Hard sphere model

Interaction Potential

The hard sphere interaction potential is given by

V\left(r\right)=\left\{{\begin{array}{lll}\infty &;&r<\sigma \\0&;&r\geq \sigma \end{array}}\right.

where $V\left(r\right)$ is the potential energy between two spheres at a distance $r$ , and $\sigma$ is the diameter of the sphere.

Equations of state

Hard sphere fluid:

See Carnahan-Starling (three dimensions)
See Ref.1

Hard sphere solid:

See Ref. 2

Fluid-solid transition

The hard sphere fluid undergoes a fluid-solid first order transition at $\rho d^{3}=0.94$ , $\eta _{A}={\frac {\pi \rho d^{3}}{6}}=0.49218$ .

William G. Hoover and Francis H. Ree "Melting Transition and Communal Entropy for Hard Spheres", Journal of Chemical Physics 49 pp. 3609-3617 (1968)

First ever simulations of hard spheres

Related systems

Other dimensions

1-dimensional case: hard rods.
2-dimensional case: hard disks.

Data

Virial coefficients of hard spheres and hard disks are to be found in the table.

Experimental results

For results obtained from the Colloidal Disorder - Order Transition (CDOT) experiments performed on-board the Space Shuttles Columbia and Discovery see Ref. 3.

References

Hard sphere model

Contents

Interaction Potential

Equations of state

Fluid-solid transition

First ever simulations of hard spheres

Related systems

Other dimensions

Data

Experimental results

References

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Hard sphere model

Interaction Potential

Equations of state

Fluid-solid transition

First ever simulations of hard spheres

Related systems

Other dimensions

Data

Experimental results

References

Navigation menu

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