scholarly journals Percus–Yevick structure factors made simple

2020 ◽  
Vol 53 (6) ◽  
pp. 1570-1582
Author(s):  
Robert Botet ◽  
Sylvie Kwok ◽  
Bernard Cabane
Keyword(s):  
Colloidal Particles ◽  
Mean Field ◽  
Spatial Arrangement ◽  
Measured Signal ◽  
X Ray Scattering ◽  
Internal Phase ◽  
Structure Factors ◽  
Unique Method ◽  
Truncated Normal ◽  
Spherical Droplets

Measuring the structure factor, S(q), of a dispersion of particles by small-angle X-ray scattering provides a unique method to investigate the spatial arrangement of colloidal particles. However, it is impossible to find the exact location of the particles from S(q) because some information is inherently lacking in the measured signal. The two standard ways to analyse an experimental S(q) are then to compare it either with structure factors computed from simulated systems or with analytical ones calculated from approximated systems. However, such approaches may prove inadequate for dispersions of variously polydisperse particles. While Vrij, Bloom and Stell established a mean-field approach that could yield fairly accurate approximations for experimental S(q), this solution has remained underused because of its mathematical complexity. In the present work, the complete Percus–Yevick solution for general polydisperse hard-sphere systems is derived in a concise form that is straightforward to use. The form of the solution has been simplified enough to provide experimentalists with ready solutions of several commonly encountered particle-radius distributions in real systems (Schulz, truncated normal and inverse Gaussian). The approach is also illustrated with a case study of the exponential radius distribution. Finally, the application of the proposed solution to the power-law radius distribution is discussed in detail by comparing the calculations with experimentally measured S(q) for an Apollonian packing of spherical droplets recently reported in high-internal-phase-ratio emulsions.

scholarly journals Complex fluids: the physics of emulsions

2017 ◽  
Author(s):  
M. Cates
Keyword(s):  
Interfacial Tension ◽  
Colloidal Particles ◽  
Ostwald Ripening ◽  
Equations Of Motion ◽  
Mean Field Theory ◽  
Mean Field ◽  
Fluid Mixture ◽  
Phase Separation Kinetics ◽  
Spherical Droplets

These lectures start with the mean field theory for a symmetric binary fluid mixture, addressing interfacial tension, the stress tensor, and the equations of motion (Model H). We then consider the phase separation kinetics of such a mixture: coalescence, Ostwald ripening, its prevention by trapped species, coarsening of bicontinuous states, and the role of shear flow. The third topic addressed is the stabilization of emulsions by using surfactants to reduce or even eliminate the interfacial tension between phases; the physics of bending energy, which becomes relevant in the latter case, is then presented briefly. The final topic is the creation of long-lived metastable emulsions by adsorption of colloidal particles or nanoparticles at the fluid–fluid interface; alongside spherical droplets, these methods can be used to create a range of unconventional structures with potentially interesting properties that are only now being explored.

scholarly journals Mixed-order phase transition in a colloidal crystal

2017 ◽  
Vol 114 (49) ◽  
pp. 12906-12909 ◽  
Author(s):  
Ricard Alert ◽  
Pietro Tierno ◽  
Jaume Casademunt
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Colloidal Particles ◽  
Colloidal Crystal ◽  
Equilibrium Phase ◽  
Mean Field ◽  
Critical Dimension ◽  
Colloidal System ◽  
Test Bed ◽  
Mixed Order

Mixed-order phase transitions display a discontinuity in the order parameter like first-order transitions yet feature critical behavior like second-order transitions. Such transitions have been predicted for a broad range of equilibrium and nonequilibrium systems, but their experimental observation has remained elusive. Here, we analytically predict and experimentally realize a mixed-order equilibrium phase transition. Specifically, a discontinuous solid–solid transition in a 2D crystal of paramagnetic colloidal particles is induced by a magnetic field H. At the transition field Hs, the energy landscape of the system becomes completely flat, which causes diverging fluctuations and correlation length ξ∝|H2−Hs2|−1/2. Mean-field critical exponents are predicted, since the upper critical dimension of the transition is du=2. Our colloidal system provides an experimental test bed to probe the unconventional properties of mixed-order phase transitions.

FitGISAXS: software package for modelling and analysis of GISAXS data using IGOR Pro

2010 ◽  
Vol 43 (4) ◽  
pp. 929-936 ◽  
Author(s):  
David Babonneau
Keyword(s):  
Software Package ◽  
Form Factors ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Scattering Data ◽  
Stratified Medium ◽  
X Ray ◽  
X Ray Scattering ◽  
Structure Factors ◽  
Scripting Language

A software package for performing modelling and analysis of GISAXS (grazing-incidence small-angle X-ray scattering) data within the distorted-wave Born approximation has been developed using the IGOR Pro scripting language (http://www.wavemetrics.com). The tool suite uses a slab-model approach with the Abélès matrix method to calculate X-ray reflectivity curves, electric field intensity distributions and GISAXS intensities from supported or buried scatterers arranged in two or three dimensions in a stratified medium. Models are included to calculate the scattered intensity for monodisperse, polydisperse and interacting particles with various size distributions, form factors and structure factors. The source code for the entire package is freely available, allowing anyone to develop additional tools.

