2D pair distribution function analysis of anisotropic small-angle scattering patterns from elongated nano-composite hydrogels

Soft Matter ◽  
2017 ◽  
Vol 13 (17) ◽  
pp. 3076-3083 ◽  
Author(s):  
Kengo Nishi ◽  
Mitsuhiro Shibayama
Keyword(s):  
Distribution Function ◽  
Small Angle ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Small Angle Scattering ◽  
Nano Composite ◽  
Composite Hydrogels ◽  
Angle Scattering

scholarly journals SASPDF: pair distribution function analysis of nanoparticle assemblies from small-angle scattering data

2020 ◽  
Vol 53 (3) ◽  
pp. 699-709 ◽  
Author(s):  
Chia-Hao Liu ◽  
Eric M. Janke ◽  
Ruipen Li ◽  
Pavol Juhás ◽  
Oleg Gang ◽  
...  
Keyword(s):  
Distribution Function ◽  
Small Angle ◽  
Pair Distribution Function ◽  
Function Analysis ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Nanoparticle Assemblies ◽  
Angle Scattering ◽  
Pdf Analysis ◽  
Crystallite Sizes

SASPDF, a method for characterizing the structure of nanoparticle assemblies (NPAs), is presented. The method is an extension of the atomic pair distribution function (PDF) analysis to the small-angle scattering (SAS) regime. The PDFgetS3 software package for computing the PDF from SAS data is also presented. An application of the SASPDF method to characterize structures of representative NPA samples with different levels of structural order is then demonstrated. The SASPDF method quantitatively yields information such as structure, disorder and crystallite sizes of ordered NPA samples. The method was also used to successfully model the data from a disordered NPA sample. The SASPDF method offers the possibility of more quantitative characterizations of NPA structures for a wide class of samples.

Influence of neglected small-angle scattering in radial distribution function analysis

1971 ◽  
Vol 4 (4) ◽  
pp. 277-283 ◽  
Author(s):  
G. S. Cargill
Keyword(s):  
Distribution Function ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Small Angle ◽  
Function Analysis ◽  
Small Angle Scattering ◽  
Density Fluctuations ◽  
Atomic Density ◽  
X Ray ◽  
Angle Scattering

Materials containing inhomogeneities (density-fluctuations) of much greater than atomic size produce scattering at very small angles, which may go unobserved in many X-ray, electron, and neutron scattering experiments. For liquids and for amorphous and polycrystalline solids composed of one atomic species, an approximate expression for the reduced radial distribution function obtained from intensity measurements which neglect the small-angle scattering is shown to be Gexp(r) = 4πr{ρ(r) − ρ0[1 + (\overline {\eta^2}η2(ω)/ρ0 2)γ(ω, r)]} where ρ(r) is the atomic distribution function, ρ0 is the average atomic density, \overline {\eta^2}(ω) is the average square of atomic density fluctuations, γ(ω,r) is the density fluctuation correlation function, and ω is a volume element larger than the average atomic volume but smaller than the scale of long-range density fluctuations. This expression is also valid for systems composed of more than one type of atom where ρ(r) is a weighted average of pair distribution functions and [\overline {\eta^2}(ω)/ρ0 2]γ(ω,r) for X-ray scattering describes electron density fluctuations The neglect of small-angle scattering gives rise to a G exp(r) which appears, from its slope at small r, to correspond to a material of greater average atomic density ρ0,exp than that of the sample being studied. These results are illustrated by application to fluid argon (ρ0,exp/ρ0 = 1.17 near the critical point), to amorphous silicon (ρ0,exp/ρ0 = 1.13), and to phase separated PbO–B2O3 glasses (ρ0,exp/ρ0 = 1.07 for 24 wt. % PbO).

Theoretical Background

2018 ◽  
Author(s):  
Eaton E. Lattman ◽  
Thomas D. Grant ◽  
Edward H. Snell
Keyword(s):  
Distribution Function ◽  
Small Angle ◽  
Pair Distribution Function ◽  
Structural Information ◽  
Geometric Theory ◽  
Theoretical Background ◽  
Simple Description ◽  
Angle Scattering ◽  
Rigorous Treatment ◽  
Theoretical Foundations

This chapter describes the basic background for small angle scattering starting with a simple description of the experiment and geometric theory of scattering. It describes the nature of the data produced and the information contained within that data and how relationship between real and reciprocal space in the context of solution scattering. The concept of spherical averaging is described along with its implications and effects on the available structural information from experiment. The chapter describes important fundamental concepts in solution scattering such as the pair distribution function, contrast, and resolution and information content. The chapter is presented so as to promote an intuitive understanding of the theoretical foundations of solution scattering, rather than a rigorous treatment of them.

scholarly journals An exact inversion method for extracting orientation ordering by small-angle scattering

2021 ◽  
Vol 23 (7) ◽  
pp. 4120-4132
Author(s):  
Guan-Rong Huang ◽  
Jan Michael Carrillo ◽  
Yangyang Wang ◽  
Changwoo Do ◽  
Lionel Porcar ◽  
...  
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Small Angle ◽  
Orientation Distribution ◽  
Small Angle Scattering ◽  
Inversion Method ◽  
Angle Scattering ◽  
Orientation Ordering

We outline a nonparametric inversion strategy for determining the orientation distribution function (ODF) of sheared interacting rods using small-angle scattering techniques.

scholarly journals ATSAS 3.0: expanded functionality and new tools for small-angle scattering data analysis

2021 ◽  
Vol 54 (1) ◽  
Author(s):  
Karen Manalastas-Cantos ◽  
Petr V. Konarev ◽  
Nelly R. Hajizadeh ◽  
Alexey G. Kikhney ◽  
Maxim V. Petoukhov ◽  
...  
Keyword(s):  
Distribution Function ◽  
Small Angle ◽  
Small Angle Scattering ◽  
Distance Distribution ◽  
Scattering Data ◽  
Mode Analysis ◽  
Distance Distribution Function ◽  
Search Volume ◽  
Angle Scattering ◽  
Pair Distance Distribution Function

The ATSAS software suite encompasses a number of programs for the processing, visualization, analysis and modelling of small-angle scattering data, with a focus on the data measured from biological macromolecules. Here, new developments in the ATSAS 3.0 package are described. They include IMSIM, for simulating isotropic 2D scattering patterns; IMOP, to perform operations on 2D images and masks; DATRESAMPLE, a method for variance estimation of structural invariants through parametric resampling; DATFT, which computes the pair distance distribution function by a direct Fourier transform of the scattering data; PDDFFIT, to compute the scattering data from a pair distance distribution function, allowing comparison with the experimental data; a new module in DATMW for Bayesian consensus-based concentration-independent molecular weight estimation; DATMIF, an ab initio shape analysis method that optimizes the search model directly against the scattering data; DAMEMB, an application to set up the initial search volume for multiphase modelling of membrane proteins; ELLLIP, to perform quasi-atomistic modelling of liposomes with elliptical shapes; NMATOR, which models conformational changes in nucleic acid structures through normal mode analysis in torsion angle space; DAMMIX, which reconstructs the shape of an unknown intermediate in an evolving system; and LIPMIX and BILMIX, for modelling multilamellar and asymmetric lipid vesicles, respectively. In addition, technical updates were deployed to facilitate maintainability of the package, which include porting the PRIMUS graphical interface to Qt5, updating SASpy – a PyMOL plugin to run a subset of ATSAS tools – to be both Python 2 and 3 compatible, and adding utilities to facilitate mmCIF compatibility in future ATSAS releases. All these features are implemented in ATSAS 3.0, freely available for academic users at https://www.embl-hamburg.de/biosaxs/software.html.

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