scholarly journals Microscale Fragmentation and Small-Angle Scattering from Mass Fractals

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
E. M. Anitas
Keyword(s):  
Power Law ◽  
Small Angle ◽  
Structure Factor ◽  
Structural Information ◽  
Small Angle Scattering ◽  
Fragmentation Model ◽  
Scattering Method ◽  
Power Law Decay ◽  
Angle Scattering ◽  
Polydisperse Structure

Using the small-angle scattering method, we calculate here the mono- and polydisperse structure factor from an idealized fragmentation model based on the concept of renormalization. The system consists of a large number of fractal microobjects which are randomly oriented and whose positions are uncorrelated. It is shown that, in the fractal region, the monodisperse form factor is characterized by a generalized power-law decay (i.e., a succession of maxima and minima superimposed on a simple power-law decay) and whose scattering exponent coincides with the fractal dimension of the scatterer. The present analysis of the scattering structure factor allows us to obtain the number of fragments resulted at a given iteration. The results could be used to obtain additional structural information about systems obtained through microscale fragmentation processes.

Information retrieval from X-ray small-angle scattering with polychromatic (`white') synchrotron radiation

1983 ◽  
Vol 16 (1) ◽  
pp. 42-46 ◽  
Author(s):  
O. Glatter ◽  
P. Laggner
Keyword(s):  
Synchrotron Radiation ◽  
Small Angle ◽  
Particle Shape ◽  
Structural Information ◽  
Small Angle Scattering ◽  
Radius Of Gyration ◽  
X Ray ◽  
Angle Scattering ◽  
Slit Length ◽  
Hinge Bending

The possibilities of obtaining structural information from X-ray small-angle scattering experiments with `white' polychromatic synchrotron radiation using line collimation are investigated by numerical simulation. Theoretical scattering curves of geometrical models were smeared with the appropriate wavelength distributions and slit-length functions, afflicted by statistical noise, and then evaluated by identical methods as normally used for experimental data, as described previously [program ITP; Glatter (1977). J. Appl. Cryst. 10, 415–421]. It is shown that even for a wavelength distribution of 50% half width, the information content is not limited to the parameters derived from the central part of the scattering curves, i.e. the radius of gyration and the zero-angle intensity, but also allows qualitative information on particle shape via the distance distribution function p(r). By a `hinge-bending model' consisting of two cylinders linked together at different angles it is demonstrated that changes in the radius of gyration amounting to less than 5% can be detected and quantified, and the qualitative changes in particle shape be reproduced.

Small-angle scattering of interacting particles. II. Generalized indirect Fourier transformation under consideration of the effective structure factor for polydisperse systems

1999 ◽  
Vol 32 (2) ◽  
pp. 197-209 ◽  
Author(s):  
B. Weyerich ◽  
J. Brunner-Popela ◽  
O. Glatter
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Structure Factor ◽  
Fourier Transformation ◽  
Hard Spheres ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Model Free ◽  
Angle Scattering ◽  
The Gift

The indirect Fourier transformation (IFT) is the method of choice for the model-free evaluation of small-angle scattering data. Unfortunately, this technique is only useful for dilute solutions because, for higher concentrations, particle interactions can no longer be neglected. Thus an advanced technique was developed as a generalized version, the so-called generalized indirect Fourier transformation (GIFT). It is based on the simultaneous determination of the form factor, representing the intraparticle contributions, and the structure factor, describing the interparticle contributions. The former can be determined absolutely free from model assumptions, whereas the latter has to be calculated according to an adequate model. In this paper, various models for the structure factor are compared,e.g.the effective structure factor for polydisperse hard spheres, the averaged structure factor, the local monodisperse approximation and the decoupling approximation. Furthermore, the structure factor for polydisperse rod-like particles is presented. As the model-free evaluation of small-angle scattering data is an essential point of the GIFT technique, the use of a structure factor without any influence of the form amplitude is advisable, at least during the first evaluation procedure. Therefore, a series of simulations are performed to check the possibility of the representation of various structure factors (such as the effective structure factor for hard spheres or the structure factor for rod-like particles) by the less exact but much simpler averaged structure factor. In all the observed cases, it was possible to recover the exact form factor with a free determined parameter set for the structure factor. The resulting parameters of the averaged structure factor have to be understood as apparent model parameters and therefore have only limited physical relevance. Thus the GIFT represents a technique for the model independent evaluation of scattering data with a minimum ofa prioriinformation.

