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Journal ArticleDOI

Percus-Yevick Equation for Hard Spheres with Surface Adhesion

15 Sep 1968-Journal of Chemical Physics (American Institute of PhysicsAIP)-Vol. 49, Iss: 6, pp 2770-2774
TL;DR: In this paper, it was 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.
Abstract: 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.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the analysis and modeling of small-angle scattering data from colloidal particles or polymers in solution are discussed and the basic principles of linear and non-linear least-squares methods are summarized with emphasis on applications in the analysis of small angle scattering data, including indirect Fourier transformation, square root deconvolution, size distribution determinations, and modeling.

1,361 citations

Journal ArticleDOI
TL;DR: Small-angle scattering (SAS) of x-rays and neutrons is a fundamental tool in the study of biological macromolecules as mentioned in this paper, which allows one to study the structure of native particles in near physiological environments and analyse structural changes in response to variations in external conditions.
Abstract: 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.

907 citations

Journal ArticleDOI
15 Nov 1992-EPL
TL;DR: In this article, a new treatment of the phase behaviour of a colloid + nonadsorbing polymer mixture is described and calculated phase diagrams show marked polymer partitioning between coexisting phases, an effect not considered in the usual effective potential approaches to this problem.
Abstract: 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.

846 citations

MonographDOI
01 Nov 2011
TL;DR: In this paper, the authors introduce colloid science and rheology, and present an overview of colloid physics and its applications in viscoelastic media. But they do not discuss the role of non-spherical particles.
Abstract: 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.

792 citations

Journal ArticleDOI
TL;DR: This work provides 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.
Abstract: 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...

611 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the three-dimensional classical many-body system is approximated by the use of collective coordinates, through the assumed knowledge of two-body correlation functions, and a self-consistent formulation is available for determining the correlation function.
Abstract: The three-dimensional classical many-body system is approximated by the use of collective coordinates, through the assumed knowledge of two-body correlation functions. The resulting approximate statistical state is used to obtain the two-body correlation function. Thus, a self-consistent formulation is available for determining the correlation function. Then, the self-consistent integral equation is solved in virial expansion, and the thermodynamic quantities of the system thereby ascertained. The first three virial coefficients are exactly reproduced, while the fourth is nearly correct, as evidenced by numerical results for the case of hard spheres.

2,358 citations

Journal ArticleDOI
TL;DR: In this article, a method for solving the simultaneous classical equation of motion of several hundred particles by means of fast electronic computers is described. But the method is not suitable for large numbers of particles.
Abstract: The method consists of solving exactly the simultaneous classical equation of motion of several hundred particles by means of fast electronic computers. (W.L.H.)

2,250 citations

Journal ArticleDOI
TL;DR: In this article, the equation of state and pair distribution for the Percus- Yevick integral equation for the radiai distribution function of a classical fluid are obtained in closed form for the prototype of interacting hard spheres.
Abstract: ABS>The equation of state and the pair distribution for the Percus- Yevick integral equation for the radiai distribution function of a classical fluid are obtained in closed form for the prototype of interacting hard spheres. (D.C.W.)

1,420 citations

Journal ArticleDOI
TL;DR: In this paper, the authors compared theory and experiment for behavior very near critical points, and suggested that scaling laws provide a promising approach to understand phenomena near the critical point, but that they are by no means proved or disproved by the existing experimental data.
Abstract: This paper compares theory and experiment for behavior very near critical points. The primary experimental results are the "critical indices" which describe singularities in various thermodynamic derivatives and correlation functions. These indices are tabulated and compared with theory. The basic theoretical ideas are introduced via the molecular field approach, which brings in the concept of an order parameter and suggests that there are close relations among different phase transition problems. Although this theory is qualitatively correct it is quantitatively wrong, it predicts the wrong values of the critical indices. Another theoretical approach, the "scaling law" concept, which predicts relations among these indices, is described. The experimental evidence for and against the scaling laws is assessed. It is suggested that the scaling laws provide a promising approach to understanding phenomena near the critical point, but that they are by no means proved or disproved by the existing experimental data.

1,189 citations

Journal ArticleDOI
TL;DR: In this paper, simple and exact expressions for the compressibility and pressure equations of state predicted by the Percus-Yevick equation for hard spheres were found for Wainwright and Alder.
Abstract: Simple and exact expressions have been found for the compressibility and pressure equations of state predicted by the Percus—Yevick equation for hard spheres. The equations of state are in good agreement with the machine calculations of Wainwright and Alder, and Wood, Parker, and Jacobson.

987 citations