19.
In view of the fact that the oral administration of finasteride (FIN) has resulted in various undesirable systemic side effects, the topical application of polystyrene and poly(acrylic acid)-based polymersomes (underexplored system) was investigated. Undecorated PS139-b-PAA17 and PS404-b-PAA63 vesic
PMID 24262075

Japanese Journal

Role of molecular weight in shish-kebab formation during drawing by small-angle neutron and X-ray scattering

Polymer journal 49(12), 831-837, 2017-12
NAID 40021392017

Crystal structure of the flexible tandem repeat domain of bacterial cellulose synthesis subunit C

Scientific reports 7, 13018, 2017-10-12
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Re-Evaluation of Calibration and Measurement Capabilities of Pitch Calibration Systems Designed by Using the Diffraction Method (Special Issue on Intelligent Measurement for Advanced Production Engineering)