Assessment of Small-Angle and Angle-Averaged Structure Factor for Monitoring Electrostatic Colloidal Interactions Using Multiply Scattered Light

2002 ◽  
Vol 251 (2) ◽  
pp. 434-442 ◽  
Author(s):  
Yingqing Huang ◽  
E.M. Sevick-Muraca
Keyword(s):  
Small Angle ◽  
Structure Factor ◽  
Scattered Light ◽  
Colloidal Interactions

Small Angle Neutron Scatitering Study of Sol-Gel Glasses

1989 ◽  
Vol 166 ◽  
Author(s):  
P. Wiltzius ◽  
S. B. Dierker
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Structure Factor ◽  
Small Angle Neutron Scattering ◽  
Sol Gel ◽  
Scattering Data ◽  
Length Scales ◽  
Internal Interface ◽  
Porous Glasses ◽  
Gel Glasses

ABSTRACTWe present small angle neutron scattering data of porous glasses. Analysis of the structure factor shows that the morphology on length scales between 30 A and 800 A depends on fabrication procedures. Fast gelation leads to a clumpy glass, whereas slow gelation produces a random smooth internal interface.

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.

Adhesive hard-sphere colloidal dispersions. A small-angle neutron-scattering study of stickiness and the structure factor

Langmuir ◽  
1989 ◽  
Vol 5 (2) ◽  
pp. 422-428 ◽  
Author(s):  
C. G. De Kruif ◽  
P. W. Rouw ◽  
W. J. Briels ◽  
M. H. G. Duits ◽  
A. Vrij ◽  
...  
Keyword(s):  
Neutron Scattering ◽  
Small Angle ◽  
Structure Factor ◽  
Hard Sphere ◽  
Small Angle Neutron Scattering ◽  
Colloidal Dispersions ◽  
Scattering Study ◽  
Neutron Scattering Study

Ceramic Microstructure-Property Fractal-Diffractal Calculus : Static Synergetics Yield Optimization During Processing Via Real–Time Q.A.and Interactive Q.C

1986 ◽  
Vol 73 ◽  
Author(s):  
Edward Siegel
Keyword(s):  
Pattern Recognition ◽  
Diffraction Pattern ◽  
Small Angle ◽  
Structure Factor ◽  
Static Structure Factor ◽  
Scaling Relation ◽  
Static Structure ◽  
Yield Optimization ◽  
Angle Scattering ◽  
Ceramic Microstructure

ABSTRACTCeramic microstructure-property relationships dominate any and all attempts at“better ceramics through chemistry”. Required is some universal calculus to allow analytic, universal, reversible scalable computation of one from the other. Static Synergetics universality-principle provides such a flexible versatile tool, heretofore not available. It is a reexpression of the very basic three laws of thermodynamics into r-,k-,and w-domainsthe equivalence of(symmetry-breaking/defect) Pattern-recognition(the “structure”) to signal-processing(the frequency-dependent FM) properties/ Functions. More basically, it is a manifestation of Noether's theoremthe basis of mechanics and orgin of the energy continuity equation that is the thermodynamic first law. Such an algorithm, the”software”of yield optimization(quality and quantity) real-time Q.A. and(in parallel with a specificity dominated process- model)interactive Q.C.requires as “hardware”produced input the small-angle-scattering(SAS)dominated diffraction-pattern/static structure factor SSAS(k) or Fourier transform r-domain Pattern/ photomicrograph-recognition imaging(of processing-introduced property-detrimental defects(heterogeneity heirarchy)). Output are universal FM:I/f flicker(voltage and/or current)noise power spectrum, signal-to-noise ratio over dynamic rangemulti-level system dominated anomalous low temperature/frequency thermalracoustic. properties, and 1/f relaxation response susceptibility polarization catastrophe derived dielectric, electrical, optical, noise, viscoelastic/mechanicalmagnetic,...property Functions. Input can be the ubiquitous,...universal Mandelbrot fractals,dominating ceramics;output(and internal)Functions are Berry-Nye-Jakeman wdomain diffractals,dominating all properties universally.How and Why it works are detailed exactly;universality, reversibility and scalability are analytically insured for self-similar(or selfaffine) fractal scaling-relation Pattern-recognition input;approximate. deviations from universal Functions output obtains from less than perfect mathematically ideal fractal scaling-relation Pattern-recognition input.Static Synergetics provides a new practical use for external radiation small-angle-scattering(SAS) diffraction-pattern/static structure factor measurements in ceramic material microstructure-property relationships during processing

Small-angle scattering: a view on the properties, structures and structural changes of biological macromolecules in solution

2003 ◽  
Vol 36 (2) ◽  
pp. 147-227 ◽  
Author(s):  
Michel H. J. Koch ◽  
Patrice Vachette ◽  
Dmitri I. Svergun
Keyword(s):  
High Resolution ◽  
Neutron Scattering ◽  
Small Angle ◽  
Structure Factor ◽  
Structural Changes ◽  
Biological Macromolecules ◽  
Time Resolved ◽  
Scattering Intensity ◽  
X Ray ◽  
Angle Scattering