scholarly journals Scattering from generalized Cantor fractals

2010 ◽  
Vol 43 (4) ◽  
pp. 790-797 ◽  
Author(s):  
A. Yu. Cherny ◽  
E. M. Anitas ◽  
A. I. Kuklin ◽  
M. Balasoiu ◽  
V. A. Osipov
Keyword(s):  
Fractal Dimension ◽  
Small Angle ◽  
Cantor Set ◽  
Small Angle Scattering ◽  
Three Dimensions ◽  
Radius Of Gyration ◽  
Large Wave ◽  
Fractal Sets ◽  
Power Law Decay ◽  
Angle Scattering

A fractal with a variable fractal dimension, which is a generalization of the well known triadic Cantor set, is considered. In contrast with the usual Cantor set, the fractal dimension is controlled using a scaling factor, and can vary from zero to one in one dimension and from zero to three in three dimensions. The intensity profile of small-angle scattering from the generalized Cantor fractal in three dimensions is calculated. The system is generated by a set of iterative rules, each iteration corresponding to a certain fractal generation. Small-angle scattering is considered from monodispersive sets, which are randomly oriented and placed. The scattering intensities represent minima and maxima superimposed on a power law decay, with the exponent equal to the fractal dimension of the scatterer, but the minima and maxima are damped with increasing polydispersity of the fractal sets. It is shown that, for a finite generation of the fractal, the exponent changes at sufficiently large wave vectors from the fractal dimension to four, the value given by the usual Porod law. It is shown that the number of particles of which the fractal is composed can be estimated from the value of the boundary between the fractal and Porod regions. The radius of gyration of the fractal is calculated analytically.

Small-angle scattering gives direct structural information about a membrane protein inside a lipid environment

2014 ◽  
Vol 70 (2) ◽  
pp. 371-383 ◽  
Author(s):  
Søren A. R. Kynde ◽  
Nicholas Skar-Gislinge ◽  
Martin Cramer Pedersen ◽  
Søren Roi Midtgaard ◽  
Jens Baek Simonsen ◽  
...  
Keyword(s):  
Membrane Protein ◽  
Small Angle ◽  
Structural Information ◽  
Protein Localization ◽  
Hybrid Approach ◽  
Small Angle Scattering ◽  
Phospholipid Bilayer ◽  
Scattering Data ◽  
Angle Scattering ◽  
Lipid Environment

Monomeric bacteriorhodopsin (bR) reconstituted into POPC/POPG-containing nanodiscs was investigated by combined small-angle neutron and X-ray scattering. A novel hybrid approach to small-angle scattering data analysis was developed. In combination, these provided direct structural insight into membrane-protein localization in the nanodisc and into the protein–lipid interactions. It was found that bR is laterally decentred in the plane of the disc and is slightly tilted in the phospholipid bilayer. The thickness of the bilayer is reduced in response to the incorporation of bR. The observed tilt of bR is in good accordance with previously performed theoretical predictions and computer simulations based on the bR crystal structure. The result is a significant and essential step on the way to developing a general small-angle scattering-based method for determining the low-resolution structures of membrane proteins in physiologically relevant environments.

scholarly journals Determination of G.P.(1) Zone Size in Al-Cu Alloys by the X-ray Small-Angle Scattering Method

1971 ◽  
Vol 35 (10) ◽  
pp. 1001-1007 ◽  
Author(s):  
Osamu Kawano ◽  
Tetsuya Hirouchi ◽  
Hiroyuki Yoshida ◽  
Yotaro Murakami
Keyword(s):  
Small Angle ◽  
Small Angle Scattering ◽  
Scattering Method ◽  
Zone Size ◽  
X Ray ◽  
Cu Alloys ◽  
Angle Scattering

scholarly journals Small-angle scattering and the protein crystallographer: A relationship of ever-increasing interest

2014 ◽  
Vol 36 (1) ◽  
pp. 44-48 ◽  
Author(s):  
David J. Scott
Keyword(s):  
High Resolution ◽  
Small Angle ◽  
Intrinsically Disordered Proteins ◽  
Structural Information ◽  
Crystallographic Analysis ◽  
Small Angle Scattering ◽  
Disordered Proteins ◽  
Intrinsically Disordered ◽  
Angle Scattering ◽  
Relationship Of

Protein crystallography is one of the great intellectual achievements of the 20th Century, and it continues to open up new vistas of research as scientists are able to visualize in exquisite detail the molecules of Life. It has become increasingly apparent, however, that not all proteins are amenable to crystallographic analysis. These include (but are not confined to) proteins with functional flexible segments, glycoproteins and intrinsically disordered proteins. There are also proteins that, although rigid and folded, refuse to crystallize as an entire full-length construct, and hence high-resolution information has to be pieced together domain by domain. It is into this space that small-angle scattering is increasingly being used as the technique of choice with regard to attainable structural information.

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