scholarly journals Visualizing a viral genome with contrast variation small angle X-ray scattering

2020 ◽  
Vol 295 (47) ◽  
pp. 15923-15932
Author(s):  
Josue San Emeterio ◽  
Lois Pollack
Keyword(s):  
Small Angle ◽  
Viral Genome ◽  
Viral Assembly ◽  
Measured Signal ◽  
Structural Rearrangements ◽  
Contrast Variation ◽  
Time Resolved ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

Despite the threat to human health posed by some single-stranded RNA viruses, little is understood about their assembly. The goal of this work is to introduce a new tool for watching an RNA genome direct its own packaging and encapsidation by proteins. Contrast variation small-angle X-ray scattering (CV-SAXS) is a powerful tool with the potential to monitor the changing structure of a viral RNA through this assembly process. The proteins, though present, do not contribute to the measured signal. As a first step in assessing the feasibility of viral genome studies, the structure of encapsidated MS2 RNA was exclusively detected with CV-SAXS and compared with a structure derived from asymmetric cryo-EM reconstructions. Additional comparisons with free RNA highlight the significant structural rearrangements induced by capsid proteins and invite the application of time-resolved CV-SAXS to reveal interactions that result in efficient viral assembly.

X-ray Investigations of Liquid Bismuth-Copper Alloys

2000 ◽  
Vol 55 (3-4) ◽  
pp. 381-389 ◽  
Author(s):  
J. Nomssi Nzali ◽  
W. Hoyer
Keyword(s):  
Copper Alloys ◽  
X Ray Diffraction ◽  
Model Calculations ◽  
Experimental Procedure ◽  
X Ray ◽  
X Ray Scattering ◽  
Structure Factors ◽  
Reverse Monte Carlo Simulation ◽  
Square Well ◽  
Total Structure

Liquid copper, bismuth, and eleven bismuth-copper alloys were investigated at temperatures above the liquidus with X-ray diffraction. The experimental procedure was adjusted to reduce the effects of evaporation. The Faber-Ziman total structure factors S(Q) feature a splitting of the first maximum and negative values for Q around 1 Å -1 in a large concentration range. The results are compared to previous neutron diffraction results by Zaiss and Steeb, to square-well potential model calculations by Gopala Rao and Satpathy and to a simple segregation model. The segregation model reproduces the features qualitatively. Partial structure factors are assessed by fitting both neutron and X-ray scattering results with reverse Monte-Carlo simulation

scholarly journals Structure and stacking order in crystals of asymmetric dumbbell-like colloids

2015 ◽  
Vol 48 (1) ◽  
pp. 238-243 ◽  
Author(s):  
Antara Pal ◽  
Janne-Mieke Meijer ◽  
Joost R. Wolters ◽  
Willem K. Kegel ◽  
Andrei V. Petukhov
Keyword(s):  
Crystalline Structure ◽  
Diffuse Scattering ◽  
Colloidal Particles ◽  
Three Dimensional ◽  
Stacking Faults ◽  
Face Centered Cubic ◽  
Hexagonal Close Packed ◽  
Stacking Order ◽  
X Ray Scattering ◽  
Face Centered

The crystalline structure assembled out of charge-stabilized asymmetric dumbbell-like colloidal particles in ethyl alcohol by sedimentation has been probed using small-angle X-ray scattering with microradian resolution. The existence of plastic face-centered cubic crystals was inferred from the observed Bragg peaks. The presence of stacking faults and the mosaic structure of the sample lead to the appearance of diffuse scattering, forming Bragg scattering cylinders in the three-dimensional reciprocal space. The quality of the crystalline structure, as ascertained from a detailed analysis of the diffuse scattering intensity distribution, indicates the presence of only 1.5% of stacking faults between the hexagonal close-packed layers.

Count rates and structure factors in anomalous soft x-ray scattering from cuprate superconductors

2002 ◽  
Author(s):  
Peter M. Abbamonte ◽  
L. Venema ◽  
A. Rusydi ◽  
G. Logvenov ◽  
Ivan Bozovic ◽  
...  
Keyword(s):  
Cuprate Superconductors ◽  
X Ray ◽  
X Ray Scattering ◽  
Structure Factors ◽  
Ray Scattering

Structural studies of nematic and smectic phases

1983 ◽  
Vol 309 (1507) ◽  
pp. 145-153 ◽  
Keyword(s):  
Liquid Crystal ◽  
Mean Field ◽  
Structural Studies ◽  
X Ray ◽  
Smectic A ◽  
Smectic C ◽  
X Ray Scattering ◽  
Smectic Phases ◽  
Crystal Phases ◽  
Field Behaviour

The information about liquid crystal phases that can be obtained by light scattering and by high-resolution X-ray scattering is reviewed. Results for the nematic-smectic A transition suggest the de Gennes-McMillan model is correct, but adequate theoretical solutions to the model remain elusive. Recent results on the smectic A to smectic C transition are presented that show unambiguously that it exhibits classic mean-field behaviour and this is explained by a Ginzburg criterion argument. Some preliminary results of a study of a nematic-smectic A transition in a lyotropic material are given and indicate similarity to thermotropic materials.

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