1. Introduction 1482. Basics of X-ray and neutron scattering 1492.1 Elastic scattering of electromagnetic radiation by a single electron 1492.2 Scattering by assemblies of electrons 1512.3 Anomalous scattering and long wavelengths 1532.4 Neutron scattering 1532.5 Transmission and attenuation 1553. Small-angle scattering from solutions 1563.1 Instrumentation 1563.2 The experimental scattering pattern 1573.3 Basic scattering functions 1593.4 Global structural parameters 1613.4.1 Monodisperse systems 1613.4.2 Polydisperse systems and mixtures 1633.5 Characteristic functions 1644. Modelling 1664.1 Spherical harmonics 1664.2 Shannon sampling 1694.3 Shape determination 1704.3.1 Modelling with few parameters: molecular envelopes 1714.3.2 Modelling with many parameters: bead models 1734.4 Modelling domain structure and missing parts of high-resolution models 1784.5 Computing scattering patterns from atomic models 1844.6 Rigid-body refinement 1875. Applications 1905.1 Contrast variation studies of ribosomes 1905.2 Structural changes and catalytic activity of the allosteric enzyme ATCase 1916. Interactions between molecules in solution 2036.1 Linearizing the problem for moderate interactions: the second virial coefficient 2046.2 Determination of the structure factor 2057. Time-resolved measurements 2118. Conclusions 2159. Acknowledgements 21610. References 216A self-contained presentation of the main concepts and methods for interpretation of X-ray and neutron-scattering patterns of biological macromolecules in solution, including a reminder of the basics of X-ray and neutron scattering and a brief overview of relevant aspects of modern instrumentation, is given. For monodisperse solutions the experimental data yield the scattering intensity of the macromolecules, which depends on the contrast between the solvent and the particles as well as on their shape and internal scattering density fluctuations, and the structure factor, which is related to the interactions between macromolecules. After a brief analysis of the information content of the scattering intensity, the two main approaches for modelling the shape and/or structure of macromolecules and the global minimization schemes used in the calculations are presented. The first approach is based, in its more advanced version, on the spherical harmonics approximation and relies on few parameters, whereas the second one uses bead models with thousands of parameters. Extensions of bead modelling can be used to model domain structure and missing parts in high-resolution structures. Methods for computing the scattering patterns from atomic models including the contribution of the hydration shell are discussed and examples are given, which also illustrate that significant differences sometimes exist between crystal and solution structures. These differences are in some cases explainable in terms of rigid-body motions of parts of the structures. Results of two extensive studies – on ribosomes and on the allosteric protein aspartate transcarbamoylase – illustrate the application of the various methods. The unique bridge between equilibrium structures and thermodynamic or kinetic aspects provided by scattering techniques is illustrated by modelling of intermolecular interactions, including crystallization, based on an analysis of the structure factor and recent time-resolved work on assembly and protein folding.

Particles small angle forward-scattered light measurement based on photovoltaic cell microflow cytometer

2013 ◽  
Vol 35 (2-3) ◽  
pp. 337-344 ◽  
Author(s):  
Han-Taw Chen ◽  
Lung-Ming Fu ◽  
Hsing-Hui Huang ◽  
Wei-En Shu ◽  
Yao-Nan Wang
Keyword(s):  
Small Angle ◽  
Scattered Light ◽  
Photovoltaic Cell ◽  
Light Measurement ◽  
Microflow Cytometer

SMALL ANGLE SCATTERING AND STRUCTURE FACTOR NEUTRON MEASUREMENTS OF AN AMORPHOUS Al70Si17Fe13 ALLOY

1985 ◽  
Vol 46 (C8) ◽  
pp. C8-461-C8-466 ◽  
Author(s):  
J. M. Dubois ◽  
K. Dehghan ◽  
C. Janot ◽  
P. Chieux ◽  
B. Chenal
Keyword(s):  
Small Angle ◽  
Structure Factor ◽  
Small Angle Scattering ◽  
Angle Scattering

Assessment of structure factors for analysis of small-angle scattering data from desired or undesired aggregates

2020 ◽  
Vol 53 (4) ◽  
pp. 991-1005
Author(s):  
Andreas Haahr Larsen ◽  
Jan Skov Pedersen ◽  
Lise Arleth
Keyword(s):  
Small Angle ◽  
Structure Factor ◽  
Protein Structures ◽  
Simulated Data ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Spherical Cluster ◽  
Structure Factors ◽  
Angle Scattering ◽  
Aggregation Processes

Aggregation processes are central features of many systems ranging from colloids and polymers to inorganic nanoparticles and biological systems. Some aggregated structures are controlled and desirable, e.g. in the design of size-controlled clustered nanoparticles or some protein-based drugs. In other cases, the aggregates are undesirable, e.g. protein aggregation involved in neurodegenerative diseases or in vitro studies of single protein structures. In either case, experimental and analytical tools are needed to cast light on the aggregation processes. Aggregation processes can be studied with small-angle scattering, but analytical descriptions of the aggregates are needed for detailed structural analysis. This paper presents a list of useful small-angle scattering structure factors, including a novel structure factor for a spherical cluster with local correlations between the constituent particles. Several of the structure factors were renormalized to get correct limit values in both the high-q and low-q limit, where q is the modulus of the scattering vector. The structure factors were critically evaluated against simulated data. Structure factors describing fractal aggregates provided approximate descriptions of the simulated data for all tested structures, from linear to globular aggregates. The addition of a correlation hole for the constituent particles in the fractal structure factors significantly improved the fits in all cases. Linear aggregates were best described by a linear structure factor and globular aggregates by the newly derived spherical cluster structure factor. As a central point, it is shown that the structure factors could be used to take aggregation contributions into account for samples of monomeric protein containing a minor fraction of aggregated protein. After applying structure factors in the analysis, the correct structure and oligomeric state of the protein were determined. Thus, by careful use of the presented structure factors, important structural information can be retrieved from small-angle scattering data, both when aggregates are desired and when they are undesired.

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