Hard ellipsoid model
Hard ellipsoids represent a natural choice for an anisotropic model. Ellipsoids can be produced from an affine transformation of the hard sphere model. However, in difference to the hard sphere model, which has fluid and solid phases, the hard ellipsoid model is also able to produce a nematic phase.
The general ellipsoid, also called a triaxial ellipsoid, is a quadratic surface which is given in Cartesian coordinates by
where , and define the lengths of the axis.
The most widely used overlap algorithm is that of Perram and Wertheim .
and the surface area is given by
where is an elliptic integral of the first kind and is an elliptic integral of the second kind, with the amplitude being
and the moduli
where the anisotropy parameters, and , are
The volume of the ellipsoid is given by the well known
Maximum packing fraction
Equation of state
- Main article: Hard ellipsoid equation of state
- Main article: Hard ellipsoids: virial coefficients
One of the first phase diagrams of the hard ellipsoid model was that of Frenkel and Mulder (Figure 6 in ). Camp and Allen later studied biaxial ellipsoids . It has recently been shown   that the SM2 structure is more stable than the face centered cubic structure for aspect ratios and densities .
Hard ellipse model
- Main article: Hard ellipse model (2-dimensional ellipsoids)
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- Wen-Sheng Xu , Yan-Wei Li , Zhao-Yan Sun and Li-Jia An "Hard ellipses: Equation of state, structure, and self-diffusion", Journal of Chemical Physics 139 024501 (2013)