http://wwwcourses.sens.buffalo.edu/ce435/Pedersen97.pdf

Analysis of small-angle scattering data from colloids and polymer solutions: modeling and least-squares fitting

Small-angle scattering (SAS) of x-rays and neutrons is a fundamental tool in the study of biological macromolecules. The major advantage of the method lies in its ability to provide structural information about partially or completely disordered systems. SAS allows one to study the structure of native particles in near physiological environments and to analyse structural changes in response to variations in external conditions. In this review we concentrate on SAS studies of isotropic systems, in particular, solutions of biological macromolecules, an area where major progress has been achieved during the last decade. Solution scattering studies are especially important, given the challenge of the ‘post-genomic’ era with vast numbers of protein sequences becoming available. Numerous structural initiatives aim at large-scale expression and purification of proteins for subsequent structure determination using x-ray crystallography and NMR spectroscopy. Because of the requirement of good crystals for crystallography and the low molecular mass requirement of NMR, a significant fraction of proteins cannot be analysed using these two high-resolution methods. Progress in SAS instrumentation and novel analysis methods, which substantially improve the resolution and reliability of the structural models, makes the method an important complementary tool for these initiatives. The review covers the basics of x-ray and neutron SAS, instrumentation, mathematical methods used in data analysis and major modelling techniques. Examples of applications of SAS to different types of biomolecules (proteins, nucleic acids, macromolecular complexes, polyelectrolytes) are presented. A brief account of the new opportunities offered by third and fourth generation synchrotron radiation sources (time-resolved studies, coherent scattering and single molecule scattering) is also given.

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Small-angle scattering studies of biological macromolecules in solution

A new treatment of the phase behaviour of a colloid + nonadsorbing polymer mixture is described. The calculated phase diagrams show marked polymer partitioning between coexisting phases, an effect not considered in the usual effective-potential approaches to this problem. We also predict that under certain conditions an area of three-phase coexistence should appear in the phase diagram.

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Phase Behaviour of Colloid + Polymer Mixtures

1. Introduction to colloid science and rheology 2. Hydrodynamic effects 3. Brownian hard spheres 4. Stable colloidal suspensions 5. Non-spherical particles 6. Weakly flocculated suspensions 7. Thixotropy 8. Shear thickening 9. Rheometry of suspensions 10. Suspensions in viscoelastic media 11. Advanced topics.

Colloidal Suspension Rheology

X-ray scattering is a structural characterization tool that has impacted diverse fields of study. It is unique in its ability to examine materials in real time and under realistic sample environments, enabling researchers to understand morphology at nanometer and angstrom length scales using complementary small and wide angle X-ray scattering (SAXS, WAXS), respectively. Herein, we focus on the use of SAXS to examine nanoscale particulate systems. We provide a theoretical foundation for X-ray scattering, considering both form factor and structure factor, as well as the use of correlation functions, which may be used to determine a particle’s size, size distribution, shape, and organization into hierarchical structures. The theory is expanded upon with contemporary use cases. Both transmission and reflection (grazing incidence) geometries are addressed, as well as the combination of SAXS with other X-ray and non-X-ray characterization tools. We conclude with an examination of several key areas of research w...

Small Angle X-ray Scattering for Nanoparticle Research

It is shown that the Percus–Yevick approximation can be solved analytically for a potential consisting of a hard core together with a rectangular attractive well, provided that a certain limit is taken in which the range of the well becomes zero and its depth infinite. The results show a first‐order phase transition which appears to be of the type observed numerically for the Lennard‐Jones 12–6 potential.

R. J. Baxter

Papers

Percus-Yevick Equation for Hard Spheres with Surface Adhesion