Playing with Marbles: Structural and Thermodynamic Properties of Hard-Sphere Systems

@article{Santos2013PlayingWM,
  title={Playing with Marbles: Structural and Thermodynamic Properties of Hard-Sphere Systems},
  author={Andr{\'e}s Santos},
  journal={arXiv: Soft Condensed Matter},
  year={2013}
}
These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere potential or closely related model potentials. The exact statistical-mechanical properties of one-dimensional systems, the issue of thermodynamic (in)consistency among different routes in the context of several approximate theories, and the construction of analytical… Expand
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References

SHOWING 1-10 OF 115 REFERENCES
Alternative Approaches to the Equilibrium Properties of Hard-Sphere Liquids
An overview of some analytical approaches to the computation of the structural and thermodynamic properties of single component and multicomponent hard-sphere fluids is provided. For the structuralExpand
Theory and Simulation of Hard-Sphere Fluids and Related Systems
Structure of Hard Spheres and Related Systems.- to the Thermodynamics of Hard Spheres and Related Systems.- Equations of State for Hard Spheres and Hard Disks.- Application of Hard-Sphere andExpand
Thermodynamics and structure of a fluid of hard rods, disks, spheres, or hyperspheres from rescaled virial expansions.
  • Baus, Colot
  • Physics, Medicine
  • Physical review. A, General physics
  • 1987
By rescaling the exact low-density results practical expressions are obtained for the equation of state and the direct correlation function of a fluid of hard D-spheres allowing a unified treatmentExpand
A square-well model for the structural and thermodynamic properties of simple colloidal systems
A model for the radial distribution function g(r) of a square-well fluid of variable width previously proposed [Yuste and Santos, J. Chem. Phys. 101, 2355 (1994)] is revisited and simplified. TheExpand
Structure of ternary additive hard-sphere fluid mixtures.
TLDR
Very good agreement between the results of the first two approaches and simulation is observed, with a noticeable improvement over the Percus-Yevick predictions especially near contact. Expand
Structure of hard-sphere metastable fluids.
  • Yuste, Haro, Santos
  • Physics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1996
TLDR
A rational-function approximation method to analytically derive the radial distribution function g(r ) and the structure factorS(q) of a hard-sphere fluid is revisited and shows the existence of a threshold density, beyond which no meaningful fluid structure can be derived. Expand
Structure of hard-hypersphere fluids in odd dimensions.
The structural properties of single component fluids of hard hyperspheres in odd space dimensionalities d are studied with an analytical approximation method that generalizes the rational functionExpand
Analysis of Classical Statistical Mechanics by Means of Collective Coordinates
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 approximateExpand
Equilibrium fluid-solid coexistence of hard spheres.
We present a tethered Monte Carlo simulation of the crystallization of hard spheres. Our method boosts the traditional umbrella sampling to the point of making practical the study of constrainedExpand
The penetrable-sphere fluid in the high-temperature, high-density limit
Abstract We consider a fluid of d -dimensional spherical particles interacting via a pair potential φ ( r ) which takes a finite value ϵ if the two spheres are overlapped ( r σ ) and 0 otherwise.Expand
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