Hard spheres

In statistical mechanical, hard spheres are widely used as model particles in fluids and solids. They are defined simply as impenetrable spheres that cannot overlap in space. They mimic the extremely strong ("infinitely elastic bouncing") repulsion that atoms and spherical molecules experience at very close distances. Hard spheres systems are studied by analytical means, by molecular dynamics simulations, and by the experimental study of certain model systems.

Beside being a model of theoretical significance, the hard-sphere system is used as a basis in the formulation of several modern, predictive equations of state for real fluids through the statistical associating fluid theory (SAFT) approach, and models for transport properties in gases through Chapman–Enskog theory.

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Formal definition Hard spheres of diameter $\backslash sigma$ are particles with the following pairwise interaction potential:

where $\backslash mathbf\{r\}\_1$ and $\backslash mathbf\{r\}\_2$ are the positions of the two particles.

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Hard-spheres gas The first three virial coefficients for hard spheres can be determined analytically

Higher-order ones can be determined numerically using Monte Carlo integration. We list

$$\backslash begin\{align\}\; \backslash frac\{B\_5\}$$

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